DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP221^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n005.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 09:05:53 AM UTC 2026

% Result   : Theorem 23.38s 8.82s
% Output   : Refutation 23.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   51 (  25 unt;   0 typ;   4 def)
%            Number of atoms       :  167 (  43 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  650 (  23   ~;  24   |;   0   &; 593   @)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :   85 (  84 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  933 ( 930 usr;  61 con; 0-8 aty)
%            Number of variables   :   12 (  12   ^;   0   !;   0   ?;  12   :)

% 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,
    nat: $tType ).

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

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

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

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

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

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

thf(type_def_16,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_17,type,
    produc8923325533196201883nteger: $tType ).

thf(type_def_18,type,
    set_fi4554929511873752355omplex: $tType ).

thf(type_def_19,type,
    filter6041513312241820739omplex: $tType ).

thf(type_def_20,type,
    set_fi7789364187291644575l_real: $tType ).

thf(type_def_21,type,
    filter2146258269922977983l_real: $tType ).

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

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

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

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

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

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

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

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

thf(type_def_30,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(type_def_31,type,
    set_Pr6218003697084177305l_real: $tType ).

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

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

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

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

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

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

thf(type_def_38,type,
    set_Pr1261947904930325089at_nat: $tType ).

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

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

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

thf(type_def_42,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_54,type,
    list_P6011104703257516679at_nat: $tType ).

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

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

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

thf(type_def_58,type,
    list_Code_integer: $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_P8526636022914148096eger_o: $tType ).

thf(type_def_69,type,
    list_P3744719386663036955um_num: $tType ).

thf(type_def_70,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(type_def_71,type,
    produc334124729049499915VEBT_o: $tType ).

thf(type_def_72,type,
    list_P4547456442757143711BT_int: $tType ).

thf(type_def_73,type,
    produc4894624898956917775BT_int: $tType ).

thf(type_def_74,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(type_def_75,type,
    produc9072475918466114483BT_nat: $tType ).

thf(type_def_76,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(type_def_77,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(type_def_78,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(type_def_79,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(type_def_80,type,
    option4927543243414619207at_nat: $tType ).

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

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

thf(type_def_83,type,
    produc7248412053542808358at_nat: $tType ).

thf(type_def_84,type,
    produc4471711990508489141at_nat: $tType ).

thf(type_def_85,type,
    produc2963631642982155120at_num: $tType ).

thf(type_def_86,type,
    produc3368934014287244435at_num: $tType ).

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

thf(type_def_88,type,
    produc4411394909380815293omplex: $tType ).

thf(type_def_89,type,
    produc2422161461964618553l_real: $tType ).

thf(func_def_0,type,
    produc3368934014287244435at_num: $tType ).

thf(func_def_1,type,
    produc4471711990508489141at_nat: $tType ).

thf(func_def_2,type,
    set_fi4554929511873752355omplex: $tType ).

thf(func_def_3,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(func_def_4,type,
    produc2963631642982155120at_num: $tType ).

thf(func_def_5,type,
    produc7248412053542808358at_nat: $tType ).

thf(func_def_6,type,
    set_fi7789364187291644575l_real: $tType ).

thf(func_def_7,type,
    filter6041513312241820739omplex: $tType ).

thf(func_def_8,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(func_def_9,type,
    list_P4547456442757143711BT_int: $tType ).

thf(func_def_10,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(func_def_11,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(func_def_12,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(func_def_13,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_14,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(func_def_15,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(func_def_16,type,
    filter2146258269922977983l_real: $tType ).

thf(func_def_17,type,
    list_P8526636022914148096eger_o: $tType ).

thf(func_def_18,type,
    option4927543243414619207at_nat: $tType ).

thf(func_def_19,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(func_def_20,type,
    list_P3744719386663036955um_num: $tType ).

thf(func_def_21,type,
    list_P6011104703257516679at_nat: $tType ).

thf(func_def_22,type,
    produc9072475918466114483BT_nat: $tType ).

thf(func_def_23,type,
    produc4894624898956917775BT_int: $tType ).

thf(func_def_24,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(func_def_25,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(func_def_26,type,
    produc4411394909380815293omplex: $tType ).

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

thf(func_def_28,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(func_def_29,type,
    list_P6285523579766656935_o_nat: $tType ).

thf(func_def_30,type,
    list_P3795440434834930179_o_int: $tType ).

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

thf(func_def_32,type,
    produc334124729049499915VEBT_o: $tType ).

thf(func_def_33,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(func_def_34,type,
    produc6271795597528267376eger_o: $tType ).

thf(func_def_35,type,
    produc2422161461964618553l_real: $tType ).

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

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

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

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

thf(func_def_40,type,
    list_P4002435161011370285od_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_84,type,
    archim2889992004027027881ng_rat: rat > int ).

thf(func_def_85,type,
    archim7802044766580827645g_real: real > int ).

thf(func_def_86,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_87,type,
    archim6058952711729229775r_real: real > int ).

thf(func_def_88,type,
    archimedean_frac_rat: rat > rat ).

thf(func_def_89,type,
    archim2898591450579166408c_real: real > real ).

thf(func_def_90,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_91,type,
    archim8280529875227126926d_real: real > int ).

thf(func_def_92,type,
    binomial: nat > nat > nat ).

thf(func_def_93,type,
    gbinomial_complex: complex > nat > complex ).

thf(func_def_94,type,
    gbinomial_int: int > nat > int ).

thf(func_def_95,type,
    gbinomial_nat: nat > nat > nat ).

thf(func_def_96,type,
    gbinomial_rat: rat > nat > rat ).

thf(func_def_97,type,
    gbinomial_real: real > nat > real ).

thf(func_def_98,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_99,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_100,type,
    bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_101,type,
    bit_concat_bit: nat > int > int > int ).

thf(func_def_102,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_103,type,
    bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_104,type,
    bit_ri7632146776885996613nteger: code_integer > code_integer ).

thf(func_def_105,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_106,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(func_def_107,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_108,type,
    bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).

thf(func_def_109,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_110,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_111,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_112,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_113,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_114,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_115,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_116,type,
    bit_se2119862282449309892nteger: nat > code_integer ).

thf(func_def_117,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_118,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_119,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_120,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_121,type,
    bit_se7788150548672797655nteger: nat > code_integer > code_integer ).

thf(func_def_122,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_123,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_124,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_125,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_126,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_127,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_128,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_129,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_130,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_131,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_132,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_133,type,
    bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).

thf(func_def_134,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_135,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_136,type,
    bit_se9216721137139052372nteger: code_integer > nat > $o ).

thf(func_def_137,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_138,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_139,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_140,type,
    bit_un1837492267222099188nd_num: num > num > option_num ).

thf(func_def_141,type,
    bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_142,type,
    bit_un6178654185764691216or_num: num > num > option_num ).

thf(func_def_143,type,
    bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_144,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(func_def_145,type,
    bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_146,type,
    bit_un2480387367778600638or_num: num > num > option_num ).

thf(func_def_147,type,
    bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_148,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_149,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_150,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_151,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_152,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_153,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_154,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_155,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_156,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(func_def_157,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(func_def_158,type,
    comple4887499456419720421f_real: set_real > real ).

thf(func_def_159,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_160,type,
    complete_Sup_Sup_int: set_int > int ).

thf(func_def_161,type,
    comple1385675409528146559p_real: set_real > real ).

thf(func_def_162,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(func_def_163,type,
    arg: complex > real ).

thf(func_def_164,type,
    cis: real > complex ).

thf(func_def_165,type,
    cnj: complex > complex ).

thf(func_def_166,type,
    complex2: real > real > complex ).

thf(func_def_167,type,
    im: complex > real ).

thf(func_def_168,type,
    re: complex > real ).

thf(func_def_169,type,
    csqrt: complex > complex ).

thf(func_def_170,type,
    imaginary_unit: complex ).

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

thf(func_def_172,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(func_def_173,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(func_def_174,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(func_def_175,type,
    adjust_div: product_prod_int_int > int ).

thf(func_def_176,type,
    adjust_mod: int > int > int ).

thf(func_def_177,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_178,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_179,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_180,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_181,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_182,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_183,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_184,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_185,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_186,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_187,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_188,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_189,type,
    comm_s2602460028002588243omplex: complex > nat > complex ).

thf(func_def_190,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_191,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_192,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_193,type,
    comm_s7457072308508201937r_real: real > nat > real ).

thf(func_def_194,type,
    semiri3624122377584611663nteger: nat > code_integer ).

thf(func_def_195,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(func_def_196,type,
    semiri4449623510593786356d_enat: nat > extended_enat ).

thf(func_def_197,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(func_def_198,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_199,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(func_def_200,type,
    semiri2265585572941072030t_real: nat > real ).

thf(func_def_201,type,
    invers8013647133539491842omplex: complex > complex ).

thf(func_def_202,type,
    inverse_inverse_rat: rat > rat ).

thf(func_def_203,type,
    inverse_inverse_real: real > real ).

thf(func_def_204,type,
    at_bot_real: filter_real ).

thf(func_def_205,type,
    at_top_nat: filter_nat ).

thf(func_def_206,type,
    at_top_real: filter_real ).

thf(func_def_207,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_208,type,
    eventually_real: ( real > $o ) > filter_real > $o ).

thf(func_def_209,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(func_def_210,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

thf(func_def_211,type,
    filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).

thf(func_def_212,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(func_def_213,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(func_def_214,type,
    finite_card_o: set_o > nat ).

thf(func_def_215,type,
    finite_card_complex: set_complex > nat ).

thf(func_def_216,type,
    finite_card_int: set_int > nat ).

thf(func_def_217,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_218,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_219,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_220,type,
    finite_card_char: set_char > nat ).

thf(func_def_221,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(func_def_222,type,
    finite_finite_int: set_int > $o ).

thf(func_def_223,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_224,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(func_def_225,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(func_def_226,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_227,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(func_def_228,type,
    comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).

thf(func_def_229,type,
    id_o: $o > $o ).

thf(func_def_230,type,
    id_nat: nat > nat ).

thf(func_def_231,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_232,type,
    inj_on_nat_char: ( nat > char ) > set_nat > $o ).

thf(func_def_233,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(func_def_234,type,
    map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).

thf(func_def_235,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_236,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

thf(func_def_237,type,
    gcd_Gcd_int: set_int > int ).

thf(func_def_238,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_239,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_240,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_241,type,
    gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_242,type,
    gcd_gcd_int: int > int > int ).

thf(func_def_243,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(func_def_244,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_245,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_246,type,
    abs_abs_complex: complex > complex ).

thf(func_def_247,type,
    abs_abs_int: int > int ).

thf(func_def_248,type,
    abs_abs_rat: rat > rat ).

thf(func_def_249,type,
    abs_abs_real: real > real ).

thf(func_def_250,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_251,type,
    minus_minus_complex: complex > complex > complex ).

thf(func_def_252,type,
    minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_253,type,
    minus_minus_int: int > int > int ).

thf(func_def_254,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_255,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_256,type,
    minus_minus_real: real > real > real ).

thf(func_def_257,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(func_def_258,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_259,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_260,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_261,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(func_def_262,type,
    one_one_Code_integer: code_integer ).

thf(func_def_263,type,
    one_one_complex: complex ).

thf(func_def_264,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(func_def_265,type,
    one_one_int: int ).

thf(func_def_266,type,
    one_one_nat: nat ).

thf(func_def_267,type,
    one_one_rat: rat ).

thf(func_def_268,type,
    one_one_real: real ).

thf(func_def_269,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_270,type,
    plus_plus_complex: complex > complex > complex ).

thf(func_def_271,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_272,type,
    plus_plus_int: int > int > int ).

thf(func_def_273,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_274,type,
    plus_plus_num: num > num > num ).

thf(func_def_275,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_276,type,
    plus_plus_real: real > real > real ).

thf(func_def_277,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_278,type,
    sgn_sgn_complex: complex > complex ).

thf(func_def_279,type,
    sgn_sgn_int: int > int ).

thf(func_def_280,type,
    sgn_sgn_rat: rat > rat ).

thf(func_def_281,type,
    sgn_sgn_real: real > real ).

thf(func_def_282,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_283,type,
    times_times_complex: complex > complex > complex ).

thf(func_def_284,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_285,type,
    times_times_int: int > int > int ).

thf(func_def_286,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_287,type,
    times_times_num: num > num > num ).

thf(func_def_288,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_289,type,
    times_times_real: real > real > real ).

thf(func_def_290,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_291,type,
    uminus1482373934393186551omplex: complex > complex ).

thf(func_def_292,type,
    uminus_uminus_int: int > int ).

thf(func_def_293,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_294,type,
    uminus_uminus_real: real > real ).

thf(func_def_295,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(func_def_296,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_297,type,
    zero_zero_complex: complex ).

thf(func_def_298,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(func_def_299,type,
    zero_zero_int: int ).

thf(func_def_300,type,
    zero_zero_nat: nat ).

thf(func_def_301,type,
    zero_zero_rat: rat ).

thf(func_def_302,type,
    zero_zero_real: real ).

thf(func_def_303,type,
    groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_304,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_305,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_306,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_307,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_308,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(func_def_309,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_310,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(func_def_311,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_312,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_313,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_314,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(func_def_315,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_316,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_317,type,
    groups7108830773950497114d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).

thf(func_def_318,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_319,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_320,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_321,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(func_def_322,type,
    groups6381953495645901045omplex: ( product_prod_nat_nat > complex ) > set_Pr1261947904930325089at_nat > complex ).

thf(func_def_323,type,
    groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_324,type,
    groups4567486121110086003t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).

thf(func_def_325,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(func_def_326,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(func_def_327,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(func_def_328,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_329,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_330,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(func_def_331,type,
    groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_332,type,
    groups766887009212190081x_real: ( complex > real ) > set_complex > real ).

thf(func_def_333,type,
    groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).

thf(func_def_334,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_335,type,
    groups2316167850115554303t_real: ( int > real ) > set_int > real ).

thf(func_def_336,type,
    groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_337,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_338,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_339,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_340,type,
    groups129246275422532515t_real: ( nat > real ) > set_nat > real ).

thf(func_def_341,type,
    groups713298508707869441omplex: ( real > complex ) > set_real > complex ).

thf(func_def_342,type,
    groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_343,type,
    groups1681761925125756287l_real: ( real > real ) > set_real > real ).

thf(func_def_344,type,
    groups3417619833198082522nteger: ( $o > code_integer ) > code_integer > list_o > code_integer ).

thf(func_def_345,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(func_def_346,type,
    groups9119017779487936845_o_nat: ( $o > nat ) > nat > list_o > nat ).

thf(func_def_347,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_348,type,
    the_int: ( int > $o ) > int ).

thf(func_def_349,type,
    the_real: ( real > $o ) > real ).

thf(func_def_350,type,
    if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).

thf(func_def_351,type,
    if_nat_int_int: $o > ( nat > int > int ) > ( nat > int > int ) > nat > int > int ).

thf(func_def_352,type,
    if_nat_nat_nat: $o > ( nat > nat > nat ) > ( nat > nat > nat ) > nat > nat > nat ).

thf(func_def_353,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_354,type,
    if_complex: $o > complex > complex > complex ).

thf(func_def_355,type,
    if_int: $o > int > int > int ).

thf(func_def_356,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_357,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(func_def_358,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_359,type,
    if_num: $o > num > num > num ).

thf(func_def_360,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_361,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_362,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_363,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_364,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_365,type,
    if_rat: $o > rat > rat > rat ).

thf(func_def_366,type,
    if_real: $o > real > real > real ).

thf(func_def_367,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(func_def_368,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_369,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_370,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(func_def_371,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_372,type,
    nat2: int > nat ).

thf(func_def_373,type,
    ring_11222124179247155820nteger: set_Code_integer ).

thf(func_def_374,type,
    ring_1_Ints_complex: set_complex ).

thf(func_def_375,type,
    ring_1_Ints_int: set_int ).

thf(func_def_376,type,
    ring_1_Ints_rat: set_rat ).

thf(func_def_377,type,
    ring_1_Ints_real: set_real ).

thf(func_def_378,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_379,type,
    ring_17405671764205052669omplex: int > complex ).

thf(func_def_380,type,
    ring_1_of_int_int: int > int ).

thf(func_def_381,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_382,type,
    ring_1_of_int_real: int > real ).

thf(func_def_383,type,
    inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_384,type,
    inf_inf_nat: nat > nat > nat ).

thf(func_def_385,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_386,type,
    sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_387,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_388,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_389,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_390,type,
    bfun_nat_real: ( nat > real ) > filter_nat > $o ).

thf(func_def_391,type,
    at_infinity_real: filter_real ).

thf(func_def_392,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_393,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_394,type,
    concat_o: list_list_o > list_o ).

thf(func_def_395,type,
    concat_int: list_list_int > list_int ).

thf(func_def_396,type,
    concat_nat: list_list_nat > list_nat ).

thf(func_def_397,type,
    concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_398,type,
    distinct_int: list_int > $o ).

thf(func_def_399,type,
    distinct_nat: list_nat > $o ).

thf(func_def_400,type,
    drop_nat: nat > list_nat > list_nat ).

thf(func_def_401,type,
    linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).

thf(func_def_402,type,
    linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_403,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_404,type,
    cons_int: int > list_int > list_int ).

thf(func_def_405,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_406,type,
    nil_int: list_int ).

thf(func_def_407,type,
    nil_nat: list_nat ).

thf(func_def_408,type,
    hd_nat: list_nat > nat ).

thf(func_def_409,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_410,type,
    set_o2: list_o > set_o ).

thf(func_def_411,type,
    set_complex2: list_complex > set_complex ).

thf(func_def_412,type,
    set_int2: list_int > set_int ).

thf(func_def_413,type,
    set_list_o2: list_list_o > set_list_o ).

thf(func_def_414,type,
    set_list_int2: list_list_int > set_list_int ).

thf(func_def_415,type,
    set_list_nat2: list_list_nat > set_list_nat ).

thf(func_def_416,type,
    set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).

thf(func_def_417,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_418,type,
    set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_419,type,
    set_real2: list_real > set_real ).

thf(func_def_420,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_421,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(func_def_422,type,
    tl_nat: list_nat > list_nat ).

thf(func_def_423,type,
    nth_o: list_o > nat > $o ).

thf(func_def_424,type,
    nth_Code_integer: list_Code_integer > nat > code_integer ).

thf(func_def_425,type,
    nth_complex: list_complex > nat > complex ).

thf(func_def_426,type,
    nth_int: list_int > nat > int ).

thf(func_def_427,type,
    nth_list_nat: list_list_nat > nat > list_nat ).

thf(func_def_428,type,
    nth_nat: list_nat > nat > nat ).

thf(func_def_429,type,
    nth_num: list_num > nat > num ).

thf(func_def_430,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(func_def_431,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(func_def_432,type,
    nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).

thf(func_def_433,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(func_def_434,type,
    nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).

thf(func_def_435,type,
    nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).

thf(func_def_436,type,
    nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).

thf(func_def_437,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(func_def_438,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(func_def_439,type,
    nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).

thf(func_def_440,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(func_def_441,type,
    nth_real: list_real > nat > real ).

thf(func_def_442,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_443,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(func_def_444,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(func_def_445,type,
    product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).

thf(func_def_446,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(func_def_447,type,
    produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).

thf(func_def_448,type,
    product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).

thf(func_def_449,type,
    produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).

thf(func_def_450,type,
    product_num_num: list_num > list_num > list_P3744719386663036955um_num ).

thf(func_def_451,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(func_def_452,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(func_def_453,type,
    produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).

thf(func_def_454,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(func_def_455,type,
    remdups_nat: list_nat > list_nat ).

thf(func_def_456,type,
    replicate_o: nat > $o > list_o ).

thf(func_def_457,type,
    replicate_complex: nat > complex > list_complex ).

thf(func_def_458,type,
    replicate_int: nat > int > list_int ).

thf(func_def_459,type,
    replicate_nat: nat > nat > list_nat ).

thf(func_def_460,type,
    replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).

thf(func_def_461,type,
    replicate_real: nat > real > list_real ).

thf(func_def_462,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_463,type,
    sorted_wrt_int: ( int > int > $o ) > list_int > $o ).

thf(func_def_464,type,
    sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(func_def_465,type,
    subseqs_o: list_o > list_list_o ).

thf(func_def_466,type,
    subseqs_int: list_int > list_list_int ).

thf(func_def_467,type,
    subseqs_nat: list_nat > list_list_nat ).

thf(func_def_468,type,
    subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).

thf(func_def_469,type,
    take_nat: nat > list_nat > list_nat ).

thf(func_def_470,type,
    upt: nat > nat > list_nat ).

thf(func_def_471,type,
    upto: int > int > list_int ).

thf(func_def_472,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_473,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_474,type,
    suc: nat > nat ).

thf(func_def_475,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_476,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(func_def_477,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_478,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_479,type,
    pred: nat > nat ).

thf(func_def_480,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_481,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(func_def_482,type,
    semiri4216267220026989637d_enat: nat > extended_enat ).

thf(func_def_483,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_484,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_485,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_486,type,
    semiri5074537144036343181t_real: nat > real ).

thf(func_def_487,type,
    semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).

thf(func_def_488,type,
    semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).

thf(func_def_489,type,
    semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).

thf(func_def_490,type,
    semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).

thf(func_def_491,type,
    semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).

thf(func_def_492,type,
    size_size_list_o: list_o > nat ).

thf(func_def_493,type,
    size_s3445333598471063425nteger: list_Code_integer > nat ).

thf(func_def_494,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(func_def_495,type,
    size_size_list_int: list_int > nat ).

thf(func_def_496,type,
    size_s2710708370519433104list_o: list_list_o > nat ).

thf(func_def_497,type,
    size_s533118279054570080st_int: list_list_int > nat ).

thf(func_def_498,type,
    size_s3023201423986296836st_nat: list_list_nat > nat ).

thf(func_def_499,type,
    size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).

thf(func_def_500,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_501,type,
    size_size_list_num: list_num > nat ).

thf(func_def_502,type,
    size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).

thf(func_def_503,type,
    size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).

thf(func_def_504,type,
    size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).

thf(func_def_505,type,
    size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).

thf(func_def_506,type,
    size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).

thf(func_def_507,type,
    size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).

thf(func_def_508,type,
    size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).

thf(func_def_509,type,
    size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).

thf(func_def_510,type,
    size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).

thf(func_def_511,type,
    size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).

thf(func_def_512,type,
    size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).

thf(func_def_513,type,
    size_size_list_real: list_real > nat ).

thf(func_def_514,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(func_def_515,type,
    size_size_num: num > nat ).

thf(func_def_516,type,
    size_size_option_num: option_num > nat ).

thf(func_def_517,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(func_def_518,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(func_def_519,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_520,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_521,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_522,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_523,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_524,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_525,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_526,type,
    nat_triangle: nat > nat ).

thf(func_def_527,type,
    root: nat > real > real ).

thf(func_def_528,type,
    sqrt: real > real ).

thf(func_def_529,type,
    bitM: num > num ).

thf(func_def_530,type,
    inc: num > num ).

thf(func_def_531,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_532,type,
    neg_nu7009210354673126013omplex: complex > complex ).

thf(func_def_533,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_534,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_535,type,
    neg_numeral_dbl_real: real > real ).

thf(func_def_536,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_537,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(func_def_538,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_539,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_540,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(func_def_541,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_542,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(func_def_543,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_544,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_545,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(func_def_546,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_547,type,
    bit0: num > num ).

thf(func_def_548,type,
    bit1: num > num ).

thf(func_def_549,type,
    one: num ).

thf(func_def_550,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_551,type,
    size_num: num > nat ).

thf(func_def_552,type,
    num_of_nat: nat > num ).

thf(func_def_553,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_554,type,
    numera6690914467698888265omplex: num > complex ).

thf(func_def_555,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(func_def_556,type,
    numeral_numeral_int: num > int ).

thf(func_def_557,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_558,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_559,type,
    numeral_numeral_real: num > real ).

thf(func_def_560,type,
    pow: num > num > num ).

thf(func_def_561,type,
    pred_numeral: num > nat ).

thf(func_def_562,type,
    sqr: num > num ).

thf(func_def_563,type,
    none_num: option_num ).

thf(func_def_564,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(func_def_565,type,
    some_num: num > option_num ).

thf(func_def_566,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(func_def_567,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(func_def_568,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_569,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_570,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_571,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(func_def_572,type,
    size_option_num: ( num > nat ) > option_num > nat ).

thf(func_def_573,type,
    size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).

thf(func_def_574,type,
    bot_bo4199563552545308370d_enat: extended_enat ).

thf(func_def_575,type,
    bot_bot_nat: nat ).

thf(func_def_576,type,
    bot_bot_set_int: set_int ).

thf(func_def_577,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_578,type,
    ord_less_complex_o: ( complex > $o ) > ( complex > $o ) > $o ).

thf(func_def_579,type,
    ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_580,type,
    ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_581,type,
    ord_le549003669493604880_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).

thf(func_def_582,type,
    ord_less_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_583,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_584,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(func_def_585,type,
    ord_less_int: int > int > $o ).

thf(func_def_586,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_587,type,
    ord_less_num: num > num > $o ).

thf(func_def_588,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_589,type,
    ord_less_real: real > real > $o ).

thf(func_def_590,type,
    ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_591,type,
    ord_less_set_complex: set_complex > set_complex > $o ).

thf(func_def_592,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_593,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_594,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(func_def_595,type,
    ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_596,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_597,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_598,type,
    ord_less_set_set_int: set_set_int > set_set_int > $o ).

thf(func_def_599,type,
    ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).

thf(func_def_600,type,
    ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_601,type,
    ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_602,type,
    ord_le704812498762024988_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).

thf(func_def_603,type,
    ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_604,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_605,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(func_def_606,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(func_def_607,type,
    ord_le4104064031414453916r_real: filter_real > filter_real > $o ).

thf(func_def_608,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_609,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_610,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_611,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_612,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_613,type,
    ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_614,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(func_def_615,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_616,type,
    ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).

thf(func_def_617,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_618,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(func_def_619,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_620,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(func_def_621,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_622,type,
    ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).

thf(func_def_623,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_624,type,
    ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_625,type,
    ord_max_int: int > int > int ).

thf(func_def_626,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_627,type,
    ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_628,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_629,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(func_def_630,type,
    order_9091379641038594480t_real: ( nat > real ) > $o ).

thf(func_def_631,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(func_def_632,type,
    order_mono_nat_real: ( nat > real ) > $o ).

thf(func_def_633,type,
    order_5726023648592871131at_nat: ( nat > nat ) > $o ).

thf(func_def_634,type,
    order_7092887310737990675l_real: ( real > real ) > $o ).

thf(func_def_635,type,
    top_top_set_o: set_o ).

thf(func_def_636,type,
    top_top_set_nat: set_nat ).

thf(func_def_637,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_638,type,
    top_top_set_real: set_real ).

thf(func_def_639,type,
    top_top_set_char: set_char ).

thf(func_def_640,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_641,type,
    power_power_complex: complex > nat > complex ).

thf(func_def_642,type,
    power_8040749407984259932d_enat: extended_enat > nat > extended_enat ).

thf(func_def_643,type,
    power_power_int: int > nat > int ).

thf(func_def_644,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_645,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_646,type,
    power_power_real: real > nat > real ).

thf(func_def_647,type,
    produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).

thf(func_def_648,type,
    produc851828971589881931at_num: ( nat > num > num ) > produc2963631642982155120at_num > produc3368934014287244435at_num ).

thf(func_def_649,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(func_def_650,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(func_def_651,type,
    product_Pair_o_nat: $o > nat > product_prod_o_nat ).

thf(func_def_652,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(func_def_653,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_654,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_655,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_656,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_657,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_658,type,
    produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(func_def_659,type,
    produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).

thf(func_def_660,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_661,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(func_def_662,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(func_def_663,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(func_def_664,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(func_def_665,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(func_def_666,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_667,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_668,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_669,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_670,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_671,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_672,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(func_def_673,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_674,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_675,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_676,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_677,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_678,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_679,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_680,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_681,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_682,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(func_def_683,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_684,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_685,type,
    produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).

thf(func_def_686,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(func_def_687,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_688,type,
    fract: int > int > rat ).

thf(func_def_689,type,
    rep_Rat: rat > product_prod_int_int ).

thf(func_def_690,type,
    field_5140801741446780682s_real: set_real ).

thf(func_def_691,type,
    field_7254667332652039916t_real: rat > real ).

thf(func_def_692,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_693,type,
    positive: rat > $o ).

thf(func_def_694,type,
    real_V2521375963428798218omplex: set_complex ).

thf(func_def_695,type,
    real_V470468836141973256s_real: set_real ).

thf(func_def_696,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(func_def_697,type,
    real_V975177566351809787t_real: real > real > real ).

thf(func_def_698,type,
    real_V1022390504157884413omplex: complex > real ).

thf(func_def_699,type,
    real_V7735802525324610683m_real: real > real ).

thf(func_def_700,type,
    real_V4546457046886955230omplex: real > complex ).

thf(func_def_701,type,
    real_V1803761363581548252l_real: real > real ).

thf(func_def_702,type,
    real_V2046097035970521341omplex: real > complex > complex ).

thf(func_def_703,type,
    real_V1485227260804924795R_real: real > real > real ).

thf(func_def_704,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_705,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(func_def_706,type,
    divide_divide_int: int > int > int ).

thf(func_def_707,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_708,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_709,type,
    divide_divide_real: real > real > real ).

thf(func_def_710,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_711,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(func_def_712,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_713,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_714,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_715,type,
    dvd_dvd_real: real > real > $o ).

thf(func_def_716,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_717,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_718,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_719,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_720,type,
    zero_n1201886186963655149omplex: $o > complex ).

thf(func_def_721,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_722,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_723,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(func_def_724,type,
    zero_n3304061248610475627l_real: $o > real ).

thf(func_def_725,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(func_def_726,type,
    suminf_int: ( nat > int ) > int ).

thf(func_def_727,type,
    suminf_nat: ( nat > nat ) > nat ).

thf(func_def_728,type,
    suminf_real: ( nat > real ) > real ).

thf(func_def_729,type,
    summable_complex: ( nat > complex ) > $o ).

thf(func_def_730,type,
    summable_int: ( nat > int ) > $o ).

thf(func_def_731,type,
    summable_nat: ( nat > nat ) > $o ).

thf(func_def_732,type,
    summable_real: ( nat > real ) > $o ).

thf(func_def_733,type,
    sums_complex: ( nat > complex ) > complex > $o ).

thf(func_def_734,type,
    sums_int: ( nat > int ) > int > $o ).

thf(func_def_735,type,
    sums_nat: ( nat > nat ) > nat > $o ).

thf(func_def_736,type,
    sums_real: ( nat > real ) > real > $o ).

thf(func_def_737,type,
    collect_o: ( $o > $o ) > set_o ).

thf(func_def_738,type,
    collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).

thf(func_def_739,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(func_def_740,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_741,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_742,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_743,type,
    collect_num: ( num > $o ) > set_num ).

thf(func_def_744,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(func_def_745,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_746,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_747,type,
    collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).

thf(func_def_748,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(func_def_749,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_750,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(func_def_751,type,
    collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).

thf(func_def_752,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_753,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_754,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_755,type,
    image_nat_real: ( nat > real ) > set_nat > set_real ).

thf(func_def_756,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_757,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_758,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(func_def_759,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(func_def_760,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(func_def_761,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_762,type,
    insert_int: int > set_int > set_int ).

thf(func_def_763,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_764,type,
    set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).

thf(func_def_765,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_766,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_767,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_768,type,
    set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).

thf(func_def_769,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_770,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_771,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(func_def_772,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_773,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(func_def_774,type,
    set_or370866239135849197et_int: set_int > set_int > set_set_int ).

thf(func_def_775,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_776,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_777,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_778,type,
    set_ord_atLeast_real: real > set_real ).

thf(func_def_779,type,
    set_ord_atMost_int: int > set_int ).

thf(func_def_780,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_781,type,
    set_ord_atMost_num: num > set_num ).

thf(func_def_782,type,
    set_ord_atMost_rat: rat > set_rat ).

thf(func_def_783,type,
    set_ord_atMost_real: real > set_real ).

thf(func_def_784,type,
    set_or58775011639299419et_int: set_int > set_set_int ).

thf(func_def_785,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_786,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_787,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_788,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_789,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(func_def_790,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_791,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(func_def_792,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_793,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_794,type,
    set_ord_lessThan_num: num > set_num ).

thf(func_def_795,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_796,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(func_def_797,type,
    ascii_of: char > char ).

thf(func_def_798,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_799,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_800,type,
    integer_of_char: char > code_integer ).

thf(func_def_801,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_802,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(func_def_803,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(func_def_804,type,
    topolo4899668324122417113eq_int: ( nat > int ) > $o ).

thf(func_def_805,type,
    topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).

thf(func_def_806,type,
    topolo1459490580787246023eq_num: ( nat > num ) > $o ).

thf(func_def_807,type,
    topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).

thf(func_def_808,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(func_def_809,type,
    topolo3100542954746470799et_int: ( nat > set_int ) > $o ).

thf(func_def_810,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(func_def_811,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(func_def_812,type,
    topolo6517432010174082258omplex: ( nat > complex ) > $o ).

thf(func_def_813,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(func_def_814,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(func_def_815,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(func_def_816,type,
    arccos: real > real ).

thf(func_def_817,type,
    arcosh_real: real > real ).

thf(func_def_818,type,
    arcsin: real > real ).

thf(func_def_819,type,
    arctan: real > real ).

thf(func_def_820,type,
    arsinh_real: real > real ).

thf(func_def_821,type,
    artanh_real: real > real ).

thf(func_def_822,type,
    cos_complex: complex > complex ).

thf(func_def_823,type,
    cos_real: real > real ).

thf(func_def_824,type,
    cos_coeff: nat > real ).

thf(func_def_825,type,
    cosh_complex: complex > complex ).

thf(func_def_826,type,
    cosh_real: real > real ).

thf(func_def_827,type,
    cot_complex: complex > complex ).

thf(func_def_828,type,
    cot_real: real > real ).

thf(func_def_829,type,
    diffs_complex: ( nat > complex ) > nat > complex ).

thf(func_def_830,type,
    diffs_int: ( nat > int ) > nat > int ).

thf(func_def_831,type,
    diffs_real: ( nat > real ) > nat > real ).

thf(func_def_832,type,
    exp_complex: complex > complex ).

thf(func_def_833,type,
    exp_real: real > real ).

thf(func_def_834,type,
    ln_ln_real: real > real ).

thf(func_def_835,type,
    log: real > real > real ).

thf(func_def_836,type,
    pi: real ).

thf(func_def_837,type,
    powr_real: real > real > real ).

thf(func_def_838,type,
    sin_complex: complex > complex ).

thf(func_def_839,type,
    sin_real: real > real ).

thf(func_def_840,type,
    sin_coeff: nat > real ).

thf(func_def_841,type,
    sinh_complex: complex > complex ).

thf(func_def_842,type,
    sinh_real: real > real ).

thf(func_def_843,type,
    tan_complex: complex > complex ).

thf(func_def_844,type,
    tan_real: real > real ).

thf(func_def_845,type,
    tanh_complex: complex > complex ).

thf(func_def_846,type,
    tanh_real: real > real ).

thf(func_def_847,type,
    transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_848,type,
    transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_849,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(func_def_850,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_851,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(func_def_852,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(func_def_853,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(func_def_854,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_855,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(func_def_856,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(func_def_857,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_858,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(func_def_859,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_860,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(func_def_861,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_862,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(func_def_863,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_864,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(func_def_865,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(func_def_866,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_867,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_868,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_869,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_870,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_871,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(func_def_872,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_873,type,
    fChoice_real: ( real > $o ) > real ).

thf(func_def_874,type,
    member_o: $o > set_o > $o ).

thf(func_def_875,type,
    member_Code_integer: code_integer > set_Code_integer > $o ).

thf(func_def_876,type,
    member_complex: complex > set_complex > $o ).

thf(func_def_877,type,
    member_int: int > set_int > $o ).

thf(func_def_878,type,
    member_list_o: list_o > set_list_o > $o ).

thf(func_def_879,type,
    member_list_int: list_int > set_list_int > $o ).

thf(func_def_880,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_881,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(func_def_882,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_883,type,
    member_num: num > set_num > $o ).

thf(func_def_884,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_885,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_886,type,
    member_real: real > set_real > $o ).

thf(func_def_887,type,
    member_set_int: set_int > set_set_int > $o ).

thf(func_def_888,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_889,type,
    deg: nat ).

thf(func_def_890,type,
    info: option4927543243414619207at_nat ).

thf(func_def_891,type,
    m: nat ).

thf(func_def_892,type,
    ma: nat ).

thf(func_def_893,type,
    mi: nat ).

thf(func_def_894,type,
    n: nat ).

thf(func_def_895,type,
    na: nat ).

thf(func_def_896,type,
    summary: vEBT_VEBT ).

thf(func_def_897,type,
    treeList: list_VEBT_VEBT ).

thf(func_def_898,type,
    x: nat ).

thf(func_def_917,type,
    sP0: ( nat > vEBT_VEBT > $o ) > nat > $o ).

thf(func_def_918,type,
    sP1: ( nat > vEBT_VEBT > $o ) > nat > $o ).

thf(func_def_919,type,
    sP2: nat > list_VEBT_VEBT > $o ).

thf(func_def_920,type,
    sP3: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_921,type,
    sP4: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).

thf(func_def_922,type,
    sP5: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_923,type,
    sP6: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_924,type,
    sP7: nat > list_VEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_925,type,
    sP8: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_926,type,
    sP9: vEBT_VEBT > nat > $o ).

thf(func_def_927,type,
    sP10: vEBT_VEBT > nat > $o ).

thf(func_def_928,type,
    sP11: nat > vEBT_VEBT > $o ).

thf(func_def_929,type,
    sP12: vEBT_VEBT > nat > $o ).

thf(func_def_930,type,
    sP13: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).

thf(func_def_931,type,
    sP14: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).

thf(func_def_932,type,
    sP15: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > $o ).

thf(func_def_933,type,
    sP16: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > $o ).

thf(func_def_934,type,
    sP17: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > $o ).

thf(func_def_935,type,
    sP18: ( option4927543243414619207at_nat > option_num > $o ) > option_num > option4927543243414619207at_nat > $o ).

thf(func_def_936,type,
    sP19: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_937,type,
    sP20: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_938,type,
    sP21: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_939,type,
    sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_940,type,
    sP23: list_VEBT_VEBT > $o ).

thf(func_def_941,type,
    sP24: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_942,type,
    sP25: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_943,type,
    sP26: list_VEBT_VEBT > nat > $o ).

thf(func_def_944,type,
    sP27: nat > list_VEBT_VEBT > $o ).

thf(func_def_945,type,
    sP28: list_VEBT_VEBT > $o ).

thf(func_def_946,type,
    sP29: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_947,type,
    sP30: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_948,type,
    sP31: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_949,type,
    sP32: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_950,type,
    sP33: nat > nat > list_VEBT_VEBT > $o ).

thf(func_def_951,type,
    sP34: nat > list_VEBT_VEBT > $o ).

thf(func_def_952,type,
    sP35: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_953,type,
    sP36: nat > $o ).

thf(func_def_954,type,
    sK37: ( nat > vEBT_VEBT > $o ) > nat > nat ).

thf(func_def_955,type,
    sK38: nat > ( nat > vEBT_VEBT > $o ) > vEBT_VEBT ).

thf(func_def_956,type,
    sK39: list_VEBT_VEBT > ( nat > vEBT_VEBT > $o ) > nat > nat ).

thf(func_def_957,type,
    sK40: ( nat > vEBT_VEBT > $o ) > nat > list_VEBT_VEBT ).

thf(func_def_958,type,
    sK41: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_959,type,
    sK42: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_960,type,
    sK43: list_VEBT_VEBT > nat ).

thf(func_def_961,type,
    sK44: vEBT_VEBT > nat ).

thf(func_def_962,type,
    sK45: vEBT_VEBT > nat > nat ).

thf(func_def_963,type,
    sK46: vEBT_VEBT > nat > nat ).

thf(func_def_964,type,
    sK47: vEBT_VEBT > nat > nat ).

thf(func_def_965,type,
    sK48: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_966,type,
    sK49: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_967,type,
    sK50: vEBT_VEBT > nat > nat ).

thf(func_def_968,type,
    sK51: vEBT_VEBT > nat > nat ).

thf(func_def_969,type,
    sK52: nat > vEBT_VEBT > nat ).

thf(func_def_970,type,
    sK53: nat > vEBT_VEBT > nat ).

thf(func_def_971,type,
    sK54: nat > vEBT_VEBT > nat ).

thf(func_def_972,type,
    sK55: nat > vEBT_VEBT > nat ).

thf(func_def_973,type,
    sK56: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_974,type,
    sK57: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_975,type,
    sK58: nat > vEBT_VEBT > nat ).

thf(func_def_976,type,
    sK59: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_977,type,
    sK60: vEBT_VEBT > nat > nat ).

thf(func_def_978,type,
    sK61: vEBT_VEBT > nat > nat ).

thf(func_def_979,type,
    sK62: vEBT_VEBT > nat > nat ).

thf(func_def_980,type,
    sK63: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_981,type,
    sK64: vEBT_VEBT > nat > nat ).

thf(func_def_982,type,
    sK65: vEBT_VEBT > nat > nat ).

thf(func_def_983,type,
    sK66: vEBT_VEBT > nat > nat ).

thf(func_def_984,type,
    sK67: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_985,type,
    sK68: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_986,type,
    sK69: nat > list_VEBT_VEBT > nat ).

thf(func_def_987,type,
    sK70: nat > list_VEBT_VEBT > nat ).

thf(func_def_988,type,
    sK71: vEBT_VEBT > $o ).

thf(func_def_989,type,
    sK72: vEBT_VEBT > $o ).

thf(func_def_990,type,
    sK73: ( list_VEBT_VEBT > $o ) > list_VEBT_VEBT ).

thf(func_def_991,type,
    sK74: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_992,type,
    sK75: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_993,type,
    sK76: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_994,type,
    sK77: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > num ).

thf(func_def_995,type,
    sK78: nat > nat ).

thf(func_def_996,type,
    sK79: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_997,type,
    sK80: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > product_prod_nat_nat ).

thf(func_def_998,type,
    sK81: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > num ).

thf(func_def_999,type,
    sK82: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1000,type,
    sK83: list_VEBT_VEBT > vEBT_VEBT > nat > nat ).

thf(func_def_1001,type,
    sK84: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1002,type,
    sK85: list_VEBT_VEBT > nat ).

thf(func_def_1003,type,
    sK86: nat > nat > list_VEBT_VEBT > nat > nat > nat ).

thf(func_def_1004,type,
    sK87: nat > nat > list_VEBT_VEBT > nat > nat > nat ).

thf(func_def_1005,type,
    sK88: list_VEBT_VEBT > nat > nat ).

thf(func_def_1006,type,
    sK89: nat > list_VEBT_VEBT ).

thf(func_def_1007,type,
    sK90: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_1008,type,
    sK91: vEBT_VEBT > nat ).

thf(func_def_1009,type,
    sK92: vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_1010,type,
    sK93: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1011,type,
    sK94: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1012,type,
    sK95: vEBT_VEBT > $o ).

thf(func_def_1013,type,
    sK96: vEBT_VEBT > $o ).

thf(func_def_1014,type,
    sK97: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1015,type,
    sK98: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1016,type,
    sK99: list_VEBT_VEBT > nat ).

thf(func_def_1017,type,
    sK100: vEBT_VEBT > nat ).

thf(func_def_1018,type,
    sK101: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1019,type,
    sK102: list_VEBT_VEBT > nat > nat ).

thf(func_def_1020,type,
    sK103: nat > list_VEBT_VEBT > nat > nat > nat > nat ).

thf(func_def_1021,type,
    sK104: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_1022,type,
    sK105: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1023,type,
    sK106: list_VEBT_VEBT > nat ).

thf(func_def_1024,type,
    sK107: list_VEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_1025,type,
    sK108: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_1026,type,
    sK109: list_VEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_1028,type,
    ph111: 
      !>[X0: $tType] : X0 ).

thf(f24320,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f23760,f23786,f23801,f24316,f24319]) ).

thf(f24319,plain,
    ~ spl110_1,
    inference(avatar_contradiction_clause,[status(thm)],[f24318]) ).

thf(f24318,plain,
    ( $false
    | ~ spl110_1 ),
    inference(trivial_inequality_removal,[status(thm)],[f24317]) ).

thf(f24317,plain,
    ( ( $false = $true )
    | ~ spl110_1 ),
    inference(forward_demodulation,[status(thm)],[f23756,f23665]) ).

thf(f23665,plain,
    ( $false
    = ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23663]) ).

thf(f23663,plain,
    ( $true
   != ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x )
      | ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f23567]) ).

thf(f23567,plain,
    ( $true
   != ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_VEBT_membermima @ Y0 @ Y1 )
          | ( vEBT_V5719532721284313246member @ Y0 @ Y1 ) )
      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary )
      @ x ) ),
    inference(definition_unfolding,[status(thm)],[f23489,f23355,f23427]) ).

thf(f23427,plain,
    ( info
    = ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ),
    inference(cnf_transformation,[status(thm)],[f737]) ).

thf(f737,axiom,
    ( info
    = ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_736__C5_Ohyps_C_I12_J) ).

thf(f23355,plain,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_VEBT_membermima @ Y0 @ Y1 )
          | ( vEBT_V5719532721284313246member @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f11806]) ).

thf(f11806,plain,
    ( vEBT_V8194947554948674370ptions
    = ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_VEBT_membermima @ Y0 @ Y1 )
          | ( vEBT_V5719532721284313246member @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f11805]) ).

thf(f11805,plain,
    ( ( ^ [X0: vEBT_VEBT,X1: nat] :
          ( ( vEBT_V5719532721284313246member @ X0 @ X1 )
          | ( vEBT_VEBT_membermima @ X0 @ X1 ) ) )
    = vEBT_V8194947554948674370ptions ),
    inference(rectify,[status(thm)],[f1]) ).

thf(f1,axiom,
    ( ( ^ [X0: vEBT_VEBT,X1: nat] :
          ( ( vEBT_V5719532721284313246member @ X0 @ X1 )
          | ( vEBT_VEBT_membermima @ X0 @ X1 ) ) )
    = vEBT_V8194947554948674370ptions ),
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_0_both__member__options__def) ).

thf(f23489,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f23091]) ).

thf(f23091,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
   != $true ),
    inference(flattening,[status(thm)],[f15733]) ).

thf(f15733,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
   != $true ),
    inference(fool_elimination,[status(thm)],[f15732]) ).

thf(f15732,plain,
    ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ),
    inference(rectify,[status(thm)],[f10250]) ).

thf(f10250,negated_conjecture,
    ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ),
    inference(negated_conjecture,[status(cth)],[f10249]) ).

thf(f10249,conjecture,
    vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x,
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',conj_0) ).

thf(f23756,plain,
    ( ( $true
      = ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) )
    | ~ spl110_1 ),
    inference(avatar_component_clause,[status(thm)],[f23755]) ).

thf(f23755,definition,
    ( spl110_1
  <=> ( $true
      = ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ) ),
    introduced(definition,[new_symbols(naming,[spl110_1])],[avatar_definition]) ).

thf(f24316,plain,
    ~ spl110_8,
    inference(avatar_contradiction_clause,[status(thm)],[f24315]) ).

thf(f24315,plain,
    ( $false
    | ~ spl110_8 ),
    inference(trivial_inequality_removal,[status(thm)],[f24314]) ).

thf(f24314,plain,
    ( ( $false = $true )
    | ~ spl110_8 ),
    inference(forward_demodulation,[status(thm)],[f23779,f23664]) ).

thf(f23664,plain,
    ( $false
    = ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23663]) ).

thf(f23779,plain,
    ( ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x )
      = $true )
    | ~ spl110_8 ),
    inference(avatar_component_clause,[status(thm)],[f23778]) ).

thf(f23778,definition,
    ( spl110_8
  <=> ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl110_8])],[avatar_definition]) ).

thf(f23801,plain,
    ( ~ spl110_9
    | spl110_8 ),
    inference(avatar_split_clause,[status(thm)],[f23566,f23778,f23782]) ).

thf(f23782,definition,
    ( spl110_9
  <=> ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl110_9])],[avatar_definition]) ).

thf(f23566,plain,
    ( ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x )
      = $true )
    | ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
     != $true ) ),
    inference(definition_unfolding,[status(thm)],[f23488,f23427]) ).

thf(f23488,plain,
    ( ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true )
    | ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
     != $true ) ),
    inference(cnf_transformation,[status(thm)],[f23132]) ).

thf(f23132,plain,
    ( ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true )
    | ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
     != $true ) ),
    inference(ennf_transformation,[status(thm)],[f23076]) ).

thf(f23076,plain,
    ( ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
      = $true )
   => ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true ) ),
    inference(fool_elimination,[status(thm)],[f23075]) ).

thf(f23075,plain,
    ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
   => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
    inference(rectify,[status(thm)],[f8]) ).

thf(f8,axiom,
    ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
   => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062) ).

thf(f23786,plain,
    ( spl110_9
    | spl110_2 ),
    inference(avatar_split_clause,[status(thm)],[f23699,f23758,f23782]) ).

thf(f23758,definition,
    ( spl110_2
  <=> ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl110_2])],[avatar_definition]) ).

thf(f23699,plain,
    ( ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
      = $true )
    | ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23698]) ).

thf(f23698,plain,
    ( ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
      | ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) ) )
    = $true ),
    inference(beta_eta_normalization,[status(thm)],[f23559]) ).

thf(f23559,plain,
    ( ( ^ [Y0: vEBT_VEBT,Y1: nat] :
          ( ( vEBT_VEBT_membermima @ Y0 @ Y1 )
          | ( vEBT_V5719532721284313246member @ Y0 @ Y1 ) )
      @ ( 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 ) ) ) ) )
    = $true ),
    inference(definition_unfolding,[status(thm)],[f23452,f23355]) ).

thf(f23452,plain,
    ( ( 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 ) ) ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f19232]) ).

thf(f19232,plain,
    ( ( 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 ) ) ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f19231]) ).

thf(f19231,plain,
    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 ) ) ) ),
    inference(rectify,[status(thm)],[f12]) ).

thf(f12,axiom,
    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 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_11_assms_I3_J) ).

thf(f23760,plain,
    ( spl110_1
    | ~ spl110_2 ),
    inference(avatar_split_clause,[status(thm)],[f23568,f23758,f23755]) ).

thf(f23568,plain,
    ( ( $true
      = ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ x ) )
    | ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
     != $true ) ),
    inference(definition_unfolding,[status(thm)],[f23492,f23427]) ).

thf(f23492,plain,
    ( ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
     != $true )
    | ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true ) ),
    inference(cnf_transformation,[status(thm)],[f23126]) ).

thf(f23126,plain,
    ( ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
     != $true )
    | ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true ) ),
    inference(ennf_transformation,[status(thm)],[f18374]) ).

thf(f18374,plain,
    ( ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
      = $true )
   => ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
      = $true ) ),
    inference(fool_elimination,[status(thm)],[f18373]) ).

thf(f18373,plain,
    ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
   => ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
    inference(rectify,[status(thm)],[f9]) ).

thf(f9,axiom,
    ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
   => ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP221^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.11/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34  % Computer : n005.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Thu Feb 26 07:37:14 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46  ---- Original DTF file ---
% 0.18/0.46  thf(spec,logic,$$dhol).
% 0.18/0.46  %------------------------------------------------------------------------------
% 0.18/0.46  % File     : ITP221^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.18/0.46  % Domain   : Interactive Theorem Proving
% 0.18/0.46  % Problem  : Sledgehammer problem VEBT_Definitions 00493_022399
% 0.18/0.46  % Version  : [Des22] axioms.
% 0.18/0.46  % English  :
% 0.18/0.46  
% 0.18/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.46  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.18/0.46  % Source   : [Des22]
% 0.18/0.46  % Names    : 0063_VEBT_Definitions_00493_022399 [Des22]
% 0.18/0.46  
% 0.18/0.46  % Status   : Theorem
% 0.18/0.46  % Rating   : ? v9.2.1
% 0.18/0.46  % Syntax   : Number of formulae    : 11148 (6201 unt; 899 typ;   0 def)
% 0.18/0.46  %            Number of atoms       : 25899 (11696 equ;   0 cnn)
% 0.18/0.46  %            Maximal formula atoms :   71 (   2 avg)
% 0.18/0.46  %            Number of connectives : 104223 (2335   ~; 517   |;1426   &;91503   @)
% 0.18/0.46  %                                         (   0 <=>;8442  =>;   0  <=;   0 <~>)
% 0.18/0.46  %            Maximal formula depth :   39 (   5 avg)
% 0.18/0.46  %            Number of types       :   85 (  84 usr)
% 0.18/0.46  %            Number of type conns  : 2723 (2723   >;   0   *;   0   +;   0  <<)
% 0.18/0.46  %            Number of symbols     :  818 ( 815 usr;  57 con; 0-8 aty)
% 0.18/0.46  %            Number of variables   : 23152 (1825   ^;20748   !; 579   ?;23152   :)
% 0.18/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.18/0.46  
% 0.18/0.46  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.18/0.46  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.18/0.46  %            proofs - 
% 0.18/0.46  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.18/0.46  %            2022-02-17 17:39:15.009
% 0.18/0.46  % Bugfixes : Added ()s around negated sides of equations.
% 0.18/0.46  %------------------------------------------------------------------------------
% 0.18/0.46  % Could-be-implicit typings (84)
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% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 0.18/0.46      inf_inf_nat: nat > nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 0.18/0.46      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 0.18/0.46      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.18/0.46      sup_sup_nat: nat > nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.18/0.46      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 0.18/0.46      lattic8265883725875713057ax_nat: set_nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.18/0.46      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 0.18/0.46      at_infinity_real: filter_real ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 0.18/0.46      append_int: list_int > list_int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.18/0.46      append_nat: list_nat > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oconcat_001_Eo,type,
% 0.18/0.46      concat_o: list_list_o > list_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 0.18/0.46      concat_int: list_list_int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 0.18/0.46      concat_nat: list_list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 0.18/0.46      distinct_int: list_int > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 0.18/0.46      distinct_nat: list_nat > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 0.18/0.46      drop_nat: nat > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 0.18/0.46      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.18/0.46      linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 0.18/0.46      linord2614967742042102400et_nat: set_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 0.18/0.46      cons_int: int > list_int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.18/0.46      cons_nat: nat > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 0.18/0.46      nil_int: list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.18/0.46      nil_nat: list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 0.18/0.46      hd_nat: list_nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.18/0.46      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 0.18/0.46      set_o2: list_o > set_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 0.18/0.46      set_complex2: list_complex > set_complex ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 0.18/0.46      set_int2: list_int > set_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 0.18/0.46      set_list_o2: list_list_o > set_list_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 0.18/0.46      set_list_int2: list_list_int > set_list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 0.18/0.46      set_list_nat2: list_list_nat > set_list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.18/0.46      set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.18/0.46      set_nat2: list_nat > set_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.46      set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 0.18/0.46      set_real2: list_real > set_real ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 0.18/0.46      tl_nat: list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001_Eo,type,
% 0.18/0.46      nth_o: list_o > nat > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 0.18/0.46      nth_Code_integer: list_Code_integer > nat > code_integer ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 0.18/0.46      nth_complex: list_complex > nat > complex ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 0.18/0.46      nth_int: list_int > nat > int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 0.18/0.46      nth_list_nat: list_list_nat > nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.18/0.46      nth_nat: list_nat > nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 0.18/0.46      nth_num: list_num > nat > num ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.18/0.46      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.18/0.46      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 0.18/0.46      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.18/0.46      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.18/0.46      nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.46      nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.18/0.46      nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.18/0.46      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.18/0.46      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.18/0.46      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.18/0.46      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.18/0.46      nth_real: list_real > nat > real ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 0.18/0.46      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 0.18/0.46      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 0.18/0.46      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 0.18/0.46      produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 0.18/0.46      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 0.18/0.46      product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.18/0.46      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.18/0.46      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.18/0.46      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 0.18/0.46      remdups_nat: list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001_Eo,type,
% 0.18/0.46      replicate_o: nat > $o > list_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 0.18/0.46      replicate_complex: nat > complex > list_complex ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 0.18/0.46      replicate_int: nat > int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 0.18/0.46      replicate_nat: nat > nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.46      replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 0.18/0.46      replicate_real: nat > real > list_real ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 0.18/0.46      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.18/0.46      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osubseqs_001_Eo,type,
% 0.18/0.46      subseqs_o: list_o > list_list_o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 0.18/0.46      subseqs_int: list_int > list_list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 0.18/0.46      subseqs_nat: list_nat > list_list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.46      subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.18/0.46      take_nat: nat > list_nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oupt,type,
% 0.18/0.46      upt: nat > nat > list_nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oupto,type,
% 0.18/0.46      upto: int > int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oupto__aux,type,
% 0.18/0.46      upto_aux: int > int > list_int > list_int ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_List_Oupto__rel,type,
% 0.18/0.46      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_OSuc,type,
% 0.18/0.46      suc: nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.46      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.18/0.46      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.18/0.46      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.18/0.46      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Onat_Opred,type,
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% 0.18/0.46  
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% 0.18/0.46      semiri1316708129612266289at_nat: nat > nat ).
% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
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% 0.18/0.46  
% 0.18/0.46  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.18/0.46      semiri5074537144036343181t_real: nat > real ).
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% 0.18/0.46  
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% 0.18/0.46  
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% 0.18/0.46      nat_list_encode: list_nat > nat ).
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% 0.18/0.46      nat_list_encode_rel: list_nat > list_nat > $o ).
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% 0.18/0.46      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
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% 0.18/0.46  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
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% 0.18/0.46      nat_set_encode: set_nat > nat ).
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% 0.18/0.46      nat_triangle: nat > nat ).
% 0.18/0.46  
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% 0.18/0.47      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 0.18/0.47      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.18/0.47      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.18/0.47      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.18/0.47      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.18/0.47      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.18/0.47      vEBT_VEBT_high: nat > nat > nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.18/0.47      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.18/0.47      vEBT_VEBT_low: nat > nat > nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.18/0.47      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.18/0.47      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.18/0.47      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.18/0.47      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.18/0.47      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.18/0.47      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.18/0.47      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.18/0.47      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.18/0.47      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.18/0.47      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.18/0.47      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.18/0.47      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.18/0.47      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.47      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.18/0.47      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.18/0.47      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_Wellfounded_Opred__nat,type,
% 0.18/0.47      pred_nat: set_Pr1261947904930325089at_nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 0.18/0.47      fChoice_real: ( real > $o ) > real ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001_Eo,type,
% 0.18/0.47      member_o: $o > set_o > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 0.18/0.47      member_Code_integer: code_integer > set_Code_integer > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.18/0.47      member_complex: complex > set_complex > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Int__Oint,type,
% 0.18/0.47      member_int: int > set_int > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 0.18/0.47      member_list_o: list_o > set_list_o > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 0.18/0.47      member_list_int: list_int > set_list_int > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.18/0.47      member_list_nat: list_nat > set_list_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.18/0.47      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Nat__Onat,type,
% 0.18/0.47      member_nat: nat > set_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Num__Onum,type,
% 0.18/0.47      member_num: num > set_num > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.18/0.47      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Rat__Orat,type,
% 0.18/0.47      member_rat: rat > set_rat > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Real__Oreal,type,
% 0.18/0.47      member_real: real > set_real > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 0.18/0.47      member_set_int: set_int > set_set_int > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.18/0.47      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_deg,type,
% 0.18/0.47      deg: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_info,type,
% 0.18/0.47      info: option4927543243414619207at_nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_m____,type,
% 0.18/0.47      m: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_ma____,type,
% 0.18/0.47      ma: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_mi____,type,
% 0.18/0.47      mi: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_n,type,
% 0.18/0.47      n: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_na____,type,
% 0.18/0.47      na: nat ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_summary,type,
% 0.18/0.47      summary: vEBT_VEBT ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_treeList,type,
% 0.18/0.47      treeList: list_VEBT_VEBT ).
% 0.18/0.47  
% 0.18/0.47  thf(sy_v_x,type,
% 0.18/0.47      x: nat ).
% 0.18/0.47  
% 0.18/0.47  % Relevant facts (10210)
% 0.18/0.47  thf(fact_0_both__member__options__def,axiom,
% 0.18/0.47      ( vEBT_V8194947554948674370ptions
% 0.18/0.47      = ( ^ [T: vEBT_VEBT,X: nat] :
% 0.18/0.47            ( ( vEBT_V5719532721284313246member @ T @ X )
% 0.18/0.47            | ( vEBT_VEBT_membermima @ T @ X ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % both_member_options_def
% 0.18/0.47  thf(fact_1__092_060open_0621_A_060_Adeg_092_060close_062,axiom,
% 0.18/0.47      ord_less_nat @ one_one_nat @ deg ).
% 0.18/0.47  
% 0.18/0.47  % \<open>1 < deg\<close>
% 0.18/0.47  thf(fact_2_VEBT_Oinject_I1_J,axiom,
% 0.18/0.47      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 0.18/0.47        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.18/0.47          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.18/0.47        = ( ( X11 = Y11 )
% 0.18/0.47          & ( X12 = Y12 )
% 0.18/0.47          & ( X13 = Y13 )
% 0.18/0.47          & ( X14 = Y14 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % VEBT.inject(1)
% 0.18/0.47  thf(fact_3__C5_Ohyps_C_I3_J,axiom,
% 0.18/0.47      ( ( summary
% 0.18/0.47        = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 0.18/0.47     => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(3)
% 0.18/0.47  thf(fact_4__C5_Ohyps_C_I2_J,axiom,
% 0.18/0.47      vEBT_invar_vebt @ summary @ m ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(2)
% 0.18/0.47  thf(fact_5_assms_I1_J,axiom,
% 0.18/0.47      vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ n ).
% 0.18/0.47  
% 0.18/0.47  % assms(1)
% 0.18/0.47  thf(fact_6_assms_I2_J,axiom,
% 0.18/0.47      ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.18/0.47  
% 0.18/0.47  % assms(2)
% 0.18/0.47  thf(fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 0.18/0.47      ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
% 0.18/0.47     => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 0.18/0.47  
% 0.18/0.47  % \<open>naive_member (treeList ! high x (deg div 2)) (low x (deg div 2)) \<Longrightarrow> naive_member (Node info deg treeList summary) x\<close>
% 0.18/0.47  thf(fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 0.18/0.47      ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
% 0.18/0.47     => ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 0.18/0.47  
% 0.18/0.47  % \<open>membermima (treeList ! high x (deg div 2)) (low x (deg div 2)) \<Longrightarrow> membermima (Node info deg treeList summary) x\<close>
% 0.18/0.47  thf(fact_9__092_060open_062high_Ax_A_Ideg_Adiv_A2_J_A_060_A2_A_094_Am_092_060close_062,axiom,
% 0.18/0.47      ord_less_nat @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 0.18/0.47  
% 0.18/0.47  % \<open>high x (deg div 2) < 2 ^ m\<close>
% 0.18/0.47  thf(fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
% 0.18/0.47      ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
% 0.18/0.47      | ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % \<open>membermima (treeList ! high x (deg div 2)) (low x (deg div 2)) \<or> naive_member (treeList ! high x (deg div 2)) (low x (deg div 2))\<close>
% 0.18/0.47  thf(fact_11_assms_I3_J,axiom,
% 0.18/0.47      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 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % assms(3)
% 0.18/0.47  thf(fact_12__C5_Ohyps_C_I1_J,axiom,
% 0.18/0.47      ! [X2: vEBT_VEBT] :
% 0.18/0.47        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.18/0.47       => ( ( vEBT_invar_vebt @ X2 @ na )
% 0.18/0.47          & ( ( X2
% 0.18/0.47              = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 0.18/0.47           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(1)
% 0.18/0.47  thf(fact_13__C5_Ohyps_C_I7_J,axiom,
% 0.18/0.47      ! [I: nat] :
% 0.18/0.47        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.18/0.47       => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X3 ) )
% 0.18/0.47          = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(7)
% 0.18/0.47  thf(fact_14__C5_Ohyps_C_I6_J,axiom,
% 0.18/0.47      ( deg
% 0.18/0.47      = ( plus_plus_nat @ na @ m ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(6)
% 0.18/0.47  thf(fact_15__C5_Ohyps_C_I10_J,axiom,
% 0.18/0.47      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(10)
% 0.18/0.47  thf(fact_16_high__def,axiom,
% 0.18/0.47      ( vEBT_VEBT_high
% 0.18/0.47      = ( ^ [X: nat,N: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % high_def
% 0.18/0.47  thf(fact_17_high__bound__aux,axiom,
% 0.18/0.47      ! [Ma: nat,N2: nat,M: nat] :
% 0.18/0.47        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 0.18/0.47       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % high_bound_aux
% 0.18/0.47  thf(fact_18__C5_Ohyps_C_I8_J,axiom,
% 0.18/0.47      ( ( mi = ma )
% 0.18/0.47     => ! [X2: vEBT_VEBT] :
% 0.18/0.47          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.18/0.47         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(8)
% 0.18/0.47  thf(fact_19__C5_Ohyps_C_I5_J,axiom,
% 0.18/0.47      ( m
% 0.18/0.47      = ( suc @ na ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(5)
% 0.18/0.47  thf(fact_20__C5_Ohyps_C_I4_J,axiom,
% 0.18/0.47      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.18/0.47      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(4)
% 0.18/0.47  thf(fact_21_in__children__def,axiom,
% 0.18/0.47      ( vEBT_V5917875025757280293ildren
% 0.18/0.47      = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N ) ) @ ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % in_children_def
% 0.18/0.47  thf(fact_22_add__self__div__2,axiom,
% 0.18/0.47      ! [M: nat] :
% 0.18/0.47        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47        = M ) ).
% 0.18/0.47  
% 0.18/0.47  % add_self_div_2
% 0.18/0.47  thf(fact_23__C5_Ohyps_C_I11_J,axiom,
% 0.18/0.47      ( ( mi != ma )
% 0.18/0.47     => ! [I: nat] :
% 0.18/0.47          ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.18/0.47         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.18/0.47                = I )
% 0.18/0.47             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.18/0.47            & ! [X2: nat] :
% 0.18/0.47                ( ( ( ( vEBT_VEBT_high @ X2 @ na )
% 0.18/0.47                    = I )
% 0.18/0.47                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
% 0.18/0.47               => ( ( ord_less_nat @ mi @ X2 )
% 0.18/0.47                  & ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(11)
% 0.18/0.47  thf(fact_24_one__add__one,axiom,
% 0.18/0.47      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.18/0.47      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_25_one__add__one,axiom,
% 0.18/0.47      ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 0.18/0.47      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_26_one__add__one,axiom,
% 0.18/0.47      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.18/0.47      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_27_one__add__one,axiom,
% 0.18/0.47      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.18/0.47      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_28_one__add__one,axiom,
% 0.18/0.47      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.18/0.47      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_29_one__add__one,axiom,
% 0.18/0.47      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.18/0.47      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_add_one
% 0.18/0.47  thf(fact_30_power__strict__increasing__iff,axiom,
% 0.18/0.47      ! [B: real,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ B )
% 0.18/0.47       => ( ( ord_less_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 0.18/0.47          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing_iff
% 0.18/0.47  thf(fact_31_power__strict__increasing__iff,axiom,
% 0.18/0.47      ! [B: rat,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ B )
% 0.18/0.47       => ( ( ord_less_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 0.18/0.47          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing_iff
% 0.18/0.47  thf(fact_32_power__strict__increasing__iff,axiom,
% 0.18/0.47      ! [B: nat,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ B )
% 0.18/0.47       => ( ( ord_less_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 0.18/0.47          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing_iff
% 0.18/0.47  thf(fact_33_power__strict__increasing__iff,axiom,
% 0.18/0.47      ! [B: int,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ B )
% 0.18/0.47       => ( ( ord_less_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 0.18/0.47          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing_iff
% 0.18/0.47  thf(fact_34_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.18/0.47        = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_35_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 0.18/0.47        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_36_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 0.18/0.47        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_37_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 0.18/0.47        = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_38_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.18/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_39_numeral__plus__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.18/0.47        = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_one
% 0.18/0.47  thf(fact_40_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_41_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_42_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 0.18/0.47        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_43_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_44_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_45_one__plus__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral
% 0.18/0.47  thf(fact_46_one__less__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_less_numeral_iff
% 0.18/0.47  thf(fact_47_one__less__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_less_numeral_iff
% 0.18/0.47  thf(fact_48_one__less__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_less_numeral_iff
% 0.18/0.47  thf(fact_49_one__less__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_less_numeral_iff
% 0.18/0.47  thf(fact_50_one__less__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ one @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_less_numeral_iff
% 0.18/0.47  thf(fact_51_power__inject__exp,axiom,
% 0.18/0.47      ! [A: real,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.18/0.47       => ( ( ( power_power_real @ A @ M )
% 0.18/0.47            = ( power_power_real @ A @ N2 ) )
% 0.18/0.47          = ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_inject_exp
% 0.18/0.47  thf(fact_52_power__inject__exp,axiom,
% 0.18/0.47      ! [A: rat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.18/0.47       => ( ( ( power_power_rat @ A @ M )
% 0.18/0.47            = ( power_power_rat @ A @ N2 ) )
% 0.18/0.47          = ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_inject_exp
% 0.18/0.47  thf(fact_53_power__inject__exp,axiom,
% 0.18/0.47      ! [A: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.18/0.47       => ( ( ( power_power_nat @ A @ M )
% 0.18/0.47            = ( power_power_nat @ A @ N2 ) )
% 0.18/0.47          = ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_inject_exp
% 0.18/0.47  thf(fact_54_power__inject__exp,axiom,
% 0.18/0.47      ! [A: int,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.18/0.47       => ( ( ( power_power_int @ A @ M )
% 0.18/0.47            = ( power_power_int @ A @ N2 ) )
% 0.18/0.47          = ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_inject_exp
% 0.18/0.47  thf(fact_55_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_rat @ N2 )
% 0.18/0.47          = one_one_rat )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_56_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numera1916890842035813515d_enat @ N2 )
% 0.18/0.47          = one_on7984719198319812577d_enat )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_57_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numera6690914467698888265omplex @ N2 )
% 0.18/0.47          = one_one_complex )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_58_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_real @ N2 )
% 0.18/0.47          = one_one_real )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_59_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_nat @ N2 )
% 0.18/0.47          = one_one_nat )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_60_numeral__eq__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_int @ N2 )
% 0.18/0.47          = one_one_int )
% 0.18/0.47        = ( N2 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_one_iff
% 0.18/0.47  thf(fact_61_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_one_rat
% 0.18/0.47          = ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_62_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_on7984719198319812577d_enat
% 0.18/0.47          = ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_63_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_one_complex
% 0.18/0.47          = ( numera6690914467698888265omplex @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_64_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_one_real
% 0.18/0.47          = ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_65_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_one_nat
% 0.18/0.47          = ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_66_one__eq__numeral__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( one_one_int
% 0.18/0.47          = ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( one = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_eq_numeral_iff
% 0.18/0.47  thf(fact_67_div__exp__eq,axiom,
% 0.18/0.47      ! [A: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.18/0.47        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % div_exp_eq
% 0.18/0.47  thf(fact_68_div__exp__eq,axiom,
% 0.18/0.47      ! [A: int,M: nat,N2: nat] :
% 0.18/0.47        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.18/0.47        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % div_exp_eq
% 0.18/0.47  thf(fact_69_div__exp__eq,axiom,
% 0.18/0.47      ! [A: code_integer,M: nat,N2: nat] :
% 0.18/0.47        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.18/0.47        = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % div_exp_eq
% 0.18/0.47  thf(fact_70_even__odd__cases,axiom,
% 0.18/0.47      ! [X4: nat] :
% 0.18/0.47        ( ! [N3: nat] :
% 0.18/0.47            ( X4
% 0.18/0.47           != ( plus_plus_nat @ N3 @ N3 ) )
% 0.18/0.47       => ~ ! [N3: nat] :
% 0.18/0.47              ( X4
% 0.18/0.47             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % even_odd_cases
% 0.18/0.47  thf(fact_71__C5_Ohyps_C_I9_J,axiom,
% 0.18/0.47      ord_less_eq_nat @ mi @ ma ).
% 0.18/0.47  
% 0.18/0.47  % "5.hyps"(9)
% 0.18/0.47  thf(fact_72_inthall,axiom,
% 0.18/0.47      ! [Xs: list_real,P: real > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: real] :
% 0.18/0.47            ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_73_inthall,axiom,
% 0.18/0.47      ! [Xs: list_complex,P: complex > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: complex] :
% 0.18/0.47            ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_complex @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_74_inthall,axiom,
% 0.18/0.47      ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: product_prod_nat_nat] :
% 0.18/0.47            ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_75_inthall,axiom,
% 0.18/0.47      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: vEBT_VEBT] :
% 0.18/0.47            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_76_inthall,axiom,
% 0.18/0.47      ! [Xs: list_o,P: $o > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: $o] :
% 0.18/0.47            ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_77_inthall,axiom,
% 0.18/0.47      ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: nat] :
% 0.18/0.47            ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_78_inthall,axiom,
% 0.18/0.47      ! [Xs: list_int,P: int > $o,N2: nat] :
% 0.18/0.47        ( ! [X5: int] :
% 0.18/0.47            ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 0.18/0.47           => ( P @ X5 ) )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.18/0.47         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % inthall
% 0.18/0.47  thf(fact_79_numeral__eq__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( numera1916890842035813515d_enat @ M )
% 0.18/0.47          = ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_iff
% 0.18/0.47  thf(fact_80_numeral__eq__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( numera6690914467698888265omplex @ M )
% 0.18/0.47          = ( numera6690914467698888265omplex @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_iff
% 0.18/0.47  thf(fact_81_numeral__eq__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_real @ M )
% 0.18/0.47          = ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_iff
% 0.18/0.47  thf(fact_82_numeral__eq__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_nat @ M )
% 0.18/0.47          = ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_iff
% 0.18/0.47  thf(fact_83_numeral__eq__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( numeral_numeral_int @ M )
% 0.18/0.47          = ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_eq_iff
% 0.18/0.47  thf(fact_84_numeral__le__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_iff
% 0.18/0.47  thf(fact_85_numeral__le__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_iff
% 0.18/0.47  thf(fact_86_numeral__le__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_iff
% 0.18/0.47  thf(fact_87_numeral__le__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_iff
% 0.18/0.47  thf(fact_88_numeral__le__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_iff
% 0.18/0.47  thf(fact_89_bits__div__by__1,axiom,
% 0.18/0.47      ! [A: nat] :
% 0.18/0.47        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % bits_div_by_1
% 0.18/0.47  thf(fact_90_bits__div__by__1,axiom,
% 0.18/0.47      ! [A: int] :
% 0.18/0.47        ( ( divide_divide_int @ A @ one_one_int )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % bits_div_by_1
% 0.18/0.47  thf(fact_91_bits__div__by__1,axiom,
% 0.18/0.47      ! [A: code_integer] :
% 0.18/0.47        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % bits_div_by_1
% 0.18/0.47  thf(fact_92_power__one,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( power_power_rat @ one_one_rat @ N2 )
% 0.18/0.47        = one_one_rat ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one
% 0.18/0.47  thf(fact_93_power__one,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( power_power_nat @ one_one_nat @ N2 )
% 0.18/0.47        = one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one
% 0.18/0.47  thf(fact_94_power__one,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( power_power_real @ one_one_real @ N2 )
% 0.18/0.47        = one_one_real ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one
% 0.18/0.47  thf(fact_95_power__one,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( power_power_int @ one_one_int @ N2 )
% 0.18/0.47        = one_one_int ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one
% 0.18/0.47  thf(fact_96_power__one,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( power_power_complex @ one_one_complex @ N2 )
% 0.18/0.47        = one_one_complex ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one
% 0.18/0.47  thf(fact_97_power__one__right,axiom,
% 0.18/0.47      ! [A: nat] :
% 0.18/0.47        ( ( power_power_nat @ A @ one_one_nat )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_right
% 0.18/0.47  thf(fact_98_power__one__right,axiom,
% 0.18/0.47      ! [A: real] :
% 0.18/0.47        ( ( power_power_real @ A @ one_one_nat )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_right
% 0.18/0.47  thf(fact_99_power__one__right,axiom,
% 0.18/0.47      ! [A: int] :
% 0.18/0.47        ( ( power_power_int @ A @ one_one_nat )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_right
% 0.18/0.47  thf(fact_100_power__one__right,axiom,
% 0.18/0.47      ! [A: complex] :
% 0.18/0.47        ( ( power_power_complex @ A @ one_one_nat )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_right
% 0.18/0.47  thf(fact_101_set__n__deg__not__0,axiom,
% 0.18/0.47      ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 0.18/0.47        ( ! [X5: vEBT_VEBT] :
% 0.18/0.47            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.47           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.18/0.47       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.18/0.47            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.47         => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % set_n_deg_not_0
% 0.18/0.47  thf(fact_102_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: rat] :
% 0.18/0.47        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.18/0.47        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_103_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: extended_enat] :
% 0.18/0.47        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 0.18/0.47        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_104_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: complex] :
% 0.18/0.47        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.18/0.47        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_105_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: real] :
% 0.18/0.47        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.18/0.47        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_106_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: nat] :
% 0.18/0.47        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.18/0.47        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_107_add__numeral__left,axiom,
% 0.18/0.47      ! [V: num,W: num,Z: int] :
% 0.18/0.47        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.18/0.47        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_numeral_left
% 0.18/0.47  thf(fact_108_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.18/0.47        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_109_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: complex,P: complex > $o] :
% 0.18/0.47        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_110_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: real,P: real > $o] :
% 0.18/0.47        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_111_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: list_nat,P: list_nat > $o] :
% 0.18/0.47        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_112_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: nat,P: nat > $o] :
% 0.18/0.47        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_113_mem__Collect__eq,axiom,
% 0.18/0.47      ! [A: int,P: int > $o] :
% 0.18/0.47        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.18/0.47        = ( P @ A ) ) ).
% 0.18/0.47  
% 0.18/0.47  % mem_Collect_eq
% 0.18/0.47  thf(fact_114_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.18/0.47        ( ( collec3392354462482085612at_nat
% 0.18/0.47          @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_115_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_complex] :
% 0.18/0.47        ( ( collect_complex
% 0.18/0.47          @ ^ [X: complex] : ( member_complex @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_116_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_real] :
% 0.18/0.47        ( ( collect_real
% 0.18/0.47          @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_117_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_list_nat] :
% 0.18/0.47        ( ( collect_list_nat
% 0.18/0.47          @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_118_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_nat] :
% 0.18/0.47        ( ( collect_nat
% 0.18/0.47          @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_119_Collect__mem__eq,axiom,
% 0.18/0.47      ! [A2: set_int] :
% 0.18/0.47        ( ( collect_int
% 0.18/0.47          @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 0.18/0.47        = A2 ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_mem_eq
% 0.18/0.47  thf(fact_120_Collect__cong,axiom,
% 0.18/0.47      ! [P: complex > $o,Q: complex > $o] :
% 0.18/0.47        ( ! [X5: complex] :
% 0.18/0.47            ( ( P @ X5 )
% 0.18/0.47            = ( Q @ X5 ) )
% 0.18/0.47       => ( ( collect_complex @ P )
% 0.18/0.47          = ( collect_complex @ Q ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_cong
% 0.18/0.47  thf(fact_121_Collect__cong,axiom,
% 0.18/0.47      ! [P: real > $o,Q: real > $o] :
% 0.18/0.47        ( ! [X5: real] :
% 0.18/0.47            ( ( P @ X5 )
% 0.18/0.47            = ( Q @ X5 ) )
% 0.18/0.47       => ( ( collect_real @ P )
% 0.18/0.47          = ( collect_real @ Q ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_cong
% 0.18/0.47  thf(fact_122_Collect__cong,axiom,
% 0.18/0.47      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.18/0.47        ( ! [X5: list_nat] :
% 0.18/0.47            ( ( P @ X5 )
% 0.18/0.47            = ( Q @ X5 ) )
% 0.18/0.47       => ( ( collect_list_nat @ P )
% 0.18/0.47          = ( collect_list_nat @ Q ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_cong
% 0.18/0.47  thf(fact_123_Collect__cong,axiom,
% 0.18/0.47      ! [P: nat > $o,Q: nat > $o] :
% 0.18/0.47        ( ! [X5: nat] :
% 0.18/0.47            ( ( P @ X5 )
% 0.18/0.47            = ( Q @ X5 ) )
% 0.18/0.47       => ( ( collect_nat @ P )
% 0.18/0.47          = ( collect_nat @ Q ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_cong
% 0.18/0.47  thf(fact_124_Collect__cong,axiom,
% 0.18/0.47      ! [P: int > $o,Q: int > $o] :
% 0.18/0.47        ( ! [X5: int] :
% 0.18/0.47            ( ( P @ X5 )
% 0.18/0.47            = ( Q @ X5 ) )
% 0.18/0.47       => ( ( collect_int @ P )
% 0.18/0.47          = ( collect_int @ Q ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Collect_cong
% 0.18/0.47  thf(fact_125_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_126_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_127_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 0.18/0.47        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_128_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_129_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_130_numeral__plus__numeral,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_plus_numeral
% 0.18/0.47  thf(fact_131_numeral__less__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_less_iff
% 0.18/0.47  thf(fact_132_numeral__less__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_less_iff
% 0.18/0.47  thf(fact_133_numeral__less__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_less_iff
% 0.18/0.47  thf(fact_134_numeral__less__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_less_iff
% 0.18/0.47  thf(fact_135_numeral__less__iff,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_less_iff
% 0.18/0.47  thf(fact_136_numeral__le__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 0.18/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_one_iff
% 0.18/0.47  thf(fact_137_numeral__le__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 0.18/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_one_iff
% 0.18/0.47  thf(fact_138_numeral__le__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 0.18/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_one_iff
% 0.18/0.47  thf(fact_139_numeral__le__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 0.18/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_one_iff
% 0.18/0.47  thf(fact_140_numeral__le__one__iff,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 0.18/0.47        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_le_one_iff
% 0.18/0.47  thf(fact_141_Suc__numeral,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 0.18/0.47        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_numeral
% 0.18/0.47  thf(fact_142_power__increasing__iff,axiom,
% 0.18/0.47      ! [B: real,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ B )
% 0.18/0.47       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 0.18/0.47          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing_iff
% 0.18/0.47  thf(fact_143_power__increasing__iff,axiom,
% 0.18/0.47      ! [B: rat,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ B )
% 0.18/0.47       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 0.18/0.47          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing_iff
% 0.18/0.47  thf(fact_144_power__increasing__iff,axiom,
% 0.18/0.47      ! [B: nat,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ B )
% 0.18/0.47       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 0.18/0.47          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing_iff
% 0.18/0.47  thf(fact_145_power__increasing__iff,axiom,
% 0.18/0.47      ! [B: int,X4: nat,Y: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ B )
% 0.18/0.47       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 0.18/0.47          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing_iff
% 0.18/0.47  thf(fact_146_add__2__eq__Suc_H,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47        = ( suc @ ( suc @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_2_eq_Suc'
% 0.18/0.47  thf(fact_147_add__2__eq__Suc,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.18/0.47        = ( suc @ ( suc @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_2_eq_Suc
% 0.18/0.47  thf(fact_148_Suc__1,axiom,
% 0.18/0.47      ( ( suc @ one_one_nat )
% 0.18/0.47      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_1
% 0.18/0.47  thf(fact_149_div2__Suc__Suc,axiom,
% 0.18/0.47      ! [M: nat] :
% 0.18/0.47        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % div2_Suc_Suc
% 0.18/0.47  thf(fact_150_Suc__div__le__mono,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_div_le_mono
% 0.18/0.47  thf(fact_151_add__One__commute,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( plus_plus_num @ one @ N2 )
% 0.18/0.47        = ( plus_plus_num @ N2 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_One_commute
% 0.18/0.47  thf(fact_152_le__numeral__extra_I4_J,axiom,
% 0.18/0.47      ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.18/0.47  
% 0.18/0.47  % le_numeral_extra(4)
% 0.18/0.47  thf(fact_153_le__numeral__extra_I4_J,axiom,
% 0.18/0.47      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.18/0.47  
% 0.18/0.47  % le_numeral_extra(4)
% 0.18/0.47  thf(fact_154_le__numeral__extra_I4_J,axiom,
% 0.18/0.47      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.18/0.47  
% 0.18/0.47  % le_numeral_extra(4)
% 0.18/0.47  thf(fact_155_le__numeral__extra_I4_J,axiom,
% 0.18/0.47      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.18/0.47  
% 0.18/0.47  % le_numeral_extra(4)
% 0.18/0.47  thf(fact_156_div__le__dividend,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 0.18/0.47  
% 0.18/0.47  % div_le_dividend
% 0.18/0.47  thf(fact_157_div__le__mono,axiom,
% 0.18/0.47      ! [M: nat,N2: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.47       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % div_le_mono
% 0.18/0.47  thf(fact_158_power__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: real] :
% 0.18/0.47        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.18/0.47         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing
% 0.18/0.47  thf(fact_159_power__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: rat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.18/0.47         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing
% 0.18/0.47  thf(fact_160_power__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.18/0.47         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing
% 0.18/0.47  thf(fact_161_power__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: int] :
% 0.18/0.47        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.18/0.47         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_increasing
% 0.18/0.47  thf(fact_162_power__le__imp__le__exp,axiom,
% 0.18/0.47      ! [A: real,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.18/0.47       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_le_imp_le_exp
% 0.18/0.47  thf(fact_163_power__le__imp__le__exp,axiom,
% 0.18/0.47      ! [A: rat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.18/0.47       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_le_imp_le_exp
% 0.18/0.47  thf(fact_164_power__le__imp__le__exp,axiom,
% 0.18/0.47      ! [A: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.18/0.47       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_le_imp_le_exp
% 0.18/0.47  thf(fact_165_power__le__imp__le__exp,axiom,
% 0.18/0.47      ! [A: int,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.18/0.47       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_le_imp_le_exp
% 0.18/0.47  thf(fact_166_Suc__nat__number__of__add,axiom,
% 0.18/0.47      ! [V: num,N2: nat] :
% 0.18/0.47        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 0.18/0.47        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_nat_number_of_add
% 0.18/0.47  thf(fact_167_one__le__numeral,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_numeral
% 0.18/0.47  thf(fact_168_one__le__numeral,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_numeral
% 0.18/0.47  thf(fact_169_one__le__numeral,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_numeral
% 0.18/0.47  thf(fact_170_one__le__numeral,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_numeral
% 0.18/0.47  thf(fact_171_one__le__numeral,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_numeral
% 0.18/0.47  thf(fact_172_one__le__power,axiom,
% 0.18/0.47      ! [A: real,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.18/0.47       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_power
% 0.18/0.47  thf(fact_173_one__le__power,axiom,
% 0.18/0.47      ! [A: rat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.18/0.47       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_power
% 0.18/0.47  thf(fact_174_one__le__power,axiom,
% 0.18/0.47      ! [A: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.18/0.47       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_power
% 0.18/0.47  thf(fact_175_one__le__power,axiom,
% 0.18/0.47      ! [A: int,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.18/0.47       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_le_power
% 0.18/0.47  thf(fact_176_power__gt1,axiom,
% 0.18/0.47      ! [A: real,N2: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.18/0.47       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_gt1
% 0.18/0.47  thf(fact_177_power__gt1,axiom,
% 0.18/0.47      ! [A: rat,N2: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.18/0.47       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_gt1
% 0.18/0.47  thf(fact_178_power__gt1,axiom,
% 0.18/0.47      ! [A: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.18/0.47       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_gt1
% 0.18/0.47  thf(fact_179_power__gt1,axiom,
% 0.18/0.47      ! [A: int,N2: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.18/0.47       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_gt1
% 0.18/0.47  thf(fact_180_power2__nat__le__imp__le,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 0.18/0.47       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power2_nat_le_imp_le
% 0.18/0.47  thf(fact_181_power2__nat__le__eq__le,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.18/0.47        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power2_nat_le_eq_le
% 0.18/0.47  thf(fact_182_self__le__ge2__pow,axiom,
% 0.18/0.47      ! [K: nat,M: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.18/0.47       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % self_le_ge2_pow
% 0.18/0.47  thf(fact_183_is__num__normalize_I1_J,axiom,
% 0.18/0.47      ! [A: real,B: real,C: real] :
% 0.18/0.47        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.18/0.47        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % is_num_normalize(1)
% 0.18/0.47  thf(fact_184_is__num__normalize_I1_J,axiom,
% 0.18/0.47      ! [A: rat,B: rat,C: rat] :
% 0.18/0.47        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.18/0.47        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % is_num_normalize(1)
% 0.18/0.47  thf(fact_185_is__num__normalize_I1_J,axiom,
% 0.18/0.47      ! [A: int,B: int,C: int] :
% 0.18/0.47        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.18/0.47        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % is_num_normalize(1)
% 0.18/0.47  thf(fact_186_ex__power__ivl2,axiom,
% 0.18/0.47      ! [B: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.18/0.47       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.18/0.47         => ? [N3: nat] :
% 0.18/0.47              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.18/0.47              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % ex_power_ivl2
% 0.18/0.47  thf(fact_187_ex__power__ivl1,axiom,
% 0.18/0.47      ! [B: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.18/0.47       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.18/0.47         => ? [N3: nat] :
% 0.18/0.47              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.18/0.47              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % ex_power_ivl1
% 0.18/0.47  thf(fact_188_less__numeral__extra_I4_J,axiom,
% 0.18/0.47      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.18/0.47  
% 0.18/0.47  % less_numeral_extra(4)
% 0.18/0.47  thf(fact_189_less__numeral__extra_I4_J,axiom,
% 0.18/0.47      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.18/0.47  
% 0.18/0.47  % less_numeral_extra(4)
% 0.18/0.47  thf(fact_190_less__numeral__extra_I4_J,axiom,
% 0.18/0.47      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % less_numeral_extra(4)
% 0.18/0.47  thf(fact_191_less__numeral__extra_I4_J,axiom,
% 0.18/0.47      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.18/0.47  
% 0.18/0.47  % less_numeral_extra(4)
% 0.18/0.47  thf(fact_192_power__divide,axiom,
% 0.18/0.47      ! [A: real,B: real,N2: nat] :
% 0.18/0.47        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 0.18/0.47        = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_divide
% 0.18/0.47  thf(fact_193_power__divide,axiom,
% 0.18/0.47      ! [A: complex,B: complex,N2: nat] :
% 0.18/0.47        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 0.18/0.47        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_divide
% 0.18/0.47  thf(fact_194_not__numeral__less__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 0.18/0.47  
% 0.18/0.47  % not_numeral_less_one
% 0.18/0.47  thf(fact_195_not__numeral__less__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 0.18/0.47  
% 0.18/0.47  % not_numeral_less_one
% 0.18/0.47  thf(fact_196_not__numeral__less__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 0.18/0.47  
% 0.18/0.47  % not_numeral_less_one
% 0.18/0.47  thf(fact_197_not__numeral__less__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % not_numeral_less_one
% 0.18/0.47  thf(fact_198_not__numeral__less__one,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 0.18/0.47  
% 0.18/0.47  % not_numeral_less_one
% 0.18/0.47  thf(fact_199_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X4 ) )
% 0.18/0.47        = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_200_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X4 ) )
% 0.18/0.47        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_201_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X4 ) )
% 0.18/0.47        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_202_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X4 ) )
% 0.18/0.47        = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_203_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X4 ) )
% 0.18/0.47        = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_204_one__plus__numeral__commute,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X4 ) )
% 0.18/0.47        = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 0.18/0.47  
% 0.18/0.47  % one_plus_numeral_commute
% 0.18/0.47  thf(fact_205_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_206_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_207_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_208_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_209_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_210_numeral__Bit0,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0
% 0.18/0.47  thf(fact_211_numeral__One,axiom,
% 0.18/0.47      ( ( numeral_numeral_rat @ one )
% 0.18/0.47      = one_one_rat ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_212_numeral__One,axiom,
% 0.18/0.47      ( ( numera1916890842035813515d_enat @ one )
% 0.18/0.47      = one_on7984719198319812577d_enat ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_213_numeral__One,axiom,
% 0.18/0.47      ( ( numera6690914467698888265omplex @ one )
% 0.18/0.47      = one_one_complex ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_214_numeral__One,axiom,
% 0.18/0.47      ( ( numeral_numeral_real @ one )
% 0.18/0.47      = one_one_real ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_215_numeral__One,axiom,
% 0.18/0.47      ( ( numeral_numeral_nat @ one )
% 0.18/0.47      = one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_216_numeral__One,axiom,
% 0.18/0.47      ( ( numeral_numeral_int @ one )
% 0.18/0.47      = one_one_int ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_One
% 0.18/0.47  thf(fact_217_divide__numeral__1,axiom,
% 0.18/0.47      ! [A: real] :
% 0.18/0.47        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % divide_numeral_1
% 0.18/0.47  thf(fact_218_divide__numeral__1,axiom,
% 0.18/0.47      ! [A: complex] :
% 0.18/0.47        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.18/0.47        = A ) ).
% 0.18/0.47  
% 0.18/0.47  % divide_numeral_1
% 0.18/0.47  thf(fact_219_power__one__over,axiom,
% 0.18/0.47      ! [A: rat,N2: nat] :
% 0.18/0.47        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 0.18/0.47        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_over
% 0.18/0.47  thf(fact_220_power__one__over,axiom,
% 0.18/0.47      ! [A: real,N2: nat] :
% 0.18/0.47        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 0.18/0.47        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_over
% 0.18/0.47  thf(fact_221_power__one__over,axiom,
% 0.18/0.47      ! [A: complex,N2: nat] :
% 0.18/0.47        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 0.18/0.47        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_one_over
% 0.18/0.47  thf(fact_222_numerals_I1_J,axiom,
% 0.18/0.47      ( ( numeral_numeral_nat @ one )
% 0.18/0.47      = one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % numerals(1)
% 0.18/0.47  thf(fact_223_numeral__Bit0__div__2,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47        = ( numeral_numeral_nat @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0_div_2
% 0.18/0.47  thf(fact_224_numeral__Bit0__div__2,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.18/0.47        = ( numeral_numeral_int @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0_div_2
% 0.18/0.47  thf(fact_225_numeral__Bit0__div__2,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.18/0.47        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % numeral_Bit0_div_2
% 0.18/0.47  thf(fact_226_power__strict__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: real] :
% 0.18/0.47        ( ( ord_less_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_real @ one_one_real @ A )
% 0.18/0.47         => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing
% 0.18/0.47  thf(fact_227_power__strict__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: rat] :
% 0.18/0.47        ( ( ord_less_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.18/0.47         => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing
% 0.18/0.47  thf(fact_228_power__strict__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: nat] :
% 0.18/0.47        ( ( ord_less_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.18/0.47         => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing
% 0.18/0.47  thf(fact_229_power__strict__increasing,axiom,
% 0.18/0.47      ! [N2: nat,N4: nat,A: int] :
% 0.18/0.47        ( ( ord_less_nat @ N2 @ N4 )
% 0.18/0.47       => ( ( ord_less_int @ one_one_int @ A )
% 0.18/0.47         => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_strict_increasing
% 0.18/0.47  thf(fact_230_power__less__imp__less__exp,axiom,
% 0.18/0.47      ! [A: real,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_real @ one_one_real @ A )
% 0.18/0.47       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_less_imp_less_exp
% 0.18/0.47  thf(fact_231_power__less__imp__less__exp,axiom,
% 0.18/0.47      ! [A: rat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_rat @ one_one_rat @ A )
% 0.18/0.47       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_less_imp_less_exp
% 0.18/0.47  thf(fact_232_power__less__imp__less__exp,axiom,
% 0.18/0.47      ! [A: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ one_one_nat @ A )
% 0.18/0.47       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_less_imp_less_exp
% 0.18/0.47  thf(fact_233_power__less__imp__less__exp,axiom,
% 0.18/0.47      ! [A: int,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_int @ one_one_int @ A )
% 0.18/0.47       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.18/0.47         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % power_less_imp_less_exp
% 0.18/0.47  thf(fact_234_one__power2,axiom,
% 0.18/0.47      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47      = one_one_rat ) ).
% 0.18/0.47  
% 0.18/0.47  % one_power2
% 0.18/0.47  thf(fact_235_one__power2,axiom,
% 0.18/0.47      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47      = one_one_nat ) ).
% 0.18/0.47  
% 0.18/0.47  % one_power2
% 0.18/0.47  thf(fact_236_one__power2,axiom,
% 0.18/0.47      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47      = one_one_real ) ).
% 0.18/0.47  
% 0.18/0.47  % one_power2
% 0.18/0.47  thf(fact_237_one__power2,axiom,
% 0.18/0.47      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47      = one_one_int ) ).
% 0.18/0.47  
% 0.18/0.47  % one_power2
% 0.18/0.47  thf(fact_238_one__power2,axiom,
% 0.18/0.47      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.47      = one_one_complex ) ).
% 0.18/0.47  
% 0.18/0.47  % one_power2
% 0.18/0.47  thf(fact_239_nat__1__add__1,axiom,
% 0.18/0.47      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.18/0.47      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_1_add_1
% 0.18/0.47  thf(fact_240_less__exp,axiom,
% 0.18/0.47      ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_exp
% 0.18/0.47  thf(fact_241_semiring__norm_I76_J,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(76)
% 0.18/0.47  thf(fact_242_semiring__norm_I2_J,axiom,
% 0.18/0.47      ( ( plus_plus_num @ one @ one )
% 0.18/0.47      = ( bit0 @ one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(2)
% 0.18/0.47  thf(fact_243_field__less__half__sum,axiom,
% 0.18/0.47      ! [X4: rat,Y: rat] :
% 0.18/0.47        ( ( ord_less_rat @ X4 @ Y )
% 0.18/0.47       => ( ord_less_rat @ X4 @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % field_less_half_sum
% 0.18/0.47  thf(fact_244_field__less__half__sum,axiom,
% 0.18/0.47      ! [X4: real,Y: real] :
% 0.18/0.47        ( ( ord_less_real @ X4 @ Y )
% 0.18/0.47       => ( ord_less_real @ X4 @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % field_less_half_sum
% 0.18/0.47  thf(fact_245_semiring__norm_I75_J,axiom,
% 0.18/0.47      ! [M: num] :
% 0.18/0.47        ~ ( ord_less_num @ M @ one ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(75)
% 0.18/0.47  thf(fact_246_semiring__norm_I78_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( ord_less_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(78)
% 0.18/0.47  thf(fact_247_semiring__norm_I6_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(6)
% 0.18/0.47  thf(fact_248_nat__add__left__cancel__le,axiom,
% 0.18/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_add_left_cancel_le
% 0.18/0.47  thf(fact_249_nat__add__left__cancel__less,axiom,
% 0.18/0.47      ! [K: nat,M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.18/0.47        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_add_left_cancel_less
% 0.18/0.47  thf(fact_250_add__Suc__right,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 0.18/0.47        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % add_Suc_right
% 0.18/0.47  thf(fact_251_enat__ord__number_I2_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % enat_ord_number(2)
% 0.18/0.47  thf(fact_252_Suc__le__mono,axiom,
% 0.18/0.47      ! [N2: nat,M: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.18/0.47        = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_le_mono
% 0.18/0.47  thf(fact_253_Suc__less__eq,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.18/0.47        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_less_eq
% 0.18/0.47  thf(fact_254_semiring__norm_I87_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ( bit0 @ M )
% 0.18/0.47          = ( bit0 @ N2 ) )
% 0.18/0.47        = ( M = N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(87)
% 0.18/0.47  thf(fact_255_nat_Oinject,axiom,
% 0.18/0.47      ! [X22: nat,Y2: nat] :
% 0.18/0.47        ( ( ( suc @ X22 )
% 0.18/0.47          = ( suc @ Y2 ) )
% 0.18/0.47        = ( X22 = Y2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat.inject
% 0.18/0.47  thf(fact_256_old_Onat_Oinject,axiom,
% 0.18/0.47      ! [Nat: nat,Nat2: nat] :
% 0.18/0.47        ( ( ( suc @ Nat )
% 0.18/0.47          = ( suc @ Nat2 ) )
% 0.18/0.47        = ( Nat = Nat2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % old.nat.inject
% 0.18/0.47  thf(fact_257_semiring__norm_I85_J,axiom,
% 0.18/0.47      ! [M: num] :
% 0.18/0.47        ( ( bit0 @ M )
% 0.18/0.47       != one ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(85)
% 0.18/0.47  thf(fact_258_semiring__norm_I83_J,axiom,
% 0.18/0.47      ! [N2: num] :
% 0.18/0.47        ( one
% 0.18/0.47       != ( bit0 @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(83)
% 0.18/0.47  thf(fact_259_lessI,axiom,
% 0.18/0.47      ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % lessI
% 0.18/0.47  thf(fact_260_Suc__mono,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.47       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_mono
% 0.18/0.47  thf(fact_261_semiring__norm_I71_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(71)
% 0.18/0.47  thf(fact_262_semiring__norm_I68_J,axiom,
% 0.18/0.47      ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(68)
% 0.18/0.47  thf(fact_263_semiring__norm_I69_J,axiom,
% 0.18/0.47      ! [M: num] :
% 0.18/0.47        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.18/0.47  
% 0.18/0.47  % semiring_norm(69)
% 0.18/0.47  thf(fact_264_enat__ord__number_I1_J,axiom,
% 0.18/0.47      ! [M: num,N2: num] :
% 0.18/0.47        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.18/0.47        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % enat_ord_number(1)
% 0.18/0.47  thf(fact_265_enat__less__induct,axiom,
% 0.18/0.47      ! [P: extended_enat > $o,N2: extended_enat] :
% 0.18/0.47        ( ! [N3: extended_enat] :
% 0.18/0.47            ( ! [M2: extended_enat] :
% 0.18/0.47                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 0.18/0.47               => ( P @ M2 ) )
% 0.18/0.47           => ( P @ N3 ) )
% 0.18/0.47       => ( P @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % enat_less_induct
% 0.18/0.47  thf(fact_266_le__num__One__iff,axiom,
% 0.18/0.47      ! [X4: num] :
% 0.18/0.47        ( ( ord_less_eq_num @ X4 @ one )
% 0.18/0.47        = ( X4 = one ) ) ).
% 0.18/0.47  
% 0.18/0.47  % le_num_One_iff
% 0.18/0.47  thf(fact_267_two__realpow__ge__one,axiom,
% 0.18/0.47      ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % two_realpow_ge_one
% 0.18/0.47  thf(fact_268_Suc__inject,axiom,
% 0.18/0.47      ! [X4: nat,Y: nat] :
% 0.18/0.47        ( ( ( suc @ X4 )
% 0.18/0.47          = ( suc @ Y ) )
% 0.18/0.47       => ( X4 = Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_inject
% 0.18/0.47  thf(fact_269_n__not__Suc__n,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ( N2
% 0.18/0.47       != ( suc @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % n_not_Suc_n
% 0.18/0.47  thf(fact_270_nat__neq__iff,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( M != N2 )
% 0.18/0.47        = ( ( ord_less_nat @ M @ N2 )
% 0.18/0.47          | ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_neq_iff
% 0.18/0.47  thf(fact_271_less__not__refl,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.18/0.47  
% 0.18/0.47  % less_not_refl
% 0.18/0.47  thf(fact_272_less__not__refl2,axiom,
% 0.18/0.47      ! [N2: nat,M: nat] :
% 0.18/0.47        ( ( ord_less_nat @ N2 @ M )
% 0.18/0.47       => ( M != N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_not_refl2
% 0.18/0.47  thf(fact_273_less__not__refl3,axiom,
% 0.18/0.47      ! [S: nat,T2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ S @ T2 )
% 0.18/0.47       => ( S != T2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_not_refl3
% 0.18/0.47  thf(fact_274_less__irrefl__nat,axiom,
% 0.18/0.47      ! [N2: nat] :
% 0.18/0.47        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.18/0.47  
% 0.18/0.47  % less_irrefl_nat
% 0.18/0.47  thf(fact_275_nat__less__induct,axiom,
% 0.18/0.47      ! [P: nat > $o,N2: nat] :
% 0.18/0.47        ( ! [N3: nat] :
% 0.18/0.47            ( ! [M2: nat] :
% 0.18/0.47                ( ( ord_less_nat @ M2 @ N3 )
% 0.18/0.47               => ( P @ M2 ) )
% 0.18/0.47           => ( P @ N3 ) )
% 0.18/0.47       => ( P @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_less_induct
% 0.18/0.47  thf(fact_276_infinite__descent,axiom,
% 0.18/0.47      ! [P: nat > $o,N2: nat] :
% 0.18/0.47        ( ! [N3: nat] :
% 0.18/0.47            ( ~ ( P @ N3 )
% 0.18/0.47           => ? [M2: nat] :
% 0.18/0.47                ( ( ord_less_nat @ M2 @ N3 )
% 0.18/0.47                & ~ ( P @ M2 ) ) )
% 0.18/0.47       => ( P @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % infinite_descent
% 0.18/0.47  thf(fact_277_linorder__neqE__nat,axiom,
% 0.18/0.47      ! [X4: nat,Y: nat] :
% 0.18/0.47        ( ( X4 != Y )
% 0.18/0.47       => ( ~ ( ord_less_nat @ X4 @ Y )
% 0.18/0.47         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % linorder_neqE_nat
% 0.18/0.47  thf(fact_278_le__refl,axiom,
% 0.18/0.47      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 0.18/0.47  
% 0.18/0.47  % le_refl
% 0.18/0.47  thf(fact_279_le__trans,axiom,
% 0.18/0.47      ! [I2: nat,J: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.47       => ( ( ord_less_eq_nat @ J @ K )
% 0.18/0.47         => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % le_trans
% 0.18/0.47  thf(fact_280_eq__imp__le,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( M = N2 )
% 0.18/0.47       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % eq_imp_le
% 0.18/0.47  thf(fact_281_le__antisym,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.47       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.18/0.47         => ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % le_antisym
% 0.18/0.47  thf(fact_282_nat__le__linear,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.47        | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.18/0.47  
% 0.18/0.47  % nat_le_linear
% 0.18/0.47  thf(fact_283_Nat_Oex__has__greatest__nat,axiom,
% 0.18/0.47      ! [P: nat > $o,K: nat,B: nat] :
% 0.18/0.47        ( ( P @ K )
% 0.18/0.47       => ( ! [Y3: nat] :
% 0.18/0.47              ( ( P @ Y3 )
% 0.18/0.47             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.18/0.47         => ? [X5: nat] :
% 0.18/0.47              ( ( P @ X5 )
% 0.18/0.47              & ! [Y4: nat] :
% 0.18/0.47                  ( ( P @ Y4 )
% 0.18/0.47                 => ( ord_less_eq_nat @ Y4 @ X5 ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Nat.ex_has_greatest_nat
% 0.18/0.47  thf(fact_284_size__neq__size__imp__neq,axiom,
% 0.18/0.47      ! [X4: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 0.18/0.47        ( ( ( size_s6755466524823107622T_VEBT @ X4 )
% 0.18/0.47         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 0.18/0.47       => ( X4 != Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % size_neq_size_imp_neq
% 0.18/0.47  thf(fact_285_size__neq__size__imp__neq,axiom,
% 0.18/0.47      ! [X4: list_o,Y: list_o] :
% 0.18/0.47        ( ( ( size_size_list_o @ X4 )
% 0.18/0.47         != ( size_size_list_o @ Y ) )
% 0.18/0.47       => ( X4 != Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % size_neq_size_imp_neq
% 0.18/0.47  thf(fact_286_size__neq__size__imp__neq,axiom,
% 0.18/0.47      ! [X4: list_nat,Y: list_nat] :
% 0.18/0.47        ( ( ( size_size_list_nat @ X4 )
% 0.18/0.47         != ( size_size_list_nat @ Y ) )
% 0.18/0.47       => ( X4 != Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % size_neq_size_imp_neq
% 0.18/0.47  thf(fact_287_size__neq__size__imp__neq,axiom,
% 0.18/0.47      ! [X4: list_int,Y: list_int] :
% 0.18/0.47        ( ( ( size_size_list_int @ X4 )
% 0.18/0.47         != ( size_size_list_int @ Y ) )
% 0.18/0.47       => ( X4 != Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % size_neq_size_imp_neq
% 0.18/0.47  thf(fact_288_size__neq__size__imp__neq,axiom,
% 0.18/0.47      ! [X4: num,Y: num] :
% 0.18/0.47        ( ( ( size_size_num @ X4 )
% 0.18/0.47         != ( size_size_num @ Y ) )
% 0.18/0.47       => ( X4 != Y ) ) ).
% 0.18/0.47  
% 0.18/0.47  % size_neq_size_imp_neq
% 0.18/0.47  thf(fact_289_Nat_OlessE,axiom,
% 0.18/0.47      ! [I2: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_nat @ I2 @ K )
% 0.18/0.47       => ( ( K
% 0.18/0.47           != ( suc @ I2 ) )
% 0.18/0.47         => ~ ! [J2: nat] :
% 0.18/0.47                ( ( ord_less_nat @ I2 @ J2 )
% 0.18/0.47               => ( K
% 0.18/0.47                 != ( suc @ J2 ) ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Nat.lessE
% 0.18/0.47  thf(fact_290_Suc__lessD,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 0.18/0.47       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_lessD
% 0.18/0.47  thf(fact_291_Suc__lessE,axiom,
% 0.18/0.47      ! [I2: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 0.18/0.47       => ~ ! [J2: nat] :
% 0.18/0.47              ( ( ord_less_nat @ I2 @ J2 )
% 0.18/0.47             => ( K
% 0.18/0.47               != ( suc @ J2 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_lessE
% 0.18/0.47  thf(fact_292_Suc__lessI,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.47       => ( ( ( suc @ M )
% 0.18/0.47           != N2 )
% 0.18/0.47         => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_lessI
% 0.18/0.47  thf(fact_293_less__SucE,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.47       => ( ~ ( ord_less_nat @ M @ N2 )
% 0.18/0.47         => ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_SucE
% 0.18/0.47  thf(fact_294_less__SucI,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.47       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_SucI
% 0.18/0.47  thf(fact_295_Ex__less__Suc,axiom,
% 0.18/0.47      ! [N2: nat,P: nat > $o] :
% 0.18/0.47        ( ( ? [I3: nat] :
% 0.18/0.47              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.47              & ( P @ I3 ) ) )
% 0.18/0.47        = ( ( P @ N2 )
% 0.18/0.47          | ? [I3: nat] :
% 0.18/0.47              ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.47              & ( P @ I3 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Ex_less_Suc
% 0.18/0.47  thf(fact_296_less__Suc__eq,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.47        = ( ( ord_less_nat @ M @ N2 )
% 0.18/0.47          | ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_Suc_eq
% 0.18/0.47  thf(fact_297_not__less__eq,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 0.18/0.47        = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % not_less_eq
% 0.18/0.47  thf(fact_298_All__less__Suc,axiom,
% 0.18/0.47      ! [N2: nat,P: nat > $o] :
% 0.18/0.47        ( ( ! [I3: nat] :
% 0.18/0.47              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.47             => ( P @ I3 ) ) )
% 0.18/0.47        = ( ( P @ N2 )
% 0.18/0.47          & ! [I3: nat] :
% 0.18/0.47              ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.47             => ( P @ I3 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % All_less_Suc
% 0.18/0.47  thf(fact_299_Suc__less__eq2,axiom,
% 0.18/0.47      ! [N2: nat,M: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.18/0.47        = ( ? [M3: nat] :
% 0.18/0.47              ( ( M
% 0.18/0.47                = ( suc @ M3 ) )
% 0.18/0.47              & ( ord_less_nat @ N2 @ M3 ) ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_less_eq2
% 0.18/0.47  thf(fact_300_less__antisym,axiom,
% 0.18/0.47      ! [N2: nat,M: nat] :
% 0.18/0.47        ( ~ ( ord_less_nat @ N2 @ M )
% 0.18/0.47       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.47         => ( M = N2 ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_antisym
% 0.18/0.47  thf(fact_301_Suc__less__SucD,axiom,
% 0.18/0.47      ! [M: nat,N2: nat] :
% 0.18/0.47        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.18/0.47       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.47  
% 0.18/0.47  % Suc_less_SucD
% 0.18/0.47  thf(fact_302_less__trans__Suc,axiom,
% 0.18/0.47      ! [I2: nat,J: nat,K: nat] :
% 0.18/0.47        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.47       => ( ( ord_less_nat @ J @ K )
% 0.18/0.47         => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 0.18/0.47  
% 0.18/0.47  % less_trans_Suc
% 0.18/0.47  thf(fact_303_less__Suc__induct,axiom,
% 0.18/0.47      ! [I2: nat,J: nat,P: nat > nat > $o] :
% 0.18/0.47        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.47       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 0.18/0.47         => ( ! [I4: nat,J2: nat,K2: nat] :
% 0.18/0.47                ( ( ord_less_nat @ I4 @ J2 )
% 0.18/0.47               => ( ( ord_less_nat @ J2 @ K2 )
% 0.18/0.47                 => ( ( P @ I4 @ J2 )
% 0.18/0.48                   => ( ( P @ J2 @ K2 )
% 0.18/0.48                     => ( P @ I4 @ K2 ) ) ) ) )
% 0.18/0.48           => ( P @ I2 @ J ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_Suc_induct
% 0.18/0.48  thf(fact_304_strict__inc__induct,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,P: nat > $o] :
% 0.18/0.48        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48       => ( ! [I4: nat] :
% 0.18/0.48              ( ( J
% 0.18/0.48                = ( suc @ I4 ) )
% 0.18/0.48             => ( P @ I4 ) )
% 0.18/0.48         => ( ! [I4: nat] :
% 0.18/0.48                ( ( ord_less_nat @ I4 @ J )
% 0.18/0.48               => ( ( P @ ( suc @ I4 ) )
% 0.18/0.48                 => ( P @ I4 ) ) )
% 0.18/0.48           => ( P @ I2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % strict_inc_induct
% 0.18/0.48  thf(fact_305_not__less__less__Suc__eq,axiom,
% 0.18/0.48      ! [N2: nat,M: nat] :
% 0.18/0.48        ( ~ ( ord_less_nat @ N2 @ M )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.48          = ( N2 = M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % not_less_less_Suc_eq
% 0.18/0.48  thf(fact_306_Suc__leD,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_leD
% 0.18/0.48  thf(fact_307_le__SucE,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.18/0.48       => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48         => ( M
% 0.18/0.48            = ( suc @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_SucE
% 0.18/0.48  thf(fact_308_le__SucI,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_SucI
% 0.18/0.48  thf(fact_309_Suc__le__D,axiom,
% 0.18/0.48      ! [N2: nat,M4: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M4 )
% 0.18/0.48       => ? [M5: nat] :
% 0.18/0.48            ( M4
% 0.18/0.48            = ( suc @ M5 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_le_D
% 0.18/0.48  thf(fact_310_le__Suc__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.18/0.48        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48          | ( M
% 0.18/0.48            = ( suc @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_Suc_eq
% 0.18/0.48  thf(fact_311_Suc__n__not__le__n,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48        ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_n_not_le_n
% 0.18/0.48  thf(fact_312_not__less__eq__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 0.18/0.48        = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 0.18/0.48  
% 0.18/0.48  % not_less_eq_eq
% 0.18/0.48  thf(fact_313_full__nat__induct,axiom,
% 0.18/0.48      ! [P: nat > $o,N2: nat] :
% 0.18/0.48        ( ! [N3: nat] :
% 0.18/0.48            ( ! [M2: nat] :
% 0.18/0.48                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 0.18/0.48               => ( P @ M2 ) )
% 0.18/0.48           => ( P @ N3 ) )
% 0.18/0.48       => ( P @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % full_nat_induct
% 0.18/0.48  thf(fact_314_nat__induct__at__least,axiom,
% 0.18/0.48      ! [M: nat,N2: nat,P: nat > $o] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ( P @ M )
% 0.18/0.48         => ( ! [N3: nat] :
% 0.18/0.48                ( ( ord_less_eq_nat @ M @ N3 )
% 0.18/0.48               => ( ( P @ N3 )
% 0.18/0.48                 => ( P @ ( suc @ N3 ) ) ) )
% 0.18/0.48           => ( P @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nat_induct_at_least
% 0.18/0.48  thf(fact_315_transitive__stepwise__le,axiom,
% 0.18/0.48      ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 0.18/0.48         => ( ! [X5: nat,Y3: nat,Z2: nat] :
% 0.18/0.48                ( ( R @ X5 @ Y3 )
% 0.18/0.48               => ( ( R @ Y3 @ Z2 )
% 0.18/0.48                 => ( R @ X5 @ Z2 ) ) )
% 0.18/0.48           => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 0.18/0.48             => ( R @ M @ N2 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % transitive_stepwise_le
% 0.18/0.48  thf(fact_316_nat__arith_Osuc1,axiom,
% 0.18/0.48      ! [A2: nat,K: nat,A: nat] :
% 0.18/0.48        ( ( A2
% 0.18/0.48          = ( plus_plus_nat @ K @ A ) )
% 0.18/0.48       => ( ( suc @ A2 )
% 0.18/0.48          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nat_arith.suc1
% 0.18/0.48  thf(fact_317_add__Suc,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 0.18/0.48        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_Suc
% 0.18/0.48  thf(fact_318_add__Suc__shift,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 0.18/0.48        = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_Suc_shift
% 0.18/0.48  thf(fact_319_nat__less__le,axiom,
% 0.18/0.48      ( ord_less_nat
% 0.18/0.48      = ( ^ [M6: nat,N: nat] :
% 0.18/0.48            ( ( ord_less_eq_nat @ M6 @ N )
% 0.18/0.48            & ( M6 != N ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nat_less_le
% 0.18/0.48  thf(fact_320_less__imp__le__nat,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_imp_le_nat
% 0.18/0.48  thf(fact_321_le__eq__less__or__eq,axiom,
% 0.18/0.48      ( ord_less_eq_nat
% 0.18/0.48      = ( ^ [M6: nat,N: nat] :
% 0.18/0.48            ( ( ord_less_nat @ M6 @ N )
% 0.18/0.48            | ( M6 = N ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_eq_less_or_eq
% 0.18/0.48  thf(fact_322_less__or__eq__imp__le,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48          | ( M = N2 ) )
% 0.18/0.48       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_or_eq_imp_le
% 0.18/0.48  thf(fact_323_le__neq__implies__less,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ( M != N2 )
% 0.18/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_neq_implies_less
% 0.18/0.48  thf(fact_324_less__mono__imp__le__mono,axiom,
% 0.18/0.48      ! [F: nat > nat,I2: nat,J: nat] :
% 0.18/0.48        ( ! [I4: nat,J2: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ J2 )
% 0.18/0.48           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48         => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_mono_imp_le_mono
% 0.18/0.48  thf(fact_325_add__lessD1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat] :
% 0.18/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 0.18/0.48       => ( ord_less_nat @ I2 @ K ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_lessD1
% 0.18/0.48  thf(fact_326_add__less__mono,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48       => ( ( ord_less_nat @ K @ L )
% 0.18/0.48         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_mono
% 0.18/0.48  thf(fact_327_not__add__less1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat] :
% 0.18/0.48        ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 0.18/0.48  
% 0.18/0.48  % not_add_less1
% 0.18/0.48  thf(fact_328_not__add__less2,axiom,
% 0.18/0.48      ! [J: nat,I2: nat] :
% 0.18/0.48        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 0.18/0.48  
% 0.18/0.48  % not_add_less2
% 0.18/0.48  thf(fact_329_add__less__mono1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat] :
% 0.18/0.48        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_mono1
% 0.18/0.48  thf(fact_330_trans__less__add1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,M: nat] :
% 0.18/0.48        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % trans_less_add1
% 0.18/0.48  thf(fact_331_trans__less__add2,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,M: nat] :
% 0.18/0.48        ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % trans_less_add2
% 0.18/0.48  thf(fact_332_less__add__eq__less,axiom,
% 0.18/0.48      ! [K: nat,L: nat,M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ K @ L )
% 0.18/0.48       => ( ( ( plus_plus_nat @ M @ L )
% 0.18/0.48            = ( plus_plus_nat @ K @ N2 ) )
% 0.18/0.48         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_eq_less
% 0.18/0.48  thf(fact_333_add__leE,axiom,
% 0.18/0.48      ! [M: nat,K: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.18/0.48       => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48           => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_leE
% 0.18/0.48  thf(fact_334_le__add1,axiom,
% 0.18/0.48      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_add1
% 0.18/0.48  thf(fact_335_le__add2,axiom,
% 0.18/0.48      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_add2
% 0.18/0.48  thf(fact_336_add__leD1,axiom,
% 0.18/0.48      ! [M: nat,K: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_leD1
% 0.18/0.48  thf(fact_337_add__leD2,axiom,
% 0.18/0.48      ! [M: nat,K: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_leD2
% 0.18/0.48  thf(fact_338_le__Suc__ex,axiom,
% 0.18/0.48      ! [K: nat,L: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ K @ L )
% 0.18/0.48       => ? [N3: nat] :
% 0.18/0.48            ( L
% 0.18/0.48            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_Suc_ex
% 0.18/0.48  thf(fact_339_add__le__mono,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ( ord_less_eq_nat @ K @ L )
% 0.18/0.48         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_mono
% 0.18/0.48  thf(fact_340_add__le__mono1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_mono1
% 0.18/0.48  thf(fact_341_trans__le__add1,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,M: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % trans_le_add1
% 0.18/0.48  thf(fact_342_trans__le__add2,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,M: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % trans_le_add2
% 0.18/0.48  thf(fact_343_nat__le__iff__add,axiom,
% 0.18/0.48      ( ord_less_eq_nat
% 0.18/0.48      = ( ^ [M6: nat,N: nat] :
% 0.18/0.48          ? [K3: nat] :
% 0.18/0.48            ( N
% 0.18/0.48            = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nat_le_iff_add
% 0.18/0.48  thf(fact_344_lift__Suc__mono__less,axiom,
% 0.18/0.48      ! [F: nat > real,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less
% 0.18/0.48  thf(fact_345_lift__Suc__mono__less,axiom,
% 0.18/0.48      ! [F: nat > rat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less
% 0.18/0.48  thf(fact_346_lift__Suc__mono__less,axiom,
% 0.18/0.48      ! [F: nat > num,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less
% 0.18/0.48  thf(fact_347_lift__Suc__mono__less,axiom,
% 0.18/0.48      ! [F: nat > nat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less
% 0.18/0.48  thf(fact_348_lift__Suc__mono__less,axiom,
% 0.18/0.48      ! [F: nat > int,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less
% 0.18/0.48  thf(fact_349_lift__Suc__mono__less__iff,axiom,
% 0.18/0.48      ! [F: nat > real,N2: nat,M: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.48          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less_iff
% 0.18/0.48  thf(fact_350_lift__Suc__mono__less__iff,axiom,
% 0.18/0.48      ! [F: nat > rat,N2: nat,M: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.48          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less_iff
% 0.18/0.48  thf(fact_351_lift__Suc__mono__less__iff,axiom,
% 0.18/0.48      ! [F: nat > num,N2: nat,M: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.48          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less_iff
% 0.18/0.48  thf(fact_352_lift__Suc__mono__less__iff,axiom,
% 0.18/0.48      ! [F: nat > nat,N2: nat,M: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.48          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less_iff
% 0.18/0.48  thf(fact_353_lift__Suc__mono__less__iff,axiom,
% 0.18/0.48      ! [F: nat > int,N2: nat,M: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.48          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_less_iff
% 0.18/0.48  thf(fact_354_lift__Suc__mono__le,axiom,
% 0.18/0.48      ! [F: nat > set_int,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_le
% 0.18/0.48  thf(fact_355_lift__Suc__mono__le,axiom,
% 0.18/0.48      ! [F: nat > rat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_le
% 0.18/0.48  thf(fact_356_lift__Suc__mono__le,axiom,
% 0.18/0.48      ! [F: nat > num,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_le
% 0.18/0.48  thf(fact_357_lift__Suc__mono__le,axiom,
% 0.18/0.48      ! [F: nat > nat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_le
% 0.18/0.48  thf(fact_358_lift__Suc__mono__le,axiom,
% 0.18/0.48      ! [F: nat > int,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_mono_le
% 0.18/0.48  thf(fact_359_lift__Suc__antimono__le,axiom,
% 0.18/0.48      ! [F: nat > set_int,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_antimono_le
% 0.18/0.48  thf(fact_360_lift__Suc__antimono__le,axiom,
% 0.18/0.48      ! [F: nat > rat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_antimono_le
% 0.18/0.48  thf(fact_361_lift__Suc__antimono__le,axiom,
% 0.18/0.48      ! [F: nat > num,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_antimono_le
% 0.18/0.48  thf(fact_362_lift__Suc__antimono__le,axiom,
% 0.18/0.48      ! [F: nat > nat,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_antimono_le
% 0.18/0.48  thf(fact_363_lift__Suc__antimono__le,axiom,
% 0.18/0.48      ! [F: nat > int,N2: nat,N5: nat] :
% 0.18/0.48        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.18/0.48       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 0.18/0.48         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % lift_Suc_antimono_le
% 0.18/0.48  thf(fact_364_le__imp__less__Suc,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_imp_less_Suc
% 0.18/0.48  thf(fact_365_less__eq__Suc__le,axiom,
% 0.18/0.48      ( ord_less_nat
% 0.18/0.48      = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_eq_Suc_le
% 0.18/0.48  thf(fact_366_less__Suc__eq__le,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.48        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_Suc_eq_le
% 0.18/0.48  thf(fact_367_le__less__Suc__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.48          = ( N2 = M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_less_Suc_eq
% 0.18/0.48  thf(fact_368_Suc__le__lessD,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.48       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_le_lessD
% 0.18/0.48  thf(fact_369_inc__induct,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,P: nat > $o] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ( P @ J )
% 0.18/0.48         => ( ! [N3: nat] :
% 0.18/0.48                ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.18/0.48               => ( ( ord_less_nat @ N3 @ J )
% 0.18/0.48                 => ( ( P @ ( suc @ N3 ) )
% 0.18/0.48                   => ( P @ N3 ) ) ) )
% 0.18/0.48           => ( P @ I2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % inc_induct
% 0.18/0.48  thf(fact_370_dec__induct,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,P: nat > $o] :
% 0.18/0.48        ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48       => ( ( P @ I2 )
% 0.18/0.48         => ( ! [N3: nat] :
% 0.18/0.48                ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.18/0.48               => ( ( ord_less_nat @ N3 @ J )
% 0.18/0.48                 => ( ( P @ N3 )
% 0.18/0.48                   => ( P @ ( suc @ N3 ) ) ) ) )
% 0.18/0.48           => ( P @ J ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dec_induct
% 0.18/0.48  thf(fact_371_Suc__le__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.48        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_le_eq
% 0.18/0.48  thf(fact_372_Suc__leI,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48       => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_leI
% 0.18/0.48  thf(fact_373_less__natE,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48       => ~ ! [Q2: nat] :
% 0.18/0.48              ( N2
% 0.18/0.48             != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_natE
% 0.18/0.48  thf(fact_374_less__add__Suc1,axiom,
% 0.18/0.48      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_Suc1
% 0.18/0.48  thf(fact_375_less__add__Suc2,axiom,
% 0.18/0.48      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_Suc2
% 0.18/0.48  thf(fact_376_less__iff__Suc__add,axiom,
% 0.18/0.48      ( ord_less_nat
% 0.18/0.48      = ( ^ [M6: nat,N: nat] :
% 0.18/0.48          ? [K3: nat] :
% 0.18/0.48            ( N
% 0.18/0.48            = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_iff_Suc_add
% 0.18/0.48  thf(fact_377_less__imp__Suc__add,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48       => ? [K2: nat] :
% 0.18/0.48            ( N2
% 0.18/0.48            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_imp_Suc_add
% 0.18/0.48  thf(fact_378_mono__nat__linear__lb,axiom,
% 0.18/0.48      ! [F: nat > nat,M: nat,K: nat] :
% 0.18/0.48        ( ! [M5: nat,N3: nat] :
% 0.18/0.48            ( ( ord_less_nat @ M5 @ N3 )
% 0.18/0.48           => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mono_nat_linear_lb
% 0.18/0.48  thf(fact_379_Suc__eq__plus1,axiom,
% 0.18/0.48      ( suc
% 0.18/0.48      = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_eq_plus1
% 0.18/0.48  thf(fact_380_plus__1__eq__Suc,axiom,
% 0.18/0.48      ( ( plus_plus_nat @ one_one_nat )
% 0.18/0.48      = suc ) ).
% 0.18/0.48  
% 0.18/0.48  % plus_1_eq_Suc
% 0.18/0.48  thf(fact_381_Suc__eq__plus1__left,axiom,
% 0.18/0.48      ( suc
% 0.18/0.48      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Suc_eq_plus1_left
% 0.18/0.48  thf(fact_382_field__sum__of__halves,axiom,
% 0.18/0.48      ! [X4: rat] :
% 0.18/0.48        ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.18/0.48        = X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % field_sum_of_halves
% 0.18/0.48  thf(fact_383_field__sum__of__halves,axiom,
% 0.18/0.48      ! [X4: real] :
% 0.18/0.48        ( ( plus_plus_real @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.18/0.48        = X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % field_sum_of_halves
% 0.18/0.48  thf(fact_384_div__by__1,axiom,
% 0.18/0.48      ! [A: rat] :
% 0.18/0.48        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_385_div__by__1,axiom,
% 0.18/0.48      ! [A: nat] :
% 0.18/0.48        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_386_div__by__1,axiom,
% 0.18/0.48      ! [A: int] :
% 0.18/0.48        ( ( divide_divide_int @ A @ one_one_int )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_387_div__by__1,axiom,
% 0.18/0.48      ! [A: real] :
% 0.18/0.48        ( ( divide_divide_real @ A @ one_one_real )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_388_div__by__1,axiom,
% 0.18/0.48      ! [A: complex] :
% 0.18/0.48        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_389_div__by__1,axiom,
% 0.18/0.48      ! [A: code_integer] :
% 0.18/0.48        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % div_by_1
% 0.18/0.48  thf(fact_390_add__less__cancel__left,axiom,
% 0.18/0.48      ! [C: real,A: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.18/0.48        = ( ord_less_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_left
% 0.18/0.48  thf(fact_391_add__less__cancel__left,axiom,
% 0.18/0.48      ! [C: rat,A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.18/0.48        = ( ord_less_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_left
% 0.18/0.48  thf(fact_392_add__less__cancel__left,axiom,
% 0.18/0.48      ! [C: nat,A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.18/0.48        = ( ord_less_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_left
% 0.18/0.48  thf(fact_393_add__less__cancel__left,axiom,
% 0.18/0.48      ! [C: int,A: int,B: int] :
% 0.18/0.48        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.18/0.48        = ( ord_less_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_left
% 0.18/0.48  thf(fact_394_add__less__cancel__right,axiom,
% 0.18/0.48      ! [A: real,C: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.18/0.48        = ( ord_less_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_right
% 0.18/0.48  thf(fact_395_add__less__cancel__right,axiom,
% 0.18/0.48      ! [A: rat,C: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.18/0.48        = ( ord_less_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_right
% 0.18/0.48  thf(fact_396_add__less__cancel__right,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.18/0.48        = ( ord_less_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_right
% 0.18/0.48  thf(fact_397_add__less__cancel__right,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.18/0.48        = ( ord_less_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_cancel_right
% 0.18/0.48  thf(fact_398_add__le__cancel__left,axiom,
% 0.18/0.48      ! [C: real,A: real,B: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.18/0.48        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_left
% 0.18/0.48  thf(fact_399_add__le__cancel__left,axiom,
% 0.18/0.48      ! [C: rat,A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.18/0.48        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_left
% 0.18/0.48  thf(fact_400_add__le__cancel__left,axiom,
% 0.18/0.48      ! [C: nat,A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.18/0.48        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_left
% 0.18/0.48  thf(fact_401_add__le__cancel__left,axiom,
% 0.18/0.48      ! [C: int,A: int,B: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.18/0.48        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_left
% 0.18/0.48  thf(fact_402_add__le__cancel__right,axiom,
% 0.18/0.48      ! [A: real,C: real,B: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.18/0.48        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_right
% 0.18/0.48  thf(fact_403_add__le__cancel__right,axiom,
% 0.18/0.48      ! [A: rat,C: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.18/0.48        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_right
% 0.18/0.48  thf(fact_404_add__le__cancel__right,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.18/0.48        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_right
% 0.18/0.48  thf(fact_405_add__le__cancel__right,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.18/0.48        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_cancel_right
% 0.18/0.48  thf(fact_406_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_real] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 0.18/0.48       => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_407_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_complex] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.18/0.48       => ( member_complex @ ( nth_complex @ Xs @ N2 ) @ ( set_complex2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_408_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_P6011104703257516679at_nat] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 0.18/0.48       => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_409_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_VEBT_VEBT] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_410_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_o] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48       => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_411_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_nat] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48       => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_412_nth__mem,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_int] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48       => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_mem
% 0.18/0.48  thf(fact_413_list__ball__nth,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48       => ( ! [X5: vEBT_VEBT] :
% 0.18/0.48              ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.48             => ( P @ X5 ) )
% 0.18/0.48         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_ball_nth
% 0.18/0.48  thf(fact_414_list__ball__nth,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_o,P: $o > $o] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48       => ( ! [X5: $o] :
% 0.18/0.48              ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 0.18/0.48             => ( P @ X5 ) )
% 0.18/0.48         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_ball_nth
% 0.18/0.48  thf(fact_415_list__ball__nth,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48       => ( ! [X5: nat] :
% 0.18/0.48              ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 0.18/0.48             => ( P @ X5 ) )
% 0.18/0.48         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_ball_nth
% 0.18/0.48  thf(fact_416_list__ball__nth,axiom,
% 0.18/0.48      ! [N2: nat,Xs: list_int,P: int > $o] :
% 0.18/0.48        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48       => ( ! [X5: int] :
% 0.18/0.48              ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 0.18/0.48             => ( P @ X5 ) )
% 0.18/0.48         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_ball_nth
% 0.18/0.48  thf(fact_417_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: real,Xs: list_real] :
% 0.18/0.48        ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 0.18/0.48              & ( ( nth_real @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_418_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: complex,Xs: list_complex] :
% 0.18/0.48        ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.18/0.48              & ( ( nth_complex @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_419_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 0.18/0.48        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 0.18/0.48              & ( ( nth_Pr7617993195940197384at_nat @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_420_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.18/0.48        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48              & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_421_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: $o,Xs: list_o] :
% 0.18/0.48        ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48              & ( ( nth_o @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_422_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: nat,Xs: list_nat] :
% 0.18/0.48        ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48              & ( ( nth_nat @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_423_in__set__conv__nth,axiom,
% 0.18/0.48      ! [X4: int,Xs: list_int] :
% 0.18/0.48        ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.18/0.48        = ( ? [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48              & ( ( nth_int @ Xs @ I3 )
% 0.18/0.48                = X4 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % in_set_conv_nth
% 0.18/0.48  thf(fact_424_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_real,P: real > $o,X4: real] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_425_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_complex,P: complex > $o,X4: complex] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_426_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X4: product_prod_nat_nat] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_427_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_428_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_o,P: $o > $o,X4: $o] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_429_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_nat,P: nat > $o,X4: nat] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_430_all__nth__imp__all__set,axiom,
% 0.18/0.48      ! [Xs: list_int,P: int > $o,X4: int] :
% 0.18/0.48        ( ! [I4: nat] :
% 0.18/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48           => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 0.18/0.48       => ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.18/0.48         => ( P @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_nth_imp_all_set
% 0.18/0.48  thf(fact_431_all__set__conv__all__nth,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.18/0.48        ( ( ! [X: vEBT_VEBT] :
% 0.18/0.48              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.48             => ( P @ X ) ) )
% 0.18/0.48        = ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48             => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_set_conv_all_nth
% 0.18/0.48  thf(fact_432_all__set__conv__all__nth,axiom,
% 0.18/0.48      ! [Xs: list_o,P: $o > $o] :
% 0.18/0.48        ( ( ! [X: $o] :
% 0.18/0.48              ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.18/0.48             => ( P @ X ) ) )
% 0.18/0.48        = ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48             => ( P @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_set_conv_all_nth
% 0.18/0.48  thf(fact_433_all__set__conv__all__nth,axiom,
% 0.18/0.48      ! [Xs: list_nat,P: nat > $o] :
% 0.18/0.48        ( ( ! [X: nat] :
% 0.18/0.48              ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.18/0.48             => ( P @ X ) ) )
% 0.18/0.48        = ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48             => ( P @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_set_conv_all_nth
% 0.18/0.48  thf(fact_434_all__set__conv__all__nth,axiom,
% 0.18/0.48      ! [Xs: list_int,P: int > $o] :
% 0.18/0.48        ( ( ! [X: int] :
% 0.18/0.48              ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.18/0.48             => ( P @ X ) ) )
% 0.18/0.48        = ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48             => ( P @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % all_set_conv_all_nth
% 0.18/0.48  thf(fact_435_gt__half__sum,axiom,
% 0.18/0.48      ! [A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % gt_half_sum
% 0.18/0.48  thf(fact_436_gt__half__sum,axiom,
% 0.18/0.48      ! [A: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % gt_half_sum
% 0.18/0.48  thf(fact_437_less__half__sum,axiom,
% 0.18/0.48      ! [A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_half_sum
% 0.18/0.48  thf(fact_438_less__half__sum,axiom,
% 0.18/0.48      ! [A: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_half_sum
% 0.18/0.48  thf(fact_439_add__right__cancel,axiom,
% 0.18/0.48      ! [B: real,A: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ B @ A )
% 0.18/0.48          = ( plus_plus_real @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_cancel
% 0.18/0.48  thf(fact_440_add__right__cancel,axiom,
% 0.18/0.48      ! [B: rat,A: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ B @ A )
% 0.18/0.48          = ( plus_plus_rat @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_cancel
% 0.18/0.48  thf(fact_441_add__right__cancel,axiom,
% 0.18/0.48      ! [B: nat,A: nat,C: nat] :
% 0.18/0.48        ( ( ( plus_plus_nat @ B @ A )
% 0.18/0.48          = ( plus_plus_nat @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_cancel
% 0.18/0.48  thf(fact_442_add__right__cancel,axiom,
% 0.18/0.48      ! [B: int,A: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ B @ A )
% 0.18/0.48          = ( plus_plus_int @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_cancel
% 0.18/0.48  thf(fact_443_add__left__cancel,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ A @ B )
% 0.18/0.48          = ( plus_plus_real @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_cancel
% 0.18/0.48  thf(fact_444_add__left__cancel,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ A @ B )
% 0.18/0.48          = ( plus_plus_rat @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_cancel
% 0.18/0.48  thf(fact_445_add__left__cancel,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ( plus_plus_nat @ A @ B )
% 0.18/0.48          = ( plus_plus_nat @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_cancel
% 0.18/0.48  thf(fact_446_add__left__cancel,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ A @ B )
% 0.18/0.48          = ( plus_plus_int @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_cancel
% 0.18/0.48  thf(fact_447_real__arch__pow,axiom,
% 0.18/0.48      ! [X4: real,Y: real] :
% 0.18/0.48        ( ( ord_less_real @ one_one_real @ X4 )
% 0.18/0.48       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X4 @ N3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % real_arch_pow
% 0.18/0.48  thf(fact_448_less__eq__real__def,axiom,
% 0.18/0.48      ( ord_less_eq_real
% 0.18/0.48      = ( ^ [X: real,Y5: real] :
% 0.18/0.48            ( ( ord_less_real @ X @ Y5 )
% 0.18/0.48            | ( X = Y5 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_eq_real_def
% 0.18/0.48  thf(fact_449_complete__real,axiom,
% 0.18/0.48      ! [S2: set_real] :
% 0.18/0.48        ( ? [X2: real] : ( member_real @ X2 @ S2 )
% 0.18/0.48       => ( ? [Z3: real] :
% 0.18/0.48            ! [X5: real] :
% 0.18/0.48              ( ( member_real @ X5 @ S2 )
% 0.18/0.48             => ( ord_less_eq_real @ X5 @ Z3 ) )
% 0.18/0.48         => ? [Y3: real] :
% 0.18/0.48              ( ! [X2: real] :
% 0.18/0.48                  ( ( member_real @ X2 @ S2 )
% 0.18/0.48                 => ( ord_less_eq_real @ X2 @ Y3 ) )
% 0.18/0.48              & ! [Z3: real] :
% 0.18/0.48                  ( ! [X5: real] :
% 0.18/0.48                      ( ( member_real @ X5 @ S2 )
% 0.18/0.48                     => ( ord_less_eq_real @ X5 @ Z3 ) )
% 0.18/0.48                 => ( ord_less_eq_real @ Y3 @ Z3 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % complete_real
% 0.18/0.48  thf(fact_450_linorder__neqE__linordered__idom,axiom,
% 0.18/0.48      ! [X4: real,Y: real] :
% 0.18/0.48        ( ( X4 != Y )
% 0.18/0.48       => ( ~ ( ord_less_real @ X4 @ Y )
% 0.18/0.48         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % linorder_neqE_linordered_idom
% 0.18/0.48  thf(fact_451_linorder__neqE__linordered__idom,axiom,
% 0.18/0.48      ! [X4: rat,Y: rat] :
% 0.18/0.48        ( ( X4 != Y )
% 0.18/0.48       => ( ~ ( ord_less_rat @ X4 @ Y )
% 0.18/0.48         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % linorder_neqE_linordered_idom
% 0.18/0.48  thf(fact_452_linorder__neqE__linordered__idom,axiom,
% 0.18/0.48      ! [X4: int,Y: int] :
% 0.18/0.48        ( ( X4 != Y )
% 0.18/0.48       => ( ~ ( ord_less_int @ X4 @ Y )
% 0.18/0.48         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % linorder_neqE_linordered_idom
% 0.18/0.48  thf(fact_453_linordered__field__no__ub,axiom,
% 0.18/0.48      ! [X2: real] :
% 0.18/0.48      ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 0.18/0.48  
% 0.18/0.48  % linordered_field_no_ub
% 0.18/0.48  thf(fact_454_linordered__field__no__ub,axiom,
% 0.18/0.48      ! [X2: rat] :
% 0.18/0.48      ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 0.18/0.48  
% 0.18/0.48  % linordered_field_no_ub
% 0.18/0.48  thf(fact_455_linordered__field__no__lb,axiom,
% 0.18/0.48      ! [X2: real] :
% 0.18/0.48      ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 0.18/0.48  
% 0.18/0.48  % linordered_field_no_lb
% 0.18/0.48  thf(fact_456_linordered__field__no__lb,axiom,
% 0.18/0.48      ! [X2: rat] :
% 0.18/0.48      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 0.18/0.48  
% 0.18/0.48  % linordered_field_no_lb
% 0.18/0.48  thf(fact_457_one__reorient,axiom,
% 0.18/0.48      ! [X4: complex] :
% 0.18/0.48        ( ( one_one_complex = X4 )
% 0.18/0.48        = ( X4 = one_one_complex ) ) ).
% 0.18/0.48  
% 0.18/0.48  % one_reorient
% 0.18/0.48  thf(fact_458_one__reorient,axiom,
% 0.18/0.48      ! [X4: real] :
% 0.18/0.48        ( ( one_one_real = X4 )
% 0.18/0.48        = ( X4 = one_one_real ) ) ).
% 0.18/0.48  
% 0.18/0.48  % one_reorient
% 0.18/0.48  thf(fact_459_one__reorient,axiom,
% 0.18/0.48      ! [X4: rat] :
% 0.18/0.48        ( ( one_one_rat = X4 )
% 0.18/0.48        = ( X4 = one_one_rat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % one_reorient
% 0.18/0.48  thf(fact_460_one__reorient,axiom,
% 0.18/0.48      ! [X4: nat] :
% 0.18/0.48        ( ( one_one_nat = X4 )
% 0.18/0.48        = ( X4 = one_one_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % one_reorient
% 0.18/0.48  thf(fact_461_one__reorient,axiom,
% 0.18/0.48      ! [X4: int] :
% 0.18/0.48        ( ( one_one_int = X4 )
% 0.18/0.48        = ( X4 = one_one_int ) ) ).
% 0.18/0.48  
% 0.18/0.48  % one_reorient
% 0.18/0.48  thf(fact_462_add__right__imp__eq,axiom,
% 0.18/0.48      ! [B: real,A: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ B @ A )
% 0.18/0.48          = ( plus_plus_real @ C @ A ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_imp_eq
% 0.18/0.48  thf(fact_463_add__right__imp__eq,axiom,
% 0.18/0.48      ! [B: rat,A: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ B @ A )
% 0.18/0.48          = ( plus_plus_rat @ C @ A ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_imp_eq
% 0.18/0.48  thf(fact_464_add__right__imp__eq,axiom,
% 0.18/0.48      ! [B: nat,A: nat,C: nat] :
% 0.18/0.48        ( ( ( plus_plus_nat @ B @ A )
% 0.18/0.48          = ( plus_plus_nat @ C @ A ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_imp_eq
% 0.18/0.48  thf(fact_465_add__right__imp__eq,axiom,
% 0.18/0.48      ! [B: int,A: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ B @ A )
% 0.18/0.48          = ( plus_plus_int @ C @ A ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_imp_eq
% 0.18/0.48  thf(fact_466_add__left__imp__eq,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ A @ B )
% 0.18/0.48          = ( plus_plus_real @ A @ C ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_imp_eq
% 0.18/0.48  thf(fact_467_add__left__imp__eq,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ A @ B )
% 0.18/0.48          = ( plus_plus_rat @ A @ C ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_imp_eq
% 0.18/0.48  thf(fact_468_add__left__imp__eq,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ( plus_plus_nat @ A @ B )
% 0.18/0.48          = ( plus_plus_nat @ A @ C ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_imp_eq
% 0.18/0.48  thf(fact_469_add__left__imp__eq,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ A @ B )
% 0.18/0.48          = ( plus_plus_int @ A @ C ) )
% 0.18/0.48       => ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_imp_eq
% 0.18/0.48  thf(fact_470_add_Oleft__commute,axiom,
% 0.18/0.48      ! [B: real,A: real,C: real] :
% 0.18/0.48        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.18/0.48        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_commute
% 0.18/0.48  thf(fact_471_add_Oleft__commute,axiom,
% 0.18/0.48      ! [B: rat,A: rat,C: rat] :
% 0.18/0.48        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.18/0.48        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_commute
% 0.18/0.48  thf(fact_472_add_Oleft__commute,axiom,
% 0.18/0.48      ! [B: nat,A: nat,C: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.18/0.48        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_commute
% 0.18/0.48  thf(fact_473_add_Oleft__commute,axiom,
% 0.18/0.48      ! [B: int,A: int,C: int] :
% 0.18/0.48        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.18/0.48        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_commute
% 0.18/0.48  thf(fact_474_add_Ocommute,axiom,
% 0.18/0.48      ( plus_plus_real
% 0.18/0.48      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.commute
% 0.18/0.48  thf(fact_475_add_Ocommute,axiom,
% 0.18/0.48      ( plus_plus_rat
% 0.18/0.48      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.commute
% 0.18/0.48  thf(fact_476_add_Ocommute,axiom,
% 0.18/0.48      ( plus_plus_nat
% 0.18/0.48      = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.commute
% 0.18/0.48  thf(fact_477_add_Ocommute,axiom,
% 0.18/0.48      ( plus_plus_int
% 0.18/0.48      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.commute
% 0.18/0.48  thf(fact_478_add_Oright__cancel,axiom,
% 0.18/0.48      ! [B: real,A: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ B @ A )
% 0.18/0.48          = ( plus_plus_real @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.right_cancel
% 0.18/0.48  thf(fact_479_add_Oright__cancel,axiom,
% 0.18/0.48      ! [B: rat,A: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ B @ A )
% 0.18/0.48          = ( plus_plus_rat @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.right_cancel
% 0.18/0.48  thf(fact_480_add_Oright__cancel,axiom,
% 0.18/0.48      ! [B: int,A: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ B @ A )
% 0.18/0.48          = ( plus_plus_int @ C @ A ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.right_cancel
% 0.18/0.48  thf(fact_481_add_Oleft__cancel,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ( plus_plus_real @ A @ B )
% 0.18/0.48          = ( plus_plus_real @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_cancel
% 0.18/0.48  thf(fact_482_add_Oleft__cancel,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ( plus_plus_rat @ A @ B )
% 0.18/0.48          = ( plus_plus_rat @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_cancel
% 0.18/0.48  thf(fact_483_add_Oleft__cancel,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ( plus_plus_int @ A @ B )
% 0.18/0.48          = ( plus_plus_int @ A @ C ) )
% 0.18/0.48        = ( B = C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.left_cancel
% 0.18/0.48  thf(fact_484_add_Oassoc,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.assoc
% 0.18/0.48  thf(fact_485_add_Oassoc,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.assoc
% 0.18/0.48  thf(fact_486_add_Oassoc,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.assoc
% 0.18/0.48  thf(fact_487_add_Oassoc,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add.assoc
% 0.18/0.48  thf(fact_488_group__cancel_Oadd2,axiom,
% 0.18/0.48      ! [B3: real,K: real,B: real,A: real] :
% 0.18/0.48        ( ( B3
% 0.18/0.48          = ( plus_plus_real @ K @ B ) )
% 0.18/0.48       => ( ( plus_plus_real @ A @ B3 )
% 0.18/0.48          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add2
% 0.18/0.48  thf(fact_489_group__cancel_Oadd2,axiom,
% 0.18/0.48      ! [B3: rat,K: rat,B: rat,A: rat] :
% 0.18/0.48        ( ( B3
% 0.18/0.48          = ( plus_plus_rat @ K @ B ) )
% 0.18/0.48       => ( ( plus_plus_rat @ A @ B3 )
% 0.18/0.48          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add2
% 0.18/0.48  thf(fact_490_group__cancel_Oadd2,axiom,
% 0.18/0.48      ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.18/0.48        ( ( B3
% 0.18/0.48          = ( plus_plus_nat @ K @ B ) )
% 0.18/0.48       => ( ( plus_plus_nat @ A @ B3 )
% 0.18/0.48          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add2
% 0.18/0.48  thf(fact_491_group__cancel_Oadd2,axiom,
% 0.18/0.48      ! [B3: int,K: int,B: int,A: int] :
% 0.18/0.48        ( ( B3
% 0.18/0.48          = ( plus_plus_int @ K @ B ) )
% 0.18/0.48       => ( ( plus_plus_int @ A @ B3 )
% 0.18/0.48          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add2
% 0.18/0.48  thf(fact_492_group__cancel_Oadd1,axiom,
% 0.18/0.48      ! [A2: real,K: real,A: real,B: real] :
% 0.18/0.48        ( ( A2
% 0.18/0.48          = ( plus_plus_real @ K @ A ) )
% 0.18/0.48       => ( ( plus_plus_real @ A2 @ B )
% 0.18/0.48          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add1
% 0.18/0.48  thf(fact_493_group__cancel_Oadd1,axiom,
% 0.18/0.48      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.18/0.48        ( ( A2
% 0.18/0.48          = ( plus_plus_rat @ K @ A ) )
% 0.18/0.48       => ( ( plus_plus_rat @ A2 @ B )
% 0.18/0.48          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add1
% 0.18/0.48  thf(fact_494_group__cancel_Oadd1,axiom,
% 0.18/0.48      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.18/0.48        ( ( A2
% 0.18/0.48          = ( plus_plus_nat @ K @ A ) )
% 0.18/0.48       => ( ( plus_plus_nat @ A2 @ B )
% 0.18/0.48          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add1
% 0.18/0.48  thf(fact_495_group__cancel_Oadd1,axiom,
% 0.18/0.48      ! [A2: int,K: int,A: int,B: int] :
% 0.18/0.48        ( ( A2
% 0.18/0.48          = ( plus_plus_int @ K @ A ) )
% 0.18/0.48       => ( ( plus_plus_int @ A2 @ B )
% 0.18/0.48          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % group_cancel.add1
% 0.18/0.48  thf(fact_496_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ( plus_plus_real @ I2 @ K )
% 0.18/0.48          = ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(4)
% 0.18/0.48  thf(fact_497_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ( plus_plus_rat @ I2 @ K )
% 0.18/0.48          = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(4)
% 0.18/0.48  thf(fact_498_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ( plus_plus_nat @ I2 @ K )
% 0.18/0.48          = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(4)
% 0.18/0.48  thf(fact_499_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ( plus_plus_int @ I2 @ K )
% 0.18/0.48          = ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(4)
% 0.18/0.48  thf(fact_500_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % ab_semigroup_add_class.add_ac(1)
% 0.18/0.48  thf(fact_501_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % ab_semigroup_add_class.add_ac(1)
% 0.18/0.48  thf(fact_502_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % ab_semigroup_add_class.add_ac(1)
% 0.18/0.48  thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % ab_semigroup_add_class.add_ac(1)
% 0.18/0.48  thf(fact_504_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_real,B3: set_real] :
% 0.18/0.48        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: real] :
% 0.18/0.48              ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.18/0.48             => ( member_real @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_505_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_complex,B3: set_complex] :
% 0.18/0.48        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: complex] :
% 0.18/0.48              ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 0.18/0.48             => ( member_complex @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_506_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_P6011104703257516679at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.18/0.48        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: product_prod_nat_nat] :
% 0.18/0.48              ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.18/0.48             => ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_507_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 0.18/0.48        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: vEBT_VEBT] :
% 0.18/0.48              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.18/0.48             => ( member_VEBT_VEBT @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_508_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_nat,B3: set_nat] :
% 0.18/0.48        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: nat] :
% 0.18/0.48              ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.18/0.48             => ( member_nat @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_509_subset__code_I1_J,axiom,
% 0.18/0.48      ! [Xs: list_int,B3: set_int] :
% 0.18/0.48        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 0.18/0.48        = ( ! [X: int] :
% 0.18/0.48              ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.18/0.48             => ( member_int @ X @ B3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_code(1)
% 0.18/0.48  thf(fact_510_neq__if__length__neq,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.18/0.48        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.18/0.48         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.18/0.48       => ( Xs != Ys ) ) ).
% 0.18/0.48  
% 0.18/0.48  % neq_if_length_neq
% 0.18/0.48  thf(fact_511_neq__if__length__neq,axiom,
% 0.18/0.48      ! [Xs: list_o,Ys: list_o] :
% 0.18/0.48        ( ( ( size_size_list_o @ Xs )
% 0.18/0.48         != ( size_size_list_o @ Ys ) )
% 0.18/0.48       => ( Xs != Ys ) ) ).
% 0.18/0.48  
% 0.18/0.48  % neq_if_length_neq
% 0.18/0.48  thf(fact_512_neq__if__length__neq,axiom,
% 0.18/0.48      ! [Xs: list_nat,Ys: list_nat] :
% 0.18/0.48        ( ( ( size_size_list_nat @ Xs )
% 0.18/0.48         != ( size_size_list_nat @ Ys ) )
% 0.18/0.48       => ( Xs != Ys ) ) ).
% 0.18/0.48  
% 0.18/0.48  % neq_if_length_neq
% 0.18/0.48  thf(fact_513_neq__if__length__neq,axiom,
% 0.18/0.48      ! [Xs: list_int,Ys: list_int] :
% 0.18/0.48        ( ( ( size_size_list_int @ Xs )
% 0.18/0.48         != ( size_size_list_int @ Ys ) )
% 0.18/0.48       => ( Xs != Ys ) ) ).
% 0.18/0.48  
% 0.18/0.48  % neq_if_length_neq
% 0.18/0.48  thf(fact_514_Ex__list__of__length,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48      ? [Xs2: list_VEBT_VEBT] :
% 0.18/0.48        ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.18/0.48        = N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % Ex_list_of_length
% 0.18/0.48  thf(fact_515_Ex__list__of__length,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48      ? [Xs2: list_o] :
% 0.18/0.48        ( ( size_size_list_o @ Xs2 )
% 0.18/0.48        = N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % Ex_list_of_length
% 0.18/0.48  thf(fact_516_Ex__list__of__length,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48      ? [Xs2: list_nat] :
% 0.18/0.48        ( ( size_size_list_nat @ Xs2 )
% 0.18/0.48        = N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % Ex_list_of_length
% 0.18/0.48  thf(fact_517_Ex__list__of__length,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48      ? [Xs2: list_int] :
% 0.18/0.48        ( ( size_size_list_int @ Xs2 )
% 0.18/0.48        = N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % Ex_list_of_length
% 0.18/0.48  thf(fact_518_add__le__imp__le__right,axiom,
% 0.18/0.48      ! [A: real,C: real,B: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.18/0.48       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_right
% 0.18/0.48  thf(fact_519_add__le__imp__le__right,axiom,
% 0.18/0.48      ! [A: rat,C: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.18/0.48       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_right
% 0.18/0.48  thf(fact_520_add__le__imp__le__right,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.18/0.48       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_right
% 0.18/0.48  thf(fact_521_add__le__imp__le__right,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.18/0.48       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_right
% 0.18/0.48  thf(fact_522_add__le__imp__le__left,axiom,
% 0.18/0.48      ! [C: real,A: real,B: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.18/0.48       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_left
% 0.18/0.48  thf(fact_523_add__le__imp__le__left,axiom,
% 0.18/0.48      ! [C: rat,A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.18/0.48       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_left
% 0.18/0.48  thf(fact_524_add__le__imp__le__left,axiom,
% 0.18/0.48      ! [C: nat,A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.18/0.48       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_left
% 0.18/0.48  thf(fact_525_add__le__imp__le__left,axiom,
% 0.18/0.48      ! [C: int,A: int,B: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.18/0.48       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_imp_le_left
% 0.18/0.48  thf(fact_526_le__iff__add,axiom,
% 0.18/0.48      ( ord_less_eq_nat
% 0.18/0.48      = ( ^ [A3: nat,B2: nat] :
% 0.18/0.48          ? [C2: nat] :
% 0.18/0.48            ( B2
% 0.18/0.48            = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_iff_add
% 0.18/0.48  thf(fact_527_add__right__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.18/0.48       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_mono
% 0.18/0.48  thf(fact_528_add__right__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.18/0.48       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_mono
% 0.18/0.48  thf(fact_529_add__right__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_mono
% 0.18/0.48  thf(fact_530_add__right__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.18/0.48       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_right_mono
% 0.18/0.48  thf(fact_531_less__eqE,axiom,
% 0.18/0.48      ! [A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.48       => ~ ! [C3: nat] :
% 0.18/0.48              ( B
% 0.18/0.48             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_eqE
% 0.18/0.48  thf(fact_532_add__left__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.18/0.48       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_mono
% 0.18/0.48  thf(fact_533_add__left__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.18/0.48       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_mono
% 0.18/0.48  thf(fact_534_add__left__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_mono
% 0.18/0.48  thf(fact_535_add__left__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.18/0.48       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_left_mono
% 0.18/0.48  thf(fact_536_add__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_real @ C @ D )
% 0.18/0.48         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono
% 0.18/0.48  thf(fact_537_add__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_rat @ C @ D )
% 0.18/0.48         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono
% 0.18/0.48  thf(fact_538_add__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_nat @ C @ D )
% 0.18/0.48         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono
% 0.18/0.48  thf(fact_539_add__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_int @ C @ D )
% 0.18/0.48         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono
% 0.18/0.48  thf(fact_540_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(1)
% 0.18/0.48  thf(fact_541_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(1)
% 0.18/0.48  thf(fact_542_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(1)
% 0.18/0.48  thf(fact_543_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(1)
% 0.18/0.48  thf(fact_544_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_eq_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(2)
% 0.18/0.48  thf(fact_545_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_eq_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(2)
% 0.18/0.48  thf(fact_546_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_eq_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(2)
% 0.18/0.48  thf(fact_547_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_eq_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(2)
% 0.18/0.48  thf(fact_548_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(3)
% 0.18/0.48  thf(fact_549_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(3)
% 0.18/0.48  thf(fact_550_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(3)
% 0.18/0.48  thf(fact_551_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_semiring(3)
% 0.18/0.48  thf(fact_552_add__less__imp__less__right,axiom,
% 0.18/0.48      ! [A: real,C: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.18/0.48       => ( ord_less_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_right
% 0.18/0.48  thf(fact_553_add__less__imp__less__right,axiom,
% 0.18/0.48      ! [A: rat,C: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.18/0.48       => ( ord_less_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_right
% 0.18/0.48  thf(fact_554_add__less__imp__less__right,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.18/0.48       => ( ord_less_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_right
% 0.18/0.48  thf(fact_555_add__less__imp__less__right,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.18/0.48       => ( ord_less_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_right
% 0.18/0.48  thf(fact_556_add__less__imp__less__left,axiom,
% 0.18/0.48      ! [C: real,A: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.18/0.48       => ( ord_less_real @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_left
% 0.18/0.48  thf(fact_557_add__less__imp__less__left,axiom,
% 0.18/0.48      ! [C: rat,A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.18/0.48       => ( ord_less_rat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_left
% 0.18/0.48  thf(fact_558_add__less__imp__less__left,axiom,
% 0.18/0.48      ! [C: nat,A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.18/0.48       => ( ord_less_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_left
% 0.18/0.48  thf(fact_559_add__less__imp__less__left,axiom,
% 0.18/0.48      ! [C: int,A: int,B: int] :
% 0.18/0.48        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.18/0.48       => ( ord_less_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_imp_less_left
% 0.18/0.48  thf(fact_560_add__strict__right__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_right_mono
% 0.18/0.48  thf(fact_561_add__strict__right__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_right_mono
% 0.18/0.48  thf(fact_562_add__strict__right__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ord_less_nat @ A @ B )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_right_mono
% 0.18/0.48  thf(fact_563_add__strict__right__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ord_less_int @ A @ B )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_right_mono
% 0.18/0.48  thf(fact_564_add__strict__left__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_left_mono
% 0.18/0.48  thf(fact_565_add__strict__left__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_left_mono
% 0.18/0.48  thf(fact_566_add__strict__left__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( ord_less_nat @ A @ B )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_left_mono
% 0.18/0.48  thf(fact_567_add__strict__left__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( ord_less_int @ A @ B )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_left_mono
% 0.18/0.48  thf(fact_568_add__strict__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ( ord_less_real @ C @ D )
% 0.18/0.48         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_mono
% 0.18/0.48  thf(fact_569_add__strict__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ( ord_less_rat @ C @ D )
% 0.18/0.48         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_mono
% 0.18/0.48  thf(fact_570_add__strict__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.18/0.48        ( ( ord_less_nat @ A @ B )
% 0.18/0.48       => ( ( ord_less_nat @ C @ D )
% 0.18/0.48         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_mono
% 0.18/0.48  thf(fact_571_add__strict__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.18/0.48        ( ( ord_less_int @ A @ B )
% 0.18/0.48       => ( ( ord_less_int @ C @ D )
% 0.18/0.48         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_strict_mono
% 0.18/0.48  thf(fact_572_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_real @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(1)
% 0.18/0.48  thf(fact_573_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_rat @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(1)
% 0.18/0.48  thf(fact_574_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(1)
% 0.18/0.48  thf(fact_575_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_int @ I2 @ J )
% 0.18/0.48          & ( K = L ) )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(1)
% 0.18/0.48  thf(fact_576_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(2)
% 0.18/0.48  thf(fact_577_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(2)
% 0.18/0.48  thf(fact_578_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(2)
% 0.18/0.48  thf(fact_579_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( I2 = J )
% 0.18/0.48          & ( ord_less_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(2)
% 0.18/0.48  thf(fact_580_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_real @ I2 @ J )
% 0.18/0.48          & ( ord_less_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(5)
% 0.18/0.48  thf(fact_581_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_rat @ I2 @ J )
% 0.18/0.48          & ( ord_less_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(5)
% 0.18/0.48  thf(fact_582_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48          & ( ord_less_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(5)
% 0.18/0.48  thf(fact_583_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_int @ I2 @ J )
% 0.18/0.48          & ( ord_less_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(5)
% 0.18/0.48  thf(fact_584_add__divide__distrib,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat] :
% 0.18/0.48        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_divide_distrib
% 0.18/0.48  thf(fact_585_add__divide__distrib,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real] :
% 0.18/0.48        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_divide_distrib
% 0.18/0.48  thf(fact_586_add__divide__distrib,axiom,
% 0.18/0.48      ! [A: complex,B: complex,C: complex] :
% 0.18/0.48        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.18/0.48        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_divide_distrib
% 0.18/0.48  thf(fact_587_length__induct,axiom,
% 0.18/0.48      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 0.18/0.48        ( ! [Xs2: list_VEBT_VEBT] :
% 0.18/0.48            ( ! [Ys2: list_VEBT_VEBT] :
% 0.18/0.48                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.18/0.48               => ( P @ Ys2 ) )
% 0.18/0.48           => ( P @ Xs2 ) )
% 0.18/0.48       => ( P @ Xs ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_induct
% 0.18/0.48  thf(fact_588_length__induct,axiom,
% 0.18/0.48      ! [P: list_o > $o,Xs: list_o] :
% 0.18/0.48        ( ! [Xs2: list_o] :
% 0.18/0.48            ( ! [Ys2: list_o] :
% 0.18/0.48                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 0.18/0.48               => ( P @ Ys2 ) )
% 0.18/0.48           => ( P @ Xs2 ) )
% 0.18/0.48       => ( P @ Xs ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_induct
% 0.18/0.48  thf(fact_589_length__induct,axiom,
% 0.18/0.48      ! [P: list_nat > $o,Xs: list_nat] :
% 0.18/0.48        ( ! [Xs2: list_nat] :
% 0.18/0.48            ( ! [Ys2: list_nat] :
% 0.18/0.48                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 0.18/0.48               => ( P @ Ys2 ) )
% 0.18/0.48           => ( P @ Xs2 ) )
% 0.18/0.48       => ( P @ Xs ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_induct
% 0.18/0.48  thf(fact_590_length__induct,axiom,
% 0.18/0.48      ! [P: list_int > $o,Xs: list_int] :
% 0.18/0.48        ( ! [Xs2: list_int] :
% 0.18/0.48            ( ! [Ys2: list_int] :
% 0.18/0.48                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 0.18/0.48               => ( P @ Ys2 ) )
% 0.18/0.48           => ( P @ Xs2 ) )
% 0.18/0.48       => ( P @ Xs ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_induct
% 0.18/0.48  thf(fact_591_add__less__le__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_real @ C @ D )
% 0.18/0.48         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_le_mono
% 0.18/0.48  thf(fact_592_add__less__le__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_rat @ C @ D )
% 0.18/0.48         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_le_mono
% 0.18/0.48  thf(fact_593_add__less__le__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.18/0.48        ( ( ord_less_nat @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_nat @ C @ D )
% 0.18/0.48         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_le_mono
% 0.18/0.48  thf(fact_594_add__less__le__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.18/0.48        ( ( ord_less_int @ A @ B )
% 0.18/0.48       => ( ( ord_less_eq_int @ C @ D )
% 0.18/0.48         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_less_le_mono
% 0.18/0.48  thf(fact_595_add__le__less__mono,axiom,
% 0.18/0.48      ! [A: real,B: real,C: real,D: real] :
% 0.18/0.48        ( ( ord_less_eq_real @ A @ B )
% 0.18/0.48       => ( ( ord_less_real @ C @ D )
% 0.18/0.48         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_less_mono
% 0.18/0.48  thf(fact_596_add__le__less__mono,axiom,
% 0.18/0.48      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.18/0.48        ( ( ord_less_eq_rat @ A @ B )
% 0.18/0.48       => ( ( ord_less_rat @ C @ D )
% 0.18/0.48         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_less_mono
% 0.18/0.48  thf(fact_597_add__le__less__mono,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.48       => ( ( ord_less_nat @ C @ D )
% 0.18/0.48         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_less_mono
% 0.18/0.48  thf(fact_598_add__le__less__mono,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int,D: int] :
% 0.18/0.48        ( ( ord_less_eq_int @ A @ B )
% 0.18/0.48       => ( ( ord_less_int @ C @ D )
% 0.18/0.48         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_le_less_mono
% 0.18/0.48  thf(fact_599_add__mono__thms__linordered__field_I3_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_real @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(3)
% 0.18/0.48  thf(fact_600_add__mono__thms__linordered__field_I3_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_rat @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(3)
% 0.18/0.48  thf(fact_601_add__mono__thms__linordered__field_I3_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_nat @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(3)
% 0.18/0.48  thf(fact_602_add__mono__thms__linordered__field_I3_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_int @ I2 @ J )
% 0.18/0.48          & ( ord_less_eq_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(3)
% 0.18/0.48  thf(fact_603_add__mono__thms__linordered__field_I4_J,axiom,
% 0.18/0.48      ! [I2: real,J: real,K: real,L: real] :
% 0.18/0.48        ( ( ( ord_less_eq_real @ I2 @ J )
% 0.18/0.48          & ( ord_less_real @ K @ L ) )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(4)
% 0.18/0.48  thf(fact_604_add__mono__thms__linordered__field_I4_J,axiom,
% 0.18/0.48      ! [I2: rat,J: rat,K: rat,L: rat] :
% 0.18/0.48        ( ( ( ord_less_eq_rat @ I2 @ J )
% 0.18/0.48          & ( ord_less_rat @ K @ L ) )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(4)
% 0.18/0.48  thf(fact_605_add__mono__thms__linordered__field_I4_J,axiom,
% 0.18/0.48      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.18/0.48        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.48          & ( ord_less_nat @ K @ L ) )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(4)
% 0.18/0.48  thf(fact_606_add__mono__thms__linordered__field_I4_J,axiom,
% 0.18/0.48      ! [I2: int,J: int,K: int,L: int] :
% 0.18/0.48        ( ( ( ord_less_eq_int @ I2 @ J )
% 0.18/0.48          & ( ord_less_int @ K @ L ) )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono_thms_linordered_field(4)
% 0.18/0.48  thf(fact_607_add__mono1,axiom,
% 0.18/0.48      ! [A: real,B: real] :
% 0.18/0.48        ( ( ord_less_real @ A @ B )
% 0.18/0.48       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono1
% 0.18/0.48  thf(fact_608_add__mono1,axiom,
% 0.18/0.48      ! [A: rat,B: rat] :
% 0.18/0.48        ( ( ord_less_rat @ A @ B )
% 0.18/0.48       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono1
% 0.18/0.48  thf(fact_609_add__mono1,axiom,
% 0.18/0.48      ! [A: nat,B: nat] :
% 0.18/0.48        ( ( ord_less_nat @ A @ B )
% 0.18/0.48       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono1
% 0.18/0.48  thf(fact_610_add__mono1,axiom,
% 0.18/0.48      ! [A: int,B: int] :
% 0.18/0.48        ( ( ord_less_int @ A @ B )
% 0.18/0.48       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % add_mono1
% 0.18/0.48  thf(fact_611_less__add__one,axiom,
% 0.18/0.48      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_one
% 0.18/0.48  thf(fact_612_less__add__one,axiom,
% 0.18/0.48      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_one
% 0.18/0.48  thf(fact_613_less__add__one,axiom,
% 0.18/0.48      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_one
% 0.18/0.48  thf(fact_614_less__add__one,axiom,
% 0.18/0.48      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.18/0.48  
% 0.18/0.48  % less_add_one
% 0.18/0.48  thf(fact_615_list__eq__iff__nth__eq,axiom,
% 0.18/0.48      ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 0.18/0.48      = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.18/0.48            ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.18/0.48              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.18/0.48            & ! [I3: nat] :
% 0.18/0.48                ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.18/0.48               => ( ( nth_VEBT_VEBT @ Xs3 @ I3 )
% 0.18/0.48                  = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_eq_iff_nth_eq
% 0.18/0.48  thf(fact_616_list__eq__iff__nth__eq,axiom,
% 0.18/0.48      ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 0.18/0.48      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 0.18/0.48            ( ( ( size_size_list_o @ Xs3 )
% 0.18/0.48              = ( size_size_list_o @ Ys3 ) )
% 0.18/0.48            & ! [I3: nat] :
% 0.18/0.48                ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) )
% 0.18/0.48               => ( ( nth_o @ Xs3 @ I3 )
% 0.18/0.48                  = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_eq_iff_nth_eq
% 0.18/0.48  thf(fact_617_list__eq__iff__nth__eq,axiom,
% 0.18/0.48      ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 0.18/0.48      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 0.18/0.48            ( ( ( size_size_list_nat @ Xs3 )
% 0.18/0.48              = ( size_size_list_nat @ Ys3 ) )
% 0.18/0.48            & ! [I3: nat] :
% 0.18/0.48                ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) )
% 0.18/0.48               => ( ( nth_nat @ Xs3 @ I3 )
% 0.18/0.48                  = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_eq_iff_nth_eq
% 0.18/0.48  thf(fact_618_list__eq__iff__nth__eq,axiom,
% 0.18/0.48      ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 0.18/0.48      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 0.18/0.48            ( ( ( size_size_list_int @ Xs3 )
% 0.18/0.48              = ( size_size_list_int @ Ys3 ) )
% 0.18/0.48            & ! [I3: nat] :
% 0.18/0.48                ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) )
% 0.18/0.48               => ( ( nth_int @ Xs3 @ I3 )
% 0.18/0.48                  = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % list_eq_iff_nth_eq
% 0.18/0.48  thf(fact_619_Skolem__list__nth,axiom,
% 0.18/0.48      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 0.18/0.48        ( ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48             => ? [X3: vEBT_VEBT] : ( P @ I3 @ X3 ) ) )
% 0.18/0.48        = ( ? [Xs3: list_VEBT_VEBT] :
% 0.18/0.48              ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.18/0.48                = K )
% 0.18/0.48              & ! [I3: nat] :
% 0.18/0.48                  ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48                 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Skolem_list_nth
% 0.18/0.48  thf(fact_620_Skolem__list__nth,axiom,
% 0.18/0.48      ! [K: nat,P: nat > $o > $o] :
% 0.18/0.48        ( ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48             => ? [X3: $o] : ( P @ I3 @ X3 ) ) )
% 0.18/0.48        = ( ? [Xs3: list_o] :
% 0.18/0.48              ( ( ( size_size_list_o @ Xs3 )
% 0.18/0.48                = K )
% 0.18/0.48              & ! [I3: nat] :
% 0.18/0.48                  ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48                 => ( P @ I3 @ ( nth_o @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Skolem_list_nth
% 0.18/0.48  thf(fact_621_Skolem__list__nth,axiom,
% 0.18/0.48      ! [K: nat,P: nat > nat > $o] :
% 0.18/0.48        ( ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48             => ? [X3: nat] : ( P @ I3 @ X3 ) ) )
% 0.18/0.48        = ( ? [Xs3: list_nat] :
% 0.18/0.48              ( ( ( size_size_list_nat @ Xs3 )
% 0.18/0.48                = K )
% 0.18/0.48              & ! [I3: nat] :
% 0.18/0.48                  ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48                 => ( P @ I3 @ ( nth_nat @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Skolem_list_nth
% 0.18/0.48  thf(fact_622_Skolem__list__nth,axiom,
% 0.18/0.48      ! [K: nat,P: nat > int > $o] :
% 0.18/0.48        ( ( ! [I3: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48             => ? [X3: int] : ( P @ I3 @ X3 ) ) )
% 0.18/0.48        = ( ? [Xs3: list_int] :
% 0.18/0.48              ( ( ( size_size_list_int @ Xs3 )
% 0.18/0.48                = K )
% 0.18/0.48              & ! [I3: nat] :
% 0.18/0.48                  ( ( ord_less_nat @ I3 @ K )
% 0.18/0.48                 => ( P @ I3 @ ( nth_int @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % Skolem_list_nth
% 0.18/0.48  thf(fact_623_nth__equalityI,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.18/0.48        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.18/0.48          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.18/0.48       => ( ! [I4: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.18/0.48             => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 0.18/0.48                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 0.18/0.48         => ( Xs = Ys ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_equalityI
% 0.18/0.48  thf(fact_624_nth__equalityI,axiom,
% 0.18/0.48      ! [Xs: list_o,Ys: list_o] :
% 0.18/0.48        ( ( ( size_size_list_o @ Xs )
% 0.18/0.48          = ( size_size_list_o @ Ys ) )
% 0.18/0.48       => ( ! [I4: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 0.18/0.48             => ( ( nth_o @ Xs @ I4 )
% 0.18/0.48                = ( nth_o @ Ys @ I4 ) ) )
% 0.18/0.48         => ( Xs = Ys ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_equalityI
% 0.18/0.48  thf(fact_625_nth__equalityI,axiom,
% 0.18/0.48      ! [Xs: list_nat,Ys: list_nat] :
% 0.18/0.48        ( ( ( size_size_list_nat @ Xs )
% 0.18/0.48          = ( size_size_list_nat @ Ys ) )
% 0.18/0.48       => ( ! [I4: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 0.18/0.48             => ( ( nth_nat @ Xs @ I4 )
% 0.18/0.48                = ( nth_nat @ Ys @ I4 ) ) )
% 0.18/0.48         => ( Xs = Ys ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_equalityI
% 0.18/0.48  thf(fact_626_nth__equalityI,axiom,
% 0.18/0.48      ! [Xs: list_int,Ys: list_int] :
% 0.18/0.48        ( ( ( size_size_list_int @ Xs )
% 0.18/0.48          = ( size_size_list_int @ Ys ) )
% 0.18/0.48       => ( ! [I4: nat] :
% 0.18/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 0.18/0.48             => ( ( nth_int @ Xs @ I4 )
% 0.18/0.48                = ( nth_int @ Ys @ I4 ) ) )
% 0.18/0.48         => ( Xs = Ys ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % nth_equalityI
% 0.18/0.48  thf(fact_627_discrete,axiom,
% 0.18/0.48      ( ord_less_nat
% 0.18/0.48      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % discrete
% 0.18/0.48  thf(fact_628_discrete,axiom,
% 0.18/0.48      ( ord_less_int
% 0.18/0.48      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % discrete
% 0.18/0.48  thf(fact_629_buildup__nothing__in__leaf,axiom,
% 0.18/0.48      ! [N2: nat,X4: nat] :
% 0.18/0.48        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % buildup_nothing_in_leaf
% 0.18/0.48  thf(fact_630_low__def,axiom,
% 0.18/0.48      ( vEBT_VEBT_low
% 0.18/0.48      = ( ^ [X: nat,N: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % low_def
% 0.18/0.48  thf(fact_631_buildup__nothing__in__min__max,axiom,
% 0.18/0.48      ! [N2: nat,X4: nat] :
% 0.18/0.48        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % buildup_nothing_in_min_max
% 0.18/0.48  thf(fact_632_invar__vebt_Ointros_I3_J,axiom,
% 0.18/0.48      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.18/0.48        ( ! [X5: vEBT_VEBT] :
% 0.18/0.48            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.18/0.48       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.18/0.48         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.18/0.48              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48           => ( ( M
% 0.18/0.48                = ( suc @ N2 ) )
% 0.18/0.48             => ( ( Deg
% 0.18/0.48                  = ( plus_plus_nat @ N2 @ M ) )
% 0.18/0.48               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.18/0.48                 => ( ! [X5: vEBT_VEBT] :
% 0.18/0.48                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 0.18/0.48                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % invar_vebt.intros(3)
% 0.18/0.48  thf(fact_633_invar__vebt_Ointros_I2_J,axiom,
% 0.18/0.48      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.18/0.48        ( ! [X5: vEBT_VEBT] :
% 0.18/0.48            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.18/0.48       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.18/0.48         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.18/0.48              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48           => ( ( M = N2 )
% 0.18/0.48             => ( ( Deg
% 0.18/0.48                  = ( plus_plus_nat @ N2 @ M ) )
% 0.18/0.48               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.18/0.48                 => ( ! [X5: vEBT_VEBT] :
% 0.18/0.48                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 0.18/0.48                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % invar_vebt.intros(2)
% 0.18/0.48  thf(fact_634_dbl__simps_I3_J,axiom,
% 0.18/0.48      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.18/0.48      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(3)
% 0.18/0.48  thf(fact_635_dbl__simps_I3_J,axiom,
% 0.18/0.48      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.18/0.48      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(3)
% 0.18/0.48  thf(fact_636_dbl__simps_I3_J,axiom,
% 0.18/0.48      ( ( neg_numeral_dbl_real @ one_one_real )
% 0.18/0.48      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(3)
% 0.18/0.48  thf(fact_637_dbl__simps_I3_J,axiom,
% 0.18/0.48      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.18/0.48      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(3)
% 0.18/0.48  thf(fact_638_power__numeral,axiom,
% 0.18/0.48      ! [K: num,L: num] :
% 0.18/0.48        ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.18/0.48        = ( numera1916890842035813515d_enat @ ( pow @ K @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_numeral
% 0.18/0.48  thf(fact_639_power__numeral,axiom,
% 0.18/0.48      ! [K: num,L: num] :
% 0.18/0.48        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.18/0.48        = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_numeral
% 0.18/0.48  thf(fact_640_power__numeral,axiom,
% 0.18/0.48      ! [K: num,L: num] :
% 0.18/0.48        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.18/0.48        = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_numeral
% 0.18/0.48  thf(fact_641_power__numeral,axiom,
% 0.18/0.48      ! [K: num,L: num] :
% 0.18/0.48        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.18/0.48        = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_numeral
% 0.18/0.48  thf(fact_642_power__numeral,axiom,
% 0.18/0.48      ! [K: num,L: num] :
% 0.18/0.48        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 0.18/0.48        = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_numeral
% 0.18/0.48  thf(fact_643_valid__eq2,axiom,
% 0.18/0.48      ! [T2: vEBT_VEBT,D: nat] :
% 0.18/0.48        ( ( vEBT_VEBT_valid @ T2 @ D )
% 0.18/0.48       => ( vEBT_invar_vebt @ T2 @ D ) ) ).
% 0.18/0.48  
% 0.18/0.48  % valid_eq2
% 0.18/0.48  thf(fact_644_valid__eq,axiom,
% 0.18/0.48      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.18/0.48  
% 0.18/0.48  % valid_eq
% 0.18/0.48  thf(fact_645_valid__eq1,axiom,
% 0.18/0.48      ! [T2: vEBT_VEBT,D: nat] :
% 0.18/0.48        ( ( vEBT_invar_vebt @ T2 @ D )
% 0.18/0.48       => ( vEBT_VEBT_valid @ T2 @ D ) ) ).
% 0.18/0.48  
% 0.18/0.48  % valid_eq1
% 0.18/0.48  thf(fact_646_zdiv__numeral__Bit0,axiom,
% 0.18/0.48      ! [V: num,W: num] :
% 0.18/0.48        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.18/0.48        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % zdiv_numeral_Bit0
% 0.18/0.48  thf(fact_647_mod__mod__trivial,axiom,
% 0.18/0.48      ! [A: nat,B: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.18/0.48        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_mod_trivial
% 0.18/0.48  thf(fact_648_mod__mod__trivial,axiom,
% 0.18/0.48      ! [A: int,B: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.18/0.48        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_mod_trivial
% 0.18/0.48  thf(fact_649_mod__mod__trivial,axiom,
% 0.18/0.48      ! [A: code_integer,B: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.18/0.48        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_mod_trivial
% 0.18/0.48  thf(fact_650_mod__add__self1,axiom,
% 0.18/0.48      ! [B: nat,A: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.18/0.48        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self1
% 0.18/0.48  thf(fact_651_mod__add__self1,axiom,
% 0.18/0.48      ! [B: int,A: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.18/0.48        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self1
% 0.18/0.48  thf(fact_652_mod__add__self1,axiom,
% 0.18/0.48      ! [B: code_integer,A: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.18/0.48        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self1
% 0.18/0.48  thf(fact_653_mod__add__self2,axiom,
% 0.18/0.48      ! [A: nat,B: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.18/0.48        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self2
% 0.18/0.48  thf(fact_654_mod__add__self2,axiom,
% 0.18/0.48      ! [A: int,B: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.18/0.48        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self2
% 0.18/0.48  thf(fact_655_mod__add__self2,axiom,
% 0.18/0.48      ! [A: code_integer,B: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.18/0.48        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_self2
% 0.18/0.48  thf(fact_656_mod__less,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ M @ N2 )
% 0.18/0.48       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.18/0.48          = M ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_less
% 0.18/0.48  thf(fact_657_dbl__simps_I5_J,axiom,
% 0.18/0.48      ! [K: num] :
% 0.18/0.48        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.18/0.48        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(5)
% 0.18/0.48  thf(fact_658_dbl__simps_I5_J,axiom,
% 0.18/0.48      ! [K: num] :
% 0.18/0.48        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.18/0.48        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(5)
% 0.18/0.48  thf(fact_659_dbl__simps_I5_J,axiom,
% 0.18/0.48      ! [K: num] :
% 0.18/0.48        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 0.18/0.48        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_simps(5)
% 0.18/0.48  thf(fact_660_bits__one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_nat ) ).
% 0.18/0.48  
% 0.18/0.48  % bits_one_mod_two_eq_one
% 0.18/0.48  thf(fact_661_bits__one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_int ) ).
% 0.18/0.48  
% 0.18/0.48  % bits_one_mod_two_eq_one
% 0.18/0.48  thf(fact_662_bits__one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_Code_integer ) ).
% 0.18/0.48  
% 0.18/0.48  % bits_one_mod_two_eq_one
% 0.18/0.48  thf(fact_663_one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_nat ) ).
% 0.18/0.48  
% 0.18/0.48  % one_mod_two_eq_one
% 0.18/0.48  thf(fact_664_one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_int ) ).
% 0.18/0.48  
% 0.18/0.48  % one_mod_two_eq_one
% 0.18/0.48  thf(fact_665_one__mod__two__eq__one,axiom,
% 0.18/0.48      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.18/0.48      = one_one_Code_integer ) ).
% 0.18/0.48  
% 0.18/0.48  % one_mod_two_eq_one
% 0.18/0.48  thf(fact_666_mod2__Suc__Suc,axiom,
% 0.18/0.48      ! [M: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.48        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod2_Suc_Suc
% 0.18/0.48  thf(fact_667_mod__add__eq,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_eq
% 0.18/0.48  thf(fact_668_mod__add__eq,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_eq
% 0.18/0.48  thf(fact_669_mod__add__eq,axiom,
% 0.18/0.48      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_eq
% 0.18/0.48  thf(fact_670_mod__add__cong,axiom,
% 0.18/0.48      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 0.18/0.48        ( ( ( modulo_modulo_nat @ A @ C )
% 0.18/0.48          = ( modulo_modulo_nat @ A4 @ C ) )
% 0.18/0.48       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.18/0.48            = ( modulo_modulo_nat @ B4 @ C ) )
% 0.18/0.48         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.18/0.48            = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_cong
% 0.18/0.48  thf(fact_671_mod__add__cong,axiom,
% 0.18/0.48      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.18/0.48        ( ( ( modulo_modulo_int @ A @ C )
% 0.18/0.48          = ( modulo_modulo_int @ A4 @ C ) )
% 0.18/0.48       => ( ( ( modulo_modulo_int @ B @ C )
% 0.18/0.48            = ( modulo_modulo_int @ B4 @ C ) )
% 0.18/0.48         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.18/0.48            = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_cong
% 0.18/0.48  thf(fact_672_mod__add__cong,axiom,
% 0.18/0.48      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.18/0.48        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.18/0.48          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.18/0.48       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.18/0.48            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.18/0.48         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.18/0.48            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_cong
% 0.18/0.48  thf(fact_673_mod__add__left__eq,axiom,
% 0.18/0.48      ! [A: nat,C: nat,B: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.18/0.48        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_left_eq
% 0.18/0.48  thf(fact_674_mod__add__left__eq,axiom,
% 0.18/0.48      ! [A: int,C: int,B: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.18/0.48        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_left_eq
% 0.18/0.48  thf(fact_675_mod__add__left__eq,axiom,
% 0.18/0.48      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.18/0.48        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_left_eq
% 0.18/0.48  thf(fact_676_mod__add__right__eq,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_right_eq
% 0.18/0.48  thf(fact_677_mod__add__right__eq,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_right_eq
% 0.18/0.48  thf(fact_678_mod__add__right__eq,axiom,
% 0.18/0.48      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.18/0.48        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_add_right_eq
% 0.18/0.48  thf(fact_679_power__mod,axiom,
% 0.18/0.48      ! [A: nat,B: nat,N2: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 0.18/0.48        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_mod
% 0.18/0.48  thf(fact_680_power__mod,axiom,
% 0.18/0.48      ! [A: int,B: int,N2: nat] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 0.18/0.48        = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_mod
% 0.18/0.48  thf(fact_681_power__mod,axiom,
% 0.18/0.48      ! [A: code_integer,B: code_integer,N2: nat] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N2 ) @ B )
% 0.18/0.48        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ B ) ) ).
% 0.18/0.48  
% 0.18/0.48  % power_mod
% 0.18/0.48  thf(fact_682_mod__Suc__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 0.18/0.48        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_Suc_eq
% 0.18/0.48  thf(fact_683_mod__Suc__Suc__eq,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 0.18/0.48        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_Suc_Suc_eq
% 0.18/0.48  thf(fact_684_mod__less__eq__dividend,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_less_eq_dividend
% 0.18/0.48  thf(fact_685_cong__exp__iff__simps_I9_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num,N2: num] :
% 0.18/0.48        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.18/0.48          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.18/0.48        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.18/0.48          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(9)
% 0.18/0.48  thf(fact_686_cong__exp__iff__simps_I9_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num,N2: num] :
% 0.18/0.48        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.18/0.48          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.18/0.48        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.18/0.48          = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(9)
% 0.18/0.48  thf(fact_687_cong__exp__iff__simps_I9_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num,N2: num] :
% 0.18/0.48        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.18/0.48          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.18/0.48        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.18/0.48          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(9)
% 0.18/0.48  thf(fact_688_cong__exp__iff__simps_I4_J,axiom,
% 0.18/0.48      ! [M: num,N2: num] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 0.18/0.48        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(4)
% 0.18/0.48  thf(fact_689_cong__exp__iff__simps_I4_J,axiom,
% 0.18/0.48      ! [M: num,N2: num] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 0.18/0.48        = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(4)
% 0.18/0.48  thf(fact_690_cong__exp__iff__simps_I4_J,axiom,
% 0.18/0.48      ! [M: num,N2: num] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 0.18/0.48        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(4)
% 0.18/0.48  thf(fact_691_cong__exp__iff__simps_I8_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(8)
% 0.18/0.48  thf(fact_692_cong__exp__iff__simps_I8_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(8)
% 0.18/0.48  thf(fact_693_cong__exp__iff__simps_I8_J,axiom,
% 0.18/0.48      ! [M: num,Q3: num] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(8)
% 0.18/0.48  thf(fact_694_cong__exp__iff__simps_I6_J,axiom,
% 0.18/0.48      ! [Q3: num,N2: num] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(6)
% 0.18/0.48  thf(fact_695_cong__exp__iff__simps_I6_J,axiom,
% 0.18/0.48      ! [Q3: num,N2: num] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(6)
% 0.18/0.48  thf(fact_696_cong__exp__iff__simps_I6_J,axiom,
% 0.18/0.48      ! [Q3: num,N2: num] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.18/0.48       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % cong_exp_iff_simps(6)
% 0.18/0.48  thf(fact_697_div__add1__eq,axiom,
% 0.18/0.48      ! [A: nat,B: nat,C: nat] :
% 0.18/0.48        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.18/0.48        = ( 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 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_add1_eq
% 0.18/0.48  thf(fact_698_div__add1__eq,axiom,
% 0.18/0.48      ! [A: int,B: int,C: int] :
% 0.18/0.48        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.18/0.48        = ( 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 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_add1_eq
% 0.18/0.48  thf(fact_699_div__add1__eq,axiom,
% 0.18/0.48      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.18/0.48        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.18/0.48        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_add1_eq
% 0.18/0.48  thf(fact_700_mod__induct,axiom,
% 0.18/0.48      ! [P: nat > $o,N2: nat,P2: nat,M: nat] :
% 0.18/0.48        ( ( P @ N2 )
% 0.18/0.48       => ( ( ord_less_nat @ N2 @ P2 )
% 0.18/0.48         => ( ( ord_less_nat @ M @ P2 )
% 0.18/0.48           => ( ! [N3: nat] :
% 0.18/0.48                  ( ( ord_less_nat @ N3 @ P2 )
% 0.18/0.48                 => ( ( P @ N3 )
% 0.18/0.48                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 0.18/0.48             => ( P @ M ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_induct
% 0.18/0.48  thf(fact_701_mod__Suc__le__divisor,axiom,
% 0.18/0.48      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 0.18/0.48  
% 0.18/0.48  % mod_Suc_le_divisor
% 0.18/0.48  thf(fact_702_dbl__def,axiom,
% 0.18/0.48      ( neg_numeral_dbl_real
% 0.18/0.48      = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_def
% 0.18/0.48  thf(fact_703_dbl__def,axiom,
% 0.18/0.48      ( neg_numeral_dbl_rat
% 0.18/0.48      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_def
% 0.18/0.48  thf(fact_704_dbl__def,axiom,
% 0.18/0.48      ( neg_numeral_dbl_int
% 0.18/0.48      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % dbl_def
% 0.18/0.48  thf(fact_705_pow_Osimps_I1_J,axiom,
% 0.18/0.48      ! [X4: num] :
% 0.18/0.48        ( ( pow @ X4 @ one )
% 0.18/0.48        = X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % pow.simps(1)
% 0.18/0.48  thf(fact_706_bounded__Max__nat,axiom,
% 0.18/0.48      ! [P: nat > $o,X4: nat,M7: nat] :
% 0.18/0.48        ( ( P @ X4 )
% 0.18/0.48       => ( ! [X5: nat] :
% 0.18/0.48              ( ( P @ X5 )
% 0.18/0.48             => ( ord_less_eq_nat @ X5 @ M7 ) )
% 0.18/0.48         => ~ ! [M5: nat] :
% 0.18/0.48                ( ( P @ M5 )
% 0.18/0.48               => ~ ! [X2: nat] :
% 0.18/0.48                      ( ( P @ X2 )
% 0.18/0.48                     => ( ord_less_eq_nat @ X2 @ M5 ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % bounded_Max_nat
% 0.18/0.48  thf(fact_707_div__exp__mod__exp__eq,axiom,
% 0.18/0.48      ! [A: nat,N2: nat,M: nat] :
% 0.18/0.48        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_exp_mod_exp_eq
% 0.18/0.48  thf(fact_708_div__exp__mod__exp__eq,axiom,
% 0.18/0.48      ! [A: int,N2: nat,M: nat] :
% 0.18/0.48        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_exp_mod_exp_eq
% 0.18/0.48  thf(fact_709_div__exp__mod__exp__eq,axiom,
% 0.18/0.48      ! [A: code_integer,N2: nat,M: nat] :
% 0.18/0.48        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % div_exp_mod_exp_eq
% 0.18/0.48  thf(fact_710_buildup__gives__valid,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.48       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % buildup_gives_valid
% 0.18/0.48  thf(fact_711_psubsetI,axiom,
% 0.18/0.48      ! [A2: set_int,B3: set_int] :
% 0.18/0.48        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.18/0.48       => ( ( A2 != B3 )
% 0.18/0.48         => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % psubsetI
% 0.18/0.48  thf(fact_712_subset__antisym,axiom,
% 0.18/0.48      ! [A2: set_int,B3: set_int] :
% 0.18/0.48        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.18/0.48       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.18/0.48         => ( A2 = B3 ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subset_antisym
% 0.18/0.48  thf(fact_713_subsetI,axiom,
% 0.18/0.48      ! [A2: set_real,B3: set_real] :
% 0.18/0.48        ( ! [X5: real] :
% 0.18/0.48            ( ( member_real @ X5 @ A2 )
% 0.18/0.48           => ( member_real @ X5 @ B3 ) )
% 0.18/0.48       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subsetI
% 0.18/0.48  thf(fact_714_subsetI,axiom,
% 0.18/0.48      ! [A2: set_nat,B3: set_nat] :
% 0.18/0.48        ( ! [X5: nat] :
% 0.18/0.48            ( ( member_nat @ X5 @ A2 )
% 0.18/0.48           => ( member_nat @ X5 @ B3 ) )
% 0.18/0.48       => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subsetI
% 0.18/0.48  thf(fact_715_subsetI,axiom,
% 0.18/0.48      ! [A2: set_complex,B3: set_complex] :
% 0.18/0.48        ( ! [X5: complex] :
% 0.18/0.48            ( ( member_complex @ X5 @ A2 )
% 0.18/0.48           => ( member_complex @ X5 @ B3 ) )
% 0.18/0.48       => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subsetI
% 0.18/0.48  thf(fact_716_subsetI,axiom,
% 0.18/0.48      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.18/0.48        ( ! [X5: product_prod_nat_nat] :
% 0.18/0.48            ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 0.18/0.48           => ( member8440522571783428010at_nat @ X5 @ B3 ) )
% 0.18/0.48       => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subsetI
% 0.18/0.48  thf(fact_717_subsetI,axiom,
% 0.18/0.48      ! [A2: set_int,B3: set_int] :
% 0.18/0.48        ( ! [X5: int] :
% 0.18/0.48            ( ( member_int @ X5 @ A2 )
% 0.18/0.48           => ( member_int @ X5 @ B3 ) )
% 0.18/0.48       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % subsetI
% 0.18/0.48  thf(fact_718_verit__eq__simplify_I8_J,axiom,
% 0.18/0.48      ! [X22: num,Y2: num] :
% 0.18/0.48        ( ( ( bit0 @ X22 )
% 0.18/0.48          = ( bit0 @ Y2 ) )
% 0.18/0.48        = ( X22 = Y2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % verit_eq_simplify(8)
% 0.18/0.48  thf(fact_719_order__refl,axiom,
% 0.18/0.48      ! [X4: set_int] : ( ord_less_eq_set_int @ X4 @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % order_refl
% 0.18/0.48  thf(fact_720_order__refl,axiom,
% 0.18/0.48      ! [X4: rat] : ( ord_less_eq_rat @ X4 @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % order_refl
% 0.18/0.48  thf(fact_721_order__refl,axiom,
% 0.18/0.48      ! [X4: num] : ( ord_less_eq_num @ X4 @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % order_refl
% 0.18/0.48  thf(fact_722_order__refl,axiom,
% 0.18/0.48      ! [X4: nat] : ( ord_less_eq_nat @ X4 @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % order_refl
% 0.18/0.48  thf(fact_723_order__refl,axiom,
% 0.18/0.48      ! [X4: int] : ( ord_less_eq_int @ X4 @ X4 ) ).
% 0.18/0.48  
% 0.18/0.48  % order_refl
% 0.18/0.48  thf(fact_724_dual__order_Orefl,axiom,
% 0.18/0.48      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.18/0.48  
% 0.18/0.48  % dual_order.refl
% 0.18/0.48  thf(fact_725_dual__order_Orefl,axiom,
% 0.18/0.48      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.18/0.48  
% 0.18/0.48  % dual_order.refl
% 0.18/0.48  thf(fact_726_dual__order_Orefl,axiom,
% 0.18/0.48      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.18/0.48  
% 0.18/0.48  % dual_order.refl
% 0.18/0.48  thf(fact_727_dual__order_Orefl,axiom,
% 0.18/0.48      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.18/0.48  
% 0.18/0.48  % dual_order.refl
% 0.18/0.48  thf(fact_728_dual__order_Orefl,axiom,
% 0.18/0.48      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.18/0.48  
% 0.18/0.48  % dual_order.refl
% 0.18/0.48  thf(fact_729_mod2__gr__0,axiom,
% 0.18/0.48      ! [M: nat] :
% 0.18/0.48        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.18/0.48        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.18/0.48          = one_one_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % mod2_gr_0
% 0.18/0.48  thf(fact_730_length__subseqs,axiom,
% 0.18/0.48      ! [Xs: list_VEBT_VEBT] :
% 0.18/0.48        ( ( size_s8217280938318005548T_VEBT @ ( subseqs_VEBT_VEBT @ Xs ) )
% 0.18/0.48        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_subseqs
% 0.18/0.48  thf(fact_731_length__subseqs,axiom,
% 0.18/0.48      ! [Xs: list_o] :
% 0.18/0.48        ( ( size_s2710708370519433104list_o @ ( subseqs_o @ Xs ) )
% 0.18/0.48        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_subseqs
% 0.18/0.48  thf(fact_732_length__subseqs,axiom,
% 0.18/0.48      ! [Xs: list_nat] :
% 0.18/0.48        ( ( size_s3023201423986296836st_nat @ ( subseqs_nat @ Xs ) )
% 0.18/0.48        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_subseqs
% 0.18/0.48  thf(fact_733_length__subseqs,axiom,
% 0.18/0.48      ! [Xs: list_int] :
% 0.18/0.48        ( ( size_s533118279054570080st_int @ ( subseqs_int @ Xs ) )
% 0.18/0.48        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % length_subseqs
% 0.18/0.48  thf(fact_734_invar__vebt_Ointros_I5_J,axiom,
% 0.18/0.48      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.18/0.48        ( ! [X5: vEBT_VEBT] :
% 0.18/0.48            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.18/0.48       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.18/0.48         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.18/0.48              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48           => ( ( M
% 0.18/0.48                = ( suc @ N2 ) )
% 0.18/0.48             => ( ( Deg
% 0.18/0.48                  = ( plus_plus_nat @ N2 @ M ) )
% 0.18/0.48               => ( ! [I4: nat] :
% 0.18/0.48                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 0.18/0.48                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.18/0.48                 => ( ( ( Mi = Ma )
% 0.18/0.48                     => ! [X5: vEBT_VEBT] :
% 0.18/0.48                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.18/0.48                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 0.18/0.48                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.18/0.48                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.18/0.48                       => ( ( ( Mi != Ma )
% 0.18/0.48                           => ! [I4: nat] :
% 0.18/0.48                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.18/0.48                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 0.18/0.48                                      = I4 )
% 0.18/0.48                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 0.18/0.48                                  & ! [X5: nat] :
% 0.18/0.48                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 0.18/0.48                                          = I4 )
% 0.18/0.48                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 0.18/0.48                                     => ( ( ord_less_nat @ Mi @ X5 )
% 0.18/0.48                                        & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 0.18/0.48                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.48  
% 0.18/0.48  % invar_vebt.intros(5)
% 0.18/0.48  thf(fact_735_deg__not__0,axiom,
% 0.18/0.48      ! [T2: vEBT_VEBT,N2: nat] :
% 0.18/0.48        ( ( vEBT_invar_vebt @ T2 @ N2 )
% 0.18/0.48       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.18/0.48  
% 0.18/0.48  % deg_not_0
% 0.18/0.48  thf(fact_736__C5_Ohyps_C_I12_J,axiom,
% 0.18/0.48      ( ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) )
% 0.18/0.48      = info ) ).
% 0.18/0.48  
% 0.18/0.48  % "5.hyps"(12)
% 0.18/0.48  thf(fact_737_le__zero__eq,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.18/0.48        = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % le_zero_eq
% 0.18/0.48  thf(fact_738_not__gr__zero,axiom,
% 0.18/0.48      ! [N2: nat] :
% 0.18/0.48        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.18/0.48        = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.48  
% 0.18/0.48  % not_gr_zero
% 0.18/0.48  thf(fact_739_add__0,axiom,
% 0.18/0.48      ! [A: complex] :
% 0.18/0.48        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % add_0
% 0.18/0.48  thf(fact_740_add__0,axiom,
% 0.18/0.48      ! [A: real] :
% 0.18/0.48        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % add_0
% 0.18/0.48  thf(fact_741_add__0,axiom,
% 0.18/0.48      ! [A: rat] :
% 0.18/0.48        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % add_0
% 0.18/0.48  thf(fact_742_add__0,axiom,
% 0.18/0.48      ! [A: nat] :
% 0.18/0.48        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.18/0.48        = A ) ).
% 0.18/0.48  
% 0.18/0.48  % add_0
% 0.18/0.48  thf(fact_743_add__0,axiom,
% 0.18/0.48      ! [A: int] :
% 0.18/0.48        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add_0
% 0.18/0.49  thf(fact_744_zero__eq__add__iff__both__eq__0,axiom,
% 0.18/0.49      ! [X4: nat,Y: nat] :
% 0.18/0.49        ( ( zero_zero_nat
% 0.18/0.49          = ( plus_plus_nat @ X4 @ Y ) )
% 0.18/0.49        = ( ( X4 = zero_zero_nat )
% 0.18/0.49          & ( Y = zero_zero_nat ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_eq_add_iff_both_eq_0
% 0.18/0.49  thf(fact_745_add__eq__0__iff__both__eq__0,axiom,
% 0.18/0.49      ! [X4: nat,Y: nat] :
% 0.18/0.49        ( ( ( plus_plus_nat @ X4 @ Y )
% 0.18/0.49          = zero_zero_nat )
% 0.18/0.49        = ( ( X4 = zero_zero_nat )
% 0.18/0.49          & ( Y = zero_zero_nat ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_eq_0_iff_both_eq_0
% 0.18/0.49  thf(fact_746_add__cancel__right__right,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_complex @ A @ B ) )
% 0.18/0.49        = ( B = zero_zero_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_right
% 0.18/0.49  thf(fact_747_add__cancel__right__right,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_real @ A @ B ) )
% 0.18/0.49        = ( B = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_right
% 0.18/0.49  thf(fact_748_add__cancel__right__right,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_rat @ A @ B ) )
% 0.18/0.49        = ( B = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_right
% 0.18/0.49  thf(fact_749_add__cancel__right__right,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_nat @ A @ B ) )
% 0.18/0.49        = ( B = zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_right
% 0.18/0.49  thf(fact_750_add__cancel__right__right,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_int @ A @ B ) )
% 0.18/0.49        = ( B = zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_right
% 0.18/0.49  thf(fact_751_add__cancel__right__left,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_complex @ B @ A ) )
% 0.18/0.49        = ( B = zero_zero_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_left
% 0.18/0.49  thf(fact_752_add__cancel__right__left,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_real @ B @ A ) )
% 0.18/0.49        = ( B = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_left
% 0.18/0.49  thf(fact_753_add__cancel__right__left,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_rat @ B @ A ) )
% 0.18/0.49        = ( B = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_left
% 0.18/0.49  thf(fact_754_add__cancel__right__left,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_nat @ B @ A ) )
% 0.18/0.49        = ( B = zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_left
% 0.18/0.49  thf(fact_755_add__cancel__right__left,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( A
% 0.18/0.49          = ( plus_plus_int @ B @ A ) )
% 0.18/0.49        = ( B = zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_right_left
% 0.18/0.49  thf(fact_756_add__cancel__left__right,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( ( plus_plus_complex @ A @ B )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_right
% 0.18/0.49  thf(fact_757_add__cancel__left__right,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ( plus_plus_real @ A @ B )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_right
% 0.18/0.49  thf(fact_758_add__cancel__left__right,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ( plus_plus_rat @ A @ B )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_right
% 0.18/0.49  thf(fact_759_add__cancel__left__right,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ( plus_plus_nat @ A @ B )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_right
% 0.18/0.49  thf(fact_760_add__cancel__left__right,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ( plus_plus_int @ A @ B )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_right
% 0.18/0.49  thf(fact_761_add__cancel__left__left,axiom,
% 0.18/0.49      ! [B: complex,A: complex] :
% 0.18/0.49        ( ( ( plus_plus_complex @ B @ A )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_left
% 0.18/0.49  thf(fact_762_add__cancel__left__left,axiom,
% 0.18/0.49      ! [B: real,A: real] :
% 0.18/0.49        ( ( ( plus_plus_real @ B @ A )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_left
% 0.18/0.49  thf(fact_763_add__cancel__left__left,axiom,
% 0.18/0.49      ! [B: rat,A: rat] :
% 0.18/0.49        ( ( ( plus_plus_rat @ B @ A )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_left
% 0.18/0.49  thf(fact_764_add__cancel__left__left,axiom,
% 0.18/0.49      ! [B: nat,A: nat] :
% 0.18/0.49        ( ( ( plus_plus_nat @ B @ A )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_left
% 0.18/0.49  thf(fact_765_add__cancel__left__left,axiom,
% 0.18/0.49      ! [B: int,A: int] :
% 0.18/0.49        ( ( ( plus_plus_int @ B @ A )
% 0.18/0.49          = A )
% 0.18/0.49        = ( B = zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_cancel_left_left
% 0.18/0.49  thf(fact_766_double__zero__sym,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( zero_zero_real
% 0.18/0.49          = ( plus_plus_real @ A @ A ) )
% 0.18/0.49        = ( A = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_zero_sym
% 0.18/0.49  thf(fact_767_double__zero__sym,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( zero_zero_rat
% 0.18/0.49          = ( plus_plus_rat @ A @ A ) )
% 0.18/0.49        = ( A = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_zero_sym
% 0.18/0.49  thf(fact_768_double__zero__sym,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( zero_zero_int
% 0.18/0.49          = ( plus_plus_int @ A @ A ) )
% 0.18/0.49        = ( A = zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_zero_sym
% 0.18/0.49  thf(fact_769_add_Oright__neutral,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add.right_neutral
% 0.18/0.49  thf(fact_770_add_Oright__neutral,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add.right_neutral
% 0.18/0.49  thf(fact_771_add_Oright__neutral,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add.right_neutral
% 0.18/0.49  thf(fact_772_add_Oright__neutral,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add.right_neutral
% 0.18/0.49  thf(fact_773_add_Oright__neutral,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % add.right_neutral
% 0.18/0.49  thf(fact_774_division__ring__divide__zero,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.18/0.49        = zero_zero_rat ) ).
% 0.18/0.49  
% 0.18/0.49  % division_ring_divide_zero
% 0.18/0.49  thf(fact_775_division__ring__divide__zero,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.18/0.49        = zero_zero_real ) ).
% 0.18/0.49  
% 0.18/0.49  % division_ring_divide_zero
% 0.18/0.49  thf(fact_776_division__ring__divide__zero,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.18/0.49        = zero_zero_complex ) ).
% 0.18/0.49  
% 0.18/0.49  % division_ring_divide_zero
% 0.18/0.49  thf(fact_777_divide__cancel__right,axiom,
% 0.18/0.49      ! [A: rat,C: rat,B: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ A @ C )
% 0.18/0.49          = ( divide_divide_rat @ B @ C ) )
% 0.18/0.49        = ( ( C = zero_zero_rat )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_right
% 0.18/0.49  thf(fact_778_divide__cancel__right,axiom,
% 0.18/0.49      ! [A: real,C: real,B: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ A @ C )
% 0.18/0.49          = ( divide_divide_real @ B @ C ) )
% 0.18/0.49        = ( ( C = zero_zero_real )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_right
% 0.18/0.49  thf(fact_779_divide__cancel__right,axiom,
% 0.18/0.49      ! [A: complex,C: complex,B: complex] :
% 0.18/0.49        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.18/0.49          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.18/0.49        = ( ( C = zero_zero_complex )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_right
% 0.18/0.49  thf(fact_780_divide__cancel__left,axiom,
% 0.18/0.49      ! [C: rat,A: rat,B: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ C @ A )
% 0.18/0.49          = ( divide_divide_rat @ C @ B ) )
% 0.18/0.49        = ( ( C = zero_zero_rat )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_left
% 0.18/0.49  thf(fact_781_divide__cancel__left,axiom,
% 0.18/0.49      ! [C: real,A: real,B: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ C @ A )
% 0.18/0.49          = ( divide_divide_real @ C @ B ) )
% 0.18/0.49        = ( ( C = zero_zero_real )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_left
% 0.18/0.49  thf(fact_782_divide__cancel__left,axiom,
% 0.18/0.49      ! [C: complex,A: complex,B: complex] :
% 0.18/0.49        ( ( ( divide1717551699836669952omplex @ C @ A )
% 0.18/0.49          = ( divide1717551699836669952omplex @ C @ B ) )
% 0.18/0.49        = ( ( C = zero_zero_complex )
% 0.18/0.49          | ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_cancel_left
% 0.18/0.49  thf(fact_783_div__by__0,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.18/0.49        = zero_zero_rat ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_784_div__by__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_785_div__by__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_786_div__by__0,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.18/0.49        = zero_zero_real ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_787_div__by__0,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.18/0.49        = zero_zero_complex ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_788_div__by__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % div_by_0
% 0.18/0.49  thf(fact_789_divide__eq__0__iff,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ A @ B )
% 0.18/0.49          = zero_zero_rat )
% 0.18/0.49        = ( ( A = zero_zero_rat )
% 0.18/0.49          | ( B = zero_zero_rat ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_0_iff
% 0.18/0.49  thf(fact_790_divide__eq__0__iff,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ A @ B )
% 0.18/0.49          = zero_zero_real )
% 0.18/0.49        = ( ( A = zero_zero_real )
% 0.18/0.49          | ( B = zero_zero_real ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_0_iff
% 0.18/0.49  thf(fact_791_divide__eq__0__iff,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.18/0.49          = zero_zero_complex )
% 0.18/0.49        = ( ( A = zero_zero_complex )
% 0.18/0.49          | ( B = zero_zero_complex ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_0_iff
% 0.18/0.49  thf(fact_792_div__0,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.18/0.49        = zero_zero_rat ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_793_div__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_794_div__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_795_div__0,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( divide_divide_real @ zero_zero_real @ A )
% 0.18/0.49        = zero_zero_real ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_796_div__0,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.18/0.49        = zero_zero_complex ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_797_div__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % div_0
% 0.18/0.49  thf(fact_798_bits__div__by__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_by_0
% 0.18/0.49  thf(fact_799_bits__div__by__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_by_0
% 0.18/0.49  thf(fact_800_bits__div__by__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_by_0
% 0.18/0.49  thf(fact_801_bits__div__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_0
% 0.18/0.49  thf(fact_802_bits__div__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_0
% 0.18/0.49  thf(fact_803_bits__div__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_div_0
% 0.18/0.49  thf(fact_804_bits__mod__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_mod_0
% 0.18/0.49  thf(fact_805_bits__mod__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_mod_0
% 0.18/0.49  thf(fact_806_bits__mod__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % bits_mod_0
% 0.18/0.49  thf(fact_807_mod__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_0
% 0.18/0.49  thf(fact_808_mod__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_0
% 0.18/0.49  thf(fact_809_mod__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_0
% 0.18/0.49  thf(fact_810_mod__by__0,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_by_0
% 0.18/0.49  thf(fact_811_mod__by__0,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_by_0
% 0.18/0.49  thf(fact_812_mod__by__0,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 0.18/0.49        = A ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_by_0
% 0.18/0.49  thf(fact_813_mod__self,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( modulo_modulo_nat @ A @ A )
% 0.18/0.49        = zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_self
% 0.18/0.49  thf(fact_814_mod__self,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( modulo_modulo_int @ A @ A )
% 0.18/0.49        = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_self
% 0.18/0.49  thf(fact_815_mod__self,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( modulo364778990260209775nteger @ A @ A )
% 0.18/0.49        = zero_z3403309356797280102nteger ) ).
% 0.18/0.49  
% 0.18/0.49  % mod_self
% 0.18/0.49  thf(fact_816_less__nat__zero__code,axiom,
% 0.18/0.49      ! [N2: nat] :
% 0.18/0.49        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.18/0.49  
% 0.18/0.49  % less_nat_zero_code
% 0.18/0.49  thf(fact_817_neq0__conv,axiom,
% 0.18/0.49      ! [N2: nat] :
% 0.18/0.49        ( ( N2 != zero_zero_nat )
% 0.18/0.49        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.18/0.49  
% 0.18/0.49  % neq0_conv
% 0.18/0.49  thf(fact_818_bot__nat__0_Onot__eq__extremum,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( A != zero_zero_nat )
% 0.18/0.49        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % bot_nat_0.not_eq_extremum
% 0.18/0.49  thf(fact_819_le0,axiom,
% 0.18/0.49      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.18/0.49  
% 0.18/0.49  % le0
% 0.18/0.49  thf(fact_820_bot__nat__0_Oextremum,axiom,
% 0.18/0.49      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.18/0.49  
% 0.18/0.49  % bot_nat_0.extremum
% 0.18/0.49  thf(fact_821_Nat_Oadd__0__right,axiom,
% 0.18/0.49      ! [M: nat] :
% 0.18/0.49        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.18/0.49        = M ) ).
% 0.18/0.49  
% 0.18/0.49  % Nat.add_0_right
% 0.18/0.49  thf(fact_822_add__is__0,axiom,
% 0.18/0.49      ! [M: nat,N2: nat] :
% 0.18/0.49        ( ( ( plus_plus_nat @ M @ N2 )
% 0.18/0.49          = zero_zero_nat )
% 0.18/0.49        = ( ( M = zero_zero_nat )
% 0.18/0.49          & ( N2 = zero_zero_nat ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_is_0
% 0.18/0.49  thf(fact_823_dbl__simps_I2_J,axiom,
% 0.18/0.49      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 0.18/0.49      = zero_zero_complex ) ).
% 0.18/0.49  
% 0.18/0.49  % dbl_simps(2)
% 0.18/0.49  thf(fact_824_dbl__simps_I2_J,axiom,
% 0.18/0.49      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.18/0.49      = zero_zero_real ) ).
% 0.18/0.49  
% 0.18/0.49  % dbl_simps(2)
% 0.18/0.49  thf(fact_825_dbl__simps_I2_J,axiom,
% 0.18/0.49      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.18/0.49      = zero_zero_rat ) ).
% 0.18/0.49  
% 0.18/0.49  % dbl_simps(2)
% 0.18/0.49  thf(fact_826_dbl__simps_I2_J,axiom,
% 0.18/0.49      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.18/0.49      = zero_zero_int ) ).
% 0.18/0.49  
% 0.18/0.49  % dbl_simps(2)
% 0.18/0.49  thf(fact_827_mi__ma__2__deg,axiom,
% 0.18/0.49      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 0.18/0.49        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 0.18/0.49       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.18/0.49          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % mi_ma_2_deg
% 0.18/0.49  thf(fact_828_add__le__same__cancel1,axiom,
% 0.18/0.49      ! [B: real,A: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel1
% 0.18/0.49  thf(fact_829_add__le__same__cancel1,axiom,
% 0.18/0.49      ! [B: rat,A: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel1
% 0.18/0.49  thf(fact_830_add__le__same__cancel1,axiom,
% 0.18/0.49      ! [B: nat,A: nat] :
% 0.18/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel1
% 0.18/0.49  thf(fact_831_add__le__same__cancel1,axiom,
% 0.18/0.49      ! [B: int,A: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel1
% 0.18/0.49  thf(fact_832_add__le__same__cancel2,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel2
% 0.18/0.49  thf(fact_833_add__le__same__cancel2,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel2
% 0.18/0.49  thf(fact_834_add__le__same__cancel2,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel2
% 0.18/0.49  thf(fact_835_add__le__same__cancel2,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_le_same_cancel2
% 0.18/0.49  thf(fact_836_le__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.18/0.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel1
% 0.18/0.49  thf(fact_837_le__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.18/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel1
% 0.18/0.49  thf(fact_838_le__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.18/0.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel1
% 0.18/0.49  thf(fact_839_le__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.18/0.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel1
% 0.18/0.49  thf(fact_840_le__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.18/0.49        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel2
% 0.18/0.49  thf(fact_841_le__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.18/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel2
% 0.18/0.49  thf(fact_842_le__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.18/0.49        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel2
% 0.18/0.49  thf(fact_843_le__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.18/0.49        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % le_add_same_cancel2
% 0.18/0.49  thf(fact_844_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.18/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.18/0.49  thf(fact_845_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.18/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.18/0.49  thf(fact_846_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.18/0.49        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_le_zero_iff_single_add_le_zero
% 0.18/0.49  thf(fact_847_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.18/0.49        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.18/0.49  thf(fact_848_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.18/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.18/0.49  thf(fact_849_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.18/0.49        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_le_double_add_iff_zero_le_single_add
% 0.18/0.49  thf(fact_850_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.18/0.49        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.18/0.49  thf(fact_851_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.18/0.49        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.18/0.49  thf(fact_852_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.18/0.49        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_less_double_add_iff_zero_less_single_add
% 0.18/0.49  thf(fact_853_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.18/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.18/0.49  thf(fact_854_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.18/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.18/0.49  thf(fact_855_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.18/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % double_add_less_zero_iff_single_add_less_zero
% 0.18/0.49  thf(fact_856_less__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.18/0.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel2
% 0.18/0.49  thf(fact_857_less__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.18/0.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel2
% 0.18/0.49  thf(fact_858_less__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.18/0.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel2
% 0.18/0.49  thf(fact_859_less__add__same__cancel2,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.18/0.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel2
% 0.18/0.49  thf(fact_860_less__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.18/0.49        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel1
% 0.18/0.49  thf(fact_861_less__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.18/0.49        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel1
% 0.18/0.49  thf(fact_862_less__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.18/0.49        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel1
% 0.18/0.49  thf(fact_863_less__add__same__cancel1,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.18/0.49        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.18/0.49  
% 0.18/0.49  % less_add_same_cancel1
% 0.18/0.49  thf(fact_864_add__less__same__cancel2,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel2
% 0.18/0.49  thf(fact_865_add__less__same__cancel2,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel2
% 0.18/0.49  thf(fact_866_add__less__same__cancel2,axiom,
% 0.18/0.49      ! [A: nat,B: nat] :
% 0.18/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel2
% 0.18/0.49  thf(fact_867_add__less__same__cancel2,axiom,
% 0.18/0.49      ! [A: int,B: int] :
% 0.18/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.18/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel2
% 0.18/0.49  thf(fact_868_add__less__same__cancel1,axiom,
% 0.18/0.49      ! [B: real,A: real] :
% 0.18/0.49        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel1
% 0.18/0.49  thf(fact_869_add__less__same__cancel1,axiom,
% 0.18/0.49      ! [B: rat,A: rat] :
% 0.18/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel1
% 0.18/0.49  thf(fact_870_add__less__same__cancel1,axiom,
% 0.18/0.49      ! [B: nat,A: nat] :
% 0.18/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel1
% 0.18/0.49  thf(fact_871_add__less__same__cancel1,axiom,
% 0.18/0.49      ! [B: int,A: int] :
% 0.18/0.49        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.18/0.49        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % add_less_same_cancel1
% 0.18/0.49  thf(fact_872_zero__eq__1__divide__iff,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( zero_zero_rat
% 0.18/0.49          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.18/0.49        = ( A = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_eq_1_divide_iff
% 0.18/0.49  thf(fact_873_zero__eq__1__divide__iff,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( zero_zero_real
% 0.18/0.49          = ( divide_divide_real @ one_one_real @ A ) )
% 0.18/0.49        = ( A = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % zero_eq_1_divide_iff
% 0.18/0.49  thf(fact_874_one__divide__eq__0__iff,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.18/0.49          = zero_zero_rat )
% 0.18/0.49        = ( A = zero_zero_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % one_divide_eq_0_iff
% 0.18/0.49  thf(fact_875_one__divide__eq__0__iff,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ one_one_real @ A )
% 0.18/0.49          = zero_zero_real )
% 0.18/0.49        = ( A = zero_zero_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % one_divide_eq_0_iff
% 0.18/0.49  thf(fact_876_eq__divide__eq__1,axiom,
% 0.18/0.49      ! [B: rat,A: rat] :
% 0.18/0.49        ( ( one_one_rat
% 0.18/0.49          = ( divide_divide_rat @ B @ A ) )
% 0.18/0.49        = ( ( A != zero_zero_rat )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % eq_divide_eq_1
% 0.18/0.49  thf(fact_877_eq__divide__eq__1,axiom,
% 0.18/0.49      ! [B: real,A: real] :
% 0.18/0.49        ( ( one_one_real
% 0.18/0.49          = ( divide_divide_real @ B @ A ) )
% 0.18/0.49        = ( ( A != zero_zero_real )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % eq_divide_eq_1
% 0.18/0.49  thf(fact_878_divide__eq__eq__1,axiom,
% 0.18/0.49      ! [B: rat,A: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ B @ A )
% 0.18/0.49          = one_one_rat )
% 0.18/0.49        = ( ( A != zero_zero_rat )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_eq_1
% 0.18/0.49  thf(fact_879_divide__eq__eq__1,axiom,
% 0.18/0.49      ! [B: real,A: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ B @ A )
% 0.18/0.49          = one_one_real )
% 0.18/0.49        = ( ( A != zero_zero_real )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_eq_1
% 0.18/0.49  thf(fact_880_divide__self__if,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( ( A = zero_zero_rat )
% 0.18/0.49         => ( ( divide_divide_rat @ A @ A )
% 0.18/0.49            = zero_zero_rat ) )
% 0.18/0.49        & ( ( A != zero_zero_rat )
% 0.18/0.49         => ( ( divide_divide_rat @ A @ A )
% 0.18/0.49            = one_one_rat ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self_if
% 0.18/0.49  thf(fact_881_divide__self__if,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( ( A = zero_zero_real )
% 0.18/0.49         => ( ( divide_divide_real @ A @ A )
% 0.18/0.49            = zero_zero_real ) )
% 0.18/0.49        & ( ( A != zero_zero_real )
% 0.18/0.49         => ( ( divide_divide_real @ A @ A )
% 0.18/0.49            = one_one_real ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self_if
% 0.18/0.49  thf(fact_882_divide__self__if,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( ( A = zero_zero_complex )
% 0.18/0.49         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.18/0.49            = zero_zero_complex ) )
% 0.18/0.49        & ( ( A != zero_zero_complex )
% 0.18/0.49         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.18/0.49            = one_one_complex ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self_if
% 0.18/0.49  thf(fact_883_divide__self,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( A != zero_zero_rat )
% 0.18/0.49       => ( ( divide_divide_rat @ A @ A )
% 0.18/0.49          = one_one_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self
% 0.18/0.49  thf(fact_884_divide__self,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( A != zero_zero_real )
% 0.18/0.49       => ( ( divide_divide_real @ A @ A )
% 0.18/0.49          = one_one_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self
% 0.18/0.49  thf(fact_885_divide__self,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( A != zero_zero_complex )
% 0.18/0.49       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.18/0.49          = one_one_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_self
% 0.18/0.49  thf(fact_886_one__eq__divide__iff,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( one_one_rat
% 0.18/0.49          = ( divide_divide_rat @ A @ B ) )
% 0.18/0.49        = ( ( B != zero_zero_rat )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % one_eq_divide_iff
% 0.18/0.49  thf(fact_887_one__eq__divide__iff,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( one_one_real
% 0.18/0.49          = ( divide_divide_real @ A @ B ) )
% 0.18/0.49        = ( ( B != zero_zero_real )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % one_eq_divide_iff
% 0.18/0.49  thf(fact_888_one__eq__divide__iff,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( one_one_complex
% 0.18/0.49          = ( divide1717551699836669952omplex @ A @ B ) )
% 0.18/0.49        = ( ( B != zero_zero_complex )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % one_eq_divide_iff
% 0.18/0.49  thf(fact_889_div__self,axiom,
% 0.18/0.49      ! [A: rat] :
% 0.18/0.49        ( ( A != zero_zero_rat )
% 0.18/0.49       => ( ( divide_divide_rat @ A @ A )
% 0.18/0.49          = one_one_rat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_890_div__self,axiom,
% 0.18/0.49      ! [A: nat] :
% 0.18/0.49        ( ( A != zero_zero_nat )
% 0.18/0.49       => ( ( divide_divide_nat @ A @ A )
% 0.18/0.49          = one_one_nat ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_891_div__self,axiom,
% 0.18/0.49      ! [A: int] :
% 0.18/0.49        ( ( A != zero_zero_int )
% 0.18/0.49       => ( ( divide_divide_int @ A @ A )
% 0.18/0.49          = one_one_int ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_892_div__self,axiom,
% 0.18/0.49      ! [A: real] :
% 0.18/0.49        ( ( A != zero_zero_real )
% 0.18/0.49       => ( ( divide_divide_real @ A @ A )
% 0.18/0.49          = one_one_real ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_893_div__self,axiom,
% 0.18/0.49      ! [A: complex] :
% 0.18/0.49        ( ( A != zero_zero_complex )
% 0.18/0.49       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.18/0.49          = one_one_complex ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_894_div__self,axiom,
% 0.18/0.49      ! [A: code_integer] :
% 0.18/0.49        ( ( A != zero_z3403309356797280102nteger )
% 0.18/0.49       => ( ( divide6298287555418463151nteger @ A @ A )
% 0.18/0.49          = one_one_Code_integer ) ) ).
% 0.18/0.49  
% 0.18/0.49  % div_self
% 0.18/0.49  thf(fact_895_divide__eq__1__iff,axiom,
% 0.18/0.49      ! [A: rat,B: rat] :
% 0.18/0.49        ( ( ( divide_divide_rat @ A @ B )
% 0.18/0.49          = one_one_rat )
% 0.18/0.49        = ( ( B != zero_zero_rat )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_1_iff
% 0.18/0.49  thf(fact_896_divide__eq__1__iff,axiom,
% 0.18/0.49      ! [A: real,B: real] :
% 0.18/0.49        ( ( ( divide_divide_real @ A @ B )
% 0.18/0.49          = one_one_real )
% 0.18/0.49        = ( ( B != zero_zero_real )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_1_iff
% 0.18/0.49  thf(fact_897_divide__eq__1__iff,axiom,
% 0.18/0.49      ! [A: complex,B: complex] :
% 0.18/0.49        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.18/0.49          = one_one_complex )
% 0.18/0.49        = ( ( B != zero_zero_complex )
% 0.18/0.49          & ( A = B ) ) ) ).
% 0.18/0.49  
% 0.18/0.49  % divide_eq_1_iff
% 0.29/0.49  thf(fact_898_power__0__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 0.29/0.49        = zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_Suc
% 0.29/0.49  thf(fact_899_power__0__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_Suc
% 0.29/0.49  thf(fact_900_power__0__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 0.29/0.49        = zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_Suc
% 0.29/0.49  thf(fact_901_power__0__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_Suc
% 0.29/0.49  thf(fact_902_power__0__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 0.29/0.49        = zero_zero_complex ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_Suc
% 0.29/0.49  thf(fact_903_power__zero__numeral,axiom,
% 0.29/0.49      ! [K: num] :
% 0.29/0.49        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.49        = zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % power_zero_numeral
% 0.29/0.49  thf(fact_904_power__zero__numeral,axiom,
% 0.29/0.49      ! [K: num] :
% 0.29/0.49        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % power_zero_numeral
% 0.29/0.49  thf(fact_905_power__zero__numeral,axiom,
% 0.29/0.49      ! [K: num] :
% 0.29/0.49        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 0.29/0.49        = zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % power_zero_numeral
% 0.29/0.49  thf(fact_906_power__zero__numeral,axiom,
% 0.29/0.49      ! [K: num] :
% 0.29/0.49        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % power_zero_numeral
% 0.29/0.49  thf(fact_907_power__zero__numeral,axiom,
% 0.29/0.49      ! [K: num] :
% 0.29/0.49        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 0.29/0.49        = zero_zero_complex ) ).
% 0.29/0.49  
% 0.29/0.49  % power_zero_numeral
% 0.29/0.49  thf(fact_908_mod__by__1,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_by_1
% 0.29/0.49  thf(fact_909_mod__by__1,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_by_1
% 0.29/0.49  thf(fact_910_mod__by__1,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.29/0.49        = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_by_1
% 0.29/0.49  thf(fact_911_bits__mod__by__1,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_by_1
% 0.29/0.49  thf(fact_912_bits__mod__by__1,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_by_1
% 0.29/0.49  thf(fact_913_bits__mod__by__1,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.29/0.49        = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_by_1
% 0.29/0.49  thf(fact_914_bits__mod__div__trivial,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_div_trivial
% 0.29/0.49  thf(fact_915_bits__mod__div__trivial,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_div_trivial
% 0.29/0.49  thf(fact_916_bits__mod__div__trivial,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.29/0.49        = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_mod_div_trivial
% 0.29/0.49  thf(fact_917_mod__div__trivial,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_div_trivial
% 0.29/0.49  thf(fact_918_mod__div__trivial,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.29/0.49        = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_div_trivial
% 0.29/0.49  thf(fact_919_mod__div__trivial,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.29/0.49        = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_div_trivial
% 0.29/0.49  thf(fact_920_power__Suc0__right,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % power_Suc0_right
% 0.29/0.49  thf(fact_921_power__Suc0__right,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % power_Suc0_right
% 0.29/0.49  thf(fact_922_power__Suc0__right,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % power_Suc0_right
% 0.29/0.49  thf(fact_923_power__Suc0__right,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % power_Suc0_right
% 0.29/0.49  thf(fact_924_less__Suc0,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_Suc0
% 0.29/0.49  thf(fact_925_zero__less__Suc,axiom,
% 0.29/0.49      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_Suc
% 0.29/0.49  thf(fact_926_add__gr__0,axiom,
% 0.29/0.49      ! [M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.49        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.49          | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_gr_0
% 0.29/0.49  thf(fact_927_less__one,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ N2 @ one_one_nat )
% 0.29/0.49        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_one
% 0.29/0.49  thf(fact_928_div__by__Suc__0,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = M ) ).
% 0.29/0.49  
% 0.29/0.49  % div_by_Suc_0
% 0.29/0.49  thf(fact_929_div__less,axiom,
% 0.29/0.49      ! [M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.49       => ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.49          = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % div_less
% 0.29/0.49  thf(fact_930_power__Suc__0,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.49        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_Suc_0
% 0.29/0.49  thf(fact_931_nat__power__eq__Suc__0__iff,axiom,
% 0.29/0.49      ! [X4: nat,M: nat] :
% 0.29/0.49        ( ( ( power_power_nat @ X4 @ M )
% 0.29/0.49          = ( suc @ zero_zero_nat ) )
% 0.29/0.49        = ( ( M = zero_zero_nat )
% 0.29/0.49          | ( X4
% 0.29/0.49            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % nat_power_eq_Suc_0_iff
% 0.29/0.49  thf(fact_932_nat__zero__less__power__iff,axiom,
% 0.29/0.49      ! [X4: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X4 @ N2 ) )
% 0.29/0.49        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.49          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % nat_zero_less_power_iff
% 0.29/0.49  thf(fact_933_mod__by__Suc__0,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_by_Suc_0
% 0.29/0.49  thf(fact_934_zero__le__divide__1__iff,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.29/0.49        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_divide_1_iff
% 0.29/0.49  thf(fact_935_zero__le__divide__1__iff,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.49        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_divide_1_iff
% 0.29/0.49  thf(fact_936_divide__le__0__1__iff,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.29/0.49        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_0_1_iff
% 0.29/0.49  thf(fact_937_divide__le__0__1__iff,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.49        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_0_1_iff
% 0.29/0.49  thf(fact_938_zero__less__divide__1__iff,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.49        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_divide_1_iff
% 0.29/0.49  thf(fact_939_zero__less__divide__1__iff,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.29/0.49        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_divide_1_iff
% 0.29/0.49  thf(fact_940_less__divide__eq__1__pos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.49          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_1_pos
% 0.29/0.49  thf(fact_941_less__divide__eq__1__pos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.49          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_1_pos
% 0.29/0.49  thf(fact_942_less__divide__eq__1__neg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.49          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_1_neg
% 0.29/0.49  thf(fact_943_less__divide__eq__1__neg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.49          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % less_divide_eq_1_neg
% 0.29/0.49  thf(fact_944_divide__less__eq__1__pos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.49          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_1_pos
% 0.29/0.49  thf(fact_945_divide__less__eq__1__pos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.49          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_1_pos
% 0.29/0.49  thf(fact_946_divide__less__eq__1__neg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.49          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_1_neg
% 0.29/0.49  thf(fact_947_divide__less__eq__1__neg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.49          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_eq_1_neg
% 0.29/0.49  thf(fact_948_divide__less__0__1__iff,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.49        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_0_1_iff
% 0.29/0.49  thf(fact_949_divide__less__0__1__iff,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.29/0.49        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_less_0_1_iff
% 0.29/0.49  thf(fact_950_power__eq__0__iff,axiom,
% 0.29/0.49      ! [A: rat,N2: nat] :
% 0.29/0.49        ( ( ( power_power_rat @ A @ N2 )
% 0.29/0.49          = zero_zero_rat )
% 0.29/0.49        = ( ( A = zero_zero_rat )
% 0.29/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_0_iff
% 0.29/0.49  thf(fact_951_power__eq__0__iff,axiom,
% 0.29/0.49      ! [A: nat,N2: nat] :
% 0.29/0.49        ( ( ( power_power_nat @ A @ N2 )
% 0.29/0.49          = zero_zero_nat )
% 0.29/0.49        = ( ( A = zero_zero_nat )
% 0.29/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_0_iff
% 0.29/0.49  thf(fact_952_power__eq__0__iff,axiom,
% 0.29/0.49      ! [A: real,N2: nat] :
% 0.29/0.49        ( ( ( power_power_real @ A @ N2 )
% 0.29/0.49          = zero_zero_real )
% 0.29/0.49        = ( ( A = zero_zero_real )
% 0.29/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_0_iff
% 0.29/0.49  thf(fact_953_power__eq__0__iff,axiom,
% 0.29/0.49      ! [A: int,N2: nat] :
% 0.29/0.49        ( ( ( power_power_int @ A @ N2 )
% 0.29/0.49          = zero_zero_int )
% 0.29/0.49        = ( ( A = zero_zero_int )
% 0.29/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_0_iff
% 0.29/0.49  thf(fact_954_power__eq__0__iff,axiom,
% 0.29/0.49      ! [A: complex,N2: nat] :
% 0.29/0.49        ( ( ( power_power_complex @ A @ N2 )
% 0.29/0.49          = zero_zero_complex )
% 0.29/0.49        = ( ( A = zero_zero_complex )
% 0.29/0.49          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_0_iff
% 0.29/0.49  thf(fact_955_le__divide__eq__1__pos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.49          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_1_pos
% 0.29/0.49  thf(fact_956_le__divide__eq__1__pos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.49          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_1_pos
% 0.29/0.49  thf(fact_957_le__divide__eq__1__neg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.49          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_1_neg
% 0.29/0.49  thf(fact_958_le__divide__eq__1__neg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.49          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_divide_eq_1_neg
% 0.29/0.49  thf(fact_959_divide__le__eq__1__pos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.49          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_1_pos
% 0.29/0.49  thf(fact_960_divide__le__eq__1__pos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.49          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_1_pos
% 0.29/0.49  thf(fact_961_divide__le__eq__1__neg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.49          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_1_neg
% 0.29/0.49  thf(fact_962_divide__le__eq__1__neg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.49          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_eq_1_neg
% 0.29/0.49  thf(fact_963_power__strict__decreasing__iff,axiom,
% 0.29/0.49      ! [B: real,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.49       => ( ( ord_less_real @ B @ one_one_real )
% 0.29/0.49         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_decreasing_iff
% 0.29/0.49  thf(fact_964_power__strict__decreasing__iff,axiom,
% 0.29/0.49      ! [B: rat,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.49       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.29/0.49         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_decreasing_iff
% 0.29/0.49  thf(fact_965_power__strict__decreasing__iff,axiom,
% 0.29/0.49      ! [B: nat,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.49       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.29/0.49         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_decreasing_iff
% 0.29/0.49  thf(fact_966_power__strict__decreasing__iff,axiom,
% 0.29/0.49      ! [B: int,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.49       => ( ( ord_less_int @ B @ one_one_int )
% 0.29/0.49         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_decreasing_iff
% 0.29/0.49  thf(fact_967_power__mono__iff,axiom,
% 0.29/0.49      ! [A: real,B: real,N2: nat] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.49              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_mono_iff
% 0.29/0.49  thf(fact_968_power__mono__iff,axiom,
% 0.29/0.49      ! [A: rat,B: rat,N2: nat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.29/0.49              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_mono_iff
% 0.29/0.49  thf(fact_969_power__mono__iff,axiom,
% 0.29/0.49      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.29/0.49              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_mono_iff
% 0.29/0.49  thf(fact_970_power__mono__iff,axiom,
% 0.29/0.49      ! [A: int,B: int,N2: nat] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.29/0.49              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_mono_iff
% 0.29/0.49  thf(fact_971_zero__eq__power2,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49          = zero_zero_rat )
% 0.29/0.49        = ( A = zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_eq_power2
% 0.29/0.49  thf(fact_972_zero__eq__power2,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49          = zero_zero_nat )
% 0.29/0.49        = ( A = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_eq_power2
% 0.29/0.49  thf(fact_973_zero__eq__power2,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49          = zero_zero_real )
% 0.29/0.49        = ( A = zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_eq_power2
% 0.29/0.49  thf(fact_974_zero__eq__power2,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49          = zero_zero_int )
% 0.29/0.49        = ( A = zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_eq_power2
% 0.29/0.49  thf(fact_975_zero__eq__power2,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49          = zero_zero_complex )
% 0.29/0.49        = ( A = zero_zero_complex ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_eq_power2
% 0.29/0.49  thf(fact_976_one__div__two__eq__zero,axiom,
% 0.29/0.49      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % one_div_two_eq_zero
% 0.29/0.49  thf(fact_977_one__div__two__eq__zero,axiom,
% 0.29/0.49      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % one_div_two_eq_zero
% 0.29/0.49  thf(fact_978_one__div__two__eq__zero,axiom,
% 0.29/0.49      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % one_div_two_eq_zero
% 0.29/0.49  thf(fact_979_bits__1__div__2,axiom,
% 0.29/0.49      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_1_div_2
% 0.29/0.49  thf(fact_980_bits__1__div__2,axiom,
% 0.29/0.49      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_1_div_2
% 0.29/0.49  thf(fact_981_bits__1__div__2,axiom,
% 0.29/0.49      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.49      = zero_z3403309356797280102nteger ) ).
% 0.29/0.49  
% 0.29/0.49  % bits_1_div_2
% 0.29/0.49  thf(fact_982_power__decreasing__iff,axiom,
% 0.29/0.49      ! [B: real,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.49       => ( ( ord_less_real @ B @ one_one_real )
% 0.29/0.49         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_decreasing_iff
% 0.29/0.49  thf(fact_983_power__decreasing__iff,axiom,
% 0.29/0.49      ! [B: rat,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.49       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.29/0.49         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_decreasing_iff
% 0.29/0.49  thf(fact_984_power__decreasing__iff,axiom,
% 0.29/0.49      ! [B: nat,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.49       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.29/0.49         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_decreasing_iff
% 0.29/0.49  thf(fact_985_power__decreasing__iff,axiom,
% 0.29/0.49      ! [B: int,M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.49       => ( ( ord_less_int @ B @ one_one_int )
% 0.29/0.49         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 0.29/0.49            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_decreasing_iff
% 0.29/0.49  thf(fact_986_power2__eq__iff__nonneg,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.49         => ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49            = ( X4 = Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_eq_iff_nonneg
% 0.29/0.49  thf(fact_987_power2__eq__iff__nonneg,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.49         => ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49            = ( X4 = Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_eq_iff_nonneg
% 0.29/0.49  thf(fact_988_power2__eq__iff__nonneg,axiom,
% 0.29/0.49      ! [X4: nat,Y: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.49         => ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49            = ( X4 = Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_eq_iff_nonneg
% 0.29/0.49  thf(fact_989_power2__eq__iff__nonneg,axiom,
% 0.29/0.49      ! [X4: int,Y: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.49         => ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49            = ( X4 = Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_eq_iff_nonneg
% 0.29/0.49  thf(fact_990_power2__less__eq__zero__iff,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.29/0.49        = ( A = zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_less_eq_zero_iff
% 0.29/0.49  thf(fact_991_power2__less__eq__zero__iff,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.29/0.49        = ( A = zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_less_eq_zero_iff
% 0.29/0.49  thf(fact_992_power2__less__eq__zero__iff,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.29/0.49        = ( A = zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power2_less_eq_zero_iff
% 0.29/0.49  thf(fact_993_zero__less__power2,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49        = ( A != zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_power2
% 0.29/0.49  thf(fact_994_zero__less__power2,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49        = ( A != zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_power2
% 0.29/0.49  thf(fact_995_zero__less__power2,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49        = ( A != zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_power2
% 0.29/0.49  thf(fact_996_sum__power2__eq__zero__iff,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49          = zero_zero_rat )
% 0.29/0.49        = ( ( X4 = zero_zero_rat )
% 0.29/0.49          & ( Y = zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % sum_power2_eq_zero_iff
% 0.29/0.49  thf(fact_997_sum__power2__eq__zero__iff,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49          = zero_zero_real )
% 0.29/0.49        = ( ( X4 = zero_zero_real )
% 0.29/0.49          & ( Y = zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % sum_power2_eq_zero_iff
% 0.29/0.49  thf(fact_998_sum__power2__eq__zero__iff,axiom,
% 0.29/0.49      ! [X4: int,Y: int] :
% 0.29/0.49        ( ( ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.49          = zero_zero_int )
% 0.29/0.49        = ( ( X4 = zero_zero_int )
% 0.29/0.49          & ( Y = zero_zero_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % sum_power2_eq_zero_iff
% 0.29/0.49  thf(fact_999_add__self__mod__2,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.49        = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % add_self_mod_2
% 0.29/0.49  thf(fact_1000_psubsetD,axiom,
% 0.29/0.49      ! [A2: set_real,B3: set_real,C: real] :
% 0.29/0.49        ( ( ord_less_set_real @ A2 @ B3 )
% 0.29/0.49       => ( ( member_real @ C @ A2 )
% 0.29/0.49         => ( member_real @ C @ B3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % psubsetD
% 0.29/0.49  thf(fact_1001_psubsetD,axiom,
% 0.29/0.49      ! [A2: set_nat,B3: set_nat,C: nat] :
% 0.29/0.49        ( ( ord_less_set_nat @ A2 @ B3 )
% 0.29/0.49       => ( ( member_nat @ C @ A2 )
% 0.29/0.49         => ( member_nat @ C @ B3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % psubsetD
% 0.29/0.49  thf(fact_1002_psubsetD,axiom,
% 0.29/0.49      ! [A2: set_complex,B3: set_complex,C: complex] :
% 0.29/0.49        ( ( ord_less_set_complex @ A2 @ B3 )
% 0.29/0.49       => ( ( member_complex @ C @ A2 )
% 0.29/0.49         => ( member_complex @ C @ B3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % psubsetD
% 0.29/0.49  thf(fact_1003_psubsetD,axiom,
% 0.29/0.49      ! [A2: set_int,B3: set_int,C: int] :
% 0.29/0.49        ( ( ord_less_set_int @ A2 @ B3 )
% 0.29/0.49       => ( ( member_int @ C @ A2 )
% 0.29/0.49         => ( member_int @ C @ B3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % psubsetD
% 0.29/0.49  thf(fact_1004_psubsetD,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 0.29/0.49        ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 0.29/0.49       => ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.29/0.49         => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % psubsetD
% 0.29/0.49  thf(fact_1005_zero__reorient,axiom,
% 0.29/0.49      ! [X4: complex] :
% 0.29/0.49        ( ( zero_zero_complex = X4 )
% 0.29/0.49        = ( X4 = zero_zero_complex ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_reorient
% 0.29/0.49  thf(fact_1006_zero__reorient,axiom,
% 0.29/0.49      ! [X4: real] :
% 0.29/0.49        ( ( zero_zero_real = X4 )
% 0.29/0.49        = ( X4 = zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_reorient
% 0.29/0.49  thf(fact_1007_zero__reorient,axiom,
% 0.29/0.49      ! [X4: rat] :
% 0.29/0.49        ( ( zero_zero_rat = X4 )
% 0.29/0.49        = ( X4 = zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_reorient
% 0.29/0.49  thf(fact_1008_zero__reorient,axiom,
% 0.29/0.49      ! [X4: nat] :
% 0.29/0.49        ( ( zero_zero_nat = X4 )
% 0.29/0.49        = ( X4 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_reorient
% 0.29/0.49  thf(fact_1009_zero__reorient,axiom,
% 0.29/0.49      ! [X4: int] :
% 0.29/0.49        ( ( zero_zero_int = X4 )
% 0.29/0.49        = ( X4 = zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_reorient
% 0.29/0.49  thf(fact_1010_verit__sum__simplify,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % verit_sum_simplify
% 0.29/0.49  thf(fact_1011_verit__sum__simplify,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % verit_sum_simplify
% 0.29/0.49  thf(fact_1012_verit__sum__simplify,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % verit_sum_simplify
% 0.29/0.49  thf(fact_1013_verit__sum__simplify,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % verit_sum_simplify
% 0.29/0.49  thf(fact_1014_verit__sum__simplify,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % verit_sum_simplify
% 0.29/0.49  thf(fact_1015_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.29/0.49      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 0.29/0.49        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X4 )
% 0.29/0.49        = ( ( X4 = Mi )
% 0.29/0.49          | ( X4 = Ma ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % VEBT_internal.membermima.simps(3)
% 0.29/0.49  thf(fact_1016_power__0__left,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ( N2 = zero_zero_nat )
% 0.29/0.49         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.29/0.49            = one_one_rat ) )
% 0.29/0.49        & ( ( N2 != zero_zero_nat )
% 0.29/0.49         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.29/0.49            = zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_left
% 0.29/0.49  thf(fact_1017_power__0__left,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ( N2 = zero_zero_nat )
% 0.29/0.49         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.29/0.49            = one_one_nat ) )
% 0.29/0.49        & ( ( N2 != zero_zero_nat )
% 0.29/0.49         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.29/0.49            = zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_left
% 0.29/0.49  thf(fact_1018_power__0__left,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ( N2 = zero_zero_nat )
% 0.29/0.49         => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.29/0.49            = one_one_real ) )
% 0.29/0.49        & ( ( N2 != zero_zero_nat )
% 0.29/0.49         => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.29/0.49            = zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_left
% 0.29/0.49  thf(fact_1019_power__0__left,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ( N2 = zero_zero_nat )
% 0.29/0.49         => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.29/0.49            = one_one_int ) )
% 0.29/0.49        & ( ( N2 != zero_zero_nat )
% 0.29/0.49         => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.29/0.49            = zero_zero_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_left
% 0.29/0.49  thf(fact_1020_power__0__left,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ( N2 = zero_zero_nat )
% 0.29/0.49         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.29/0.49            = one_one_complex ) )
% 0.29/0.49        & ( ( N2 != zero_zero_nat )
% 0.29/0.49         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.29/0.49            = zero_zero_complex ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_0_left
% 0.29/0.49  thf(fact_1021_zero__power,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 0.29/0.49          = zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_power
% 0.29/0.49  thf(fact_1022_zero__power,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 0.29/0.49          = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_power
% 0.29/0.49  thf(fact_1023_zero__power,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( power_power_real @ zero_zero_real @ N2 )
% 0.29/0.49          = zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_power
% 0.29/0.49  thf(fact_1024_zero__power,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( power_power_int @ zero_zero_int @ N2 )
% 0.29/0.49          = zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_power
% 0.29/0.49  thf(fact_1025_zero__power,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 0.29/0.49          = zero_zero_complex ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_power
% 0.29/0.49  thf(fact_1026_zero__le,axiom,
% 0.29/0.49      ! [X4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X4 ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le
% 0.29/0.49  thf(fact_1027_le__numeral__extra_I3_J,axiom,
% 0.29/0.49      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(3)
% 0.29/0.49  thf(fact_1028_le__numeral__extra_I3_J,axiom,
% 0.29/0.49      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(3)
% 0.29/0.49  thf(fact_1029_le__numeral__extra_I3_J,axiom,
% 0.29/0.49      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(3)
% 0.29/0.49  thf(fact_1030_le__numeral__extra_I3_J,axiom,
% 0.29/0.49      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.29/0.49  
% 0.29/0.49  % le_numeral_extra(3)
% 0.29/0.49  thf(fact_1031_zero__less__iff__neq__zero,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49        = ( N2 != zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_iff_neq_zero
% 0.29/0.49  thf(fact_1032_gr__implies__not__zero,axiom,
% 0.29/0.49      ! [M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.49       => ( N2 != zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % gr_implies_not_zero
% 0.29/0.49  thf(fact_1033_not__less__zero,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_less_zero
% 0.29/0.49  thf(fact_1034_gr__zeroI,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( N2 != zero_zero_nat )
% 0.29/0.49       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % gr_zeroI
% 0.29/0.49  thf(fact_1035_less__numeral__extra_I3_J,axiom,
% 0.29/0.49      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(3)
% 0.29/0.49  thf(fact_1036_less__numeral__extra_I3_J,axiom,
% 0.29/0.49      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(3)
% 0.29/0.49  thf(fact_1037_less__numeral__extra_I3_J,axiom,
% 0.29/0.49      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(3)
% 0.29/0.49  thf(fact_1038_less__numeral__extra_I3_J,axiom,
% 0.29/0.49      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(3)
% 0.29/0.49  thf(fact_1039_field__lbound__gt__zero,axiom,
% 0.29/0.49      ! [D1: real,D2: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.29/0.49       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.29/0.49         => ? [E: real] :
% 0.29/0.49              ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.49              & ( ord_less_real @ E @ D1 )
% 0.29/0.49              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % field_lbound_gt_zero
% 0.29/0.49  thf(fact_1040_field__lbound__gt__zero,axiom,
% 0.29/0.49      ! [D1: rat,D2: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.29/0.49       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 0.29/0.49         => ? [E: rat] :
% 0.29/0.49              ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.29/0.49              & ( ord_less_rat @ E @ D1 )
% 0.29/0.49              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % field_lbound_gt_zero
% 0.29/0.49  thf(fact_1041_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_zero_rat
% 0.29/0.49       != ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1042_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_z5237406670263579293d_enat
% 0.29/0.49       != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1043_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_zero_complex
% 0.29/0.49       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1044_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_zero_real
% 0.29/0.49       != ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1045_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_zero_nat
% 0.29/0.49       != ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1046_zero__neq__numeral,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ( zero_zero_int
% 0.29/0.49       != ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_numeral
% 0.29/0.49  thf(fact_1047_zero__neq__one,axiom,
% 0.29/0.49      zero_zero_complex != one_one_complex ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_one
% 0.29/0.49  thf(fact_1048_zero__neq__one,axiom,
% 0.29/0.49      zero_zero_real != one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_one
% 0.29/0.49  thf(fact_1049_zero__neq__one,axiom,
% 0.29/0.49      zero_zero_rat != one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_one
% 0.29/0.49  thf(fact_1050_zero__neq__one,axiom,
% 0.29/0.49      zero_zero_nat != one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_one
% 0.29/0.49  thf(fact_1051_zero__neq__one,axiom,
% 0.29/0.49      zero_zero_int != one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % zero_neq_one
% 0.29/0.49  thf(fact_1052_add_Ogroup__left__neutral,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.group_left_neutral
% 0.29/0.49  thf(fact_1053_add_Ogroup__left__neutral,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.group_left_neutral
% 0.29/0.49  thf(fact_1054_add_Ogroup__left__neutral,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.group_left_neutral
% 0.29/0.49  thf(fact_1055_add_Ogroup__left__neutral,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.group_left_neutral
% 0.29/0.49  thf(fact_1056_add_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.comm_neutral
% 0.29/0.49  thf(fact_1057_add_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.comm_neutral
% 0.29/0.49  thf(fact_1058_add_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.comm_neutral
% 0.29/0.49  thf(fact_1059_add_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.comm_neutral
% 0.29/0.49  thf(fact_1060_add_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.comm_neutral
% 0.29/0.49  thf(fact_1061_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.49      ! [A: complex] :
% 0.29/0.49        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_add_class.add_0
% 0.29/0.49  thf(fact_1062_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.49      ! [A: real] :
% 0.29/0.49        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_add_class.add_0
% 0.29/0.49  thf(fact_1063_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_add_class.add_0
% 0.29/0.49  thf(fact_1064_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_add_class.add_0
% 0.29/0.49  thf(fact_1065_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_add_class.add_0
% 0.29/0.49  thf(fact_1066_power__not__zero,axiom,
% 0.29/0.49      ! [A: rat,N2: nat] :
% 0.29/0.49        ( ( A != zero_zero_rat )
% 0.29/0.49       => ( ( power_power_rat @ A @ N2 )
% 0.29/0.49         != zero_zero_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_not_zero
% 0.29/0.49  thf(fact_1067_power__not__zero,axiom,
% 0.29/0.49      ! [A: nat,N2: nat] :
% 0.29/0.49        ( ( A != zero_zero_nat )
% 0.29/0.49       => ( ( power_power_nat @ A @ N2 )
% 0.29/0.49         != zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_not_zero
% 0.29/0.49  thf(fact_1068_power__not__zero,axiom,
% 0.29/0.49      ! [A: real,N2: nat] :
% 0.29/0.49        ( ( A != zero_zero_real )
% 0.29/0.49       => ( ( power_power_real @ A @ N2 )
% 0.29/0.49         != zero_zero_real ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_not_zero
% 0.29/0.49  thf(fact_1069_power__not__zero,axiom,
% 0.29/0.49      ! [A: int,N2: nat] :
% 0.29/0.49        ( ( A != zero_zero_int )
% 0.29/0.49       => ( ( power_power_int @ A @ N2 )
% 0.29/0.49         != zero_zero_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_not_zero
% 0.29/0.49  thf(fact_1070_power__not__zero,axiom,
% 0.29/0.49      ! [A: complex,N2: nat] :
% 0.29/0.49        ( ( A != zero_zero_complex )
% 0.29/0.49       => ( ( power_power_complex @ A @ N2 )
% 0.29/0.49         != zero_zero_complex ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_not_zero
% 0.29/0.49  thf(fact_1071_num_Osize_I4_J,axiom,
% 0.29/0.49      ( ( size_size_num @ one )
% 0.29/0.49      = zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % num.size(4)
% 0.29/0.49  thf(fact_1072_vebt__buildup_Ocases,axiom,
% 0.29/0.49      ! [X4: nat] :
% 0.29/0.49        ( ( X4 != zero_zero_nat )
% 0.29/0.49       => ( ( X4
% 0.29/0.49           != ( suc @ zero_zero_nat ) )
% 0.29/0.49         => ~ ! [Va2: nat] :
% 0.29/0.49                ( X4
% 0.29/0.49               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % vebt_buildup.cases
% 0.29/0.49  thf(fact_1073_not0__implies__Suc,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( N2 != zero_zero_nat )
% 0.29/0.49       => ? [M5: nat] :
% 0.29/0.49            ( N2
% 0.29/0.49            = ( suc @ M5 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % not0_implies_Suc
% 0.29/0.49  thf(fact_1074_Zero__not__Suc,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( zero_zero_nat
% 0.29/0.49       != ( suc @ M ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Zero_not_Suc
% 0.29/0.49  thf(fact_1075_Zero__neq__Suc,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( zero_zero_nat
% 0.29/0.49       != ( suc @ M ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Zero_neq_Suc
% 0.29/0.49  thf(fact_1076_Suc__neq__Zero,axiom,
% 0.29/0.49      ! [M: nat] :
% 0.29/0.49        ( ( suc @ M )
% 0.29/0.49       != zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % Suc_neq_Zero
% 0.29/0.49  thf(fact_1077_zero__induct,axiom,
% 0.29/0.49      ! [P: nat > $o,K: nat] :
% 0.29/0.49        ( ( P @ K )
% 0.29/0.49       => ( ! [N3: nat] :
% 0.29/0.49              ( ( P @ ( suc @ N3 ) )
% 0.29/0.49             => ( P @ N3 ) )
% 0.29/0.49         => ( P @ zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_induct
% 0.29/0.49  thf(fact_1078_diff__induct,axiom,
% 0.29/0.49      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.29/0.49        ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 0.29/0.49       => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.29/0.49         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.49                ( ( P @ X5 @ Y3 )
% 0.29/0.49               => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 0.29/0.49           => ( P @ M @ N2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % diff_induct
% 0.29/0.49  thf(fact_1079_nat__induct,axiom,
% 0.29/0.49      ! [P: nat > $o,N2: nat] :
% 0.29/0.49        ( ( P @ zero_zero_nat )
% 0.29/0.49       => ( ! [N3: nat] :
% 0.29/0.49              ( ( P @ N3 )
% 0.29/0.49             => ( P @ ( suc @ N3 ) ) )
% 0.29/0.49         => ( P @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % nat_induct
% 0.29/0.49  thf(fact_1080_old_Onat_Oexhaust,axiom,
% 0.29/0.49      ! [Y: nat] :
% 0.29/0.49        ( ( Y != zero_zero_nat )
% 0.29/0.49       => ~ ! [Nat3: nat] :
% 0.29/0.49              ( Y
% 0.29/0.49             != ( suc @ Nat3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % old.nat.exhaust
% 0.29/0.49  thf(fact_1081_nat_OdiscI,axiom,
% 0.29/0.49      ! [Nat: nat,X22: nat] :
% 0.29/0.49        ( ( Nat
% 0.29/0.49          = ( suc @ X22 ) )
% 0.29/0.49       => ( Nat != zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % nat.discI
% 0.29/0.49  thf(fact_1082_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.49      ! [Nat2: nat] :
% 0.29/0.49        ( zero_zero_nat
% 0.29/0.49       != ( suc @ Nat2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % old.nat.distinct(1)
% 0.29/0.49  thf(fact_1083_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.49      ! [Nat2: nat] :
% 0.29/0.49        ( ( suc @ Nat2 )
% 0.29/0.49       != zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % old.nat.distinct(2)
% 0.29/0.49  thf(fact_1084_nat_Odistinct_I1_J,axiom,
% 0.29/0.49      ! [X22: nat] :
% 0.29/0.49        ( zero_zero_nat
% 0.29/0.49       != ( suc @ X22 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % nat.distinct(1)
% 0.29/0.49  thf(fact_1085_infinite__descent0,axiom,
% 0.29/0.49      ! [P: nat > $o,N2: nat] :
% 0.29/0.49        ( ( P @ zero_zero_nat )
% 0.29/0.49       => ( ! [N3: nat] :
% 0.29/0.49              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.49             => ( ~ ( P @ N3 )
% 0.29/0.49               => ? [M2: nat] :
% 0.29/0.49                    ( ( ord_less_nat @ M2 @ N3 )
% 0.29/0.49                    & ~ ( P @ M2 ) ) ) )
% 0.29/0.49         => ( P @ N2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % infinite_descent0
% 0.29/0.49  thf(fact_1086_gr__implies__not0,axiom,
% 0.29/0.49      ! [M: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.49       => ( N2 != zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % gr_implies_not0
% 0.29/0.49  thf(fact_1087_less__zeroE,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % less_zeroE
% 0.29/0.49  thf(fact_1088_not__less0,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_less0
% 0.29/0.49  thf(fact_1089_not__gr0,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.49        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % not_gr0
% 0.29/0.49  thf(fact_1090_gr0I,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( N2 != zero_zero_nat )
% 0.29/0.49       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % gr0I
% 0.29/0.49  thf(fact_1091_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % bot_nat_0.extremum_strict
% 0.29/0.49  thf(fact_1092_le__0__eq,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.29/0.49        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % le_0_eq
% 0.29/0.49  thf(fact_1093_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.49       => ( A = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % bot_nat_0.extremum_uniqueI
% 0.29/0.49  thf(fact_1094_bot__nat__0_Oextremum__unique,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.49        = ( A = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % bot_nat_0.extremum_unique
% 0.29/0.49  thf(fact_1095_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.49      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.29/0.49  
% 0.29/0.49  % less_eq_nat.simps(1)
% 0.29/0.49  thf(fact_1096_add__eq__self__zero,axiom,
% 0.29/0.49      ! [M: nat,N2: nat] :
% 0.29/0.49        ( ( ( plus_plus_nat @ M @ N2 )
% 0.29/0.49          = M )
% 0.29/0.49       => ( N2 = zero_zero_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_eq_self_zero
% 0.29/0.49  thf(fact_1097_plus__nat_Oadd__0,axiom,
% 0.29/0.49      ! [N2: nat] :
% 0.29/0.49        ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 0.29/0.49        = N2 ) ).
% 0.29/0.49  
% 0.29/0.49  % plus_nat.add_0
% 0.29/0.49  thf(fact_1098_power__eq__imp__eq__base,axiom,
% 0.29/0.49      ! [A: real,N2: nat,B: real] :
% 0.29/0.49        ( ( ( power_power_real @ A @ N2 )
% 0.29/0.49          = ( power_power_real @ B @ N2 ) )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.49           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49             => ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_imp_eq_base
% 0.29/0.49  thf(fact_1099_power__eq__imp__eq__base,axiom,
% 0.29/0.49      ! [A: rat,N2: nat,B: rat] :
% 0.29/0.49        ( ( ( power_power_rat @ A @ N2 )
% 0.29/0.49          = ( power_power_rat @ B @ N2 ) )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.49           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49             => ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_imp_eq_base
% 0.29/0.49  thf(fact_1100_power__eq__imp__eq__base,axiom,
% 0.29/0.49      ! [A: nat,N2: nat,B: nat] :
% 0.29/0.49        ( ( ( power_power_nat @ A @ N2 )
% 0.29/0.49          = ( power_power_nat @ B @ N2 ) )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.49           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49             => ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_imp_eq_base
% 0.29/0.49  thf(fact_1101_power__eq__imp__eq__base,axiom,
% 0.29/0.49      ! [A: int,N2: nat,B: int] :
% 0.29/0.49        ( ( ( power_power_int @ A @ N2 )
% 0.29/0.49          = ( power_power_int @ B @ N2 ) )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.49           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49             => ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_imp_eq_base
% 0.29/0.49  thf(fact_1102_power__eq__iff__eq__base,axiom,
% 0.29/0.49      ! [N2: nat,A: real,B: real] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.49           => ( ( ( power_power_real @ A @ N2 )
% 0.29/0.49                = ( power_power_real @ B @ N2 ) )
% 0.29/0.49              = ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_iff_eq_base
% 0.29/0.49  thf(fact_1103_power__eq__iff__eq__base,axiom,
% 0.29/0.49      ! [N2: nat,A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.49           => ( ( ( power_power_rat @ A @ N2 )
% 0.29/0.49                = ( power_power_rat @ B @ N2 ) )
% 0.29/0.49              = ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_iff_eq_base
% 0.29/0.49  thf(fact_1104_power__eq__iff__eq__base,axiom,
% 0.29/0.49      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.49           => ( ( ( power_power_nat @ A @ N2 )
% 0.29/0.49                = ( power_power_nat @ B @ N2 ) )
% 0.29/0.49              = ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_iff_eq_base
% 0.29/0.49  thf(fact_1105_power__eq__iff__eq__base,axiom,
% 0.29/0.49      ! [N2: nat,A: int,B: int] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.49           => ( ( ( power_power_int @ A @ N2 )
% 0.29/0.49                = ( power_power_int @ B @ N2 ) )
% 0.29/0.49              = ( A = B ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_eq_iff_eq_base
% 0.29/0.49  thf(fact_1106_power__strict__mono,axiom,
% 0.29/0.49      ! [A: real,B: real,N2: nat] :
% 0.29/0.49        ( ( ord_less_real @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_mono
% 0.29/0.49  thf(fact_1107_power__strict__mono,axiom,
% 0.29/0.49      ! [A: rat,B: rat,N2: nat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_mono
% 0.29/0.49  thf(fact_1108_power__strict__mono,axiom,
% 0.29/0.49      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.49        ( ( ord_less_nat @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_mono
% 0.29/0.49  thf(fact_1109_power__strict__mono,axiom,
% 0.29/0.49      ! [A: int,B: int,N2: nat] :
% 0.29/0.49        ( ( ord_less_int @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.49           => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % power_strict_mono
% 0.29/0.49  thf(fact_1110_zero__le__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_numeral
% 0.29/0.49  thf(fact_1111_zero__le__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_numeral
% 0.29/0.49  thf(fact_1112_zero__le__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_numeral
% 0.29/0.49  thf(fact_1113_zero__le__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_numeral
% 0.29/0.49  thf(fact_1114_zero__le__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_numeral
% 0.29/0.49  thf(fact_1115_not__numeral__le__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_le_zero
% 0.29/0.49  thf(fact_1116_not__numeral__le__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_le_zero
% 0.29/0.49  thf(fact_1117_not__numeral__le__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_le_zero
% 0.29/0.49  thf(fact_1118_not__numeral__le__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_le_zero
% 0.29/0.49  thf(fact_1119_not__numeral__le__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_le_zero
% 0.29/0.49  thf(fact_1120_not__numeral__less__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_less_zero
% 0.29/0.49  thf(fact_1121_not__numeral__less__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_less_zero
% 0.29/0.49  thf(fact_1122_not__numeral__less__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_less_zero
% 0.29/0.49  thf(fact_1123_not__numeral__less__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_less_zero
% 0.29/0.49  thf(fact_1124_not__numeral__less__zero,axiom,
% 0.29/0.49      ! [N2: num] :
% 0.29/0.49        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % not_numeral_less_zero
% 0.29/0.49  thf(fact_1125_zero__less__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_numeral
% 0.29/0.49  thf(fact_1126_zero__less__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_numeral
% 0.29/0.49  thf(fact_1127_zero__less__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_numeral
% 0.29/0.49  thf(fact_1128_zero__less__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_numeral
% 0.29/0.49  thf(fact_1129_zero__less__numeral,axiom,
% 0.29/0.49      ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_numeral
% 0.29/0.49  thf(fact_1130_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one_class.zero_le_one
% 0.29/0.49  thf(fact_1131_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one_class.zero_le_one
% 0.29/0.49  thf(fact_1132_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one_class.zero_le_one
% 0.29/0.49  thf(fact_1133_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one_class.zero_le_one
% 0.29/0.49  thf(fact_1134_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.49  thf(fact_1135_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.49  thf(fact_1136_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.49  thf(fact_1137_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.49      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.49  thf(fact_1138_not__one__le__zero,axiom,
% 0.29/0.49      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_le_zero
% 0.29/0.49  thf(fact_1139_not__one__le__zero,axiom,
% 0.29/0.49      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_le_zero
% 0.29/0.49  thf(fact_1140_not__one__le__zero,axiom,
% 0.29/0.49      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_le_zero
% 0.29/0.49  thf(fact_1141_not__one__le__zero,axiom,
% 0.29/0.49      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_le_zero
% 0.29/0.49  thf(fact_1142_add__decreasing,axiom,
% 0.29/0.49      ! [A: real,C: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ C @ B )
% 0.29/0.49         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing
% 0.29/0.49  thf(fact_1143_add__decreasing,axiom,
% 0.29/0.49      ! [A: rat,C: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.49         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing
% 0.29/0.49  thf(fact_1144_add__decreasing,axiom,
% 0.29/0.49      ! [A: nat,C: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.49       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.49         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing
% 0.29/0.49  thf(fact_1145_add__decreasing,axiom,
% 0.29/0.49      ! [A: int,C: int,B: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.49         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing
% 0.29/0.49  thf(fact_1146_add__increasing,axiom,
% 0.29/0.49      ! [A: real,B: real,C: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.49         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing
% 0.29/0.49  thf(fact_1147_add__increasing,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.49         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing
% 0.29/0.49  thf(fact_1148_add__increasing,axiom,
% 0.29/0.49      ! [A: nat,B: nat,C: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.49         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing
% 0.29/0.49  thf(fact_1149_add__increasing,axiom,
% 0.29/0.49      ! [A: int,B: int,C: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.49         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing
% 0.29/0.49  thf(fact_1150_add__decreasing2,axiom,
% 0.29/0.49      ! [C: real,A: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.49         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing2
% 0.29/0.49  thf(fact_1151_add__decreasing2,axiom,
% 0.29/0.49      ! [C: rat,A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.49         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing2
% 0.29/0.49  thf(fact_1152_add__decreasing2,axiom,
% 0.29/0.49      ! [C: nat,A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.29/0.49       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.49         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing2
% 0.29/0.49  thf(fact_1153_add__decreasing2,axiom,
% 0.29/0.49      ! [C: int,A: int,B: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.49         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_decreasing2
% 0.29/0.49  thf(fact_1154_add__increasing2,axiom,
% 0.29/0.49      ! [C: real,B: real,A: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.49       => ( ( ord_less_eq_real @ B @ A )
% 0.29/0.49         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing2
% 0.29/0.49  thf(fact_1155_add__increasing2,axiom,
% 0.29/0.49      ! [C: rat,B: rat,A: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.49       => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.49         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing2
% 0.29/0.49  thf(fact_1156_add__increasing2,axiom,
% 0.29/0.49      ! [C: nat,B: nat,A: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.49       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.49         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing2
% 0.29/0.49  thf(fact_1157_add__increasing2,axiom,
% 0.29/0.49      ! [C: int,B: int,A: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.49       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.49         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_increasing2
% 0.29/0.49  thf(fact_1158_add__nonneg__nonneg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.49         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_nonneg
% 0.29/0.49  thf(fact_1159_add__nonneg__nonneg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.49         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_nonneg
% 0.29/0.49  thf(fact_1160_add__nonneg__nonneg,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.49         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_nonneg
% 0.29/0.49  thf(fact_1161_add__nonneg__nonneg,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.49         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_nonneg
% 0.29/0.49  thf(fact_1162_add__nonpos__nonpos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.49         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_nonpos
% 0.29/0.49  thf(fact_1163_add__nonpos__nonpos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.49         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_nonpos
% 0.29/0.49  thf(fact_1164_add__nonpos__nonpos,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.49       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.49         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_nonpos
% 0.29/0.49  thf(fact_1165_add__nonpos__nonpos,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.49         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_nonpos
% 0.29/0.49  thf(fact_1166_add__nonneg__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.49         => ( ( ( plus_plus_real @ X4 @ Y )
% 0.29/0.49              = zero_zero_real )
% 0.29/0.49            = ( ( X4 = zero_zero_real )
% 0.29/0.49              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_eq_0_iff
% 0.29/0.49  thf(fact_1167_add__nonneg__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.49         => ( ( ( plus_plus_rat @ X4 @ Y )
% 0.29/0.49              = zero_zero_rat )
% 0.29/0.49            = ( ( X4 = zero_zero_rat )
% 0.29/0.49              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_eq_0_iff
% 0.29/0.49  thf(fact_1168_add__nonneg__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: nat,Y: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.49         => ( ( ( plus_plus_nat @ X4 @ Y )
% 0.29/0.49              = zero_zero_nat )
% 0.29/0.49            = ( ( X4 = zero_zero_nat )
% 0.29/0.49              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_eq_0_iff
% 0.29/0.49  thf(fact_1169_add__nonneg__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: int,Y: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.49         => ( ( ( plus_plus_int @ X4 @ Y )
% 0.29/0.49              = zero_zero_int )
% 0.29/0.49            = ( ( X4 = zero_zero_int )
% 0.29/0.49              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonneg_eq_0_iff
% 0.29/0.49  thf(fact_1170_add__nonpos__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.29/0.49         => ( ( ( plus_plus_real @ X4 @ Y )
% 0.29/0.49              = zero_zero_real )
% 0.29/0.49            = ( ( X4 = zero_zero_real )
% 0.29/0.49              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_eq_0_iff
% 0.29/0.49  thf(fact_1171_add__nonpos__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.29/0.49         => ( ( ( plus_plus_rat @ X4 @ Y )
% 0.29/0.49              = zero_zero_rat )
% 0.29/0.49            = ( ( X4 = zero_zero_rat )
% 0.29/0.49              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_eq_0_iff
% 0.29/0.49  thf(fact_1172_add__nonpos__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: nat,Y: nat] :
% 0.29/0.49        ( ( ord_less_eq_nat @ X4 @ zero_zero_nat )
% 0.29/0.49       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.29/0.49         => ( ( ( plus_plus_nat @ X4 @ Y )
% 0.29/0.49              = zero_zero_nat )
% 0.29/0.49            = ( ( X4 = zero_zero_nat )
% 0.29/0.49              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_eq_0_iff
% 0.29/0.49  thf(fact_1173_add__nonpos__eq__0__iff,axiom,
% 0.29/0.49      ! [X4: int,Y: int] :
% 0.29/0.49        ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.29/0.49         => ( ( ( plus_plus_int @ X4 @ Y )
% 0.29/0.49              = zero_zero_int )
% 0.29/0.49            = ( ( X4 = zero_zero_int )
% 0.29/0.49              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_nonpos_eq_0_iff
% 0.29/0.49  thf(fact_1174_not__one__less__zero,axiom,
% 0.29/0.49      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_less_zero
% 0.29/0.49  thf(fact_1175_not__one__less__zero,axiom,
% 0.29/0.49      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_less_zero
% 0.29/0.49  thf(fact_1176_not__one__less__zero,axiom,
% 0.29/0.49      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_less_zero
% 0.29/0.49  thf(fact_1177_not__one__less__zero,axiom,
% 0.29/0.49      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.49  
% 0.29/0.49  % not_one_less_zero
% 0.29/0.49  thf(fact_1178_zero__less__one,axiom,
% 0.29/0.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one
% 0.29/0.49  thf(fact_1179_zero__less__one,axiom,
% 0.29/0.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one
% 0.29/0.49  thf(fact_1180_zero__less__one,axiom,
% 0.29/0.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one
% 0.29/0.49  thf(fact_1181_zero__less__one,axiom,
% 0.29/0.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % zero_less_one
% 0.29/0.49  thf(fact_1182_less__numeral__extra_I1_J,axiom,
% 0.29/0.49      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(1)
% 0.29/0.49  thf(fact_1183_less__numeral__extra_I1_J,axiom,
% 0.29/0.49      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(1)
% 0.29/0.49  thf(fact_1184_less__numeral__extra_I1_J,axiom,
% 0.29/0.49      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(1)
% 0.29/0.49  thf(fact_1185_less__numeral__extra_I1_J,axiom,
% 0.29/0.49      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % less_numeral_extra(1)
% 0.29/0.49  thf(fact_1186_pos__add__strict,axiom,
% 0.29/0.49      ! [A: real,B: real,C: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_real @ B @ C )
% 0.29/0.49         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % pos_add_strict
% 0.29/0.49  thf(fact_1187_pos__add__strict,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_rat @ B @ C )
% 0.29/0.49         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % pos_add_strict
% 0.29/0.49  thf(fact_1188_pos__add__strict,axiom,
% 0.29/0.49      ! [A: nat,B: nat,C: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.49       => ( ( ord_less_nat @ B @ C )
% 0.29/0.49         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % pos_add_strict
% 0.29/0.49  thf(fact_1189_pos__add__strict,axiom,
% 0.29/0.49      ! [A: int,B: int,C: int] :
% 0.29/0.49        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.49       => ( ( ord_less_int @ B @ C )
% 0.29/0.49         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % pos_add_strict
% 0.29/0.49  thf(fact_1190_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_nat @ A @ B )
% 0.29/0.49       => ~ ! [C3: nat] :
% 0.29/0.49              ( ( B
% 0.29/0.49                = ( plus_plus_nat @ A @ C3 ) )
% 0.29/0.49             => ( C3 = zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % canonically_ordered_monoid_add_class.lessE
% 0.29/0.49  thf(fact_1191_add__pos__pos,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.49       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.49         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_pos_pos
% 0.29/0.49  thf(fact_1192_add__pos__pos,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.49       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.49         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_pos_pos
% 0.29/0.49  thf(fact_1193_add__pos__pos,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.49       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.49         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_pos_pos
% 0.29/0.49  thf(fact_1194_add__pos__pos,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.49       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.49         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_pos_pos
% 0.29/0.49  thf(fact_1195_add__neg__neg,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.49         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_neg_neg
% 0.29/0.49  thf(fact_1196_add__neg__neg,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.49         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_neg_neg
% 0.29/0.49  thf(fact_1197_add__neg__neg,axiom,
% 0.29/0.49      ! [A: nat,B: nat] :
% 0.29/0.49        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.49       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.49         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_neg_neg
% 0.29/0.49  thf(fact_1198_add__neg__neg,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.49         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_neg_neg
% 0.29/0.49  thf(fact_1199_add__less__zeroD,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.49          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_less_zeroD
% 0.29/0.49  thf(fact_1200_add__less__zeroD,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ X4 @ Y ) @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 0.29/0.49          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_less_zeroD
% 0.29/0.49  thf(fact_1201_add__less__zeroD,axiom,
% 0.29/0.49      ! [X4: int,Y: int] :
% 0.29/0.49        ( ( ord_less_int @ ( plus_plus_int @ X4 @ Y ) @ zero_zero_int )
% 0.29/0.49       => ( ( ord_less_int @ X4 @ zero_zero_int )
% 0.29/0.49          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % add_less_zeroD
% 0.29/0.49  thf(fact_1202_divide__le__0__iff,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.29/0.49        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.49          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.49            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_0_iff
% 0.29/0.49  thf(fact_1203_divide__le__0__iff,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.49        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.49          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.49            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_le_0_iff
% 0.29/0.49  thf(fact_1204_divide__right__mono,axiom,
% 0.29/0.49      ! [A: real,B: real,C: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.49         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_right_mono
% 0.29/0.49  thf(fact_1205_divide__right__mono,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.49         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_right_mono
% 0.29/0.49  thf(fact_1206_zero__le__divide__iff,axiom,
% 0.29/0.49      ! [A: real,B: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.49        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.49            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.49          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.49            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_divide_iff
% 0.29/0.49  thf(fact_1207_zero__le__divide__iff,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.49        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.49            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.29/0.49          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.49            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % zero_le_divide_iff
% 0.29/0.49  thf(fact_1208_divide__nonneg__nonneg,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.49         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonneg_nonneg
% 0.29/0.49  thf(fact_1209_divide__nonneg__nonneg,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.49         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonneg_nonneg
% 0.29/0.49  thf(fact_1210_divide__nonneg__nonpos,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.29/0.49         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonneg_nonpos
% 0.29/0.49  thf(fact_1211_divide__nonneg__nonpos,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.49       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.29/0.49         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonneg_nonpos
% 0.29/0.49  thf(fact_1212_divide__nonpos__nonneg,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.49         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonpos_nonneg
% 0.29/0.49  thf(fact_1213_divide__nonpos__nonneg,axiom,
% 0.29/0.49      ! [X4: rat,Y: rat] :
% 0.29/0.49        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.49       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.49         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % divide_nonpos_nonneg
% 0.29/0.49  thf(fact_1214_divide__nonpos__nonpos,axiom,
% 0.29/0.49      ! [X4: real,Y: real] :
% 0.29/0.49        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.49       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.29/0.49         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_nonpos_nonpos
% 0.29/0.50  thf(fact_1215_divide__nonpos__nonpos,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.50       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_nonpos_nonpos
% 0.29/0.50  thf(fact_1216_divide__right__mono__neg,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.50         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_right_mono_neg
% 0.29/0.50  thf(fact_1217_divide__right__mono__neg,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_right_mono_neg
% 0.29/0.50  thf(fact_1218_power__mono,axiom,
% 0.29/0.50      ! [A: real,B: real,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.50         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mono
% 0.29/0.50  thf(fact_1219_power__mono,axiom,
% 0.29/0.50      ! [A: rat,B: rat,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.50         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mono
% 0.29/0.50  thf(fact_1220_power__mono,axiom,
% 0.29/0.50      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.50         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mono
% 0.29/0.50  thf(fact_1221_power__mono,axiom,
% 0.29/0.50      ! [A: int,B: int,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.50         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % power_mono
% 0.29/0.50  thf(fact_1222_zero__le__power,axiom,
% 0.29/0.50      ! [A: real,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_le_power
% 0.29/0.50  thf(fact_1223_zero__le__power,axiom,
% 0.29/0.50      ! [A: rat,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_le_power
% 0.29/0.50  thf(fact_1224_zero__le__power,axiom,
% 0.29/0.50      ! [A: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_le_power
% 0.29/0.50  thf(fact_1225_zero__le__power,axiom,
% 0.29/0.50      ! [A: int,N2: nat] :
% 0.29/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_le_power
% 0.29/0.50  thf(fact_1226_divide__strict__right__mono__neg,axiom,
% 0.29/0.50      ! [B: rat,A: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ B @ A )
% 0.29/0.50       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_strict_right_mono_neg
% 0.29/0.50  thf(fact_1227_divide__strict__right__mono__neg,axiom,
% 0.29/0.50      ! [B: real,A: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ B @ A )
% 0.29/0.50       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.50         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_strict_right_mono_neg
% 0.29/0.50  thf(fact_1228_divide__strict__right__mono,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.50         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_strict_right_mono
% 0.29/0.50  thf(fact_1229_divide__strict__right__mono,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.50         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_strict_right_mono
% 0.29/0.50  thf(fact_1230_zero__less__divide__iff,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.50        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.50            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.29/0.50          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.50            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_divide_iff
% 0.29/0.50  thf(fact_1231_zero__less__divide__iff,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.50        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.50            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.29/0.50          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.50            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_divide_iff
% 0.29/0.50  thf(fact_1232_divide__less__cancel,axiom,
% 0.29/0.50      ! [A: rat,C: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.50        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.50           => ( ord_less_rat @ A @ B ) )
% 0.29/0.50          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.50           => ( ord_less_rat @ B @ A ) )
% 0.29/0.50          & ( C != zero_zero_rat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_less_cancel
% 0.29/0.50  thf(fact_1233_divide__less__cancel,axiom,
% 0.29/0.50      ! [A: real,C: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.50        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.50           => ( ord_less_real @ A @ B ) )
% 0.29/0.50          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.50           => ( ord_less_real @ B @ A ) )
% 0.29/0.50          & ( C != zero_zero_real ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_less_cancel
% 0.29/0.50  thf(fact_1234_divide__less__0__iff,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.50        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.50            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.29/0.50          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.50            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_less_0_iff
% 0.29/0.50  thf(fact_1235_divide__less__0__iff,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.29/0.50        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.50            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.29/0.50          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.50            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_less_0_iff
% 0.29/0.50  thf(fact_1236_divide__pos__pos,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.50       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.50         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_pos_pos
% 0.29/0.50  thf(fact_1237_divide__pos__pos,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.50       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.50         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_pos_pos
% 0.29/0.50  thf(fact_1238_divide__pos__neg,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.50       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_pos_neg
% 0.29/0.50  thf(fact_1239_divide__pos__neg,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.50       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.29/0.50         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_pos_neg
% 0.29/0.50  thf(fact_1240_divide__neg__pos,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 0.29/0.50       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.50         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_neg_pos
% 0.29/0.50  thf(fact_1241_divide__neg__pos,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.50       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.50         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_neg_pos
% 0.29/0.50  thf(fact_1242_divide__neg__neg,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 0.29/0.50       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_neg_neg
% 0.29/0.50  thf(fact_1243_divide__neg__neg,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.50       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.29/0.50         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % divide_neg_neg
% 0.29/0.50  thf(fact_1244_zero__less__power,axiom,
% 0.29/0.50      ! [A: real,N2: nat] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_power
% 0.29/0.50  thf(fact_1245_zero__less__power,axiom,
% 0.29/0.50      ! [A: rat,N2: nat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_power
% 0.29/0.50  thf(fact_1246_zero__less__power,axiom,
% 0.29/0.50      ! [A: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_power
% 0.29/0.50  thf(fact_1247_zero__less__power,axiom,
% 0.29/0.50      ! [A: int,N2: nat] :
% 0.29/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % zero_less_power
% 0.29/0.50  thf(fact_1248_right__inverse__eq,axiom,
% 0.29/0.50      ! [B: rat,A: rat] :
% 0.29/0.50        ( ( B != zero_zero_rat )
% 0.29/0.50       => ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.50            = one_one_rat )
% 0.29/0.50          = ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % right_inverse_eq
% 0.29/0.50  thf(fact_1249_right__inverse__eq,axiom,
% 0.29/0.50      ! [B: real,A: real] :
% 0.29/0.50        ( ( B != zero_zero_real )
% 0.29/0.50       => ( ( ( divide_divide_real @ A @ B )
% 0.29/0.50            = one_one_real )
% 0.29/0.50          = ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % right_inverse_eq
% 0.29/0.50  thf(fact_1250_right__inverse__eq,axiom,
% 0.29/0.50      ! [B: complex,A: complex] :
% 0.29/0.50        ( ( B != zero_zero_complex )
% 0.29/0.50       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.50            = one_one_complex )
% 0.29/0.50          = ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % right_inverse_eq
% 0.29/0.50  thf(fact_1251_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.50       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.29/0.50  thf(fact_1252_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.29/0.50  thf(fact_1253_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.29/0.50  thf(fact_1254_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.29/0.50      ! [B: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.50       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.29/0.50  thf(fact_1255_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.29/0.50      ! [B: int,A: int] :
% 0.29/0.50        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.50       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.29/0.50  thf(fact_1256_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.29/0.50      ! [B: code_integer,A: code_integer] :
% 0.29/0.50        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.50       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.29/0.50  thf(fact_1257_power__0,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.29/0.50        = one_one_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % power_0
% 0.29/0.50  thf(fact_1258_power__0,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.29/0.50        = one_one_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % power_0
% 0.29/0.50  thf(fact_1259_power__0,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ( ( power_power_real @ A @ zero_zero_nat )
% 0.29/0.50        = one_one_real ) ).
% 0.29/0.50  
% 0.29/0.50  % power_0
% 0.29/0.50  thf(fact_1260_power__0,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ( ( power_power_int @ A @ zero_zero_nat )
% 0.29/0.50        = one_one_int ) ).
% 0.29/0.50  
% 0.29/0.50  % power_0
% 0.29/0.50  thf(fact_1261_power__0,axiom,
% 0.29/0.50      ! [A: complex] :
% 0.29/0.50        ( ( power_power_complex @ A @ zero_zero_nat )
% 0.29/0.50        = one_one_complex ) ).
% 0.29/0.50  
% 0.29/0.50  % power_0
% 0.29/0.50  thf(fact_1262_mod__eq__self__iff__div__eq__0,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ( modulo_modulo_nat @ A @ B )
% 0.29/0.50          = A )
% 0.29/0.50        = ( ( divide_divide_nat @ A @ B )
% 0.29/0.50          = zero_zero_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mod_eq_self_iff_div_eq_0
% 0.29/0.50  thf(fact_1263_mod__eq__self__iff__div__eq__0,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.50          = A )
% 0.29/0.50        = ( ( divide_divide_int @ A @ B )
% 0.29/0.50          = zero_zero_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mod_eq_self_iff_div_eq_0
% 0.29/0.50  thf(fact_1264_mod__eq__self__iff__div__eq__0,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.50          = A )
% 0.29/0.50        = ( ( divide6298287555418463151nteger @ A @ B )
% 0.29/0.50          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mod_eq_self_iff_div_eq_0
% 0.29/0.50  thf(fact_1265_Ex__less__Suc2,axiom,
% 0.29/0.50      ! [N2: nat,P: nat > $o] :
% 0.29/0.50        ( ( ? [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/0.50              & ( P @ I3 ) ) )
% 0.29/0.50        = ( ( P @ zero_zero_nat )
% 0.29/0.50          | ? [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ N2 )
% 0.29/0.50              & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Ex_less_Suc2
% 0.29/0.50  thf(fact_1266_gr0__conv__Suc,axiom,
% 0.29/0.50      ! [N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.50        = ( ? [M6: nat] :
% 0.29/0.50              ( N2
% 0.29/0.50              = ( suc @ M6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % gr0_conv_Suc
% 0.29/0.50  thf(fact_1267_All__less__Suc2,axiom,
% 0.29/0.50      ! [N2: nat,P: nat > $o] :
% 0.29/0.50        ( ( ! [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/0.50             => ( P @ I3 ) ) )
% 0.29/0.50        = ( ( P @ zero_zero_nat )
% 0.29/0.50          & ! [I3: nat] :
% 0.29/0.50              ( ( ord_less_nat @ I3 @ N2 )
% 0.29/0.50             => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % All_less_Suc2
% 0.29/0.50  thf(fact_1268_gr0__implies__Suc,axiom,
% 0.29/0.50      ! [N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.50       => ? [M5: nat] :
% 0.29/0.50            ( N2
% 0.29/0.50            = ( suc @ M5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % gr0_implies_Suc
% 0.29/0.50  thf(fact_1269_less__Suc__eq__0__disj,axiom,
% 0.29/0.50      ! [M: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.29/0.50        = ( ( M = zero_zero_nat )
% 0.29/0.50          | ? [J3: nat] :
% 0.29/0.50              ( ( M
% 0.29/0.50                = ( suc @ J3 ) )
% 0.29/0.50              & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_Suc_eq_0_disj
% 0.29/0.50  thf(fact_1270_add__is__1,axiom,
% 0.29/0.50      ! [M: nat,N2: nat] :
% 0.29/0.50        ( ( ( plus_plus_nat @ M @ N2 )
% 0.29/0.50          = ( suc @ zero_zero_nat ) )
% 0.29/0.50        = ( ( ( M
% 0.29/0.50              = ( suc @ zero_zero_nat ) )
% 0.29/0.50            & ( N2 = zero_zero_nat ) )
% 0.29/0.50          | ( ( M = zero_zero_nat )
% 0.29/0.50            & ( N2
% 0.29/0.50              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_is_1
% 0.29/0.50  thf(fact_1271_one__is__add,axiom,
% 0.29/0.50      ! [M: nat,N2: nat] :
% 0.29/0.50        ( ( ( suc @ zero_zero_nat )
% 0.29/0.50          = ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.50        = ( ( ( M
% 0.29/0.50              = ( suc @ zero_zero_nat ) )
% 0.29/0.50            & ( N2 = zero_zero_nat ) )
% 0.29/0.50          | ( ( M = zero_zero_nat )
% 0.29/0.50            & ( N2
% 0.29/0.50              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_is_add
% 0.29/0.50  thf(fact_1272_ex__least__nat__le,axiom,
% 0.29/0.50      ! [P: nat > $o,N2: nat] :
% 0.29/0.50        ( ( P @ N2 )
% 0.29/0.50       => ( ~ ( P @ zero_zero_nat )
% 0.29/0.50         => ? [K2: nat] :
% 0.29/0.50              ( ( ord_less_eq_nat @ K2 @ N2 )
% 0.29/0.50              & ! [I: nat] :
% 0.29/0.50                  ( ( ord_less_nat @ I @ K2 )
% 0.29/0.50                 => ~ ( P @ I ) )
% 0.29/0.50              & ( P @ K2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_least_nat_le
% 0.29/0.50  thf(fact_1273_less__imp__add__positive,axiom,
% 0.29/0.50      ! [I2: nat,J: nat] :
% 0.29/0.50        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.50       => ? [K2: nat] :
% 0.29/0.50            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.29/0.50            & ( ( plus_plus_nat @ I2 @ K2 )
% 0.29/0.50              = J ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_add_positive
% 0.29/0.50  thf(fact_1274_div__less__mono,axiom,
% 0.29/0.50      ! [A2: nat,B3: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A2 @ B3 )
% 0.29/0.50       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.50         => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 0.29/0.50              = zero_zero_nat )
% 0.29/0.50           => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 0.29/0.50                = zero_zero_nat )
% 0.29/0.50             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % div_less_mono
% 0.29/0.50  thf(fact_1275_One__nat__def,axiom,
% 0.29/0.50      ( one_one_nat
% 0.29/0.50      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % One_nat_def
% 0.29/0.50  thf(fact_1276_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.29/0.50      ! [M: nat,N2: nat] :
% 0.29/0.50        ( ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.50          = zero_zero_nat )
% 0.29/0.50        = ( ( ord_less_nat @ M @ N2 )
% 0.29/0.50          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Euclidean_Division.div_eq_0_iff
% 0.29/0.50  thf(fact_1277_nat__power__less__imp__less,axiom,
% 0.29/0.50      ! [I2: nat,M: nat,N2: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 0.29/0.50       => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 0.29/0.50         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nat_power_less_imp_less
% 0.29/0.50  thf(fact_1278_mod__Suc,axiom,
% 0.29/0.50      ! [M: nat,N2: nat] :
% 0.29/0.50        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.50            = N2 )
% 0.29/0.50         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 0.29/0.50            = zero_zero_nat ) )
% 0.29/0.50        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.50           != N2 )
% 0.29/0.50         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 0.29/0.50            = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mod_Suc
% 0.29/0.50  thf(fact_1279_mod__less__divisor,axiom,
% 0.29/0.50      ! [N2: nat,M: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.50       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mod_less_divisor
% 0.29/0.50  thf(fact_1280_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.29/0.50      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.29/0.50        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 0.29/0.50  
% 0.29/0.50  % VEBT_internal.naive_member.simps(2)
% 0.29/0.50  thf(fact_1281_order__antisym__conv,axiom,
% 0.29/0.50      ! [Y: set_int,X4: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ Y @ X4 )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym_conv
% 0.29/0.50  thf(fact_1282_order__antisym__conv,axiom,
% 0.29/0.50      ! [Y: rat,X4: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.50       => ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym_conv
% 0.29/0.50  thf(fact_1283_order__antisym__conv,axiom,
% 0.29/0.50      ! [Y: num,X4: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ Y @ X4 )
% 0.29/0.50       => ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym_conv
% 0.29/0.50  thf(fact_1284_order__antisym__conv,axiom,
% 0.29/0.50      ! [Y: nat,X4: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.50       => ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym_conv
% 0.29/0.50  thf(fact_1285_order__antisym__conv,axiom,
% 0.29/0.50      ! [Y: int,X4: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ Y @ X4 )
% 0.29/0.50       => ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym_conv
% 0.29/0.50  thf(fact_1286_linorder__le__cases,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ~ ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50       => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_le_cases
% 0.29/0.50  thf(fact_1287_linorder__le__cases,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ~ ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50       => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_le_cases
% 0.29/0.50  thf(fact_1288_linorder__le__cases,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ~ ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50       => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_le_cases
% 0.29/0.50  thf(fact_1289_linorder__le__cases,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ~ ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50       => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_le_cases
% 0.29/0.50  thf(fact_1290_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1291_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1292_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1293_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1294_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1295_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1296_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1297_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1298_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1299_ord__le__eq__subst,axiom,
% 0.29/0.50      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_subst
% 0.29/0.50  thf(fact_1300_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1301_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1302_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1303_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1304_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1305_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: num,F: num > num,B: num,C: num] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1306_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1307_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: int,F: num > int,B: num,C: num] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1308_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1309_ord__eq__le__subst,axiom,
% 0.29/0.50      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_subst
% 0.29/0.50  thf(fact_1310_linorder__linear,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50        | ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_linear
% 0.29/0.50  thf(fact_1311_linorder__linear,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50        | ( ord_less_eq_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_linear
% 0.29/0.50  thf(fact_1312_linorder__linear,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50        | ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_linear
% 0.29/0.50  thf(fact_1313_linorder__linear,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50        | ( ord_less_eq_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_linear
% 0.29/0.50  thf(fact_1314_verit__la__disequality,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50        | ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.50        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_la_disequality
% 0.29/0.50  thf(fact_1315_verit__la__disequality,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50        | ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.50        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_la_disequality
% 0.29/0.50  thf(fact_1316_verit__la__disequality,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50        | ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.50        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_la_disequality
% 0.29/0.50  thf(fact_1317_verit__la__disequality,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50        | ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.50        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_la_disequality
% 0.29/0.50  thf(fact_1318_order__eq__refl,axiom,
% 0.29/0.50      ! [X4: set_int,Y: set_int] :
% 0.29/0.50        ( ( X4 = Y )
% 0.29/0.50       => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_eq_refl
% 0.29/0.50  thf(fact_1319_order__eq__refl,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( X4 = Y )
% 0.29/0.50       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_eq_refl
% 0.29/0.50  thf(fact_1320_order__eq__refl,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( X4 = Y )
% 0.29/0.50       => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_eq_refl
% 0.29/0.50  thf(fact_1321_order__eq__refl,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( X4 = Y )
% 0.29/0.50       => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_eq_refl
% 0.29/0.50  thf(fact_1322_order__eq__refl,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( X4 = Y )
% 0.29/0.50       => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_eq_refl
% 0.29/0.50  thf(fact_1323_order__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1324_order__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1325_order__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1326_order__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1327_order__subst2,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1328_order__subst2,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1329_order__subst2,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1330_order__subst2,axiom,
% 0.29/0.50      ! [A: num,B: num,F: num > int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1331_order__subst2,axiom,
% 0.29/0.50      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1332_order__subst2,axiom,
% 0.29/0.50      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst2
% 0.29/0.50  thf(fact_1333_order__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1334_order__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1335_order__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1336_order__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.50         => ( ! [X5: int,Y3: int] :
% 0.29/0.50                ( ( ord_less_eq_int @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1337_order__subst1,axiom,
% 0.29/0.50      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1338_order__subst1,axiom,
% 0.29/0.50      ! [A: num,F: num > num,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1339_order__subst1,axiom,
% 0.29/0.50      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1340_order__subst1,axiom,
% 0.29/0.50      ! [A: num,F: int > num,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.50         => ( ! [X5: int,Y3: int] :
% 0.29/0.50                ( ( ord_less_eq_int @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1341_order__subst1,axiom,
% 0.29/0.50      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1342_order__subst1,axiom,
% 0.29/0.50      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_subst1
% 0.29/0.50  thf(fact_1343_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: set_int,B2: set_int] :
% 0.29/0.50            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.29/0.50            & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Orderings.order_eq_iff
% 0.29/0.50  thf(fact_1344_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.50            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.29/0.50            & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Orderings.order_eq_iff
% 0.29/0.50  thf(fact_1345_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: num,B2: num] :
% 0.29/0.50            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.29/0.50            & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Orderings.order_eq_iff
% 0.29/0.50  thf(fact_1346_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.50            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.29/0.50            & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Orderings.order_eq_iff
% 0.29/0.50  thf(fact_1347_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: int,B2: int] :
% 0.29/0.50            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.29/0.50            & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Orderings.order_eq_iff
% 0.29/0.50  thf(fact_1348_antisym,axiom,
% 0.29/0.50      ! [A: set_int,B: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym
% 0.29/0.50  thf(fact_1349_antisym,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym
% 0.29/0.50  thf(fact_1350_antisym,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ A )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym
% 0.29/0.50  thf(fact_1351_antisym,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym
% 0.29/0.50  thf(fact_1352_antisym,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym
% 0.29/0.50  thf(fact_1353_dual__order_Otrans,axiom,
% 0.29/0.50      ! [B: set_int,A: set_int,C: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ C @ B )
% 0.29/0.50         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.trans
% 0.29/0.50  thf(fact_1354_dual__order_Otrans,axiom,
% 0.29/0.50      ! [B: rat,A: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.50         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.trans
% 0.29/0.50  thf(fact_1355_dual__order_Otrans,axiom,
% 0.29/0.50      ! [B: num,A: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_num @ C @ B )
% 0.29/0.50         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.trans
% 0.29/0.50  thf(fact_1356_dual__order_Otrans,axiom,
% 0.29/0.50      ! [B: nat,A: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.50         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.trans
% 0.29/0.50  thf(fact_1357_dual__order_Otrans,axiom,
% 0.29/0.50      ! [B: int,A: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.50         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.trans
% 0.29/0.50  thf(fact_1358_dual__order_Oantisym,axiom,
% 0.29/0.50      ! [B: set_int,A: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.antisym
% 0.29/0.50  thf(fact_1359_dual__order_Oantisym,axiom,
% 0.29/0.50      ! [B: rat,A: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.antisym
% 0.29/0.50  thf(fact_1360_dual__order_Oantisym,axiom,
% 0.29/0.50      ! [B: num,A: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.antisym
% 0.29/0.50  thf(fact_1361_dual__order_Oantisym,axiom,
% 0.29/0.50      ! [B: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.antisym
% 0.29/0.50  thf(fact_1362_dual__order_Oantisym,axiom,
% 0.29/0.50      ! [B: int,A: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.50       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.50         => ( A = B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.antisym
% 0.29/0.50  thf(fact_1363_dual__order_Oeq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: set_int,B2: set_int] :
% 0.29/0.50            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.29/0.50            & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.eq_iff
% 0.29/0.50  thf(fact_1364_dual__order_Oeq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.50            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.29/0.50            & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.eq_iff
% 0.29/0.50  thf(fact_1365_dual__order_Oeq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: num,B2: num] :
% 0.29/0.50            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.29/0.50            & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.eq_iff
% 0.29/0.50  thf(fact_1366_dual__order_Oeq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.50            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.29/0.50            & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.eq_iff
% 0.29/0.50  thf(fact_1367_dual__order_Oeq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [A3: int,B2: int] :
% 0.29/0.50            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.29/0.50            & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.eq_iff
% 0.29/0.50  thf(fact_1368_linorder__wlog,axiom,
% 0.29/0.50      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.50        ( ! [A5: rat,B5: rat] :
% 0.29/0.50            ( ( ord_less_eq_rat @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: rat,B5: rat] :
% 0.29/0.50              ( ( P @ B5 @ A5 )
% 0.29/0.50             => ( P @ A5 @ B5 ) )
% 0.29/0.50         => ( P @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_wlog
% 0.29/0.50  thf(fact_1369_linorder__wlog,axiom,
% 0.29/0.50      ! [P: num > num > $o,A: num,B: num] :
% 0.29/0.50        ( ! [A5: num,B5: num] :
% 0.29/0.50            ( ( ord_less_eq_num @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: num,B5: num] :
% 0.29/0.50              ( ( P @ B5 @ A5 )
% 0.29/0.50             => ( P @ A5 @ B5 ) )
% 0.29/0.50         => ( P @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_wlog
% 0.29/0.50  thf(fact_1370_linorder__wlog,axiom,
% 0.29/0.50      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.50        ( ! [A5: nat,B5: nat] :
% 0.29/0.50            ( ( ord_less_eq_nat @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: nat,B5: nat] :
% 0.29/0.50              ( ( P @ B5 @ A5 )
% 0.29/0.50             => ( P @ A5 @ B5 ) )
% 0.29/0.50         => ( P @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_wlog
% 0.29/0.50  thf(fact_1371_linorder__wlog,axiom,
% 0.29/0.50      ! [P: int > int > $o,A: int,B: int] :
% 0.29/0.50        ( ! [A5: int,B5: int] :
% 0.29/0.50            ( ( ord_less_eq_int @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: int,B5: int] :
% 0.29/0.50              ( ( P @ B5 @ A5 )
% 0.29/0.50             => ( P @ A5 @ B5 ) )
% 0.29/0.50         => ( P @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_wlog
% 0.29/0.50  thf(fact_1372_order__trans,axiom,
% 0.29/0.50      ! [X4: set_int,Y: set_int,Z: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.29/0.50         => ( ord_less_eq_set_int @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_trans
% 0.29/0.50  thf(fact_1373_order__trans,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.50         => ( ord_less_eq_rat @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_trans
% 0.29/0.50  thf(fact_1374_order__trans,axiom,
% 0.29/0.50      ! [X4: num,Y: num,Z: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.50         => ( ord_less_eq_num @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_trans
% 0.29/0.50  thf(fact_1375_order__trans,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat,Z: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.50         => ( ord_less_eq_nat @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_trans
% 0.29/0.50  thf(fact_1376_order__trans,axiom,
% 0.29/0.50      ! [X4: int,Y: int,Z: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.50         => ( ord_less_eq_int @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_trans
% 0.29/0.50  thf(fact_1377_order_Otrans,axiom,
% 0.29/0.50      ! [A: set_int,B: set_int,C: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ B @ C )
% 0.29/0.50         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.trans
% 0.29/0.50  thf(fact_1378_order_Otrans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.trans
% 0.29/0.50  thf(fact_1379_order_Otrans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.trans
% 0.29/0.50  thf(fact_1380_order_Otrans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.trans
% 0.29/0.50  thf(fact_1381_order_Otrans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.trans
% 0.29/0.50  thf(fact_1382_order__antisym,axiom,
% 0.29/0.50      ! [X4: set_int,Y: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ Y @ X4 )
% 0.29/0.50         => ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym
% 0.29/0.50  thf(fact_1383_order__antisym,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.50         => ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym
% 0.29/0.50  thf(fact_1384_order__antisym,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_num @ Y @ X4 )
% 0.29/0.50         => ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym
% 0.29/0.50  thf(fact_1385_order__antisym,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.50         => ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym
% 0.29/0.50  thf(fact_1386_order__antisym,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_eq_int @ Y @ X4 )
% 0.29/0.50         => ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_antisym
% 0.29/0.50  thf(fact_1387_ord__le__eq__trans,axiom,
% 0.29/0.50      ! [A: set_int,B: set_int,C: set_int] :
% 0.29/0.50        ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_trans
% 0.29/0.50  thf(fact_1388_ord__le__eq__trans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_trans
% 0.29/0.50  thf(fact_1389_ord__le__eq__trans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_trans
% 0.29/0.50  thf(fact_1390_ord__le__eq__trans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_trans
% 0.29/0.50  thf(fact_1391_ord__le__eq__trans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_le_eq_trans
% 0.29/0.50  thf(fact_1392_ord__eq__le__trans,axiom,
% 0.29/0.50      ! [A: set_int,B: set_int,C: set_int] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_eq_set_int @ B @ C )
% 0.29/0.50         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_trans
% 0.29/0.50  thf(fact_1393_ord__eq__le__trans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_trans
% 0.29/0.50  thf(fact_1394_ord__eq__le__trans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_trans
% 0.29/0.50  thf(fact_1395_ord__eq__le__trans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_trans
% 0.29/0.50  thf(fact_1396_ord__eq__le__trans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_le_trans
% 0.29/0.50  thf(fact_1397_order__class_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [X: set_int,Y5: set_int] :
% 0.29/0.50            ( ( ord_less_eq_set_int @ X @ Y5 )
% 0.29/0.50            & ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_class.order_eq_iff
% 0.29/0.50  thf(fact_1398_order__class_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [X: rat,Y5: rat] :
% 0.29/0.50            ( ( ord_less_eq_rat @ X @ Y5 )
% 0.29/0.50            & ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_class.order_eq_iff
% 0.29/0.50  thf(fact_1399_order__class_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [X: num,Y5: num] :
% 0.29/0.50            ( ( ord_less_eq_num @ X @ Y5 )
% 0.29/0.50            & ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_class.order_eq_iff
% 0.29/0.50  thf(fact_1400_order__class_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [X: nat,Y5: nat] :
% 0.29/0.50            ( ( ord_less_eq_nat @ X @ Y5 )
% 0.29/0.50            & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_class.order_eq_iff
% 0.29/0.50  thf(fact_1401_order__class_Oorder__eq__iff,axiom,
% 0.29/0.50      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.50      = ( ^ [X: int,Y5: int] :
% 0.29/0.50            ( ( ord_less_eq_int @ X @ Y5 )
% 0.29/0.50            & ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_class.order_eq_iff
% 0.29/0.50  thf(fact_1402_le__cases3,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.50        ( ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.50         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 0.29/0.50       => ( ( ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.50           => ~ ( ord_less_eq_rat @ X4 @ Z ) )
% 0.29/0.50         => ( ( ( ord_less_eq_rat @ X4 @ Z )
% 0.29/0.50             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 0.29/0.50           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 0.29/0.50               => ~ ( ord_less_eq_rat @ Y @ X4 ) )
% 0.29/0.50             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.50                 => ~ ( ord_less_eq_rat @ Z @ X4 ) )
% 0.29/0.50               => ~ ( ( ord_less_eq_rat @ Z @ X4 )
% 0.29/0.50                   => ~ ( ord_less_eq_rat @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_cases3
% 0.29/0.50  thf(fact_1403_le__cases3,axiom,
% 0.29/0.50      ! [X4: num,Y: num,Z: num] :
% 0.29/0.50        ( ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.50         => ~ ( ord_less_eq_num @ Y @ Z ) )
% 0.29/0.50       => ( ( ( ord_less_eq_num @ Y @ X4 )
% 0.29/0.50           => ~ ( ord_less_eq_num @ X4 @ Z ) )
% 0.29/0.50         => ( ( ( ord_less_eq_num @ X4 @ Z )
% 0.29/0.50             => ~ ( ord_less_eq_num @ Z @ Y ) )
% 0.29/0.50           => ( ( ( ord_less_eq_num @ Z @ Y )
% 0.29/0.50               => ~ ( ord_less_eq_num @ Y @ X4 ) )
% 0.29/0.50             => ( ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.50                 => ~ ( ord_less_eq_num @ Z @ X4 ) )
% 0.29/0.50               => ~ ( ( ord_less_eq_num @ Z @ X4 )
% 0.29/0.50                   => ~ ( ord_less_eq_num @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_cases3
% 0.29/0.50  thf(fact_1404_le__cases3,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat,Z: nat] :
% 0.29/0.50        ( ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.50         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.29/0.50       => ( ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.50           => ~ ( ord_less_eq_nat @ X4 @ Z ) )
% 0.29/0.50         => ( ( ( ord_less_eq_nat @ X4 @ Z )
% 0.29/0.50             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.29/0.50           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.29/0.50               => ~ ( ord_less_eq_nat @ Y @ X4 ) )
% 0.29/0.50             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.50                 => ~ ( ord_less_eq_nat @ Z @ X4 ) )
% 0.29/0.50               => ~ ( ( ord_less_eq_nat @ Z @ X4 )
% 0.29/0.50                   => ~ ( ord_less_eq_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_cases3
% 0.29/0.50  thf(fact_1405_le__cases3,axiom,
% 0.29/0.50      ! [X4: int,Y: int,Z: int] :
% 0.29/0.50        ( ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.50         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 0.29/0.50       => ( ( ( ord_less_eq_int @ Y @ X4 )
% 0.29/0.50           => ~ ( ord_less_eq_int @ X4 @ Z ) )
% 0.29/0.50         => ( ( ( ord_less_eq_int @ X4 @ Z )
% 0.29/0.50             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 0.29/0.50           => ( ( ( ord_less_eq_int @ Z @ Y )
% 0.29/0.50               => ~ ( ord_less_eq_int @ Y @ X4 ) )
% 0.29/0.50             => ( ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.50                 => ~ ( ord_less_eq_int @ Z @ X4 ) )
% 0.29/0.50               => ~ ( ( ord_less_eq_int @ Z @ X4 )
% 0.29/0.50                   => ~ ( ord_less_eq_int @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % le_cases3
% 0.29/0.50  thf(fact_1406_nle__le,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.50        = ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.50          & ( B != A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nle_le
% 0.29/0.50  thf(fact_1407_nle__le,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.29/0.50        = ( ( ord_less_eq_num @ B @ A )
% 0.29/0.50          & ( B != A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nle_le
% 0.29/0.50  thf(fact_1408_nle__le,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.29/0.50        = ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.50          & ( B != A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nle_le
% 0.29/0.50  thf(fact_1409_nle__le,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.29/0.50        = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.50          & ( B != A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % nle_le
% 0.29/0.50  thf(fact_1410_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.50      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(2)
% 0.29/0.50  thf(fact_1411_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.50      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(2)
% 0.29/0.50  thf(fact_1412_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.50      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(2)
% 0.29/0.50  thf(fact_1413_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.50      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(2)
% 0.29/0.50  thf(fact_1414_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.50      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(2)
% 0.29/0.50  thf(fact_1415_order__less__imp__not__less,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_less
% 0.29/0.50  thf(fact_1416_order__less__imp__not__less,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_less
% 0.29/0.50  thf(fact_1417_order__less__imp__not__less,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_less
% 0.29/0.50  thf(fact_1418_order__less__imp__not__less,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_less
% 0.29/0.50  thf(fact_1419_order__less__imp__not__less,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_less
% 0.29/0.50  thf(fact_1420_order__less__imp__not__eq2,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( Y != X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq2
% 0.29/0.50  thf(fact_1421_order__less__imp__not__eq2,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( Y != X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq2
% 0.29/0.50  thf(fact_1422_order__less__imp__not__eq2,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( Y != X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq2
% 0.29/0.50  thf(fact_1423_order__less__imp__not__eq2,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( Y != X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq2
% 0.29/0.50  thf(fact_1424_order__less__imp__not__eq2,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( Y != X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq2
% 0.29/0.50  thf(fact_1425_order__less__imp__not__eq,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq
% 0.29/0.50  thf(fact_1426_order__less__imp__not__eq,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq
% 0.29/0.50  thf(fact_1427_order__less__imp__not__eq,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq
% 0.29/0.50  thf(fact_1428_order__less__imp__not__eq,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq
% 0.29/0.50  thf(fact_1429_order__less__imp__not__eq,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_not_eq
% 0.29/0.50  thf(fact_1430_linorder__less__linear,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50        | ( X4 = Y )
% 0.29/0.50        | ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_linear
% 0.29/0.50  thf(fact_1431_linorder__less__linear,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50        | ( X4 = Y )
% 0.29/0.50        | ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_linear
% 0.29/0.50  thf(fact_1432_linorder__less__linear,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50        | ( X4 = Y )
% 0.29/0.50        | ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_linear
% 0.29/0.50  thf(fact_1433_linorder__less__linear,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50        | ( X4 = Y )
% 0.29/0.50        | ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_linear
% 0.29/0.50  thf(fact_1434_linorder__less__linear,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50        | ( X4 = Y )
% 0.29/0.50        | ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_linear
% 0.29/0.50  thf(fact_1435_order__less__imp__triv,axiom,
% 0.29/0.50      ! [X4: real,Y: real,P: $o] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.50         => P ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_triv
% 0.29/0.50  thf(fact_1436_order__less__imp__triv,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat,P: $o] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_rat @ Y @ X4 )
% 0.29/0.50         => P ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_triv
% 0.29/0.50  thf(fact_1437_order__less__imp__triv,axiom,
% 0.29/0.50      ! [X4: num,Y: num,P: $o] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_num @ Y @ X4 )
% 0.29/0.50         => P ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_triv
% 0.29/0.50  thf(fact_1438_order__less__imp__triv,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat,P: $o] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_nat @ Y @ X4 )
% 0.29/0.50         => P ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_triv
% 0.29/0.50  thf(fact_1439_order__less__imp__triv,axiom,
% 0.29/0.50      ! [X4: int,Y: int,P: $o] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_int @ Y @ X4 )
% 0.29/0.50         => P ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_imp_triv
% 0.29/0.50  thf(fact_1440_order__less__not__sym,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_not_sym
% 0.29/0.50  thf(fact_1441_order__less__not__sym,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_not_sym
% 0.29/0.50  thf(fact_1442_order__less__not__sym,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_not_sym
% 0.29/0.50  thf(fact_1443_order__less__not__sym,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_not_sym
% 0.29/0.50  thf(fact_1444_order__less__not__sym,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_not_sym
% 0.29/0.50  thf(fact_1445_order__less__subst2,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1446_order__less__subst2,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1447_order__less__subst2,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > num,C: num] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1448_order__less__subst2,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1449_order__less__subst2,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > int,C: int] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1450_order__less__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1451_order__less__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1452_order__less__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1453_order__less__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1454_order__less__subst2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst2
% 0.29/0.50  thf(fact_1455_order__less__subst1,axiom,
% 0.29/0.50      ! [A: real,F: real > real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1456_order__less__subst1,axiom,
% 0.29/0.50      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1457_order__less__subst1,axiom,
% 0.29/0.50      ! [A: real,F: num > real,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1458_order__less__subst1,axiom,
% 0.29/0.50      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1459_order__less__subst1,axiom,
% 0.29/0.50      ! [A: real,F: int > real,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_int @ B @ C )
% 0.29/0.50         => ( ! [X5: int,Y3: int] :
% 0.29/0.50                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1460_order__less__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1461_order__less__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1462_order__less__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_num @ B @ C )
% 0.29/0.50         => ( ! [X5: num,Y3: num] :
% 0.29/0.50                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1463_order__less__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_nat @ B @ C )
% 0.29/0.50         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.50                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1464_order__less__subst1,axiom,
% 0.29/0.50      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_int @ B @ C )
% 0.29/0.50         => ( ! [X5: int,Y3: int] :
% 0.29/0.50                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_subst1
% 0.29/0.50  thf(fact_1465_order__less__irrefl,axiom,
% 0.29/0.50      ! [X4: real] :
% 0.29/0.50        ~ ( ord_less_real @ X4 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_irrefl
% 0.29/0.50  thf(fact_1466_order__less__irrefl,axiom,
% 0.29/0.50      ! [X4: rat] :
% 0.29/0.50        ~ ( ord_less_rat @ X4 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_irrefl
% 0.29/0.50  thf(fact_1467_order__less__irrefl,axiom,
% 0.29/0.50      ! [X4: num] :
% 0.29/0.50        ~ ( ord_less_num @ X4 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_irrefl
% 0.29/0.50  thf(fact_1468_order__less__irrefl,axiom,
% 0.29/0.50      ! [X4: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ X4 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_irrefl
% 0.29/0.50  thf(fact_1469_order__less__irrefl,axiom,
% 0.29/0.50      ! [X4: int] :
% 0.29/0.50        ~ ( ord_less_int @ X4 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_irrefl
% 0.29/0.50  thf(fact_1470_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1471_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1472_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > num,C: num] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1473_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1474_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: real,B: real,F: real > int,C: int] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1475_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1476_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1477_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1478_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1479_ord__less__eq__subst,axiom,
% 0.29/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ( F @ B )
% 0.29/0.50            = C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_subst
% 0.29/0.50  thf(fact_1480_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: real,F: real > real,B: real,C: real] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1481_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1482_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: num,F: real > num,B: real,C: real] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1483_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: nat,F: real > nat,B: real,C: real] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1484_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: int,F: real > int,B: real,C: real] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ! [X5: real,Y3: real] :
% 0.29/0.50                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1485_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1486_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1487_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1488_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1489_ord__eq__less__subst,axiom,
% 0.29/0.50      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.29/0.50        ( ( A
% 0.29/0.50          = ( F @ B ) )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.50                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.50               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.50           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_subst
% 0.29/0.50  thf(fact_1490_order__less__trans,axiom,
% 0.29/0.50      ! [X4: real,Y: real,Z: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_real @ Y @ Z )
% 0.29/0.50         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_trans
% 0.29/0.50  thf(fact_1491_order__less__trans,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.50         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_trans
% 0.29/0.50  thf(fact_1492_order__less__trans,axiom,
% 0.29/0.50      ! [X4: num,Y: num,Z: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_num @ Y @ Z )
% 0.29/0.50         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_trans
% 0.29/0.50  thf(fact_1493_order__less__trans,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat,Z: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.50         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_trans
% 0.29/0.50  thf(fact_1494_order__less__trans,axiom,
% 0.29/0.50      ! [X4: int,Y: int,Z: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.50         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_trans
% 0.29/0.50  thf(fact_1495_order__less__asym_H,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym'
% 0.29/0.50  thf(fact_1496_order__less__asym_H,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym'
% 0.29/0.50  thf(fact_1497_order__less__asym_H,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( ord_less_num @ A @ B )
% 0.29/0.50       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym'
% 0.29/0.50  thf(fact_1498_order__less__asym_H,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A @ B )
% 0.29/0.50       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym'
% 0.29/0.50  thf(fact_1499_order__less__asym_H,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_int @ A @ B )
% 0.29/0.50       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym'
% 0.29/0.50  thf(fact_1500_linorder__neq__iff,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50        = ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50          | ( ord_less_real @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neq_iff
% 0.29/0.50  thf(fact_1501_linorder__neq__iff,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50        = ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50          | ( ord_less_rat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neq_iff
% 0.29/0.50  thf(fact_1502_linorder__neq__iff,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50        = ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50          | ( ord_less_num @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neq_iff
% 0.29/0.50  thf(fact_1503_linorder__neq__iff,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50        = ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50          | ( ord_less_nat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neq_iff
% 0.29/0.50  thf(fact_1504_linorder__neq__iff,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50        = ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50          | ( ord_less_int @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neq_iff
% 0.29/0.50  thf(fact_1505_order__less__asym,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym
% 0.29/0.50  thf(fact_1506_order__less__asym,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym
% 0.29/0.50  thf(fact_1507_order__less__asym,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym
% 0.29/0.50  thf(fact_1508_order__less__asym,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym
% 0.29/0.50  thf(fact_1509_order__less__asym,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order_less_asym
% 0.29/0.50  thf(fact_1510_linorder__neqE,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50       => ( ~ ( ord_less_real @ X4 @ Y )
% 0.29/0.50         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE
% 0.29/0.50  thf(fact_1511_linorder__neqE,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50       => ( ~ ( ord_less_rat @ X4 @ Y )
% 0.29/0.50         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE
% 0.29/0.50  thf(fact_1512_linorder__neqE,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50       => ( ~ ( ord_less_num @ X4 @ Y )
% 0.29/0.50         => ( ord_less_num @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE
% 0.29/0.50  thf(fact_1513_linorder__neqE,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50       => ( ~ ( ord_less_nat @ X4 @ Y )
% 0.29/0.50         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE
% 0.29/0.50  thf(fact_1514_linorder__neqE,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( X4 != Y )
% 0.29/0.50       => ( ~ ( ord_less_int @ X4 @ Y )
% 0.29/0.50         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_neqE
% 0.29/0.50  thf(fact_1515_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [B: real,A: real] :
% 0.29/0.50        ( ( ord_less_real @ B @ A )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1516_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [B: rat,A: rat] :
% 0.29/0.50        ( ( ord_less_rat @ B @ A )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1517_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [B: num,A: num] :
% 0.29/0.50        ( ( ord_less_num @ B @ A )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1518_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [B: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_nat @ B @ A )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1519_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [B: int,A: int] :
% 0.29/0.50        ( ( ord_less_int @ B @ A )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1520_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1521_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1522_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( ord_less_num @ A @ B )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1523_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A @ B )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1524_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_int @ A @ B )
% 0.29/0.50       => ( A != B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_implies_not_eq
% 0.29/0.50  thf(fact_1525_dual__order_Ostrict__trans,axiom,
% 0.29/0.50      ! [B: real,A: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ B @ A )
% 0.29/0.50       => ( ( ord_less_real @ C @ B )
% 0.29/0.50         => ( ord_less_real @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_trans
% 0.29/0.50  thf(fact_1526_dual__order_Ostrict__trans,axiom,
% 0.29/0.50      ! [B: rat,A: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ B @ A )
% 0.29/0.50       => ( ( ord_less_rat @ C @ B )
% 0.29/0.50         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_trans
% 0.29/0.50  thf(fact_1527_dual__order_Ostrict__trans,axiom,
% 0.29/0.50      ! [B: num,A: num,C: num] :
% 0.29/0.50        ( ( ord_less_num @ B @ A )
% 0.29/0.50       => ( ( ord_less_num @ C @ B )
% 0.29/0.50         => ( ord_less_num @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_trans
% 0.29/0.50  thf(fact_1528_dual__order_Ostrict__trans,axiom,
% 0.29/0.50      ! [B: nat,A: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_nat @ B @ A )
% 0.29/0.50       => ( ( ord_less_nat @ C @ B )
% 0.29/0.50         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_trans
% 0.29/0.50  thf(fact_1529_dual__order_Ostrict__trans,axiom,
% 0.29/0.50      ! [B: int,A: int,C: int] :
% 0.29/0.50        ( ( ord_less_int @ B @ A )
% 0.29/0.50       => ( ( ord_less_int @ C @ B )
% 0.29/0.50         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.strict_trans
% 0.29/0.50  thf(fact_1530_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 0.29/0.50        = ( ( ord_less_real @ Y @ X4 )
% 0.29/0.50          | ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_iff_gr_or_eq
% 0.29/0.50  thf(fact_1531_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 0.29/0.50        = ( ( ord_less_rat @ Y @ X4 )
% 0.29/0.50          | ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_iff_gr_or_eq
% 0.29/0.50  thf(fact_1532_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 0.29/0.50        = ( ( ord_less_num @ Y @ X4 )
% 0.29/0.50          | ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_iff_gr_or_eq
% 0.29/0.50  thf(fact_1533_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 0.29/0.50        = ( ( ord_less_nat @ Y @ X4 )
% 0.29/0.50          | ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_iff_gr_or_eq
% 0.29/0.50  thf(fact_1534_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 0.29/0.50        = ( ( ord_less_int @ Y @ X4 )
% 0.29/0.50          | ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % not_less_iff_gr_or_eq
% 0.29/0.50  thf(fact_1535_order_Ostrict__trans,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ord_less_real @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_trans
% 0.29/0.50  thf(fact_1536_order_Ostrict__trans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_trans
% 0.29/0.50  thf(fact_1537_order_Ostrict__trans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_num @ A @ B )
% 0.29/0.50       => ( ( ord_less_num @ B @ C )
% 0.29/0.50         => ( ord_less_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_trans
% 0.29/0.50  thf(fact_1538_order_Ostrict__trans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A @ B )
% 0.29/0.50       => ( ( ord_less_nat @ B @ C )
% 0.29/0.50         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_trans
% 0.29/0.50  thf(fact_1539_order_Ostrict__trans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_int @ A @ B )
% 0.29/0.50       => ( ( ord_less_int @ B @ C )
% 0.29/0.50         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.strict_trans
% 0.29/0.50  thf(fact_1540_linorder__less__wlog,axiom,
% 0.29/0.50      ! [P: real > real > $o,A: real,B: real] :
% 0.29/0.50        ( ! [A5: real,B5: real] :
% 0.29/0.50            ( ( ord_less_real @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 0.29/0.50         => ( ! [A5: real,B5: real] :
% 0.29/0.50                ( ( P @ B5 @ A5 )
% 0.29/0.50               => ( P @ A5 @ B5 ) )
% 0.29/0.50           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_wlog
% 0.29/0.50  thf(fact_1541_linorder__less__wlog,axiom,
% 0.29/0.50      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.50        ( ! [A5: rat,B5: rat] :
% 0.29/0.50            ( ( ord_less_rat @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 0.29/0.50         => ( ! [A5: rat,B5: rat] :
% 0.29/0.50                ( ( P @ B5 @ A5 )
% 0.29/0.50               => ( P @ A5 @ B5 ) )
% 0.29/0.50           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_wlog
% 0.29/0.50  thf(fact_1542_linorder__less__wlog,axiom,
% 0.29/0.50      ! [P: num > num > $o,A: num,B: num] :
% 0.29/0.50        ( ! [A5: num,B5: num] :
% 0.29/0.50            ( ( ord_less_num @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 0.29/0.50         => ( ! [A5: num,B5: num] :
% 0.29/0.50                ( ( P @ B5 @ A5 )
% 0.29/0.50               => ( P @ A5 @ B5 ) )
% 0.29/0.50           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_wlog
% 0.29/0.50  thf(fact_1543_linorder__less__wlog,axiom,
% 0.29/0.50      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.50        ( ! [A5: nat,B5: nat] :
% 0.29/0.50            ( ( ord_less_nat @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 0.29/0.50         => ( ! [A5: nat,B5: nat] :
% 0.29/0.50                ( ( P @ B5 @ A5 )
% 0.29/0.50               => ( P @ A5 @ B5 ) )
% 0.29/0.50           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_wlog
% 0.29/0.50  thf(fact_1544_linorder__less__wlog,axiom,
% 0.29/0.50      ! [P: int > int > $o,A: int,B: int] :
% 0.29/0.50        ( ! [A5: int,B5: int] :
% 0.29/0.50            ( ( ord_less_int @ A5 @ B5 )
% 0.29/0.50           => ( P @ A5 @ B5 ) )
% 0.29/0.50       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 0.29/0.50         => ( ! [A5: int,B5: int] :
% 0.29/0.50                ( ( P @ B5 @ A5 )
% 0.29/0.50               => ( P @ A5 @ B5 ) )
% 0.29/0.50           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_less_wlog
% 0.29/0.50  thf(fact_1545_exists__least__iff,axiom,
% 0.29/0.50      ( ( ^ [P3: nat > $o] :
% 0.29/0.50          ? [X6: nat] : ( P3 @ X6 ) )
% 0.29/0.50      = ( ^ [P4: nat > $o] :
% 0.29/0.50          ? [N: nat] :
% 0.29/0.50            ( ( P4 @ N )
% 0.29/0.50            & ! [M6: nat] :
% 0.29/0.50                ( ( ord_less_nat @ M6 @ N )
% 0.29/0.50               => ~ ( P4 @ M6 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % exists_least_iff
% 0.29/0.50  thf(fact_1546_dual__order_Oirrefl,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ~ ( ord_less_real @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.irrefl
% 0.29/0.50  thf(fact_1547_dual__order_Oirrefl,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ~ ( ord_less_rat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.irrefl
% 0.29/0.50  thf(fact_1548_dual__order_Oirrefl,axiom,
% 0.29/0.50      ! [A: num] :
% 0.29/0.50        ~ ( ord_less_num @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.irrefl
% 0.29/0.50  thf(fact_1549_dual__order_Oirrefl,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.irrefl
% 0.29/0.50  thf(fact_1550_dual__order_Oirrefl,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ~ ( ord_less_int @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.irrefl
% 0.29/0.50  thf(fact_1551_dual__order_Oasym,axiom,
% 0.29/0.50      ! [B: real,A: real] :
% 0.29/0.50        ( ( ord_less_real @ B @ A )
% 0.29/0.50       => ~ ( ord_less_real @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.asym
% 0.29/0.50  thf(fact_1552_dual__order_Oasym,axiom,
% 0.29/0.50      ! [B: rat,A: rat] :
% 0.29/0.50        ( ( ord_less_rat @ B @ A )
% 0.29/0.50       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.asym
% 0.29/0.50  thf(fact_1553_dual__order_Oasym,axiom,
% 0.29/0.50      ! [B: num,A: num] :
% 0.29/0.50        ( ( ord_less_num @ B @ A )
% 0.29/0.50       => ~ ( ord_less_num @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.asym
% 0.29/0.50  thf(fact_1554_dual__order_Oasym,axiom,
% 0.29/0.50      ! [B: nat,A: nat] :
% 0.29/0.50        ( ( ord_less_nat @ B @ A )
% 0.29/0.50       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.asym
% 0.29/0.50  thf(fact_1555_dual__order_Oasym,axiom,
% 0.29/0.50      ! [B: int,A: int] :
% 0.29/0.50        ( ( ord_less_int @ B @ A )
% 0.29/0.50       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dual_order.asym
% 0.29/0.50  thf(fact_1556_linorder__cases,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ~ ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( ( X4 != Y )
% 0.29/0.50         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_cases
% 0.29/0.50  thf(fact_1557_linorder__cases,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ~ ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( ( X4 != Y )
% 0.29/0.50         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_cases
% 0.29/0.50  thf(fact_1558_linorder__cases,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ~ ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( ( X4 != Y )
% 0.29/0.50         => ( ord_less_num @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_cases
% 0.29/0.50  thf(fact_1559_linorder__cases,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ~ ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( ( X4 != Y )
% 0.29/0.50         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_cases
% 0.29/0.50  thf(fact_1560_linorder__cases,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ~ ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( ( X4 != Y )
% 0.29/0.50         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % linorder_cases
% 0.29/0.50  thf(fact_1561_antisym__conv3,axiom,
% 0.29/0.50      ! [Y: real,X4: real] :
% 0.29/0.50        ( ~ ( ord_less_real @ Y @ X4 )
% 0.29/0.50       => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym_conv3
% 0.29/0.50  thf(fact_1562_antisym__conv3,axiom,
% 0.29/0.50      ! [Y: rat,X4: rat] :
% 0.29/0.50        ( ~ ( ord_less_rat @ Y @ X4 )
% 0.29/0.50       => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym_conv3
% 0.29/0.50  thf(fact_1563_antisym__conv3,axiom,
% 0.29/0.50      ! [Y: num,X4: num] :
% 0.29/0.50        ( ~ ( ord_less_num @ Y @ X4 )
% 0.29/0.50       => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym_conv3
% 0.29/0.50  thf(fact_1564_antisym__conv3,axiom,
% 0.29/0.50      ! [Y: nat,X4: nat] :
% 0.29/0.50        ( ~ ( ord_less_nat @ Y @ X4 )
% 0.29/0.50       => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym_conv3
% 0.29/0.50  thf(fact_1565_antisym__conv3,axiom,
% 0.29/0.50      ! [Y: int,X4: int] :
% 0.29/0.50        ( ~ ( ord_less_int @ Y @ X4 )
% 0.29/0.50       => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 0.29/0.50          = ( X4 = Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % antisym_conv3
% 0.29/0.50  thf(fact_1566_less__induct,axiom,
% 0.29/0.50      ! [P: nat > $o,A: nat] :
% 0.29/0.50        ( ! [X5: nat] :
% 0.29/0.50            ( ! [Y4: nat] :
% 0.29/0.50                ( ( ord_less_nat @ Y4 @ X5 )
% 0.29/0.50               => ( P @ Y4 ) )
% 0.29/0.50           => ( P @ X5 ) )
% 0.29/0.50       => ( P @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_induct
% 0.29/0.50  thf(fact_1567_ord__less__eq__trans,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_real @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_trans
% 0.29/0.50  thf(fact_1568_ord__less__eq__trans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_trans
% 0.29/0.50  thf(fact_1569_ord__less__eq__trans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( ord_less_num @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_trans
% 0.29/0.50  thf(fact_1570_ord__less__eq__trans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_trans
% 0.29/0.50  thf(fact_1571_ord__less__eq__trans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_int @ A @ B )
% 0.29/0.50       => ( ( B = C )
% 0.29/0.50         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_less_eq_trans
% 0.29/0.50  thf(fact_1572_ord__eq__less__trans,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ord_less_real @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_trans
% 0.29/0.50  thf(fact_1573_ord__eq__less__trans,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_trans
% 0.29/0.50  thf(fact_1574_ord__eq__less__trans,axiom,
% 0.29/0.50      ! [A: num,B: num,C: num] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_num @ B @ C )
% 0.29/0.50         => ( ord_less_num @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_trans
% 0.29/0.50  thf(fact_1575_ord__eq__less__trans,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_nat @ B @ C )
% 0.29/0.50         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_trans
% 0.29/0.50  thf(fact_1576_ord__eq__less__trans,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( A = B )
% 0.29/0.50       => ( ( ord_less_int @ B @ C )
% 0.29/0.50         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ord_eq_less_trans
% 0.29/0.50  thf(fact_1577_order_Oasym,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ B )
% 0.29/0.50       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.asym
% 0.29/0.50  thf(fact_1578_order_Oasym,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ A @ B )
% 0.29/0.50       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.asym
% 0.29/0.50  thf(fact_1579_order_Oasym,axiom,
% 0.29/0.50      ! [A: num,B: num] :
% 0.29/0.50        ( ( ord_less_num @ A @ B )
% 0.29/0.50       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.asym
% 0.29/0.50  thf(fact_1580_order_Oasym,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_nat @ A @ B )
% 0.29/0.50       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.asym
% 0.29/0.50  thf(fact_1581_order_Oasym,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_int @ A @ B )
% 0.29/0.50       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.50  
% 0.29/0.50  % order.asym
% 0.29/0.50  thf(fact_1582_less__imp__neq,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_neq
% 0.29/0.50  thf(fact_1583_less__imp__neq,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_neq
% 0.29/0.50  thf(fact_1584_less__imp__neq,axiom,
% 0.29/0.50      ! [X4: num,Y: num] :
% 0.29/0.50        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_neq
% 0.29/0.50  thf(fact_1585_less__imp__neq,axiom,
% 0.29/0.50      ! [X4: nat,Y: nat] :
% 0.29/0.50        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_neq
% 0.29/0.50  thf(fact_1586_less__imp__neq,axiom,
% 0.29/0.50      ! [X4: int,Y: int] :
% 0.29/0.50        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.50       => ( X4 != Y ) ) ).
% 0.29/0.50  
% 0.29/0.50  % less_imp_neq
% 0.29/0.50  thf(fact_1587_dense,axiom,
% 0.29/0.50      ! [X4: real,Y: real] :
% 0.29/0.50        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.50       => ? [Z2: real] :
% 0.29/0.50            ( ( ord_less_real @ X4 @ Z2 )
% 0.29/0.50            & ( ord_less_real @ Z2 @ Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dense
% 0.29/0.50  thf(fact_1588_dense,axiom,
% 0.29/0.50      ! [X4: rat,Y: rat] :
% 0.29/0.50        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.50       => ? [Z2: rat] :
% 0.29/0.50            ( ( ord_less_rat @ X4 @ Z2 )
% 0.29/0.50            & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % dense
% 0.29/0.50  thf(fact_1589_gt__ex,axiom,
% 0.29/0.50      ! [X4: real] :
% 0.29/0.50      ? [X_12: real] : ( ord_less_real @ X4 @ X_12 ) ).
% 0.29/0.50  
% 0.29/0.50  % gt_ex
% 0.29/0.50  thf(fact_1590_gt__ex,axiom,
% 0.29/0.50      ! [X4: rat] :
% 0.29/0.50      ? [X_12: rat] : ( ord_less_rat @ X4 @ X_12 ) ).
% 0.29/0.50  
% 0.29/0.50  % gt_ex
% 0.29/0.50  thf(fact_1591_gt__ex,axiom,
% 0.29/0.50      ! [X4: nat] :
% 0.29/0.50      ? [X_12: nat] : ( ord_less_nat @ X4 @ X_12 ) ).
% 0.29/0.50  
% 0.29/0.50  % gt_ex
% 0.29/0.50  thf(fact_1592_gt__ex,axiom,
% 0.29/0.50      ! [X4: int] :
% 0.29/0.50      ? [X_12: int] : ( ord_less_int @ X4 @ X_12 ) ).
% 0.29/0.50  
% 0.29/0.50  % gt_ex
% 0.29/0.50  thf(fact_1593_lt__ex,axiom,
% 0.29/0.50      ! [X4: real] :
% 0.29/0.50      ? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % lt_ex
% 0.29/0.50  thf(fact_1594_lt__ex,axiom,
% 0.29/0.50      ! [X4: rat] :
% 0.29/0.50      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % lt_ex
% 0.29/0.50  thf(fact_1595_lt__ex,axiom,
% 0.29/0.50      ! [X4: int] :
% 0.29/0.50      ? [Y3: int] : ( ord_less_int @ Y3 @ X4 ) ).
% 0.29/0.50  
% 0.29/0.50  % lt_ex
% 0.29/0.50  thf(fact_1596_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.50      ! [A: real] :
% 0.29/0.50        ~ ( ord_less_real @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(1)
% 0.29/0.50  thf(fact_1597_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.50      ! [A: rat] :
% 0.29/0.50        ~ ( ord_less_rat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(1)
% 0.29/0.50  thf(fact_1598_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.50      ! [A: num] :
% 0.29/0.50        ~ ( ord_less_num @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(1)
% 0.29/0.50  thf(fact_1599_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(1)
% 0.29/0.50  thf(fact_1600_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ~ ( ord_less_int @ A @ A ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_comp_simplify1(1)
% 0.29/0.50  thf(fact_1601_add__strict__increasing2,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ( ord_less_real @ B @ C )
% 0.29/0.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing2
% 0.29/0.50  thf(fact_1602_add__strict__increasing2,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ( ord_less_rat @ B @ C )
% 0.29/0.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing2
% 0.29/0.50  thf(fact_1603_add__strict__increasing2,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ( ord_less_nat @ B @ C )
% 0.29/0.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing2
% 0.29/0.50  thf(fact_1604_add__strict__increasing2,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ( ord_less_int @ B @ C )
% 0.29/0.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing2
% 0.29/0.50  thf(fact_1605_add__strict__increasing,axiom,
% 0.29/0.50      ! [A: real,B: real,C: real] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.50         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing
% 0.29/0.50  thf(fact_1606_add__strict__increasing,axiom,
% 0.29/0.50      ! [A: rat,B: rat,C: rat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.50         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing
% 0.29/0.50  thf(fact_1607_add__strict__increasing,axiom,
% 0.29/0.50      ! [A: nat,B: nat,C: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.50         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing
% 0.29/0.50  thf(fact_1608_add__strict__increasing,axiom,
% 0.29/0.50      ! [A: int,B: int,C: int] :
% 0.29/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.50         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_strict_increasing
% 0.29/0.50  thf(fact_1609_add__pos__nonneg,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_pos_nonneg
% 0.29/0.50  thf(fact_1610_add__pos__nonneg,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_pos_nonneg
% 0.29/0.50  thf(fact_1611_add__pos__nonneg,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_pos_nonneg
% 0.29/0.50  thf(fact_1612_add__pos__nonneg,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_pos_nonneg
% 0.29/0.50  thf(fact_1613_add__nonpos__neg,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.50       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.50         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonpos_neg
% 0.29/0.50  thf(fact_1614_add__nonpos__neg,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.50       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.50         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonpos_neg
% 0.29/0.50  thf(fact_1615_add__nonpos__neg,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.50       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.50         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonpos_neg
% 0.29/0.50  thf(fact_1616_add__nonpos__neg,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.50       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.50         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonpos_neg
% 0.29/0.50  thf(fact_1617_add__nonneg__pos,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.50       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.50         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonneg_pos
% 0.29/0.50  thf(fact_1618_add__nonneg__pos,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.50       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.50         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonneg_pos
% 0.29/0.50  thf(fact_1619_add__nonneg__pos,axiom,
% 0.29/0.50      ! [A: nat,B: nat] :
% 0.29/0.50        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.50       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.50         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonneg_pos
% 0.29/0.50  thf(fact_1620_add__nonneg__pos,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.50       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.50         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % add_nonneg_pos
% 0.29/0.50  thf(fact_1621_add__neg__nonpos,axiom,
% 0.29/0.50      ! [A: real,B: real] :
% 0.29/0.50        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.50       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.51         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_neg_nonpos
% 0.29/0.51  thf(fact_1622_add__neg__nonpos,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.51         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_neg_nonpos
% 0.29/0.51  thf(fact_1623_add__neg__nonpos,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.51       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.51         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_neg_nonpos
% 0.29/0.51  thf(fact_1624_add__neg__nonpos,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.51       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.51         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % add_neg_nonpos
% 0.29/0.51  thf(fact_1625_field__le__epsilon,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ! [E: real] :
% 0.29/0.51            ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.51           => ( ord_less_eq_real @ X4 @ ( plus_plus_real @ Y @ E ) ) )
% 0.29/0.51       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % field_le_epsilon
% 0.29/0.51  thf(fact_1626_field__le__epsilon,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ! [E: rat] :
% 0.29/0.51            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.29/0.51           => ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ Y @ E ) ) )
% 0.29/0.51       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % field_le_epsilon
% 0.29/0.51  thf(fact_1627_divide__nonpos__pos,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.51       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonpos_pos
% 0.29/0.51  thf(fact_1628_divide__nonpos__pos,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonpos_pos
% 0.29/0.51  thf(fact_1629_divide__nonpos__neg,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.51       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.29/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonpos_neg
% 0.29/0.51  thf(fact_1630_divide__nonpos__neg,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.51       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.29/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonpos_neg
% 0.29/0.51  thf(fact_1631_divide__nonneg__pos,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.51       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.51         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonneg_pos
% 0.29/0.51  thf(fact_1632_divide__nonneg__pos,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.51       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonneg_pos
% 0.29/0.51  thf(fact_1633_divide__nonneg__neg,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.51       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.29/0.51         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonneg_neg
% 0.29/0.51  thf(fact_1634_divide__nonneg__neg,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.51       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.29/0.51         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_nonneg_neg
% 0.29/0.51  thf(fact_1635_divide__le__cancel,axiom,
% 0.29/0.51      ! [A: real,C: real,B: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.51        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.51           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.51          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.51           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_le_cancel
% 0.29/0.51  thf(fact_1636_divide__le__cancel,axiom,
% 0.29/0.51      ! [A: rat,C: rat,B: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.51           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.51          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.51           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_le_cancel
% 0.29/0.51  thf(fact_1637_frac__less2,axiom,
% 0.29/0.51      ! [X4: real,Y: real,W: real,Z: real] :
% 0.29/0.51        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.51       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.51           => ( ( ord_less_real @ W @ Z )
% 0.29/0.51             => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_less2
% 0.29/0.51  thf(fact_1638_frac__less2,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.51       => ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.51           => ( ( ord_less_rat @ W @ Z )
% 0.29/0.51             => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_less2
% 0.29/0.51  thf(fact_1639_frac__less,axiom,
% 0.29/0.51      ! [X4: real,Y: real,W: real,Z: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.51       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.51           => ( ( ord_less_eq_real @ W @ Z )
% 0.29/0.51             => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_less
% 0.29/0.51  thf(fact_1640_frac__less,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.51       => ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.51           => ( ( ord_less_eq_rat @ W @ Z )
% 0.29/0.51             => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_less
% 0.29/0.51  thf(fact_1641_frac__le,axiom,
% 0.29/0.51      ! [Y: real,X4: real,W: real,Z: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.51       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.29/0.51           => ( ( ord_less_eq_real @ W @ Z )
% 0.29/0.51             => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_le
% 0.29/0.51  thf(fact_1642_frac__le,axiom,
% 0.29/0.51      ! [Y: rat,X4: rat,W: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.51       => ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.29/0.51           => ( ( ord_less_eq_rat @ W @ Z )
% 0.29/0.51             => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % frac_le
% 0.29/0.51  thf(fact_1643_div__positive,axiom,
% 0.29/0.51      ! [B: code_integer,A: code_integer] :
% 0.29/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.51       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.29/0.51         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_positive
% 0.29/0.51  thf(fact_1644_div__positive,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.51       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.51         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_positive
% 0.29/0.51  thf(fact_1645_div__positive,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.51       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.51         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_positive
% 0.29/0.51  thf(fact_1646_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.51       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.51         => ( ( divide6298287555418463151nteger @ A @ B )
% 0.29/0.51            = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.div_less
% 0.29/0.51  thf(fact_1647_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ A @ B )
% 0.29/0.51         => ( ( divide_divide_nat @ A @ B )
% 0.29/0.51            = zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.div_less
% 0.29/0.51  thf(fact_1648_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51       => ( ( ord_less_int @ A @ B )
% 0.29/0.51         => ( ( divide_divide_int @ A @ B )
% 0.29/0.51            = zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.div_less
% 0.29/0.51  thf(fact_1649_power__less__imp__less__base,axiom,
% 0.29/0.51      ! [A: real,N2: nat,B: real] :
% 0.29/0.51        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.51         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_less_imp_less_base
% 0.29/0.51  thf(fact_1650_power__less__imp__less__base,axiom,
% 0.29/0.51      ! [A: rat,N2: nat,B: rat] :
% 0.29/0.51        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.51         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_less_imp_less_base
% 0.29/0.51  thf(fact_1651_power__less__imp__less__base,axiom,
% 0.29/0.51      ! [A: nat,N2: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.51         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_less_imp_less_base
% 0.29/0.51  thf(fact_1652_power__less__imp__less__base,axiom,
% 0.29/0.51      ! [A: int,N2: nat,B: int] :
% 0.29/0.51        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.51         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_less_imp_less_base
% 0.29/0.51  thf(fact_1653_zero__less__two,axiom,
% 0.29/0.51      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_less_two
% 0.29/0.51  thf(fact_1654_zero__less__two,axiom,
% 0.29/0.51      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_less_two
% 0.29/0.51  thf(fact_1655_zero__less__two,axiom,
% 0.29/0.51      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_less_two
% 0.29/0.51  thf(fact_1656_zero__less__two,axiom,
% 0.29/0.51      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_less_two
% 0.29/0.51  thf(fact_1657_power__le__one,axiom,
% 0.29/0.51      ! [A: real,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.51       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.51         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_one
% 0.29/0.51  thf(fact_1658_power__le__one,axiom,
% 0.29/0.51      ! [A: rat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.51       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.51         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_one
% 0.29/0.51  thf(fact_1659_power__le__one,axiom,
% 0.29/0.51      ! [A: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.51         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_one
% 0.29/0.51  thf(fact_1660_power__le__one,axiom,
% 0.29/0.51      ! [A: int,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.51         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_one
% 0.29/0.51  thf(fact_1661_less__divide__eq__1,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51            & ( ord_less_rat @ A @ B ) )
% 0.29/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.51            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_divide_eq_1
% 0.29/0.51  thf(fact_1662_less__divide__eq__1,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51            & ( ord_less_real @ A @ B ) )
% 0.29/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.51            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_divide_eq_1
% 0.29/0.51  thf(fact_1663_divide__less__eq__1,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51            & ( ord_less_rat @ B @ A ) )
% 0.29/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.51            & ( ord_less_rat @ A @ B ) )
% 0.29/0.51          | ( A = zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_less_eq_1
% 0.29/0.51  thf(fact_1664_divide__less__eq__1,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51            & ( ord_less_real @ B @ A ) )
% 0.29/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.51            & ( ord_less_real @ A @ B ) )
% 0.29/0.51          | ( A = zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_less_eq_1
% 0.29/0.51  thf(fact_1665_div__add__self2,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( B != zero_zero_nat )
% 0.29/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.51          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self2
% 0.29/0.51  thf(fact_1666_div__add__self2,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( B != zero_zero_int )
% 0.29/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.51          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self2
% 0.29/0.51  thf(fact_1667_div__add__self2,axiom,
% 0.29/0.51      ! [B: code_integer,A: code_integer] :
% 0.29/0.51        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.29/0.51          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self2
% 0.29/0.51  thf(fact_1668_div__add__self1,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( B != zero_zero_nat )
% 0.29/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.29/0.51          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self1
% 0.29/0.51  thf(fact_1669_div__add__self1,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( B != zero_zero_int )
% 0.29/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.29/0.51          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self1
% 0.29/0.51  thf(fact_1670_div__add__self1,axiom,
% 0.29/0.51      ! [B: code_integer,A: code_integer] :
% 0.29/0.51        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.29/0.51          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_add_self1
% 0.29/0.51  thf(fact_1671_power__inject__base,axiom,
% 0.29/0.51      ! [A: real,N2: nat,B: real] :
% 0.29/0.51        ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 0.29/0.51          = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.51         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.51           => ( A = B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_inject_base
% 0.29/0.51  thf(fact_1672_power__inject__base,axiom,
% 0.29/0.51      ! [A: rat,N2: nat,B: rat] :
% 0.29/0.51        ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 0.29/0.51          = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.51         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.51           => ( A = B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_inject_base
% 0.29/0.51  thf(fact_1673_power__inject__base,axiom,
% 0.29/0.51      ! [A: nat,N2: nat,B: nat] :
% 0.29/0.51        ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 0.29/0.51          = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.51           => ( A = B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_inject_base
% 0.29/0.51  thf(fact_1674_power__inject__base,axiom,
% 0.29/0.51      ! [A: int,N2: nat,B: int] :
% 0.29/0.51        ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 0.29/0.51          = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.51           => ( A = B ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_inject_base
% 0.29/0.51  thf(fact_1675_power__le__imp__le__base,axiom,
% 0.29/0.51      ! [A: real,N2: nat,B: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.51         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_imp_le_base
% 0.29/0.51  thf(fact_1676_power__le__imp__le__base,axiom,
% 0.29/0.51      ! [A: rat,N2: nat,B: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.51         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_imp_le_base
% 0.29/0.51  thf(fact_1677_power__le__imp__le__base,axiom,
% 0.29/0.51      ! [A: nat,N2: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.51         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_imp_le_base
% 0.29/0.51  thf(fact_1678_power__le__imp__le__base,axiom,
% 0.29/0.51      ! [A: int,N2: nat,B: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.51         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_le_imp_le_base
% 0.29/0.51  thf(fact_1679_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.51       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.51         => ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.51            = A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.29/0.51  thf(fact_1680_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ A @ B )
% 0.29/0.51         => ( ( modulo_modulo_nat @ A @ B )
% 0.29/0.51            = A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.29/0.51  thf(fact_1681_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51       => ( ( ord_less_int @ A @ B )
% 0.29/0.51         => ( ( modulo_modulo_int @ A @ B )
% 0.29/0.51            = A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.29/0.51  thf(fact_1682_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.29/0.51      ! [B: code_integer,A: code_integer] :
% 0.29/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.51       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.29/0.51  thf(fact_1683_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.51       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.29/0.51  thf(fact_1684_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.51       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.29/0.51  thf(fact_1685_in__mono,axiom,
% 0.29/0.51      ! [A2: set_real,B3: set_real,X4: real] :
% 0.29/0.51        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.29/0.51       => ( ( member_real @ X4 @ A2 )
% 0.29/0.51         => ( member_real @ X4 @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_mono
% 0.29/0.51  thf(fact_1686_in__mono,axiom,
% 0.29/0.51      ! [A2: set_nat,B3: set_nat,X4: nat] :
% 0.29/0.51        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.29/0.51       => ( ( member_nat @ X4 @ A2 )
% 0.29/0.51         => ( member_nat @ X4 @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_mono
% 0.29/0.51  thf(fact_1687_in__mono,axiom,
% 0.29/0.51      ! [A2: set_complex,B3: set_complex,X4: complex] :
% 0.29/0.51        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.29/0.51       => ( ( member_complex @ X4 @ A2 )
% 0.29/0.51         => ( member_complex @ X4 @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_mono
% 0.29/0.51  thf(fact_1688_in__mono,axiom,
% 0.29/0.51      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] :
% 0.29/0.51        ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 0.29/0.51       => ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 0.29/0.51         => ( member8440522571783428010at_nat @ X4 @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_mono
% 0.29/0.51  thf(fact_1689_in__mono,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int,X4: int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ( member_int @ X4 @ A2 )
% 0.29/0.51         => ( member_int @ X4 @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_mono
% 0.29/0.51  thf(fact_1690_subsetD,axiom,
% 0.29/0.51      ! [A2: set_real,B3: set_real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.29/0.51       => ( ( member_real @ C @ A2 )
% 0.29/0.51         => ( member_real @ C @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subsetD
% 0.29/0.51  thf(fact_1691_subsetD,axiom,
% 0.29/0.51      ! [A2: set_nat,B3: set_nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.29/0.51       => ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( member_nat @ C @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subsetD
% 0.29/0.51  thf(fact_1692_subsetD,axiom,
% 0.29/0.51      ! [A2: set_complex,B3: set_complex,C: complex] :
% 0.29/0.51        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.29/0.51       => ( ( member_complex @ C @ A2 )
% 0.29/0.51         => ( member_complex @ C @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subsetD
% 0.29/0.51  thf(fact_1693_subsetD,axiom,
% 0.29/0.51      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 0.29/0.51        ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 0.29/0.51       => ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.29/0.51         => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subsetD
% 0.29/0.51  thf(fact_1694_subsetD,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( member_int @ C @ B3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subsetD
% 0.29/0.51  thf(fact_1695_equalityE,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int] :
% 0.29/0.51        ( ( A2 = B3 )
% 0.29/0.51       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51           => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equalityE
% 0.29/0.51  thf(fact_1696_subset__eq,axiom,
% 0.29/0.51      ( ord_less_eq_set_real
% 0.29/0.51      = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.51          ! [X: real] :
% 0.29/0.51            ( ( member_real @ X @ A6 )
% 0.29/0.51           => ( member_real @ X @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_eq
% 0.29/0.51  thf(fact_1697_subset__eq,axiom,
% 0.29/0.51      ( ord_less_eq_set_nat
% 0.29/0.51      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.51          ! [X: nat] :
% 0.29/0.51            ( ( member_nat @ X @ A6 )
% 0.29/0.51           => ( member_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_eq
% 0.29/0.51  thf(fact_1698_subset__eq,axiom,
% 0.29/0.51      ( ord_le211207098394363844omplex
% 0.29/0.51      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.29/0.51          ! [X: complex] :
% 0.29/0.51            ( ( member_complex @ X @ A6 )
% 0.29/0.51           => ( member_complex @ X @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_eq
% 0.29/0.51  thf(fact_1699_subset__eq,axiom,
% 0.29/0.51      ( ord_le3146513528884898305at_nat
% 0.29/0.51      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.29/0.51          ! [X: product_prod_nat_nat] :
% 0.29/0.51            ( ( member8440522571783428010at_nat @ X @ A6 )
% 0.29/0.51           => ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_eq
% 0.29/0.51  thf(fact_1700_subset__eq,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51          ! [X: int] :
% 0.29/0.51            ( ( member_int @ X @ A6 )
% 0.29/0.51           => ( member_int @ X @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_eq
% 0.29/0.51  thf(fact_1701_equalityD1,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int] :
% 0.29/0.51        ( ( A2 = B3 )
% 0.29/0.51       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equalityD1
% 0.29/0.51  thf(fact_1702_equalityD2,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int] :
% 0.29/0.51        ( ( A2 = B3 )
% 0.29/0.51       => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equalityD2
% 0.29/0.51  thf(fact_1703_subset__iff,axiom,
% 0.29/0.51      ( ord_less_eq_set_real
% 0.29/0.51      = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.51          ! [T: real] :
% 0.29/0.51            ( ( member_real @ T @ A6 )
% 0.29/0.51           => ( member_real @ T @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff
% 0.29/0.51  thf(fact_1704_subset__iff,axiom,
% 0.29/0.51      ( ord_less_eq_set_nat
% 0.29/0.51      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.51          ! [T: nat] :
% 0.29/0.51            ( ( member_nat @ T @ A6 )
% 0.29/0.51           => ( member_nat @ T @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff
% 0.29/0.51  thf(fact_1705_subset__iff,axiom,
% 0.29/0.51      ( ord_le211207098394363844omplex
% 0.29/0.51      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.29/0.51          ! [T: complex] :
% 0.29/0.51            ( ( member_complex @ T @ A6 )
% 0.29/0.51           => ( member_complex @ T @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff
% 0.29/0.51  thf(fact_1706_subset__iff,axiom,
% 0.29/0.51      ( ord_le3146513528884898305at_nat
% 0.29/0.51      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.29/0.51          ! [T: product_prod_nat_nat] :
% 0.29/0.51            ( ( member8440522571783428010at_nat @ T @ A6 )
% 0.29/0.51           => ( member8440522571783428010at_nat @ T @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff
% 0.29/0.51  thf(fact_1707_subset__iff,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51          ! [T: int] :
% 0.29/0.51            ( ( member_int @ T @ A6 )
% 0.29/0.51           => ( member_int @ T @ B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff
% 0.29/0.51  thf(fact_1708_subset__refl,axiom,
% 0.29/0.51      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_refl
% 0.29/0.51  thf(fact_1709_Collect__mono,axiom,
% 0.29/0.51      ! [P: complex > $o,Q: complex > $o] :
% 0.29/0.51        ( ! [X5: complex] :
% 0.29/0.51            ( ( P @ X5 )
% 0.29/0.51           => ( Q @ X5 ) )
% 0.29/0.51       => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono
% 0.29/0.51  thf(fact_1710_Collect__mono,axiom,
% 0.29/0.51      ! [P: real > $o,Q: real > $o] :
% 0.29/0.51        ( ! [X5: real] :
% 0.29/0.51            ( ( P @ X5 )
% 0.29/0.51           => ( Q @ X5 ) )
% 0.29/0.51       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono
% 0.29/0.51  thf(fact_1711_Collect__mono,axiom,
% 0.29/0.51      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.29/0.51        ( ! [X5: list_nat] :
% 0.29/0.51            ( ( P @ X5 )
% 0.29/0.51           => ( Q @ X5 ) )
% 0.29/0.51       => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono
% 0.29/0.51  thf(fact_1712_Collect__mono,axiom,
% 0.29/0.51      ! [P: nat > $o,Q: nat > $o] :
% 0.29/0.51        ( ! [X5: nat] :
% 0.29/0.51            ( ( P @ X5 )
% 0.29/0.51           => ( Q @ X5 ) )
% 0.29/0.51       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono
% 0.29/0.51  thf(fact_1713_Collect__mono,axiom,
% 0.29/0.51      ! [P: int > $o,Q: int > $o] :
% 0.29/0.51        ( ! [X5: int] :
% 0.29/0.51            ( ( P @ X5 )
% 0.29/0.51           => ( Q @ X5 ) )
% 0.29/0.51       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono
% 0.29/0.51  thf(fact_1714_subset__trans,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.29/0.51         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_trans
% 0.29/0.51  thf(fact_1715_set__eq__subset,axiom,
% 0.29/0.51      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.51            & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_eq_subset
% 0.29/0.51  thf(fact_1716_Collect__mono__iff,axiom,
% 0.29/0.51      ! [P: complex > $o,Q: complex > $o] :
% 0.29/0.51        ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 0.29/0.51        = ( ! [X: complex] :
% 0.29/0.51              ( ( P @ X )
% 0.29/0.51             => ( Q @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono_iff
% 0.29/0.51  thf(fact_1717_Collect__mono__iff,axiom,
% 0.29/0.51      ! [P: real > $o,Q: real > $o] :
% 0.29/0.51        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 0.29/0.51        = ( ! [X: real] :
% 0.29/0.51              ( ( P @ X )
% 0.29/0.51             => ( Q @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono_iff
% 0.29/0.51  thf(fact_1718_Collect__mono__iff,axiom,
% 0.29/0.51      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.29/0.51        ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 0.29/0.51        = ( ! [X: list_nat] :
% 0.29/0.51              ( ( P @ X )
% 0.29/0.51             => ( Q @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono_iff
% 0.29/0.51  thf(fact_1719_Collect__mono__iff,axiom,
% 0.29/0.51      ! [P: nat > $o,Q: nat > $o] :
% 0.29/0.51        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 0.29/0.51        = ( ! [X: nat] :
% 0.29/0.51              ( ( P @ X )
% 0.29/0.51             => ( Q @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono_iff
% 0.29/0.51  thf(fact_1720_Collect__mono__iff,axiom,
% 0.29/0.51      ! [P: int > $o,Q: int > $o] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 0.29/0.51        = ( ! [X: int] :
% 0.29/0.51              ( ( P @ X )
% 0.29/0.51             => ( Q @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_mono_iff
% 0.29/0.51  thf(fact_1721_subset__iff__psubset__eq,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51            ( ( ord_less_set_int @ A6 @ B6 )
% 0.29/0.51            | ( A6 = B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_iff_psubset_eq
% 0.29/0.51  thf(fact_1722_subset__psubset__trans,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ( ord_less_set_int @ B3 @ C4 )
% 0.29/0.51         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_psubset_trans
% 0.29/0.51  thf(fact_1723_subset__not__subset__eq,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.51            & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % subset_not_subset_eq
% 0.29/0.51  thf(fact_1724_psubset__subset__trans,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.29/0.51         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % psubset_subset_trans
% 0.29/0.51  thf(fact_1725_psubset__imp__subset,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ A2 @ B3 )
% 0.29/0.51       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % psubset_imp_subset
% 0.29/0.51  thf(fact_1726_psubset__eq,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.51            & ( A6 != B6 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % psubset_eq
% 0.29/0.51  thf(fact_1727_psubsetE,axiom,
% 0.29/0.51      ! [A2: set_int,B3: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ A2 @ B3 )
% 0.29/0.51       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.51           => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % psubsetE
% 0.29/0.51  thf(fact_1728_cong__exp__iff__simps_I2_J,axiom,
% 0.29/0.51      ! [N2: num,Q3: num] :
% 0.29/0.51        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.51          = zero_zero_nat )
% 0.29/0.51        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.29/0.51          = zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(2)
% 0.29/0.51  thf(fact_1729_cong__exp__iff__simps_I2_J,axiom,
% 0.29/0.51      ! [N2: num,Q3: num] :
% 0.29/0.51        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.51          = zero_zero_int )
% 0.29/0.51        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 0.29/0.51          = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(2)
% 0.29/0.51  thf(fact_1730_cong__exp__iff__simps_I2_J,axiom,
% 0.29/0.51      ! [N2: num,Q3: num] :
% 0.29/0.51        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.51          = zero_z3403309356797280102nteger )
% 0.29/0.51        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.29/0.51          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(2)
% 0.29/0.51  thf(fact_1731_cong__exp__iff__simps_I1_J,axiom,
% 0.29/0.51      ! [N2: num] :
% 0.29/0.51        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 0.29/0.51        = zero_zero_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(1)
% 0.29/0.51  thf(fact_1732_cong__exp__iff__simps_I1_J,axiom,
% 0.29/0.51      ! [N2: num] :
% 0.29/0.51        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 0.29/0.51        = zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(1)
% 0.29/0.51  thf(fact_1733_cong__exp__iff__simps_I1_J,axiom,
% 0.29/0.51      ! [N2: num] :
% 0.29/0.51        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 0.29/0.51        = zero_z3403309356797280102nteger ) ).
% 0.29/0.51  
% 0.29/0.51  % cong_exp_iff_simps(1)
% 0.29/0.51  thf(fact_1734_numeral__1__eq__Suc__0,axiom,
% 0.29/0.51      ( ( numeral_numeral_nat @ one )
% 0.29/0.51      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_1_eq_Suc_0
% 0.29/0.51  thf(fact_1735_num_Osize_I5_J,axiom,
% 0.29/0.51      ! [X22: num] :
% 0.29/0.51        ( ( size_size_num @ ( bit0 @ X22 ) )
% 0.29/0.51        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % num.size(5)
% 0.29/0.51  thf(fact_1736_ex__least__nat__less,axiom,
% 0.29/0.51      ! [P: nat > $o,N2: nat] :
% 0.29/0.51        ( ( P @ N2 )
% 0.29/0.51       => ( ~ ( P @ zero_zero_nat )
% 0.29/0.51         => ? [K2: nat] :
% 0.29/0.51              ( ( ord_less_nat @ K2 @ N2 )
% 0.29/0.51              & ! [I: nat] :
% 0.29/0.51                  ( ( ord_less_eq_nat @ I @ K2 )
% 0.29/0.51                 => ~ ( P @ I ) )
% 0.29/0.51              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % ex_least_nat_less
% 0.29/0.51  thf(fact_1737_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: real,Xs: list_real] :
% 0.29/0.51        ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1738_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: complex,Xs: list_complex] :
% 0.29/0.51        ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1739_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1740_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.29/0.51        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1741_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: $o,Xs: list_o] :
% 0.29/0.51        ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1742_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: nat,Xs: list_nat] :
% 0.29/0.51        ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1743_length__pos__if__in__set,axiom,
% 0.29/0.51      ! [X4: int,Xs: list_int] :
% 0.29/0.51        ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.29/0.51       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % length_pos_if_in_set
% 0.29/0.51  thf(fact_1744_nat__induct__non__zero,axiom,
% 0.29/0.51      ! [N2: nat,P: nat > $o] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51       => ( ( P @ one_one_nat )
% 0.29/0.51         => ( ! [N3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.51               => ( ( P @ N3 )
% 0.29/0.51                 => ( P @ ( suc @ N3 ) ) ) )
% 0.29/0.51           => ( P @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_induct_non_zero
% 0.29/0.51  thf(fact_1745_power__gt__expt,axiom,
% 0.29/0.51      ! [N2: nat,K: nat] :
% 0.29/0.51        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.51       => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_gt_expt
% 0.29/0.51  thf(fact_1746_div__greater__zero__iff,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.51        = ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.51          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_greater_zero_iff
% 0.29/0.51  thf(fact_1747_div__le__mono2,axiom,
% 0.29/0.51      ! [M: nat,N2: nat,K: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.51       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.51         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_le_mono2
% 0.29/0.51  thf(fact_1748_nat__one__le__power,axiom,
% 0.29/0.51      ! [I2: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 0.29/0.51       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nat_one_le_power
% 0.29/0.51  thf(fact_1749_mod__le__divisor,axiom,
% 0.29/0.51      ! [N2: nat,M: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mod_le_divisor
% 0.29/0.51  thf(fact_1750_div__eq__dividend__iff,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.51       => ( ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.51            = M )
% 0.29/0.51          = ( N2 = one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_eq_dividend_iff
% 0.29/0.51  thf(fact_1751_div__less__dividend,axiom,
% 0.29/0.51      ! [N2: nat,M: nat] :
% 0.29/0.51        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.51         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % div_less_dividend
% 0.29/0.51  thf(fact_1752_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.29/0.51      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 0.29/0.51        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 0.29/0.51  
% 0.29/0.51  % VEBT_internal.membermima.simps(2)
% 0.29/0.51  thf(fact_1753_le__divide__eq__1,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.29/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51            & ( ord_less_eq_real @ A @ B ) )
% 0.29/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.51            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_divide_eq_1
% 0.29/0.51  thf(fact_1754_le__divide__eq__1,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51            & ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.51            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % le_divide_eq_1
% 0.29/0.51  thf(fact_1755_divide__le__eq__1,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.29/0.51        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51            & ( ord_less_eq_real @ B @ A ) )
% 0.29/0.51          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.51            & ( ord_less_eq_real @ A @ B ) )
% 0.29/0.51          | ( A = zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_le_eq_1
% 0.29/0.51  thf(fact_1756_divide__le__eq__1,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.51        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51            & ( ord_less_eq_rat @ B @ A ) )
% 0.29/0.51          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.51            & ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.51          | ( A = zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divide_le_eq_1
% 0.29/0.51  thf(fact_1757_power__Suc__le__self,axiom,
% 0.29/0.51      ! [A: real,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.51       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.51         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_le_self
% 0.29/0.51  thf(fact_1758_power__Suc__le__self,axiom,
% 0.29/0.51      ! [A: rat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.51       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.51         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_le_self
% 0.29/0.51  thf(fact_1759_power__Suc__le__self,axiom,
% 0.29/0.51      ! [A: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.51         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_le_self
% 0.29/0.51  thf(fact_1760_power__Suc__le__self,axiom,
% 0.29/0.51      ! [A: int,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.51         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_le_self
% 0.29/0.51  thf(fact_1761_power__Suc__less__one,axiom,
% 0.29/0.51      ! [A: real,N2: nat] :
% 0.29/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51       => ( ( ord_less_real @ A @ one_one_real )
% 0.29/0.51         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_less_one
% 0.29/0.51  thf(fact_1762_power__Suc__less__one,axiom,
% 0.29/0.51      ! [A: rat,N2: nat] :
% 0.29/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.29/0.51         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_less_one
% 0.29/0.51  thf(fact_1763_power__Suc__less__one,axiom,
% 0.29/0.51      ! [A: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.29/0.51         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_less_one
% 0.29/0.51  thf(fact_1764_power__Suc__less__one,axiom,
% 0.29/0.51      ! [A: int,N2: nat] :
% 0.29/0.51        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.51       => ( ( ord_less_int @ A @ one_one_int )
% 0.29/0.51         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_Suc_less_one
% 0.29/0.51  thf(fact_1765_power__strict__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: real] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51         => ( ( ord_less_real @ A @ one_one_real )
% 0.29/0.51           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_strict_decreasing
% 0.29/0.51  thf(fact_1766_power__strict__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: rat] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.29/0.51           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_strict_decreasing
% 0.29/0.51  thf(fact_1767_power__strict__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.51         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.29/0.51           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_strict_decreasing
% 0.29/0.51  thf(fact_1768_power__strict__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: int] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.51         => ( ( ord_less_int @ A @ one_one_int )
% 0.29/0.51           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_strict_decreasing
% 0.29/0.51  thf(fact_1769_power__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: real] :
% 0.29/0.51        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.51         => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.51           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_decreasing
% 0.29/0.51  thf(fact_1770_power__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: rat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.51         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.51           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_decreasing
% 0.29/0.51  thf(fact_1771_power__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.51         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.51           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_decreasing
% 0.29/0.51  thf(fact_1772_power__decreasing,axiom,
% 0.29/0.51      ! [N2: nat,N4: nat,A: int] :
% 0.29/0.51        ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.51         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.51           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power_decreasing
% 0.29/0.51  thf(fact_1773_zero__power2,axiom,
% 0.29/0.51      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51      = zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_power2
% 0.29/0.51  thf(fact_1774_zero__power2,axiom,
% 0.29/0.51      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51      = zero_zero_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_power2
% 0.29/0.51  thf(fact_1775_zero__power2,axiom,
% 0.29/0.51      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51      = zero_zero_real ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_power2
% 0.29/0.51  thf(fact_1776_zero__power2,axiom,
% 0.29/0.51      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51      = zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_power2
% 0.29/0.51  thf(fact_1777_zero__power2,axiom,
% 0.29/0.51      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51      = zero_zero_complex ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_power2
% 0.29/0.51  thf(fact_1778_self__le__power,axiom,
% 0.29/0.51      ! [A: real,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % self_le_power
% 0.29/0.51  thf(fact_1779_self__le__power,axiom,
% 0.29/0.51      ! [A: rat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % self_le_power
% 0.29/0.51  thf(fact_1780_self__le__power,axiom,
% 0.29/0.51      ! [A: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % self_le_power
% 0.29/0.51  thf(fact_1781_self__le__power,axiom,
% 0.29/0.51      ! [A: int,N2: nat] :
% 0.29/0.51        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % self_le_power
% 0.29/0.51  thf(fact_1782_one__less__power,axiom,
% 0.29/0.51      ! [A: real,N2: nat] :
% 0.29/0.51        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_less_power
% 0.29/0.51  thf(fact_1783_one__less__power,axiom,
% 0.29/0.51      ! [A: rat,N2: nat] :
% 0.29/0.51        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_less_power
% 0.29/0.51  thf(fact_1784_one__less__power,axiom,
% 0.29/0.51      ! [A: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_less_power
% 0.29/0.51  thf(fact_1785_one__less__power,axiom,
% 0.29/0.51      ! [A: int,N2: nat] :
% 0.29/0.51        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_less_power
% 0.29/0.51  thf(fact_1786_numeral__2__eq__2,axiom,
% 0.29/0.51      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.51      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_2_eq_2
% 0.29/0.51  thf(fact_1787_verit__le__mono__div,axiom,
% 0.29/0.51      ! [A2: nat,B3: nat,N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ A2 @ B3 )
% 0.29/0.51       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.51         => ( ord_less_eq_nat
% 0.29/0.51            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 0.29/0.51              @ ( if_nat
% 0.29/0.51                @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 0.29/0.51                  = zero_zero_nat )
% 0.29/0.51                @ one_one_nat
% 0.29/0.51                @ zero_zero_nat ) )
% 0.29/0.51            @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_le_mono_div
% 0.29/0.51  thf(fact_1788_half__gt__zero__iff,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.29/0.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % half_gt_zero_iff
% 0.29/0.51  thf(fact_1789_half__gt__zero__iff,axiom,
% 0.29/0.51      ! [A: real] :
% 0.29/0.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % half_gt_zero_iff
% 0.29/0.51  thf(fact_1790_half__gt__zero,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.51       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % half_gt_zero
% 0.29/0.51  thf(fact_1791_half__gt__zero,axiom,
% 0.29/0.51      ! [A: real] :
% 0.29/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.51       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % half_gt_zero
% 0.29/0.51  thf(fact_1792_power2__le__imp__le,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.51         => ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_le_imp_le
% 0.29/0.51  thf(fact_1793_power2__le__imp__le,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.51         => ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_le_imp_le
% 0.29/0.51  thf(fact_1794_power2__le__imp__le,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.51         => ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_le_imp_le
% 0.29/0.51  thf(fact_1795_power2__le__imp__le,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.51         => ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_le_imp_le
% 0.29/0.51  thf(fact_1796_power2__eq__imp__eq,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.51         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.51           => ( X4 = Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_eq_imp_eq
% 0.29/0.51  thf(fact_1797_power2__eq__imp__eq,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.51         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.51           => ( X4 = Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_eq_imp_eq
% 0.29/0.51  thf(fact_1798_power2__eq__imp__eq,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 0.29/0.51         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.51           => ( X4 = Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_eq_imp_eq
% 0.29/0.51  thf(fact_1799_power2__eq__imp__eq,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.51         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.51           => ( X4 = Y ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_eq_imp_eq
% 0.29/0.51  thf(fact_1800_zero__le__power2,axiom,
% 0.29/0.51      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_le_power2
% 0.29/0.51  thf(fact_1801_zero__le__power2,axiom,
% 0.29/0.51      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_le_power2
% 0.29/0.51  thf(fact_1802_zero__le__power2,axiom,
% 0.29/0.51      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_le_power2
% 0.29/0.51  thf(fact_1803_power2__less__0,axiom,
% 0.29/0.51      ! [A: real] :
% 0.29/0.51        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_0
% 0.29/0.51  thf(fact_1804_power2__less__0,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_0
% 0.29/0.51  thf(fact_1805_power2__less__0,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_0
% 0.29/0.51  thf(fact_1806_exp__add__not__zero__imp__right,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.51         != zero_zero_nat )
% 0.29/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.51         != zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % exp_add_not_zero_imp_right
% 0.29/0.51  thf(fact_1807_exp__add__not__zero__imp__right,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.51         != zero_zero_int )
% 0.29/0.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.51         != zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % exp_add_not_zero_imp_right
% 0.29/0.51  thf(fact_1808_exp__add__not__zero__imp__left,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.51         != zero_zero_nat )
% 0.29/0.51       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.29/0.51         != zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % exp_add_not_zero_imp_left
% 0.29/0.51  thf(fact_1809_exp__add__not__zero__imp__left,axiom,
% 0.29/0.51      ! [M: nat,N2: nat] :
% 0.29/0.51        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.51         != zero_zero_int )
% 0.29/0.51       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.29/0.51         != zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % exp_add_not_zero_imp_left
% 0.29/0.51  thf(fact_1810_less__2__cases__iff,axiom,
% 0.29/0.51      ! [N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51        = ( ( N2 = zero_zero_nat )
% 0.29/0.51          | ( N2
% 0.29/0.51            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_2_cases_iff
% 0.29/0.51  thf(fact_1811_less__2__cases,axiom,
% 0.29/0.51      ! [N2: nat] :
% 0.29/0.51        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51       => ( ( N2 = zero_zero_nat )
% 0.29/0.51          | ( N2
% 0.29/0.51            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_2_cases
% 0.29/0.51  thf(fact_1812_power2__less__imp__less,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.51         => ( ord_less_real @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_imp_less
% 0.29/0.51  thf(fact_1813_power2__less__imp__less,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.51         => ( ord_less_rat @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_imp_less
% 0.29/0.51  thf(fact_1814_power2__less__imp__less,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.29/0.51         => ( ord_less_nat @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_imp_less
% 0.29/0.51  thf(fact_1815_power2__less__imp__less,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.51         => ( ord_less_int @ X4 @ Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % power2_less_imp_less
% 0.29/0.51  thf(fact_1816_sum__power2__le__zero__iff,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.29/0.51        = ( ( X4 = zero_zero_real )
% 0.29/0.51          & ( Y = zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_le_zero_iff
% 0.29/0.51  thf(fact_1817_sum__power2__le__zero__iff,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.29/0.51        = ( ( X4 = zero_zero_rat )
% 0.29/0.51          & ( Y = zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_le_zero_iff
% 0.29/0.51  thf(fact_1818_sum__power2__le__zero__iff,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.29/0.51        = ( ( X4 = zero_zero_int )
% 0.29/0.51          & ( Y = zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_le_zero_iff
% 0.29/0.51  thf(fact_1819_sum__power2__ge__zero,axiom,
% 0.29/0.51      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_ge_zero
% 0.29/0.51  thf(fact_1820_sum__power2__ge__zero,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_ge_zero
% 0.29/0.51  thf(fact_1821_sum__power2__ge__zero,axiom,
% 0.29/0.51      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_ge_zero
% 0.29/0.51  thf(fact_1822_sum__power2__gt__zero__iff,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.51        = ( ( X4 != zero_zero_real )
% 0.29/0.51          | ( Y != zero_zero_real ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_gt_zero_iff
% 0.29/0.51  thf(fact_1823_sum__power2__gt__zero__iff,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.51        = ( ( X4 != zero_zero_rat )
% 0.29/0.51          | ( Y != zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_gt_zero_iff
% 0.29/0.51  thf(fact_1824_sum__power2__gt__zero__iff,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.51        = ( ( X4 != zero_zero_int )
% 0.29/0.51          | ( Y != zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sum_power2_gt_zero_iff
% 0.29/0.51  thf(fact_1825_not__sum__power2__lt__zero,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.29/0.51  
% 0.29/0.51  % not_sum_power2_lt_zero
% 0.29/0.51  thf(fact_1826_not__sum__power2__lt__zero,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % not_sum_power2_lt_zero
% 0.29/0.51  thf(fact_1827_not__sum__power2__lt__zero,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % not_sum_power2_lt_zero
% 0.29/0.51  thf(fact_1828_bits__stable__imp__add__self,axiom,
% 0.29/0.51      ! [A: nat] :
% 0.29/0.51        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.51          = A )
% 0.29/0.51       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.51          = zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bits_stable_imp_add_self
% 0.29/0.51  thf(fact_1829_bits__stable__imp__add__self,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.51          = A )
% 0.29/0.51       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.29/0.51          = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bits_stable_imp_add_self
% 0.29/0.51  thf(fact_1830_bits__stable__imp__add__self,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.51          = A )
% 0.29/0.51       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.29/0.51          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bits_stable_imp_add_self
% 0.29/0.51  thf(fact_1831_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1832_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_set_int @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1833_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1834_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_num @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1835_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1836_order__le__imp__less__or__eq,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_int @ X4 @ Y )
% 0.29/0.51          | ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_imp_less_or_eq
% 0.29/0.51  thf(fact_1837_linorder__le__less__linear,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51        | ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_le_less_linear
% 0.29/0.51  thf(fact_1838_linorder__le__less__linear,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51        | ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_le_less_linear
% 0.29/0.51  thf(fact_1839_linorder__le__less__linear,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.51        | ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_le_less_linear
% 0.29/0.51  thf(fact_1840_linorder__le__less__linear,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.51        | ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_le_less_linear
% 0.29/0.51  thf(fact_1841_linorder__le__less__linear,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.51        | ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_le_less_linear
% 0.29/0.51  thf(fact_1842_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: real,B: real,F: real > real,C: real] :
% 0.29/0.51        ( ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: real,Y3: real] :
% 0.29/0.51                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1843_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.29/0.51        ( ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1844_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > real,C: real] :
% 0.29/0.51        ( ( ord_less_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1845_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.29/0.51        ( ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1846_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: int,B: int,F: int > real,C: real] :
% 0.29/0.51        ( ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: int,Y3: int] :
% 0.29/0.51                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1847_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: real,Y3: real] :
% 0.29/0.51                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1848_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1849_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1850_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1851_order__less__le__subst2,axiom,
% 0.29/0.51      ! [A: int,B: int,F: int > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: int,Y3: int] :
% 0.29/0.51                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst2
% 0.29/0.51  thf(fact_1852_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1853_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1854_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1855_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1856_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1857_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: real,F: num > real,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1858_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1859_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: num,F: num > num,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1860_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1861_order__less__le__subst1,axiom,
% 0.29/0.51      ! [A: int,F: num > int,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_subst1
% 0.29/0.51  thf(fact_1862_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1863_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1864_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1865_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1866_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1867_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1868_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1869_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1870_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1871_order__le__less__subst2,axiom,
% 0.29/0.51      ! [A: num,B: num,F: num > int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_eq_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst2
% 0.29/0.51  thf(fact_1872_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: real,F: real > real,B: real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_real @ B @ C )
% 0.29/0.51         => ( ! [X5: real,Y3: real] :
% 0.29/0.51                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1873_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1874_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: real,F: num > real,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1875_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_nat @ B @ C )
% 0.29/0.51         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1876_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: real,F: int > real,B: int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_int @ B @ C )
% 0.29/0.51         => ( ! [X5: int,Y3: int] :
% 0.29/0.51                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1877_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_real @ B @ C )
% 0.29/0.51         => ( ! [X5: real,Y3: real] :
% 0.29/0.51                ( ( ord_less_real @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1878_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_rat @ B @ C )
% 0.29/0.51         => ( ! [X5: rat,Y3: rat] :
% 0.29/0.51                ( ( ord_less_rat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1879_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_num @ B @ C )
% 0.29/0.51         => ( ! [X5: num,Y3: num] :
% 0.29/0.51                ( ( ord_less_num @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1880_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_nat @ B @ C )
% 0.29/0.51         => ( ! [X5: nat,Y3: nat] :
% 0.29/0.51                ( ( ord_less_nat @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1881_order__le__less__subst1,axiom,
% 0.29/0.51      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.51       => ( ( ord_less_int @ B @ C )
% 0.29/0.51         => ( ! [X5: int,Y3: int] :
% 0.29/0.51                ( ( ord_less_int @ X5 @ Y3 )
% 0.29/0.51               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 0.29/0.51           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_subst1
% 0.29/0.51  thf(fact_1882_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: real,Y: real,Z: real] :
% 0.29/0.51        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_real @ Y @ Z )
% 0.29/0.51         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1883_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int,Z: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.29/0.51         => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1884_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.51         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1885_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: num,Y: num,Z: num] :
% 0.29/0.51        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.51         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1886_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat,Z: nat] :
% 0.29/0.51        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.51         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1887_order__less__le__trans,axiom,
% 0.29/0.51      ! [X4: int,Y: int,Z: int] :
% 0.29/0.51        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.51         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le_trans
% 0.29/0.51  thf(fact_1888_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: real,Y: real,Z: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_real @ Y @ Z )
% 0.29/0.51         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1889_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int,Z: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_set_int @ Y @ Z )
% 0.29/0.51         => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1890_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.51         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1891_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: num,Y: num,Z: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_num @ Y @ Z )
% 0.29/0.51         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1892_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat,Z: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.51         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1893_order__le__less__trans,axiom,
% 0.29/0.51      ! [X4: int,Y: int,Z: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.51         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less_trans
% 0.29/0.51  thf(fact_1894_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.51         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1895_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.51         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1896_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1897_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: num,B: num] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51         => ( ord_less_num @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1898_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.51         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1899_order__neq__le__trans,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( A != B )
% 0.29/0.51       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.51         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_neq_le_trans
% 0.29/0.51  thf(fact_1900_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1901_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1902_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1903_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: num,B: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_num @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1904_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1905_order__le__neq__trans,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.51       => ( ( A != B )
% 0.29/0.51         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_neq_trans
% 0.29/0.51  thf(fact_1906_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1907_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1908_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1909_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ord_less_num @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1910_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1911_order__less__imp__le,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_int @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_imp_le
% 0.29/0.51  thf(fact_1912_linorder__not__less,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_eq_real @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_less
% 0.29/0.51  thf(fact_1913_linorder__not__less,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_less
% 0.29/0.51  thf(fact_1914_linorder__not__less,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_eq_num @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_less
% 0.29/0.51  thf(fact_1915_linorder__not__less,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_less
% 0.29/0.51  thf(fact_1916_linorder__not__less,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_eq_int @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_less
% 0.29/0.51  thf(fact_1917_linorder__not__le,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_real @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_real @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_le
% 0.29/0.51  thf(fact_1918_linorder__not__le,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_rat @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_rat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_le
% 0.29/0.51  thf(fact_1919_linorder__not__le,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_num @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_num @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_le
% 0.29/0.51  thf(fact_1920_linorder__not__le,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_nat @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_nat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_le
% 0.29/0.51  thf(fact_1921_linorder__not__le,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_int @ X4 @ Y ) )
% 0.29/0.51        = ( ord_less_int @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % linorder_not_le
% 0.29/0.51  thf(fact_1922_order__less__le,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [X: real,Y5: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1923_order__less__le,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [X: set_int,Y5: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1924_order__less__le,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [X: rat,Y5: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1925_order__less__le,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [X: num,Y5: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1926_order__less__le,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [X: nat,Y5: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1927_order__less__le,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [X: int,Y5: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ X @ Y5 )
% 0.29/0.51            & ( X != Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_less_le
% 0.29/0.51  thf(fact_1928_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_real
% 0.29/0.51      = ( ^ [X: real,Y5: real] :
% 0.29/0.51            ( ( ord_less_real @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1929_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [X: set_int,Y5: set_int] :
% 0.29/0.51            ( ( ord_less_set_int @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1930_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_rat
% 0.29/0.51      = ( ^ [X: rat,Y5: rat] :
% 0.29/0.51            ( ( ord_less_rat @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1931_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_num
% 0.29/0.51      = ( ^ [X: num,Y5: num] :
% 0.29/0.51            ( ( ord_less_num @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1932_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_nat
% 0.29/0.51      = ( ^ [X: nat,Y5: nat] :
% 0.29/0.51            ( ( ord_less_nat @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1933_order__le__less,axiom,
% 0.29/0.51      ( ord_less_eq_int
% 0.29/0.51      = ( ^ [X: int,Y5: int] :
% 0.29/0.51            ( ( ord_less_int @ X @ Y5 )
% 0.29/0.51            | ( X = Y5 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order_le_less
% 0.29/0.51  thf(fact_1934_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: real,A: real] :
% 0.29/0.51        ( ( ord_less_real @ B @ A )
% 0.29/0.51       => ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1935_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: set_int,A: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ B @ A )
% 0.29/0.51       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1936_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: rat,A: rat] :
% 0.29/0.51        ( ( ord_less_rat @ B @ A )
% 0.29/0.51       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1937_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: num,A: num] :
% 0.29/0.51        ( ( ord_less_num @ B @ A )
% 0.29/0.51       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1938_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: nat,A: nat] :
% 0.29/0.51        ( ( ord_less_nat @ B @ A )
% 0.29/0.51       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1939_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [B: int,A: int] :
% 0.29/0.51        ( ( ord_less_int @ B @ A )
% 0.29/0.51       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_implies_order
% 0.29/0.51  thf(fact_1940_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1941_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ A @ B )
% 0.29/0.51       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1942_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1943_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: num,B: num] :
% 0.29/0.51        ( ( ord_less_num @ A @ B )
% 0.29/0.51       => ( ord_less_eq_num @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1944_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ord_less_nat @ A @ B )
% 0.29/0.51       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1945_order_Ostrict__implies__order,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_implies_order
% 0.29/0.51  thf(fact_1946_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [B2: real,A3: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1947_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [B2: set_int,A3: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1948_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [B2: rat,A3: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1949_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [B2: num,A3: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1950_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [B2: nat,A3: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1951_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [B2: int,A3: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.29/0.51            & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_not
% 0.29/0.51  thf(fact_1952_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: real,A: real,C: real] :
% 0.29/0.51        ( ( ord_less_real @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_real @ C @ B )
% 0.29/0.51         => ( ord_less_real @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1953_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: set_int,A: set_int,C: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ C @ B )
% 0.29/0.51         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1954_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: rat,A: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_rat @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.51         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1955_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: num,A: num,C: num] :
% 0.29/0.51        ( ( ord_less_num @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_num @ C @ B )
% 0.29/0.51         => ( ord_less_num @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1956_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: nat,A: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_nat @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.51         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1957_dual__order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [B: int,A: int,C: int] :
% 0.29/0.51        ( ( ord_less_int @ B @ A )
% 0.29/0.51       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.51         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans2
% 0.29/0.51  thf(fact_1958_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: real,A: real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.51       => ( ( ord_less_real @ C @ B )
% 0.29/0.51         => ( ord_less_real @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1959_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: set_int,A: set_int,C: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.51       => ( ( ord_less_set_int @ C @ B )
% 0.29/0.51         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1960_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: rat,A: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.51       => ( ( ord_less_rat @ C @ B )
% 0.29/0.51         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1961_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: num,A: num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ B @ A )
% 0.29/0.51       => ( ( ord_less_num @ C @ B )
% 0.29/0.51         => ( ord_less_num @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1962_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: nat,A: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.51       => ( ( ord_less_nat @ C @ B )
% 0.29/0.51         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1963_dual__order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [B: int,A: int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.51       => ( ( ord_less_int @ C @ B )
% 0.29/0.51         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_trans1
% 0.29/0.51  thf(fact_1964_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [B2: real,A3: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1965_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [B2: set_int,A3: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1966_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [B2: rat,A3: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1967_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [B2: num,A3: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1968_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [B2: nat,A3: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1969_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [B2: int,A3: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.strict_iff_order
% 0.29/0.51  thf(fact_1970_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_real
% 0.29/0.51      = ( ^ [B2: real,A3: real] :
% 0.29/0.51            ( ( ord_less_real @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1971_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [B2: set_int,A3: set_int] :
% 0.29/0.51            ( ( ord_less_set_int @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1972_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_rat
% 0.29/0.51      = ( ^ [B2: rat,A3: rat] :
% 0.29/0.51            ( ( ord_less_rat @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1973_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_num
% 0.29/0.51      = ( ^ [B2: num,A3: num] :
% 0.29/0.51            ( ( ord_less_num @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1974_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_nat
% 0.29/0.51      = ( ^ [B2: nat,A3: nat] :
% 0.29/0.51            ( ( ord_less_nat @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1975_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_int
% 0.29/0.51      = ( ^ [B2: int,A3: int] :
% 0.29/0.51            ( ( ord_less_int @ B2 @ A3 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dual_order.order_iff_strict
% 0.29/0.51  thf(fact_1976_dense__le__bounded,axiom,
% 0.29/0.51      ! [X4: real,Y: real,Z: real] :
% 0.29/0.51        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.51       => ( ! [W2: real] :
% 0.29/0.51              ( ( ord_less_real @ X4 @ W2 )
% 0.29/0.51             => ( ( ord_less_real @ W2 @ Y )
% 0.29/0.51               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 0.29/0.51         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_le_bounded
% 0.29/0.51  thf(fact_1977_dense__le__bounded,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.51        ( ( ord_less_rat @ X4 @ Y )
% 0.29/0.51       => ( ! [W2: rat] :
% 0.29/0.51              ( ( ord_less_rat @ X4 @ W2 )
% 0.29/0.51             => ( ( ord_less_rat @ W2 @ Y )
% 0.29/0.51               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 0.29/0.51         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_le_bounded
% 0.29/0.51  thf(fact_1978_dense__ge__bounded,axiom,
% 0.29/0.51      ! [Z: real,X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_real @ Z @ X4 )
% 0.29/0.51       => ( ! [W2: real] :
% 0.29/0.51              ( ( ord_less_real @ Z @ W2 )
% 0.29/0.51             => ( ( ord_less_real @ W2 @ X4 )
% 0.29/0.51               => ( ord_less_eq_real @ Y @ W2 ) ) )
% 0.29/0.51         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_ge_bounded
% 0.29/0.51  thf(fact_1979_dense__ge__bounded,axiom,
% 0.29/0.51      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_rat @ Z @ X4 )
% 0.29/0.51       => ( ! [W2: rat] :
% 0.29/0.51              ( ( ord_less_rat @ Z @ W2 )
% 0.29/0.51             => ( ( ord_less_rat @ W2 @ X4 )
% 0.29/0.51               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 0.29/0.51         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_ge_bounded
% 0.29/0.51  thf(fact_1980_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [A3: real,B2: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1981_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [A3: set_int,B2: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1982_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1983_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [A3: num,B2: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1984_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1985_order_Ostrict__iff__not,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [A3: int,B2: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.29/0.51            & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_not
% 0.29/0.51  thf(fact_1986_order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( ord_less_real @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.51         => ( ord_less_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1987_order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int,C: set_int] :
% 0.29/0.51        ( ( ord_less_set_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ B @ C )
% 0.29/0.51         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1988_order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.51         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1989_order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [A: num,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.51         => ( ord_less_num @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1990_order_Ostrict__trans2,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 @ B @ C )
% 0.29/0.51         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1991_order_Ostrict__trans2,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( ord_less_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.51         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans2
% 0.29/0.51  thf(fact_1992_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: real,B: real,C: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.51       => ( ( ord_less_real @ B @ C )
% 0.29/0.51         => ( ord_less_real @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1993_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int,C: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_set_int @ B @ C )
% 0.29/0.51         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1994_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: rat,B: rat,C: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.51       => ( ( ord_less_rat @ B @ C )
% 0.29/0.51         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1995_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: num,B: num,C: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ A @ B )
% 0.29/0.51       => ( ( ord_less_num @ B @ C )
% 0.29/0.51         => ( ord_less_num @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1996_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: nat,B: nat,C: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.51       => ( ( ord_less_nat @ B @ C )
% 0.29/0.51         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1997_order_Ostrict__trans1,axiom,
% 0.29/0.51      ! [A: int,B: int,C: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.51       => ( ( ord_less_int @ B @ C )
% 0.29/0.51         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_trans1
% 0.29/0.51  thf(fact_1998_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [A3: real,B2: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_1999_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [A3: set_int,B2: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_2000_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_2001_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [A3: num,B2: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_2002_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_2003_order_Ostrict__iff__order,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [A3: int,B2: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.29/0.51            & ( A3 != B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.strict_iff_order
% 0.29/0.51  thf(fact_2004_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_real
% 0.29/0.51      = ( ^ [A3: real,B2: real] :
% 0.29/0.51            ( ( ord_less_real @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2005_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_set_int
% 0.29/0.51      = ( ^ [A3: set_int,B2: set_int] :
% 0.29/0.51            ( ( ord_less_set_int @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2006_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_rat
% 0.29/0.51      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.51            ( ( ord_less_rat @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2007_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_num
% 0.29/0.51      = ( ^ [A3: num,B2: num] :
% 0.29/0.51            ( ( ord_less_num @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2008_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_nat
% 0.29/0.51      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.51            ( ( ord_less_nat @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2009_order_Oorder__iff__strict,axiom,
% 0.29/0.51      ( ord_less_eq_int
% 0.29/0.51      = ( ^ [A3: int,B2: int] :
% 0.29/0.51            ( ( ord_less_int @ A3 @ B2 )
% 0.29/0.51            | ( A3 = B2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % order.order_iff_strict
% 0.29/0.51  thf(fact_2010_not__le__imp__less,axiom,
% 0.29/0.51      ! [Y: real,X4: real] :
% 0.29/0.51        ( ~ ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.51       => ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_le_imp_less
% 0.29/0.51  thf(fact_2011_not__le__imp__less,axiom,
% 0.29/0.51      ! [Y: rat,X4: rat] :
% 0.29/0.51        ( ~ ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.51       => ( ord_less_rat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_le_imp_less
% 0.29/0.51  thf(fact_2012_not__le__imp__less,axiom,
% 0.29/0.51      ! [Y: num,X4: num] :
% 0.29/0.51        ( ~ ( ord_less_eq_num @ Y @ X4 )
% 0.29/0.51       => ( ord_less_num @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_le_imp_less
% 0.29/0.51  thf(fact_2013_not__le__imp__less,axiom,
% 0.29/0.51      ! [Y: nat,X4: nat] :
% 0.29/0.51        ( ~ ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.51       => ( ord_less_nat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_le_imp_less
% 0.29/0.51  thf(fact_2014_not__le__imp__less,axiom,
% 0.29/0.51      ! [Y: int,X4: int] :
% 0.29/0.51        ( ~ ( ord_less_eq_int @ Y @ X4 )
% 0.29/0.51       => ( ord_less_int @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % not_le_imp_less
% 0.29/0.51  thf(fact_2015_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_real
% 0.29/0.51      = ( ^ [X: real,Y5: real] :
% 0.29/0.51            ( ( ord_less_eq_real @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2016_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_set_int
% 0.29/0.51      = ( ^ [X: set_int,Y5: set_int] :
% 0.29/0.51            ( ( ord_less_eq_set_int @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2017_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_rat
% 0.29/0.51      = ( ^ [X: rat,Y5: rat] :
% 0.29/0.51            ( ( ord_less_eq_rat @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2018_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_num
% 0.29/0.51      = ( ^ [X: num,Y5: num] :
% 0.29/0.51            ( ( ord_less_eq_num @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2019_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_nat
% 0.29/0.51      = ( ^ [X: nat,Y5: nat] :
% 0.29/0.51            ( ( ord_less_eq_nat @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2020_less__le__not__le,axiom,
% 0.29/0.51      ( ord_less_int
% 0.29/0.51      = ( ^ [X: int,Y5: int] :
% 0.29/0.51            ( ( ord_less_eq_int @ X @ Y5 )
% 0.29/0.51            & ~ ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % less_le_not_le
% 0.29/0.51  thf(fact_2021_dense__le,axiom,
% 0.29/0.51      ! [Y: real,Z: real] :
% 0.29/0.51        ( ! [X5: real] :
% 0.29/0.51            ( ( ord_less_real @ X5 @ Y )
% 0.29/0.51           => ( ord_less_eq_real @ X5 @ Z ) )
% 0.29/0.51       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_le
% 0.29/0.51  thf(fact_2022_dense__le,axiom,
% 0.29/0.51      ! [Y: rat,Z: rat] :
% 0.29/0.51        ( ! [X5: rat] :
% 0.29/0.51            ( ( ord_less_rat @ X5 @ Y )
% 0.29/0.51           => ( ord_less_eq_rat @ X5 @ Z ) )
% 0.29/0.51       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_le
% 0.29/0.51  thf(fact_2023_dense__ge,axiom,
% 0.29/0.51      ! [Z: real,Y: real] :
% 0.29/0.51        ( ! [X5: real] :
% 0.29/0.51            ( ( ord_less_real @ Z @ X5 )
% 0.29/0.51           => ( ord_less_eq_real @ Y @ X5 ) )
% 0.29/0.51       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_ge
% 0.29/0.51  thf(fact_2024_dense__ge,axiom,
% 0.29/0.51      ! [Z: rat,Y: rat] :
% 0.29/0.51        ( ! [X5: rat] :
% 0.29/0.51            ( ( ord_less_rat @ Z @ X5 )
% 0.29/0.51           => ( ord_less_eq_rat @ Y @ X5 ) )
% 0.29/0.51       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dense_ge
% 0.29/0.51  thf(fact_2025_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2026_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_set_int @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2027_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2028_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2029_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2030_antisym__conv2,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.51       => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv2
% 0.29/0.51  thf(fact_2031_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ~ ( ord_less_real @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2032_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: set_int,Y: set_int] :
% 0.29/0.51        ( ~ ( ord_less_set_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2033_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ~ ( ord_less_rat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2034_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ~ ( ord_less_num @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_num @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2035_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ~ ( ord_less_nat @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_nat @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2036_antisym__conv1,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ~ ( ord_less_int @ X4 @ Y )
% 0.29/0.51       => ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.51          = ( X4 = Y ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % antisym_conv1
% 0.29/0.51  thf(fact_2037_nless__le,axiom,
% 0.29/0.51      ! [A: real,B: real] :
% 0.29/0.51        ( ( ~ ( ord_less_real @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2038_nless__le,axiom,
% 0.29/0.51      ! [A: set_int,B: set_int] :
% 0.29/0.51        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2039_nless__le,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2040_nless__le,axiom,
% 0.29/0.51      ! [A: num,B: num] :
% 0.29/0.51        ( ( ~ ( ord_less_num @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2041_nless__le,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2042_nless__le,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.29/0.51        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % nless_le
% 0.29/0.51  thf(fact_2043_leI,axiom,
% 0.29/0.51      ! [X4: real,Y: real] :
% 0.29/0.51        ( ~ ( ord_less_real @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_real @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leI
% 0.29/0.51  thf(fact_2044_leI,axiom,
% 0.29/0.51      ! [X4: rat,Y: rat] :
% 0.29/0.51        ( ~ ( ord_less_rat @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leI
% 0.29/0.51  thf(fact_2045_leI,axiom,
% 0.29/0.51      ! [X4: num,Y: num] :
% 0.29/0.51        ( ~ ( ord_less_num @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leI
% 0.29/0.51  thf(fact_2046_leI,axiom,
% 0.29/0.51      ! [X4: nat,Y: nat] :
% 0.29/0.51        ( ~ ( ord_less_nat @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leI
% 0.29/0.51  thf(fact_2047_leI,axiom,
% 0.29/0.51      ! [X4: int,Y: int] :
% 0.29/0.51        ( ~ ( ord_less_int @ X4 @ Y )
% 0.29/0.51       => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leI
% 0.29/0.51  thf(fact_2048_leD,axiom,
% 0.29/0.51      ! [Y: real,X4: real] :
% 0.29/0.51        ( ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2049_leD,axiom,
% 0.29/0.51      ! [Y: set_int,X4: set_int] :
% 0.29/0.51        ( ( ord_less_eq_set_int @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_set_int @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2050_leD,axiom,
% 0.29/0.51      ! [Y: rat,X4: rat] :
% 0.29/0.51        ( ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_rat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2051_leD,axiom,
% 0.29/0.51      ! [Y: num,X4: num] :
% 0.29/0.51        ( ( ord_less_eq_num @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_num @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2052_leD,axiom,
% 0.29/0.51      ! [Y: nat,X4: nat] :
% 0.29/0.51        ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_nat @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2053_leD,axiom,
% 0.29/0.51      ! [Y: int,X4: int] :
% 0.29/0.51        ( ( ord_less_eq_int @ Y @ X4 )
% 0.29/0.51       => ~ ( ord_less_int @ X4 @ Y ) ) ).
% 0.29/0.51  
% 0.29/0.51  % leD
% 0.29/0.51  thf(fact_2054_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.51      ! [B4: real,A4: real] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 0.29/0.51        = ( ord_less_real @ A4 @ B4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_comp_simplify1(3)
% 0.29/0.51  thf(fact_2055_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.51      ! [B4: rat,A4: rat] :
% 0.29/0.51        ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 0.29/0.51        = ( ord_less_rat @ A4 @ B4 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_comp_simplify1(3)
% 0.29/0.51  thf(fact_2056_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.52      ! [B4: num,A4: num] :
% 0.29/0.52        ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 0.29/0.52        = ( ord_less_num @ A4 @ B4 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_comp_simplify1(3)
% 0.29/0.52  thf(fact_2057_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.52      ! [B4: nat,A4: nat] :
% 0.29/0.52        ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.29/0.52        = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_comp_simplify1(3)
% 0.29/0.52  thf(fact_2058_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.52      ! [B4: int,A4: int] :
% 0.29/0.52        ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 0.29/0.52        = ( ord_less_int @ A4 @ B4 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_comp_simplify1(3)
% 0.29/0.52  thf(fact_2059_Suc__n__div__2__gt__zero,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_n_div_2_gt_zero
% 0.29/0.52  thf(fact_2060_div__2__gt__zero,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.52       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_2_gt_zero
% 0.29/0.52  thf(fact_2061_verit__eq__simplify_I10_J,axiom,
% 0.29/0.52      ! [X22: num] :
% 0.29/0.52        ( one
% 0.29/0.52       != ( bit0 @ X22 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_eq_simplify(10)
% 0.29/0.52  thf(fact_2062_invar__vebt_Ointros_I4_J,axiom,
% 0.29/0.52      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.29/0.52        ( ! [X5: vEBT_VEBT] :
% 0.29/0.52            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.29/0.52           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.29/0.52       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.29/0.52         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.29/0.52              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.52           => ( ( M = N2 )
% 0.29/0.52             => ( ( Deg
% 0.29/0.52                  = ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.52               => ( ! [I4: nat] :
% 0.29/0.52                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.52                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 0.29/0.52                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.29/0.52                 => ( ( ( Mi = Ma )
% 0.29/0.52                     => ! [X5: vEBT_VEBT] :
% 0.29/0.52                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.29/0.52                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 0.29/0.52                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.29/0.52                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.52                       => ( ( ( Mi != Ma )
% 0.29/0.52                           => ! [I4: nat] :
% 0.29/0.52                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.52                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 0.29/0.52                                      = I4 )
% 0.29/0.52                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 0.29/0.52                                  & ! [X5: nat] :
% 0.29/0.52                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 0.29/0.52                                          = I4 )
% 0.29/0.52                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 0.29/0.52                                     => ( ( ord_less_nat @ Mi @ X5 )
% 0.29/0.52                                        & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 0.29/0.52                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % invar_vebt.intros(4)
% 0.29/0.52  thf(fact_2063_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52         != ( suc @ zero_zero_nat ) )
% 0.29/0.52        = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52          = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod2_eq_Suc_0_eq_0
% 0.29/0.52  thf(fact_2064_not__mod__2__eq__1__eq__0,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52         != one_one_nat )
% 0.29/0.52        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52          = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_1_eq_0
% 0.29/0.52  thf(fact_2065_not__mod__2__eq__1__eq__0,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.52         != one_one_int )
% 0.29/0.52        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.52          = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_1_eq_0
% 0.29/0.52  thf(fact_2066_not__mod__2__eq__1__eq__0,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.52         != one_one_Code_integer )
% 0.29/0.52        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.52          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_1_eq_0
% 0.29/0.52  thf(fact_2067_not__mod__2__eq__0__eq__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52         != zero_zero_nat )
% 0.29/0.52        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52          = one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_0_eq_1
% 0.29/0.52  thf(fact_2068_not__mod__2__eq__0__eq__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.52         != zero_zero_int )
% 0.29/0.52        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.52          = one_one_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_0_eq_1
% 0.29/0.52  thf(fact_2069_not__mod__2__eq__0__eq__1,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.52         != zero_z3403309356797280102nteger )
% 0.29/0.52        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.52          = one_one_Code_integer ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_mod_2_eq_0_eq_1
% 0.29/0.52  thf(fact_2070_invar__vebt_Osimps,axiom,
% 0.29/0.52      ( vEBT_invar_vebt
% 0.29/0.52      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 0.29/0.52            ( ( ? [A3: $o,B2: $o] :
% 0.29/0.52                  ( A1
% 0.29/0.52                  = ( vEBT_Leaf @ A3 @ B2 ) )
% 0.29/0.52              & ( A22
% 0.29/0.52                = ( suc @ zero_zero_nat ) ) )
% 0.29/0.52            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 0.29/0.52                ( ( A1
% 0.29/0.52                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ( vEBT_invar_vebt @ X @ N ) )
% 0.29/0.52                & ( vEBT_invar_vebt @ Summary2 @ N )
% 0.29/0.52                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.52                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.52                & ( A22
% 0.29/0.52                  = ( plus_plus_nat @ N @ N ) )
% 0.29/0.52                & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.52            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 0.29/0.52                ( ( A1
% 0.29/0.52                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ( vEBT_invar_vebt @ X @ N ) )
% 0.29/0.52                & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 0.29/0.52                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.52                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.29/0.52                & ( A22
% 0.29/0.52                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 0.29/0.52                & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.52            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 0.29/0.52                ( ( A1
% 0.29/0.52                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ( vEBT_invar_vebt @ X @ N ) )
% 0.29/0.52                & ( vEBT_invar_vebt @ Summary2 @ N )
% 0.29/0.52                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.52                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.52                & ( A22
% 0.29/0.52                  = ( plus_plus_nat @ N @ N ) )
% 0.29/0.52                & ! [I3: nat] :
% 0.29/0.52                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.52                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 0.29/0.52                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.29/0.52                & ( ( Mi2 = Ma2 )
% 0.29/0.52                 => ! [X: vEBT_VEBT] :
% 0.29/0.52                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.52                & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.52                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.29/0.52                & ( ( Mi2 != Ma2 )
% 0.29/0.52                 => ! [I3: nat] :
% 0.29/0.52                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.52                     => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 0.29/0.52                            = I3 )
% 0.29/0.52                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 0.29/0.52                        & ! [X: nat] :
% 0.29/0.52                            ( ( ( ( vEBT_VEBT_high @ X @ N )
% 0.29/0.52                                = I3 )
% 0.29/0.52                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 0.29/0.52                           => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.52                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) )
% 0.29/0.52            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 0.29/0.52                ( ( A1
% 0.29/0.52                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 0.29/0.52                & ! [X: vEBT_VEBT] :
% 0.29/0.52                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                   => ( vEBT_invar_vebt @ X @ N ) )
% 0.29/0.52                & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 0.29/0.52                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.29/0.52                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.29/0.52                & ( A22
% 0.29/0.52                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 0.29/0.52                & ! [I3: nat] :
% 0.29/0.52                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.29/0.52                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 0.29/0.52                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.29/0.52                & ( ( Mi2 = Ma2 )
% 0.29/0.52                 => ! [X: vEBT_VEBT] :
% 0.29/0.52                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.52                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.52                & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.52                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.29/0.52                & ( ( Mi2 != Ma2 )
% 0.29/0.52                 => ! [I3: nat] :
% 0.29/0.52                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 0.29/0.52                     => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 0.29/0.52                            = I3 )
% 0.29/0.52                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 0.29/0.52                        & ! [X: nat] :
% 0.29/0.52                            ( ( ( ( vEBT_VEBT_high @ X @ N )
% 0.29/0.52                                = I3 )
% 0.29/0.52                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 0.29/0.52                           => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.52                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % invar_vebt.simps
% 0.29/0.52  thf(fact_2071_invar__vebt_Ocases,axiom,
% 0.29/0.52      ! [A12: vEBT_VEBT,A23: nat] :
% 0.29/0.52        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 0.29/0.52       => ( ( ? [A5: $o,B5: $o] :
% 0.29/0.52                ( A12
% 0.29/0.52                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.52           => ( A23
% 0.29/0.52             != ( suc @ zero_zero_nat ) ) )
% 0.29/0.52         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 0.29/0.52                ( ( A12
% 0.29/0.52                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.52               => ( ( A23 = Deg2 )
% 0.29/0.52                 => ( ! [X2: vEBT_VEBT] :
% 0.29/0.52                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                       => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 0.29/0.52                   => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 0.29/0.52                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.52                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                       => ( ( M5 = N3 )
% 0.29/0.52                         => ( ( Deg2
% 0.29/0.52                              = ( plus_plus_nat @ N3 @ M5 ) )
% 0.29/0.52                           => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 0.29/0.52                             => ~ ! [X2: vEBT_VEBT] :
% 0.29/0.52                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                                   => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.29/0.52           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 0.29/0.52                  ( ( A12
% 0.29/0.52                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.52                 => ( ( A23 = Deg2 )
% 0.29/0.52                   => ( ! [X2: vEBT_VEBT] :
% 0.29/0.52                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                         => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 0.29/0.52                     => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 0.29/0.52                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.52                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                         => ( ( M5
% 0.29/0.52                              = ( suc @ N3 ) )
% 0.29/0.52                           => ( ( Deg2
% 0.29/0.52                                = ( plus_plus_nat @ N3 @ M5 ) )
% 0.29/0.52                             => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 0.29/0.52                               => ~ ! [X2: vEBT_VEBT] :
% 0.29/0.52                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                                     => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.29/0.52             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 0.29/0.52                    ( ( A12
% 0.29/0.52                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.52                   => ( ( A23 = Deg2 )
% 0.29/0.52                     => ( ! [X2: vEBT_VEBT] :
% 0.29/0.52                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                           => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 0.29/0.52                       => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 0.29/0.52                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.52                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                           => ( ( M5 = N3 )
% 0.29/0.52                             => ( ( Deg2
% 0.29/0.52                                  = ( plus_plus_nat @ N3 @ M5 ) )
% 0.29/0.52                               => ( ! [I: nat] :
% 0.29/0.52                                      ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 0.29/0.52                                        = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 0.29/0.52                                 => ( ( ( Mi3 = Ma3 )
% 0.29/0.52                                     => ! [X2: vEBT_VEBT] :
% 0.29/0.52                                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 0.29/0.52                                   => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.29/0.52                                     => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.52                                       => ~ ( ( Mi3 != Ma3 )
% 0.29/0.52                                           => ! [I: nat] :
% 0.29/0.52                                                ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                                               => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 0.29/0.52                                                      = I )
% 0.29/0.52                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 0.29/0.52                                                  & ! [X2: nat] :
% 0.29/0.52                                                      ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 0.29/0.52                                                          = I )
% 0.29/0.52                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 0.29/0.52                                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.29/0.52                                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.52               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 0.29/0.52                      ( ( A12
% 0.29/0.52                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.52                     => ( ( A23 = Deg2 )
% 0.29/0.52                       => ( ! [X2: vEBT_VEBT] :
% 0.29/0.52                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                             => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 0.29/0.52                         => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 0.29/0.52                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.52                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                             => ( ( M5
% 0.29/0.52                                  = ( suc @ N3 ) )
% 0.29/0.52                               => ( ( Deg2
% 0.29/0.52                                    = ( plus_plus_nat @ N3 @ M5 ) )
% 0.29/0.52                                 => ( ! [I: nat] :
% 0.29/0.52                                        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                                       => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 0.29/0.52                                          = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 0.29/0.52                                   => ( ( ( Mi3 = Ma3 )
% 0.29/0.52                                       => ! [X2: vEBT_VEBT] :
% 0.29/0.52                                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.52                                           => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 0.29/0.52                                     => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.29/0.52                                       => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.52                                         => ~ ( ( Mi3 != Ma3 )
% 0.29/0.52                                             => ! [I: nat] :
% 0.29/0.52                                                  ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 0.29/0.52                                                 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 0.29/0.52                                                        = I )
% 0.29/0.52                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 0.29/0.52                                                    & ! [X2: nat] :
% 0.29/0.52                                                        ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 0.29/0.52                                                            = I )
% 0.29/0.52                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 0.29/0.52                                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 0.29/0.52                                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % invar_vebt.cases
% 0.29/0.52  thf(fact_2072_nat__induct2,axiom,
% 0.29/0.52      ! [P: nat > $o,N2: nat] :
% 0.29/0.52        ( ( P @ zero_zero_nat )
% 0.29/0.52       => ( ( P @ one_one_nat )
% 0.29/0.52         => ( ! [N3: nat] :
% 0.29/0.52                ( ( P @ N3 )
% 0.29/0.52               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.52           => ( P @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_induct2
% 0.29/0.52  thf(fact_2073_not__Some__eq,axiom,
% 0.29/0.52      ! [X4: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( ! [Y5: product_prod_nat_nat] :
% 0.29/0.52              ( X4
% 0.29/0.52             != ( some_P7363390416028606310at_nat @ Y5 ) ) )
% 0.29/0.52        = ( X4 = none_P5556105721700978146at_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_Some_eq
% 0.29/0.52  thf(fact_2074_not__Some__eq,axiom,
% 0.29/0.52      ! [X4: option_num] :
% 0.29/0.52        ( ( ! [Y5: num] :
% 0.29/0.52              ( X4
% 0.29/0.52             != ( some_num @ Y5 ) ) )
% 0.29/0.52        = ( X4 = none_num ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_Some_eq
% 0.29/0.52  thf(fact_2075_not__None__eq,axiom,
% 0.29/0.52      ! [X4: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( X4 != none_P5556105721700978146at_nat )
% 0.29/0.52        = ( ? [Y5: product_prod_nat_nat] :
% 0.29/0.52              ( X4
% 0.29/0.52              = ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_None_eq
% 0.29/0.52  thf(fact_2076_not__None__eq,axiom,
% 0.29/0.52      ! [X4: option_num] :
% 0.29/0.52        ( ( X4 != none_num )
% 0.29/0.52        = ( ? [Y5: num] :
% 0.29/0.52              ( X4
% 0.29/0.52              = ( some_num @ Y5 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_None_eq
% 0.29/0.52  thf(fact_2077_pos2,axiom,
% 0.29/0.52      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.29/0.52  
% 0.29/0.52  % pos2
% 0.29/0.52  thf(fact_2078_double__eq__0__iff,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ A @ A )
% 0.29/0.52          = zero_zero_real )
% 0.29/0.52        = ( A = zero_zero_real ) ) ).
% 0.29/0.52  
% 0.29/0.52  % double_eq_0_iff
% 0.29/0.52  thf(fact_2079_double__eq__0__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ A @ A )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( A = zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % double_eq_0_iff
% 0.29/0.52  thf(fact_2080_double__eq__0__iff,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ A @ A )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( A = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % double_eq_0_iff
% 0.29/0.52  thf(fact_2081_div__pos__pos__trivial,axiom,
% 0.29/0.52      ! [K: int,L: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.52       => ( ( ord_less_int @ K @ L )
% 0.29/0.52         => ( ( divide_divide_int @ K @ L )
% 0.29/0.52            = zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_pos_pos_trivial
% 0.29/0.52  thf(fact_2082_div__neg__neg__trivial,axiom,
% 0.29/0.52      ! [K: int,L: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_int @ L @ K )
% 0.29/0.52         => ( ( divide_divide_int @ K @ L )
% 0.29/0.52            = zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_neg_neg_trivial
% 0.29/0.52  thf(fact_2083_VEBT_Oinject_I2_J,axiom,
% 0.29/0.52      ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 0.29/0.52        ( ( ( vEBT_Leaf @ X21 @ X222 )
% 0.29/0.52          = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 0.29/0.52        = ( ( X21 = Y21 )
% 0.29/0.52          & ( X222 = Y22 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT.inject(2)
% 0.29/0.52  thf(fact_2084_i0__less,axiom,
% 0.29/0.52      ! [N2: extended_enat] :
% 0.29/0.52        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 0.29/0.52        = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % i0_less
% 0.29/0.52  thf(fact_2085_half__nonnegative__int__iff,axiom,
% 0.29/0.52      ! [K: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.29/0.52        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.52  
% 0.29/0.52  % half_nonnegative_int_iff
% 0.29/0.52  thf(fact_2086_half__negative__int__iff,axiom,
% 0.29/0.52      ! [K: int] :
% 0.29/0.52        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.29/0.52        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % half_negative_int_iff
% 0.29/0.52  thf(fact_2087_VEBT_Osize_I4_J,axiom,
% 0.29/0.52      ! [X21: $o,X222: $o] :
% 0.29/0.52        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT.size(4)
% 0.29/0.52  thf(fact_2088_VEBT_Oexhaust,axiom,
% 0.29/0.52      ! [Y: vEBT_VEBT] :
% 0.29/0.52        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 0.29/0.52            ( Y
% 0.29/0.52           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 0.29/0.52       => ~ ! [X212: $o,X223: $o] :
% 0.29/0.52              ( Y
% 0.29/0.52             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT.exhaust
% 0.29/0.52  thf(fact_2089_VEBT_Odistinct_I1_J,axiom,
% 0.29/0.52      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 0.29/0.52        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.29/0.52       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT.distinct(1)
% 0.29/0.52  thf(fact_2090_zdiv__mono__strict,axiom,
% 0.29/0.52      ! [A2: int,B3: int,N2: int] :
% 0.29/0.52        ( ( ord_less_int @ A2 @ B3 )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.29/0.52         => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 0.29/0.52              = zero_zero_int )
% 0.29/0.52           => ( ( ( modulo_modulo_int @ B3 @ N2 )
% 0.29/0.52                = zero_zero_int )
% 0.29/0.52             => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_mono_strict
% 0.29/0.52  thf(fact_2091_div__neg__pos__less0,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_neg_pos_less0
% 0.29/0.52  thf(fact_2092_neg__imp__zdiv__neg__iff,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.29/0.52          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_imp_zdiv_neg_iff
% 0.29/0.52  thf(fact_2093_pos__imp__zdiv__neg__iff,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.29/0.52          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % pos_imp_zdiv_neg_iff
% 0.29/0.52  thf(fact_2094_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.29/0.52          = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonneg1_imp_zdiv_pos_iff
% 0.29/0.52  thf(fact_2095_pos__imp__zdiv__nonneg__iff,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.29/0.52          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % pos_imp_zdiv_nonneg_iff
% 0.29/0.52  thf(fact_2096_neg__imp__zdiv__nonneg__iff,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.29/0.52          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_imp_zdiv_nonneg_iff
% 0.29/0.52  thf(fact_2097_pos__imp__zdiv__pos__iff,axiom,
% 0.29/0.52      ! [K: int,I2: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 0.29/0.52          = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % pos_imp_zdiv_pos_iff
% 0.29/0.52  thf(fact_2098_div__nonpos__pos__le0,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_nonpos_pos_le0
% 0.29/0.52  thf(fact_2099_div__nonneg__neg__le0,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.52       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.52         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_nonneg_neg_le0
% 0.29/0.52  thf(fact_2100_verit__le__mono__div__int,axiom,
% 0.29/0.52      ! [A2: int,B3: int,N2: int] :
% 0.29/0.52        ( ( ord_less_int @ A2 @ B3 )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.29/0.52         => ( ord_less_eq_int
% 0.29/0.52            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 0.29/0.52              @ ( if_int
% 0.29/0.52                @ ( ( modulo_modulo_int @ B3 @ N2 )
% 0.29/0.52                  = zero_zero_int )
% 0.29/0.52                @ one_one_int
% 0.29/0.52                @ zero_zero_int ) )
% 0.29/0.52            @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_le_mono_div_int
% 0.29/0.52  thf(fact_2101_int__div__less__self,axiom,
% 0.29/0.52      ! [X4: int,K: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ X4 )
% 0.29/0.52       => ( ( ord_less_int @ one_one_int @ K )
% 0.29/0.52         => ( ord_less_int @ ( divide_divide_int @ X4 @ K ) @ X4 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % int_div_less_self
% 0.29/0.52  thf(fact_2102_div__positive__int,axiom,
% 0.29/0.52      ! [L: int,K: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ L @ K )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.52         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_positive_int
% 0.29/0.52  thf(fact_2103_div__int__pos__iff,axiom,
% 0.29/0.52      ! [K: int,L: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.29/0.52        = ( ( K = zero_zero_int )
% 0.29/0.52          | ( L = zero_zero_int )
% 0.29/0.52          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.52            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.29/0.52          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.52            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_int_pos_iff
% 0.29/0.52  thf(fact_2104_zdiv__mono2__neg,axiom,
% 0.29/0.52      ! [A: int,B4: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.29/0.52         => ( ( ord_less_eq_int @ B4 @ B )
% 0.29/0.52           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_mono2_neg
% 0.29/0.52  thf(fact_2105_zdiv__mono1__neg,axiom,
% 0.29/0.52      ! [A: int,A4: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ A4 )
% 0.29/0.52       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.52         => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_mono1_neg
% 0.29/0.52  thf(fact_2106_zdiv__eq__0__iff,axiom,
% 0.29/0.52      ! [I2: int,K: int] :
% 0.29/0.52        ( ( ( divide_divide_int @ I2 @ K )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( ( K = zero_zero_int )
% 0.29/0.52          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.29/0.52            & ( ord_less_int @ I2 @ K ) )
% 0.29/0.52          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.29/0.52            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_eq_0_iff
% 0.29/0.52  thf(fact_2107_zdiv__mono2,axiom,
% 0.29/0.52      ! [A: int,B4: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.29/0.52         => ( ( ord_less_eq_int @ B4 @ B )
% 0.29/0.52           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_mono2
% 0.29/0.52  thf(fact_2108_zdiv__mono1,axiom,
% 0.29/0.52      ! [A: int,A4: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ A4 )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zdiv_mono1
% 0.29/0.52  thf(fact_2109_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 0.29/0.52      ! [Uu: $o,Uv: $o,Uw: nat] :
% 0.29/0.52        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.membermima.simps(1)
% 0.29/0.52  thf(fact_2110_not__iless0,axiom,
% 0.29/0.52      ! [N2: extended_enat] :
% 0.29/0.52        ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iless0
% 0.29/0.52  thf(fact_2111_i0__lb,axiom,
% 0.29/0.52      ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 0.29/0.52  
% 0.29/0.52  % i0_lb
% 0.29/0.52  thf(fact_2112_ile0__eq,axiom,
% 0.29/0.52      ! [N2: extended_enat] :
% 0.29/0.52        ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 0.29/0.52        = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % ile0_eq
% 0.29/0.52  thf(fact_2113_realpow__pos__nth2,axiom,
% 0.29/0.52      ! [A: real,N2: nat] :
% 0.29/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.52       => ? [R2: real] :
% 0.29/0.52            ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.29/0.52            & ( ( power_power_real @ R2 @ ( suc @ N2 ) )
% 0.29/0.52              = A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % realpow_pos_nth2
% 0.29/0.52  thf(fact_2114_vebt__buildup_Osimps_I1_J,axiom,
% 0.29/0.52      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.29/0.52      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_buildup.simps(1)
% 0.29/0.52  thf(fact_2115_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.29/0.52      ! [Uu: $o,Uv: $o,D: nat] :
% 0.29/0.52        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 0.29/0.52        = ( D = one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.valid'.simps(1)
% 0.29/0.52  thf(fact_2116_realpow__pos__nth__unique,axiom,
% 0.29/0.52      ! [N2: nat,A: real] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.52         => ? [X5: real] :
% 0.29/0.52              ( ( ord_less_real @ zero_zero_real @ X5 )
% 0.29/0.52              & ( ( power_power_real @ X5 @ N2 )
% 0.29/0.52                = A )
% 0.29/0.52              & ! [Y4: real] :
% 0.29/0.52                  ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 0.29/0.52                    & ( ( power_power_real @ Y4 @ N2 )
% 0.29/0.52                      = A ) )
% 0.29/0.52                 => ( Y4 = X5 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % realpow_pos_nth_unique
% 0.29/0.52  thf(fact_2117_realpow__pos__nth,axiom,
% 0.29/0.52      ! [N2: nat,A: real] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.52         => ? [R2: real] :
% 0.29/0.52              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.29/0.52              & ( ( power_power_real @ R2 @ N2 )
% 0.29/0.52                = A ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % realpow_pos_nth
% 0.29/0.52  thf(fact_2118_invar__vebt_Ointros_I1_J,axiom,
% 0.29/0.52      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % invar_vebt.intros(1)
% 0.29/0.52  thf(fact_2119_not__exp__less__eq__0__int,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % not_exp_less_eq_0_int
% 0.29/0.52  thf(fact_2120_vebt__buildup_Osimps_I2_J,axiom,
% 0.29/0.52      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.29/0.52      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.29/0.52  
% 0.29/0.52  % vebt_buildup.simps(2)
% 0.29/0.52  thf(fact_2121_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.29/0.52      ! [A: $o,B: $o,X4: nat] :
% 0.29/0.52        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X4 )
% 0.29/0.52        = ( ( ( X4 = zero_zero_nat )
% 0.29/0.52           => A )
% 0.29/0.52          & ( ( X4 != zero_zero_nat )
% 0.29/0.52           => ( ( ( X4 = one_one_nat )
% 0.29/0.52               => B )
% 0.29/0.52              & ( X4 = one_one_nat ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % VEBT_internal.naive_member.simps(1)
% 0.29/0.52  thf(fact_2122_real__arch__pow__inv,axiom,
% 0.29/0.52      ! [Y: real,X4: real] :
% 0.29/0.52        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.52       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.52         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X4 @ N3 ) @ Y ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % real_arch_pow_inv
% 0.29/0.52  thf(fact_2123_option_Odistinct_I1_J,axiom,
% 0.29/0.52      ! [X22: product_prod_nat_nat] :
% 0.29/0.52        ( none_P5556105721700978146at_nat
% 0.29/0.52       != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.distinct(1)
% 0.29/0.52  thf(fact_2124_option_Odistinct_I1_J,axiom,
% 0.29/0.52      ! [X22: num] :
% 0.29/0.52        ( none_num
% 0.29/0.52       != ( some_num @ X22 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.distinct(1)
% 0.29/0.52  thf(fact_2125_option_OdiscI,axiom,
% 0.29/0.52      ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 0.29/0.52        ( ( Option
% 0.29/0.52          = ( some_P7363390416028606310at_nat @ X22 ) )
% 0.29/0.52       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.discI
% 0.29/0.52  thf(fact_2126_option_OdiscI,axiom,
% 0.29/0.52      ! [Option: option_num,X22: num] :
% 0.29/0.52        ( ( Option
% 0.29/0.52          = ( some_num @ X22 ) )
% 0.29/0.52       => ( Option != none_num ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.discI
% 0.29/0.52  thf(fact_2127_option_Oexhaust,axiom,
% 0.29/0.52      ! [Y: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( Y != none_P5556105721700978146at_nat )
% 0.29/0.52       => ~ ! [X23: product_prod_nat_nat] :
% 0.29/0.52              ( Y
% 0.29/0.52             != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.exhaust
% 0.29/0.52  thf(fact_2128_option_Oexhaust,axiom,
% 0.29/0.52      ! [Y: option_num] :
% 0.29/0.52        ( ( Y != none_num )
% 0.29/0.52       => ~ ! [X23: num] :
% 0.29/0.52              ( Y
% 0.29/0.52             != ( some_num @ X23 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.exhaust
% 0.29/0.52  thf(fact_2129_split__option__ex,axiom,
% 0.29/0.52      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.29/0.52          ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 0.29/0.52      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.29/0.52            ( ( P4 @ none_P5556105721700978146at_nat )
% 0.29/0.52            | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % split_option_ex
% 0.29/0.52  thf(fact_2130_split__option__ex,axiom,
% 0.29/0.52      ( ( ^ [P3: option_num > $o] :
% 0.29/0.52          ? [X6: option_num] : ( P3 @ X6 ) )
% 0.29/0.52      = ( ^ [P4: option_num > $o] :
% 0.29/0.52            ( ( P4 @ none_num )
% 0.29/0.52            | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % split_option_ex
% 0.29/0.52  thf(fact_2131_split__option__all,axiom,
% 0.29/0.52      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.29/0.52          ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 0.29/0.52      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.29/0.52            ( ( P4 @ none_P5556105721700978146at_nat )
% 0.29/0.52            & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % split_option_all
% 0.29/0.52  thf(fact_2132_split__option__all,axiom,
% 0.29/0.52      ( ( ^ [P3: option_num > $o] :
% 0.29/0.52          ! [X6: option_num] : ( P3 @ X6 ) )
% 0.29/0.52      = ( ^ [P4: option_num > $o] :
% 0.29/0.52            ( ( P4 @ none_num )
% 0.29/0.52            & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % split_option_all
% 0.29/0.52  thf(fact_2133_combine__options__cases,axiom,
% 0.29/0.52      ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( ( X4 = none_P5556105721700978146at_nat )
% 0.29/0.52         => ( P @ X4 @ Y ) )
% 0.29/0.52       => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.29/0.52           => ( P @ X4 @ Y ) )
% 0.29/0.52         => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 0.29/0.52                ( ( X4
% 0.29/0.52                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.29/0.52               => ( ( Y
% 0.29/0.52                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.29/0.52                 => ( P @ X4 @ Y ) ) )
% 0.29/0.52           => ( P @ X4 @ Y ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % combine_options_cases
% 0.29/0.52  thf(fact_2134_combine__options__cases,axiom,
% 0.29/0.52      ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 0.29/0.52        ( ( ( X4 = none_P5556105721700978146at_nat )
% 0.29/0.52         => ( P @ X4 @ Y ) )
% 0.29/0.52       => ( ( ( Y = none_num )
% 0.29/0.52           => ( P @ X4 @ Y ) )
% 0.29/0.52         => ( ! [A5: product_prod_nat_nat,B5: num] :
% 0.29/0.52                ( ( X4
% 0.29/0.52                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.29/0.52               => ( ( Y
% 0.29/0.52                    = ( some_num @ B5 ) )
% 0.29/0.52                 => ( P @ X4 @ Y ) ) )
% 0.29/0.52           => ( P @ X4 @ Y ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % combine_options_cases
% 0.29/0.52  thf(fact_2135_combine__options__cases,axiom,
% 0.29/0.52      ! [X4: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.29/0.52        ( ( ( X4 = none_num )
% 0.29/0.52         => ( P @ X4 @ Y ) )
% 0.29/0.52       => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.29/0.52           => ( P @ X4 @ Y ) )
% 0.29/0.52         => ( ! [A5: num,B5: product_prod_nat_nat] :
% 0.29/0.52                ( ( X4
% 0.29/0.52                  = ( some_num @ A5 ) )
% 0.29/0.52               => ( ( Y
% 0.29/0.52                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.29/0.52                 => ( P @ X4 @ Y ) ) )
% 0.29/0.52           => ( P @ X4 @ Y ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % combine_options_cases
% 0.29/0.52  thf(fact_2136_combine__options__cases,axiom,
% 0.29/0.52      ! [X4: option_num,P: option_num > option_num > $o,Y: option_num] :
% 0.29/0.52        ( ( ( X4 = none_num )
% 0.29/0.52         => ( P @ X4 @ Y ) )
% 0.29/0.52       => ( ( ( Y = none_num )
% 0.29/0.52           => ( P @ X4 @ Y ) )
% 0.29/0.52         => ( ! [A5: num,B5: num] :
% 0.29/0.52                ( ( X4
% 0.29/0.52                  = ( some_num @ A5 ) )
% 0.29/0.52               => ( ( Y
% 0.29/0.52                    = ( some_num @ B5 ) )
% 0.29/0.52                 => ( P @ X4 @ Y ) ) )
% 0.29/0.52           => ( P @ X4 @ Y ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % combine_options_cases
% 0.29/0.52  thf(fact_2137_option_Osize_I3_J,axiom,
% 0.29/0.52      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.29/0.52      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size(3)
% 0.29/0.52  thf(fact_2138_option_Osize_I3_J,axiom,
% 0.29/0.52      ( ( size_size_option_num @ none_num )
% 0.29/0.52      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size(3)
% 0.29/0.52  thf(fact_2139_option_Osize_I4_J,axiom,
% 0.29/0.52      ! [X22: product_prod_nat_nat] :
% 0.29/0.52        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.29/0.52        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size(4)
% 0.29/0.52  thf(fact_2140_option_Osize_I4_J,axiom,
% 0.29/0.52      ! [X22: num] :
% 0.29/0.52        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 0.29/0.52        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size(4)
% 0.29/0.52  thf(fact_2141_divides__aux__eq,axiom,
% 0.29/0.52      ! [Q3: nat,R3: nat] :
% 0.29/0.52        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 0.29/0.52        = ( R3 = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divides_aux_eq
% 0.29/0.52  thf(fact_2142_divides__aux__eq,axiom,
% 0.29/0.52      ! [Q3: int,R3: int] :
% 0.29/0.52        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.52        = ( R3 = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divides_aux_eq
% 0.29/0.52  thf(fact_2143_gcd__nat__induct,axiom,
% 0.29/0.52      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.29/0.52        ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 0.29/0.52       => ( ! [M5: nat,N3: nat] :
% 0.29/0.52              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.52             => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 0.29/0.52               => ( P @ M5 @ N3 ) ) )
% 0.29/0.52         => ( P @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % gcd_nat_induct
% 0.29/0.52  thf(fact_2144_option_Osize__gen_I2_J,axiom,
% 0.29/0.52      ! [X4: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 0.29/0.52        ( ( size_o8335143837870341156at_nat @ X4 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.29/0.52        = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size_gen(2)
% 0.29/0.52  thf(fact_2145_option_Osize__gen_I2_J,axiom,
% 0.29/0.52      ! [X4: num > nat,X22: num] :
% 0.29/0.52        ( ( size_option_num @ X4 @ ( some_num @ X22 ) )
% 0.29/0.52        = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % option.size_gen(2)
% 0.29/0.52  thf(fact_2146_even__succ__mod__exp,axiom,
% 0.29/0.52      ! [A: nat,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_mod_exp
% 0.29/0.52  thf(fact_2147_even__succ__mod__exp,axiom,
% 0.29/0.52      ! [A: int,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_mod_exp
% 0.29/0.52  thf(fact_2148_even__succ__mod__exp,axiom,
% 0.29/0.52      ! [A: code_integer,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_mod_exp
% 0.29/0.52  thf(fact_2149_even__succ__div__exp,axiom,
% 0.29/0.52      ! [A: nat,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_div_exp
% 0.29/0.52  thf(fact_2150_even__succ__div__exp,axiom,
% 0.29/0.52      ! [A: int,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_div_exp
% 0.29/0.52  thf(fact_2151_even__succ__div__exp,axiom,
% 0.29/0.52      ! [A: code_integer,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % even_succ_div_exp
% 0.29/0.52  thf(fact_2152_divmod__digit__1_I1_J,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.52       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.52         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.52           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.29/0.52              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divmod_digit_1(1)
% 0.29/0.52  thf(fact_2153_divmod__digit__1_I1_J,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.52       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.52         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.52           => ( ( 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 )
% 0.29/0.52              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divmod_digit_1(1)
% 0.29/0.52  thf(fact_2154_divmod__digit__1_I1_J,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.52         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.52           => ( ( 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 )
% 0.29/0.52              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divmod_digit_1(1)
% 0.29/0.52  thf(fact_2155_num_Osize__gen_I2_J,axiom,
% 0.29/0.52      ! [X22: num] :
% 0.29/0.52        ( ( size_num @ ( bit0 @ X22 ) )
% 0.29/0.52        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % num.size_gen(2)
% 0.29/0.52  thf(fact_2156_power__le__zero__eq__numeral,axiom,
% 0.29/0.52      ! [A: real,W: num] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.29/0.52            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_le_zero_eq_numeral
% 0.29/0.52  thf(fact_2157_power__le__zero__eq__numeral,axiom,
% 0.29/0.52      ! [A: rat,W: num] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.29/0.52            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_le_zero_eq_numeral
% 0.29/0.52  thf(fact_2158_power__le__zero__eq__numeral,axiom,
% 0.29/0.52      ! [A: int,W: num] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.29/0.52            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.52              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_le_zero_eq_numeral
% 0.29/0.52  thf(fact_2159_one__mod__2__pow__eq,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_mod_2_pow_eq
% 0.29/0.52  thf(fact_2160_one__mod__2__pow__eq,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_mod_2_pow_eq
% 0.29/0.52  thf(fact_2161_one__mod__2__pow__eq,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.52        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_mod_2_pow_eq
% 0.29/0.52  thf(fact_2162_arith__geo__mean,axiom,
% 0.29/0.52      ! [U: real,X4: real,Y: real] :
% 0.29/0.52        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52          = ( times_times_real @ X4 @ Y ) )
% 0.29/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.52           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % arith_geo_mean
% 0.29/0.52  thf(fact_2163_arith__geo__mean,axiom,
% 0.29/0.52      ! [U: rat,X4: rat,Y: rat] :
% 0.29/0.52        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.52          = ( times_times_rat @ X4 @ Y ) )
% 0.29/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.52           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % arith_geo_mean
% 0.29/0.52  thf(fact_2164_semiring__norm_I13_J,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.52        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(13)
% 0.29/0.52  thf(fact_2165_semiring__norm_I11_J,axiom,
% 0.29/0.52      ! [M: num] :
% 0.29/0.52        ( ( times_times_num @ M @ one )
% 0.29/0.52        = M ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(11)
% 0.29/0.52  thf(fact_2166_semiring__norm_I12_J,axiom,
% 0.29/0.52      ! [N2: num] :
% 0.29/0.52        ( ( times_times_num @ one @ N2 )
% 0.29/0.52        = N2 ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(12)
% 0.29/0.52  thf(fact_2167_mult__is__0,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ M @ N2 )
% 0.29/0.52          = zero_zero_nat )
% 0.29/0.52        = ( ( M = zero_zero_nat )
% 0.29/0.52          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_is_0
% 0.29/0.52  thf(fact_2168_mult__0__right,axiom,
% 0.29/0.52      ! [M: nat] :
% 0.29/0.52        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_0_right
% 0.29/0.52  thf(fact_2169_mult__cancel1,axiom,
% 0.29/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ K @ M )
% 0.29/0.52          = ( times_times_nat @ K @ N2 ) )
% 0.29/0.52        = ( ( M = N2 )
% 0.29/0.52          | ( K = zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel1
% 0.29/0.52  thf(fact_2170_mult__cancel2,axiom,
% 0.29/0.52      ! [M: nat,K: nat,N2: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ M @ K )
% 0.29/0.52          = ( times_times_nat @ N2 @ K ) )
% 0.29/0.52        = ( ( M = N2 )
% 0.29/0.52          | ( K = zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel2
% 0.29/0.52  thf(fact_2171_nat__mult__eq__1__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ M @ N2 )
% 0.29/0.52          = one_one_nat )
% 0.29/0.52        = ( ( M = one_one_nat )
% 0.29/0.52          & ( N2 = one_one_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_mult_eq_1_iff
% 0.29/0.52  thf(fact_2172_nat__1__eq__mult__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( one_one_nat
% 0.29/0.52          = ( times_times_nat @ M @ N2 ) )
% 0.29/0.52        = ( ( M = one_one_nat )
% 0.29/0.52          & ( N2 = one_one_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_1_eq_mult_iff
% 0.29/0.52  thf(fact_2173_mult__zero__left,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.29/0.52        = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_left
% 0.29/0.52  thf(fact_2174_mult__zero__left,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ zero_zero_complex @ A )
% 0.29/0.52        = zero_zero_complex ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_left
% 0.29/0.52  thf(fact_2175_mult__zero__left,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ zero_zero_real @ A )
% 0.29/0.52        = zero_zero_real ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_left
% 0.29/0.52  thf(fact_2176_mult__zero__left,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_left
% 0.29/0.52  thf(fact_2177_mult__zero__left,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ zero_zero_int @ A )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_left
% 0.29/0.52  thf(fact_2178_mult__zero__right,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.29/0.52        = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_right
% 0.29/0.52  thf(fact_2179_mult__zero__right,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( times_times_complex @ A @ zero_zero_complex )
% 0.29/0.52        = zero_zero_complex ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_right
% 0.29/0.52  thf(fact_2180_mult__zero__right,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( times_times_real @ A @ zero_zero_real )
% 0.29/0.52        = zero_zero_real ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_right
% 0.29/0.52  thf(fact_2181_mult__zero__right,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_right
% 0.29/0.52  thf(fact_2182_mult__zero__right,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( times_times_int @ A @ zero_zero_int )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_zero_right
% 0.29/0.52  thf(fact_2183_mult__eq__0__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ( times_times_rat @ A @ B )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( ( A = zero_zero_rat )
% 0.29/0.52          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_0_iff
% 0.29/0.52  thf(fact_2184_mult__eq__0__iff,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( ( times_times_complex @ A @ B )
% 0.29/0.52          = zero_zero_complex )
% 0.29/0.52        = ( ( A = zero_zero_complex )
% 0.29/0.52          | ( B = zero_zero_complex ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_0_iff
% 0.29/0.52  thf(fact_2185_mult__eq__0__iff,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( ( times_times_real @ A @ B )
% 0.29/0.52          = zero_zero_real )
% 0.29/0.52        = ( ( A = zero_zero_real )
% 0.29/0.52          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_0_iff
% 0.29/0.52  thf(fact_2186_mult__eq__0__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ A @ B )
% 0.29/0.52          = zero_zero_nat )
% 0.29/0.52        = ( ( A = zero_zero_nat )
% 0.29/0.52          | ( B = zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_0_iff
% 0.29/0.52  thf(fact_2187_mult__eq__0__iff,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ( times_times_int @ A @ B )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( ( A = zero_zero_int )
% 0.29/0.52          | ( B = zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_0_iff
% 0.29/0.52  thf(fact_2188_mult__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( times_times_rat @ C @ A )
% 0.29/0.52          = ( times_times_rat @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left
% 0.29/0.52  thf(fact_2189_mult__cancel__left,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( ( times_times_complex @ C @ A )
% 0.29/0.52          = ( times_times_complex @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left
% 0.29/0.52  thf(fact_2190_mult__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ( times_times_real @ C @ A )
% 0.29/0.52          = ( times_times_real @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left
% 0.29/0.52  thf(fact_2191_mult__cancel__left,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ C @ A )
% 0.29/0.52          = ( times_times_nat @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_nat )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left
% 0.29/0.52  thf(fact_2192_mult__cancel__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ( times_times_int @ C @ A )
% 0.29/0.52          = ( times_times_int @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left
% 0.29/0.52  thf(fact_2193_mult__cancel__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( ( times_times_rat @ A @ C )
% 0.29/0.52          = ( times_times_rat @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right
% 0.29/0.52  thf(fact_2194_mult__cancel__right,axiom,
% 0.29/0.52      ! [A: complex,C: complex,B: complex] :
% 0.29/0.52        ( ( ( times_times_complex @ A @ C )
% 0.29/0.52          = ( times_times_complex @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right
% 0.29/0.52  thf(fact_2195_mult__cancel__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( ( times_times_real @ A @ C )
% 0.29/0.52          = ( times_times_real @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right
% 0.29/0.52  thf(fact_2196_mult__cancel__right,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ A @ C )
% 0.29/0.52          = ( times_times_nat @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_nat )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right
% 0.29/0.52  thf(fact_2197_mult__cancel__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( ( times_times_int @ A @ C )
% 0.29/0.52          = ( times_times_int @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right
% 0.29/0.52  thf(fact_2198_numeral__times__numeral,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 0.29/0.52        = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_numeral
% 0.29/0.52  thf(fact_2199_numeral__times__numeral,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.52        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_numeral
% 0.29/0.52  thf(fact_2200_numeral__times__numeral,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.52        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_numeral
% 0.29/0.52  thf(fact_2201_numeral__times__numeral,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.52        = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_numeral
% 0.29/0.52  thf(fact_2202_numeral__times__numeral,axiom,
% 0.29/0.52      ! [M: num,N2: num] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.52        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_numeral
% 0.29/0.52  thf(fact_2203_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.52      ! [V: num,W: num,Z: extended_enat] :
% 0.29/0.52        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 0.29/0.52        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_numeral_left_semiring_numeral
% 0.29/0.52  thf(fact_2204_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.52      ! [V: num,W: num,Z: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.29/0.52        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_numeral_left_semiring_numeral
% 0.29/0.52  thf(fact_2205_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.52      ! [V: num,W: num,Z: real] :
% 0.29/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.29/0.52        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_numeral_left_semiring_numeral
% 0.29/0.52  thf(fact_2206_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.52      ! [V: num,W: num,Z: nat] :
% 0.29/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.52        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_numeral_left_semiring_numeral
% 0.29/0.52  thf(fact_2207_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.52      ! [V: num,W: num,Z: int] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.29/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_numeral_left_semiring_numeral
% 0.29/0.52  thf(fact_2208_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_2209_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_2210_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_2211_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_2212_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_2213_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_2214_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_2215_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_2216_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_2217_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_2218_num__double,axiom,
% 0.29/0.52      ! [N2: num] :
% 0.29/0.52        ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 0.29/0.52        = ( bit0 @ N2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % num_double
% 0.29/0.52  thf(fact_2219_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_2220_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_2221_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_2222_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_2223_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_2224_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_2225_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_2226_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_2227_dvd__0__right,axiom,
% 0.29/0.52      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2228_dvd__0__right,axiom,
% 0.29/0.52      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2229_dvd__0__right,axiom,
% 0.29/0.52      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2230_dvd__0__right,axiom,
% 0.29/0.52      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2231_dvd__0__right,axiom,
% 0.29/0.52      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2232_dvd__0__right,axiom,
% 0.29/0.52      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_right
% 0.29/0.52  thf(fact_2233_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.29/0.52        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2234_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: complex] :
% 0.29/0.52        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.29/0.52        = ( A = zero_zero_complex ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2235_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.29/0.52        = ( A = zero_zero_real ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2236_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.29/0.52        = ( A = zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2237_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.29/0.52        = ( A = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2238_dvd__0__left__iff,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.29/0.52        = ( A = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_0_left_iff
% 0.29/0.52  thf(fact_2239_dvd__add__triv__right__iff,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.29/0.52        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_right_iff
% 0.29/0.52  thf(fact_2240_dvd__add__triv__right__iff,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.29/0.52        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_right_iff
% 0.29/0.52  thf(fact_2241_dvd__add__triv__right__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.29/0.52        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_right_iff
% 0.29/0.52  thf(fact_2242_dvd__add__triv__right__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.29/0.52        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_right_iff
% 0.29/0.52  thf(fact_2243_dvd__add__triv__right__iff,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.29/0.52        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_right_iff
% 0.29/0.52  thf(fact_2244_dvd__add__triv__left__iff,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.52        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_left_iff
% 0.29/0.52  thf(fact_2245_dvd__add__triv__left__iff,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.52        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_left_iff
% 0.29/0.52  thf(fact_2246_dvd__add__triv__left__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.52        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_left_iff
% 0.29/0.52  thf(fact_2247_dvd__add__triv__left__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.52        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_left_iff
% 0.29/0.52  thf(fact_2248_dvd__add__triv__left__iff,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.52        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_triv_left_iff
% 0.29/0.52  thf(fact_2249_mult__eq__1__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ( times_times_nat @ M @ N2 )
% 0.29/0.52          = ( suc @ zero_zero_nat ) )
% 0.29/0.52        = ( ( M
% 0.29/0.52            = ( suc @ zero_zero_nat ) )
% 0.29/0.52          & ( N2
% 0.29/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_eq_1_iff
% 0.29/0.52  thf(fact_2250_one__eq__mult__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ( suc @ zero_zero_nat )
% 0.29/0.52          = ( times_times_nat @ M @ N2 ) )
% 0.29/0.52        = ( ( M
% 0.29/0.52            = ( suc @ zero_zero_nat ) )
% 0.29/0.52          & ( N2
% 0.29/0.52            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_eq_mult_iff
% 0.29/0.52  thf(fact_2251_div__dvd__div,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.52       => ( ( dvd_dvd_nat @ A @ C )
% 0.29/0.52         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 0.29/0.52            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_dvd_div
% 0.29/0.52  thf(fact_2252_div__dvd__div,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.52       => ( ( dvd_dvd_int @ A @ C )
% 0.29/0.52         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 0.29/0.52            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_dvd_div
% 0.29/0.52  thf(fact_2253_div__dvd__div,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.29/0.52         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 0.29/0.52            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_dvd_div
% 0.29/0.52  thf(fact_2254_power__mult__numeral,axiom,
% 0.29/0.52      ! [A: nat,M: num,N2: num] :
% 0.29/0.52        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.52        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_mult_numeral
% 0.29/0.52  thf(fact_2255_power__mult__numeral,axiom,
% 0.29/0.52      ! [A: real,M: num,N2: num] :
% 0.29/0.52        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.52        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_mult_numeral
% 0.29/0.52  thf(fact_2256_power__mult__numeral,axiom,
% 0.29/0.52      ! [A: int,M: num,N2: num] :
% 0.29/0.52        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.52        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_mult_numeral
% 0.29/0.52  thf(fact_2257_power__mult__numeral,axiom,
% 0.29/0.52      ! [A: complex,M: num,N2: num] :
% 0.29/0.52        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.52        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % power_mult_numeral
% 0.29/0.52  thf(fact_2258_nat__mult__less__cancel__disj,axiom,
% 0.29/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.52          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_mult_less_cancel_disj
% 0.29/0.52  thf(fact_2259_nat__0__less__mult__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.52          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_0_less_mult_iff
% 0.29/0.52  thf(fact_2260_mult__less__cancel2,axiom,
% 0.29/0.52      ! [M: nat,K: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.52          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_less_cancel2
% 0.29/0.52  thf(fact_2261_not__real__square__gt__zero,axiom,
% 0.29/0.52      ! [X4: real] :
% 0.29/0.52        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X4 @ X4 ) ) )
% 0.29/0.52        = ( X4 = zero_zero_real ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_real_square_gt_zero
% 0.29/0.52  thf(fact_2262_mult__Suc__right,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 0.29/0.52        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_Suc_right
% 0.29/0.52  thf(fact_2263_nat__mult__dvd__cancel__disj,axiom,
% 0.29/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.52        = ( ( K = zero_zero_nat )
% 0.29/0.52          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_mult_dvd_cancel_disj
% 0.29/0.52  thf(fact_2264_of__bool__less__eq__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.29/0.52        = ( P
% 0.29/0.52         => Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_eq_iff
% 0.29/0.52  thf(fact_2265_of__bool__less__eq__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.29/0.52        = ( P
% 0.29/0.52         => Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_eq_iff
% 0.29/0.52  thf(fact_2266_of__bool__less__eq__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.29/0.52        = ( P
% 0.29/0.52         => Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_eq_iff
% 0.29/0.52  thf(fact_2267_of__bool__less__eq__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.29/0.52        = ( P
% 0.29/0.52         => Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_eq_iff
% 0.29/0.52  thf(fact_2268_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n1201886186963655149omplex @ $false )
% 0.29/0.52      = zero_zero_complex ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2269_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n3304061248610475627l_real @ $false )
% 0.29/0.52      = zero_zero_real ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2270_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n2052037380579107095ol_rat @ $false )
% 0.29/0.52      = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2271_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n2687167440665602831ol_nat @ $false )
% 0.29/0.52      = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2272_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n2684676970156552555ol_int @ $false )
% 0.29/0.52      = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2273_of__bool__eq_I1_J,axiom,
% 0.29/0.52      ( ( zero_n356916108424825756nteger @ $false )
% 0.29/0.52      = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(1)
% 0.29/0.52  thf(fact_2274_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.29/0.52          = zero_zero_complex )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2275_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.29/0.52          = zero_zero_real )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2276_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2277_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.29/0.52          = zero_zero_nat )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2278_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2279_of__bool__eq__0__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n356916108424825756nteger @ P )
% 0.29/0.52          = zero_z3403309356797280102nteger )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_0_iff
% 0.29/0.52  thf(fact_2280_nat__mult__div__cancel__disj,axiom,
% 0.29/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.52        ( ( ( K = zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.52            = zero_zero_nat ) )
% 0.29/0.52        & ( ( K != zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.52            = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_mult_div_cancel_disj
% 0.29/0.52  thf(fact_2281_of__bool__less__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 0.29/0.52        = ( ~ P
% 0.29/0.52          & Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_iff
% 0.29/0.52  thf(fact_2282_of__bool__less__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.29/0.52        = ( ~ P
% 0.29/0.52          & Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_iff
% 0.29/0.52  thf(fact_2283_of__bool__less__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.29/0.52        = ( ~ P
% 0.29/0.52          & Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_iff
% 0.29/0.52  thf(fact_2284_of__bool__less__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.29/0.52        = ( ~ P
% 0.29/0.52          & Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_iff
% 0.29/0.52  thf(fact_2285_of__bool__less__iff,axiom,
% 0.29/0.52      ! [P: $o,Q: $o] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.29/0.52        = ( ~ P
% 0.29/0.52          & Q ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_iff
% 0.29/0.52  thf(fact_2286_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.29/0.52          = one_one_complex )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2287_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.29/0.52          = one_one_real )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2288_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.29/0.52          = one_one_rat )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2289_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.29/0.52          = one_one_nat )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2290_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.29/0.52          = one_one_int )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2291_of__bool__eq__1__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ( zero_n356916108424825756nteger @ P )
% 0.29/0.52          = one_one_Code_integer )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq_1_iff
% 0.29/0.52  thf(fact_2292_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n1201886186963655149omplex @ $true )
% 0.29/0.52      = one_one_complex ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2293_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n3304061248610475627l_real @ $true )
% 0.29/0.52      = one_one_real ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2294_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.29/0.52      = one_one_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2295_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.29/0.52      = one_one_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2296_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n2684676970156552555ol_int @ $true )
% 0.29/0.52      = one_one_int ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2297_of__bool__eq_I2_J,axiom,
% 0.29/0.52      ( ( zero_n356916108424825756nteger @ $true )
% 0.29/0.52      = one_one_Code_integer ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_eq(2)
% 0.29/0.52  thf(fact_2298_nat__dvd__1__iff__1,axiom,
% 0.29/0.52      ! [M: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.29/0.52        = ( M = one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_dvd_1_iff_1
% 0.29/0.52  thf(fact_2299_mult__cancel__right2,axiom,
% 0.29/0.52      ! [A: rat,C: rat] :
% 0.29/0.52        ( ( ( times_times_rat @ A @ C )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( A = one_one_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right2
% 0.29/0.52  thf(fact_2300_mult__cancel__right2,axiom,
% 0.29/0.52      ! [A: complex,C: complex] :
% 0.29/0.52        ( ( ( times_times_complex @ A @ C )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( A = one_one_complex ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right2
% 0.29/0.52  thf(fact_2301_mult__cancel__right2,axiom,
% 0.29/0.52      ! [A: real,C: real] :
% 0.29/0.52        ( ( ( times_times_real @ A @ C )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( A = one_one_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right2
% 0.29/0.52  thf(fact_2302_mult__cancel__right2,axiom,
% 0.29/0.52      ! [A: int,C: int] :
% 0.29/0.52        ( ( ( times_times_int @ A @ C )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( A = one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right2
% 0.29/0.52  thf(fact_2303_mult__cancel__right1,axiom,
% 0.29/0.52      ! [C: rat,B: rat] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_rat @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( B = one_one_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right1
% 0.29/0.52  thf(fact_2304_mult__cancel__right1,axiom,
% 0.29/0.52      ! [C: complex,B: complex] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_complex @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( B = one_one_complex ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right1
% 0.29/0.52  thf(fact_2305_mult__cancel__right1,axiom,
% 0.29/0.52      ! [C: real,B: real] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_real @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( B = one_one_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right1
% 0.29/0.52  thf(fact_2306_mult__cancel__right1,axiom,
% 0.29/0.52      ! [C: int,B: int] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_int @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( B = one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_right1
% 0.29/0.52  thf(fact_2307_mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: rat,A: rat] :
% 0.29/0.52        ( ( ( times_times_rat @ C @ A )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( A = one_one_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left2
% 0.29/0.52  thf(fact_2308_mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: complex,A: complex] :
% 0.29/0.52        ( ( ( times_times_complex @ C @ A )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( A = one_one_complex ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left2
% 0.29/0.52  thf(fact_2309_mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: real,A: real] :
% 0.29/0.52        ( ( ( times_times_real @ C @ A )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( A = one_one_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left2
% 0.29/0.52  thf(fact_2310_mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: int,A: int] :
% 0.29/0.52        ( ( ( times_times_int @ C @ A )
% 0.29/0.52          = C )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( A = one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left2
% 0.29/0.52  thf(fact_2311_mult__cancel__left1,axiom,
% 0.29/0.52      ! [C: rat,B: rat] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_rat @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( B = one_one_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left1
% 0.29/0.52  thf(fact_2312_mult__cancel__left1,axiom,
% 0.29/0.52      ! [C: complex,B: complex] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_complex @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( B = one_one_complex ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left1
% 0.29/0.52  thf(fact_2313_mult__cancel__left1,axiom,
% 0.29/0.52      ! [C: real,B: real] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_real @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( B = one_one_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left1
% 0.29/0.52  thf(fact_2314_mult__cancel__left1,axiom,
% 0.29/0.52      ! [C: int,B: int] :
% 0.29/0.52        ( ( C
% 0.29/0.52          = ( times_times_int @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( B = one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_cancel_left1
% 0.29/0.52  thf(fact_2315_sum__squares__eq__zero__iff,axiom,
% 0.29/0.52      ! [X4: rat,Y: rat] :
% 0.29/0.52        ( ( ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( ( X4 = zero_zero_rat )
% 0.29/0.52          & ( Y = zero_zero_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sum_squares_eq_zero_iff
% 0.29/0.52  thf(fact_2316_sum__squares__eq__zero__iff,axiom,
% 0.29/0.52      ! [X4: real,Y: real] :
% 0.29/0.52        ( ( ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 0.29/0.52          = zero_zero_real )
% 0.29/0.52        = ( ( X4 = zero_zero_real )
% 0.29/0.52          & ( Y = zero_zero_real ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sum_squares_eq_zero_iff
% 0.29/0.52  thf(fact_2317_sum__squares__eq__zero__iff,axiom,
% 0.29/0.52      ! [X4: int,Y: int] :
% 0.29/0.52        ( ( ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( ( X4 = zero_zero_int )
% 0.29/0.52          & ( Y = zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sum_squares_eq_zero_iff
% 0.29/0.52  thf(fact_2318_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.52  thf(fact_2319_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( C != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 0.29/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.52  thf(fact_2320_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( C != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.52  thf(fact_2321_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2322_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( B != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2323_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( B != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2324_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: real,A: real] :
% 0.29/0.52        ( ( B != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2325_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: complex,A: complex] :
% 0.29/0.52        ( ( B != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2326_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_2327_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.52  thf(fact_2328_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( C != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.52  thf(fact_2329_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( C != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.29/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.52  thf(fact_2330_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.52  thf(fact_2331_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( C != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 0.29/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.52  thf(fact_2332_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( C != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 0.29/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.52  thf(fact_2333_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( A != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2334_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( A != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2335_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( A != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2336_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: real,B: real] :
% 0.29/0.52        ( ( A != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2337_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: complex,B: complex] :
% 0.29/0.52        ( ( A != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2338_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_2339_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.52  thf(fact_2340_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( C != zero_zero_real )
% 0.29/0.52       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.52          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.52  thf(fact_2341_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( C != zero_zero_complex )
% 0.29/0.52       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.52          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.52  thf(fact_2342_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( C = zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52            = zero_zero_rat ) )
% 0.29/0.52        & ( ( C != zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_divide_mult_cancel_left_if
% 0.29/0.52  thf(fact_2343_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( ( C = zero_zero_real )
% 0.29/0.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.52            = zero_zero_real ) )
% 0.29/0.52        & ( ( C != zero_zero_real )
% 0.29/0.52         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.52            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_divide_mult_cancel_left_if
% 0.29/0.52  thf(fact_2344_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( ( C = zero_zero_complex )
% 0.29/0.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.52            = zero_zero_complex ) )
% 0.29/0.52        & ( ( C != zero_zero_complex )
% 0.29/0.52         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.52            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_divide_mult_cancel_left_if
% 0.29/0.52  thf(fact_2345_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( C != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2346_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( C != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2347_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2348_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( C != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2349_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( C != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2350_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.52          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2351_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ( C = zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52            = zero_zero_nat ) )
% 0.29/0.52        & ( ( C != zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2352_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ( C = zero_zero_int )
% 0.29/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52            = zero_zero_int ) )
% 0.29/0.52        & ( ( C != zero_zero_int )
% 0.29/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2353_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52            = zero_z3403309356797280102nteger ) )
% 0.29/0.52        & ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2354_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: rat,B: rat,V: num] :
% 0.29/0.52        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.52        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2355_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: extended_enat,B: extended_enat,V: num] :
% 0.29/0.52        ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.29/0.52        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2356_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: complex,B: complex,V: num] :
% 0.29/0.52        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.29/0.52        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2357_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: real,B: real,V: num] :
% 0.29/0.52        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.52        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2358_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: nat,B: nat,V: num] :
% 0.29/0.52        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.52        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2359_distrib__right__numeral,axiom,
% 0.29/0.52      ! [A: int,B: int,V: num] :
% 0.29/0.52        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.52        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_right_numeral
% 0.29/0.52  thf(fact_2360_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.52        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2361_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: extended_enat,C: extended_enat] :
% 0.29/0.52        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 0.29/0.52        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2362_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: complex,C: complex] :
% 0.29/0.52        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.52        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2363_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: real,C: real] :
% 0.29/0.52        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.52        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2364_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: nat,C: nat] :
% 0.29/0.52        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.52        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2365_distrib__left__numeral,axiom,
% 0.29/0.52      ! [V: num,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.52        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % distrib_left_numeral
% 0.29/0.52  thf(fact_2366_dvd__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_left
% 0.29/0.52  thf(fact_2367_dvd__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_left
% 0.29/0.52  thf(fact_2368_dvd__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: complex,A: complex,B: complex] :
% 0.29/0.52        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_left
% 0.29/0.52  thf(fact_2369_dvd__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: real,A: real,B: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_left
% 0.29/0.52  thf(fact_2370_dvd__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_left
% 0.29/0.52  thf(fact_2371_dvd__mult__cancel__right,axiom,
% 0.29/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.52          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_right
% 0.29/0.52  thf(fact_2372_dvd__mult__cancel__right,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_rat )
% 0.29/0.52          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_right
% 0.29/0.52  thf(fact_2373_dvd__mult__cancel__right,axiom,
% 0.29/0.52      ! [A: complex,C: complex,B: complex] :
% 0.29/0.52        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_complex )
% 0.29/0.52          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_right
% 0.29/0.52  thf(fact_2374_dvd__mult__cancel__right,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_real )
% 0.29/0.52          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_right
% 0.29/0.52  thf(fact_2375_dvd__mult__cancel__right,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.52        = ( ( C = zero_zero_int )
% 0.29/0.52          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_cancel_right
% 0.29/0.52  thf(fact_2376_dvd__times__left__cancel__iff,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.29/0.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_left_cancel_iff
% 0.29/0.52  thf(fact_2377_dvd__times__left__cancel__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( A != zero_zero_nat )
% 0.29/0.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.29/0.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_left_cancel_iff
% 0.29/0.52  thf(fact_2378_dvd__times__left__cancel__iff,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( A != zero_zero_int )
% 0.29/0.52       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.29/0.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_left_cancel_iff
% 0.29/0.52  thf(fact_2379_dvd__times__right__cancel__iff,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 0.29/0.52          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_right_cancel_iff
% 0.29/0.52  thf(fact_2380_dvd__times__right__cancel__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( A != zero_zero_nat )
% 0.29/0.52       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.29/0.52          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_right_cancel_iff
% 0.29/0.52  thf(fact_2381_dvd__times__right__cancel__iff,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( A != zero_zero_int )
% 0.29/0.52       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.29/0.52          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_times_right_cancel_iff
% 0.29/0.52  thf(fact_2382_unit__prod,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.52         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_prod
% 0.29/0.52  thf(fact_2383_unit__prod,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.52       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.52         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_prod
% 0.29/0.52  thf(fact_2384_unit__prod,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.52       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.52         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_prod
% 0.29/0.52  thf(fact_2385_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2386_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2387_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: complex,B: complex,C: complex] :
% 0.29/0.52        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2388_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: real,B: real,C: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2389_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2390_dvd__add__times__triv__right__iff,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.29/0.52        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_right_iff
% 0.29/0.52  thf(fact_2391_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2392_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2393_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: complex,C: complex,B: complex] :
% 0.29/0.52        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2394_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: real,C: real,B: real] :
% 0.29/0.52        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2395_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2396_dvd__add__times__triv__left__iff,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.29/0.52        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_add_times_triv_left_iff
% 0.29/0.52  thf(fact_2397_mod__mult__self1__is__0,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1_is_0
% 0.29/0.52  thf(fact_2398_mod__mult__self1__is__0,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1_is_0
% 0.29/0.52  thf(fact_2399_mod__mult__self1__is__0,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 0.29/0.52        = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1_is_0
% 0.29/0.52  thf(fact_2400_mod__mult__self2__is__0,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2_is_0
% 0.29/0.52  thf(fact_2401_mod__mult__self2__is__0,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2_is_0
% 0.29/0.52  thf(fact_2402_mod__mult__self2__is__0,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.29/0.52        = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2_is_0
% 0.29/0.52  thf(fact_2403_dvd__mult__div__cancel,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.52       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_div_cancel
% 0.29/0.52  thf(fact_2404_dvd__mult__div__cancel,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.52       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_div_cancel
% 0.29/0.52  thf(fact_2405_dvd__mult__div__cancel,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_mult_div_cancel
% 0.29/0.52  thf(fact_2406_dvd__div__mult__self,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.52       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_div_mult_self
% 0.29/0.52  thf(fact_2407_dvd__div__mult__self,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.52       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_div_mult_self
% 0.29/0.52  thf(fact_2408_dvd__div__mult__self,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_div_mult_self
% 0.29/0.52  thf(fact_2409_unit__div__1__div__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_div_1
% 0.29/0.52  thf(fact_2410_unit__div__1__div__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.52       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_div_1
% 0.29/0.52  thf(fact_2411_unit__div__1__div__1,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_div_1
% 0.29/0.52  thf(fact_2412_unit__div__1__unit,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.52       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_unit
% 0.29/0.52  thf(fact_2413_unit__div__1__unit,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.52       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_unit
% 0.29/0.52  thf(fact_2414_unit__div__1__unit,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.52       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div_1_unit
% 0.29/0.52  thf(fact_2415_unit__div,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.52       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.52         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div
% 0.29/0.52  thf(fact_2416_unit__div,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.52       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.52         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div
% 0.29/0.52  thf(fact_2417_unit__div,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.52         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % unit_div
% 0.29/0.52  thf(fact_2418_div__add,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ C @ A )
% 0.29/0.52       => ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.52         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.52            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_add
% 0.29/0.52  thf(fact_2419_div__add,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ C @ A )
% 0.29/0.52       => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.52         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.52            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_add
% 0.29/0.52  thf(fact_2420_div__add,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.29/0.52       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.29/0.52            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_add
% 0.29/0.52  thf(fact_2421_mod__mult__self1,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.29/0.52        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1
% 0.29/0.52  thf(fact_2422_mod__mult__self1,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.29/0.52        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1
% 0.29/0.52  thf(fact_2423_mod__mult__self1,axiom,
% 0.29/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.29/0.52        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self1
% 0.29/0.52  thf(fact_2424_mod__mult__self2,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.29/0.52        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2
% 0.29/0.52  thf(fact_2425_mod__mult__self2,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.29/0.52        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2
% 0.29/0.52  thf(fact_2426_mod__mult__self2,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.29/0.52        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self2
% 0.29/0.52  thf(fact_2427_mod__mult__self3,axiom,
% 0.29/0.52      ! [C: nat,B: nat,A: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.29/0.52        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self3
% 0.29/0.52  thf(fact_2428_mod__mult__self3,axiom,
% 0.29/0.52      ! [C: int,B: int,A: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.29/0.52        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self3
% 0.29/0.52  thf(fact_2429_mod__mult__self3,axiom,
% 0.29/0.52      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.29/0.52        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self3
% 0.29/0.52  thf(fact_2430_mod__mult__self4,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.29/0.52        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self4
% 0.29/0.52  thf(fact_2431_mod__mult__self4,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.29/0.52        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self4
% 0.29/0.52  thf(fact_2432_mod__mult__self4,axiom,
% 0.29/0.52      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.52        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.29/0.52        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mod_mult_self4
% 0.29/0.52  thf(fact_2433_dvd__imp__mod__0,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.52       => ( ( modulo_modulo_nat @ B @ A )
% 0.29/0.52          = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_imp_mod_0
% 0.29/0.52  thf(fact_2434_dvd__imp__mod__0,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.52       => ( ( modulo_modulo_int @ B @ A )
% 0.29/0.52          = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_imp_mod_0
% 0.29/0.52  thf(fact_2435_dvd__imp__mod__0,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.52       => ( ( modulo364778990260209775nteger @ B @ A )
% 0.29/0.52          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_imp_mod_0
% 0.29/0.52  thf(fact_2436_one__le__mult__iff,axiom,
% 0.29/0.52      ! [M: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.52        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.52          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_le_mult_iff
% 0.29/0.52  thf(fact_2437_mult__le__cancel2,axiom,
% 0.29/0.52      ! [M: nat,K: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.52         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_le_cancel2
% 0.29/0.52  thf(fact_2438_nat__mult__le__cancel__disj,axiom,
% 0.29/0.52      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.52        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.52         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nat_mult_le_cancel_disj
% 0.29/0.52  thf(fact_2439_zero__less__of__bool__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_of_bool_iff
% 0.29/0.52  thf(fact_2440_zero__less__of__bool__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_of_bool_iff
% 0.29/0.52  thf(fact_2441_zero__less__of__bool__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_of_bool_iff
% 0.29/0.52  thf(fact_2442_zero__less__of__bool__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_of_bool_iff
% 0.29/0.52  thf(fact_2443_zero__less__of__bool__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 0.29/0.52        = P ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_of_bool_iff
% 0.29/0.52  thf(fact_2444_of__bool__less__one__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_one_iff
% 0.29/0.52  thf(fact_2445_of__bool__less__one__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_one_iff
% 0.29/0.52  thf(fact_2446_of__bool__less__one__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_one_iff
% 0.29/0.52  thf(fact_2447_of__bool__less__one__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_one_iff
% 0.29/0.52  thf(fact_2448_of__bool__less__one__iff,axiom,
% 0.29/0.52      ! [P: $o] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 0.29/0.52        = ( ~ P ) ) ).
% 0.29/0.52  
% 0.29/0.52  % of_bool_less_one_iff
% 0.29/0.52  thf(fact_2449_dvd__1__left,axiom,
% 0.29/0.52      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_1_left
% 0.29/0.52  thf(fact_2450_dvd__1__iff__1,axiom,
% 0.29/0.52      ! [M: nat] :
% 0.29/0.52        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.29/0.52        = ( M
% 0.29/0.52          = ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dvd_1_iff_1
% 0.29/0.52  thf(fact_2451_div__mult__self1__is__m,axiom,
% 0.29/0.52      ! [N2: nat,M: nat] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 0.29/0.52          = M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_self1_is_m
% 0.29/0.52  thf(fact_2452_div__mult__self__is__m,axiom,
% 0.29/0.52      ! [N2: nat,M: nat] :
% 0.29/0.52        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 0.29/0.52          = M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_self_is_m
% 0.29/0.52  thf(fact_2453_Suc__0__mod__eq,axiom,
% 0.29/0.52      ! [N2: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.52        = ( zero_n2687167440665602831ol_nat
% 0.29/0.52          @ ( N2
% 0.29/0.52           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_0_mod_eq
% 0.29/0.52  thf(fact_2454_Suc__mod__mult__self1,axiom,
% 0.29/0.52      ! [M: nat,K: nat,N2: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 0.29/0.52        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_mod_mult_self1
% 0.29/0.52  thf(fact_2455_Suc__mod__mult__self2,axiom,
% 0.29/0.52      ! [M: nat,N2: nat,K: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 0.29/0.52        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_mod_mult_self2
% 0.29/0.52  thf(fact_2456_Suc__mod__mult__self3,axiom,
% 0.29/0.52      ! [K: nat,N2: nat,M: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 0.29/0.52        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_mod_mult_self3
% 0.29/0.52  thf(fact_2457_Suc__mod__mult__self4,axiom,
% 0.29/0.52      ! [N2: nat,K: nat,M: nat] :
% 0.29/0.52        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 0.29/0.52        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Suc_mod_mult_self4
% 0.29/0.52  thf(fact_2458_le__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [A: real,B: real,W: num] :
% 0.29/0.52        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.52        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_numeral1(1)
% 0.29/0.52  thf(fact_2459_le__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_numeral1(1)
% 0.29/0.52  thf(fact_2460_divide__le__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [B: real,W: num,A: real] :
% 0.29/0.52        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.29/0.53        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_le_eq_numeral1(1)
% 0.29/0.53  thf(fact_2461_divide__le__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: rat,W: num,A: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.53        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_le_eq_numeral1(1)
% 0.29/0.53  thf(fact_2462_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [A: rat,B: rat,W: num] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.53        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.53             != zero_zero_rat )
% 0.29/0.53           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 0.29/0.53              = B ) )
% 0.29/0.53          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.53              = zero_zero_rat )
% 0.29/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % eq_divide_eq_numeral1(1)
% 0.29/0.53  thf(fact_2463_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [A: real,B: real,W: num] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.53        = ( ( ( ( numeral_numeral_real @ W )
% 0.29/0.53             != zero_zero_real )
% 0.29/0.53           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 0.29/0.53              = B ) )
% 0.29/0.53          & ( ( ( numeral_numeral_real @ W )
% 0.29/0.53              = zero_zero_real )
% 0.29/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % eq_divide_eq_numeral1(1)
% 0.29/0.53  thf(fact_2464_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [A: complex,B: complex,W: num] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.53        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.53             != zero_zero_complex )
% 0.29/0.53           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.53              = B ) )
% 0.29/0.53          & ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.53              = zero_zero_complex )
% 0.29/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % eq_divide_eq_numeral1(1)
% 0.29/0.53  thf(fact_2465_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: rat,W: num,A: rat] :
% 0.29/0.53        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 0.29/0.53          = A )
% 0.29/0.53        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.53             != zero_zero_rat )
% 0.29/0.53           => ( B
% 0.29/0.53              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.53          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.53              = zero_zero_rat )
% 0.29/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_eq_numeral1(1)
% 0.29/0.53  thf(fact_2466_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: real,W: num,A: real] :
% 0.29/0.53        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 0.29/0.53          = A )
% 0.29/0.53        = ( ( ( ( numeral_numeral_real @ W )
% 0.29/0.53             != zero_zero_real )
% 0.29/0.53           => ( B
% 0.29/0.53              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 0.29/0.53          & ( ( ( numeral_numeral_real @ W )
% 0.29/0.53              = zero_zero_real )
% 0.29/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_eq_numeral1(1)
% 0.29/0.53  thf(fact_2467_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: complex,W: num,A: complex] :
% 0.29/0.53        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.53          = A )
% 0.29/0.53        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.53             != zero_zero_complex )
% 0.29/0.53           => ( B
% 0.29/0.53              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.29/0.53          & ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.53              = zero_zero_complex )
% 0.29/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_eq_eq_numeral1(1)
% 0.29/0.53  thf(fact_2468_less__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [A: rat,B: rat,W: num] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.53        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_divide_eq_numeral1(1)
% 0.29/0.53  thf(fact_2469_less__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [A: real,B: real,W: num] :
% 0.29/0.53        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.53        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_divide_eq_numeral1(1)
% 0.29/0.53  thf(fact_2470_divide__less__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: rat,W: num,A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.53        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_less_eq_numeral1(1)
% 0.29/0.53  thf(fact_2471_divide__less__eq__numeral1_I1_J,axiom,
% 0.29/0.53      ! [B: real,W: num,A: real] :
% 0.29/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.29/0.53        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_less_eq_numeral1(1)
% 0.29/0.53  thf(fact_2472_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( B != zero_zero_rat )
% 0.29/0.53       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.29/0.53          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_right
% 0.29/0.53  thf(fact_2473_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.53      ! [B: real,A: real] :
% 0.29/0.53        ( ( B != zero_zero_real )
% 0.29/0.53       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.29/0.53          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_right
% 0.29/0.53  thf(fact_2474_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.53      ! [B: complex,A: complex] :
% 0.29/0.53        ( ( B != zero_zero_complex )
% 0.29/0.53       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.29/0.53          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_right
% 0.29/0.53  thf(fact_2475_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( A != zero_zero_rat )
% 0.29/0.53       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.29/0.53          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_left
% 0.29/0.53  thf(fact_2476_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( A != zero_zero_real )
% 0.29/0.53       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.29/0.53          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_left
% 0.29/0.53  thf(fact_2477_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( A != zero_zero_complex )
% 0.29/0.53       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.29/0.53          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nonzero_divide_mult_cancel_left
% 0.29/0.53  thf(fact_2478_div__mult__self4,axiom,
% 0.29/0.53      ! [B: nat,C: nat,A: nat] :
% 0.29/0.53        ( ( B != zero_zero_nat )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.29/0.53          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self4
% 0.29/0.53  thf(fact_2479_div__mult__self4,axiom,
% 0.29/0.53      ! [B: int,C: int,A: int] :
% 0.29/0.53        ( ( B != zero_zero_int )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.29/0.53          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self4
% 0.29/0.53  thf(fact_2480_div__mult__self4,axiom,
% 0.29/0.53      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.29/0.53          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self4
% 0.29/0.53  thf(fact_2481_div__mult__self3,axiom,
% 0.29/0.53      ! [B: nat,C: nat,A: nat] :
% 0.29/0.53        ( ( B != zero_zero_nat )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.29/0.53          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self3
% 0.29/0.53  thf(fact_2482_div__mult__self3,axiom,
% 0.29/0.53      ! [B: int,C: int,A: int] :
% 0.29/0.53        ( ( B != zero_zero_int )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.29/0.53          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self3
% 0.29/0.53  thf(fact_2483_div__mult__self3,axiom,
% 0.29/0.53      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.29/0.53          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self3
% 0.29/0.53  thf(fact_2484_div__mult__self2,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( B != zero_zero_nat )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.29/0.53          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self2
% 0.29/0.53  thf(fact_2485_div__mult__self2,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( B != zero_zero_int )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.29/0.53          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self2
% 0.29/0.53  thf(fact_2486_div__mult__self2,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.29/0.53          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self2
% 0.29/0.53  thf(fact_2487_div__mult__self1,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( B != zero_zero_nat )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.29/0.53          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self1
% 0.29/0.53  thf(fact_2488_div__mult__self1,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( B != zero_zero_int )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.29/0.53          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self1
% 0.29/0.53  thf(fact_2489_div__mult__self1,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.29/0.53          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_self1
% 0.29/0.53  thf(fact_2490_unit__div__mult__self,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.29/0.53          = B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_self
% 0.29/0.53  thf(fact_2491_unit__div__mult__self,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.29/0.53          = B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_self
% 0.29/0.53  thf(fact_2492_unit__div__mult__self,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.29/0.53          = B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_self
% 0.29/0.53  thf(fact_2493_unit__mult__div__div,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.29/0.53          = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_div_div
% 0.29/0.53  thf(fact_2494_unit__mult__div__div,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.29/0.53          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_div_div
% 0.29/0.53  thf(fact_2495_unit__mult__div__div,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_div_div
% 0.29/0.53  thf(fact_2496_pow__divides__pow__iff,axiom,
% 0.29/0.53      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pow_divides_pow_iff
% 0.29/0.53  thf(fact_2497_pow__divides__pow__iff,axiom,
% 0.29/0.53      ! [N2: nat,A: int,B: int] :
% 0.29/0.53        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 0.29/0.53          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pow_divides_pow_iff
% 0.29/0.53  thf(fact_2498_zmod__numeral__Bit0,axiom,
% 0.29/0.53      ! [V: num,W: num] :
% 0.29/0.53        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.29/0.53        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmod_numeral_Bit0
% 0.29/0.53  thf(fact_2499_power__add__numeral2,axiom,
% 0.29/0.53      ! [A: complex,M: num,N2: num,B: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.29/0.53        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral2
% 0.29/0.53  thf(fact_2500_power__add__numeral2,axiom,
% 0.29/0.53      ! [A: real,M: num,N2: num,B: real] :
% 0.29/0.53        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.29/0.53        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral2
% 0.29/0.53  thf(fact_2501_power__add__numeral2,axiom,
% 0.29/0.53      ! [A: nat,M: num,N2: num,B: nat] :
% 0.29/0.53        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.29/0.53        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral2
% 0.29/0.53  thf(fact_2502_power__add__numeral2,axiom,
% 0.29/0.53      ! [A: int,M: num,N2: num,B: int] :
% 0.29/0.53        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 0.29/0.53        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral2
% 0.29/0.53  thf(fact_2503_power__add__numeral,axiom,
% 0.29/0.53      ! [A: complex,M: num,N2: num] :
% 0.29/0.53        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.29/0.53        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral
% 0.29/0.53  thf(fact_2504_power__add__numeral,axiom,
% 0.29/0.53      ! [A: real,M: num,N2: num] :
% 0.29/0.53        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.29/0.53        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral
% 0.29/0.53  thf(fact_2505_power__add__numeral,axiom,
% 0.29/0.53      ! [A: nat,M: num,N2: num] :
% 0.29/0.53        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.29/0.53        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral
% 0.29/0.53  thf(fact_2506_power__add__numeral,axiom,
% 0.29/0.53      ! [A: int,M: num,N2: num] :
% 0.29/0.53        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 0.29/0.53        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_add_numeral
% 0.29/0.53  thf(fact_2507_Suc__times__numeral__mod__eq,axiom,
% 0.29/0.53      ! [K: num,N2: nat] :
% 0.29/0.53        ( ( ( numeral_numeral_nat @ K )
% 0.29/0.53         != one_one_nat )
% 0.29/0.53       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.53          = one_one_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Suc_times_numeral_mod_eq
% 0.29/0.53  thf(fact_2508_zle__add1__eq__le,axiom,
% 0.29/0.53      ! [W: int,Z: int] :
% 0.29/0.53        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.29/0.53        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zle_add1_eq_le
% 0.29/0.53  thf(fact_2509_mod__neg__neg__trivial,axiom,
% 0.29/0.53      ! [K: int,L: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.29/0.53       => ( ( ord_less_int @ L @ K )
% 0.29/0.53         => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.53            = K ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_neg_neg_trivial
% 0.29/0.53  thf(fact_2510_mod__pos__pos__trivial,axiom,
% 0.29/0.53      ! [K: int,L: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.53       => ( ( ord_less_int @ K @ L )
% 0.29/0.53         => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.53            = K ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_pos_pos_trivial
% 0.29/0.53  thf(fact_2511_even__mult__iff,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mult_iff
% 0.29/0.53  thf(fact_2512_even__mult__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mult_iff
% 0.29/0.53  thf(fact_2513_even__mult__iff,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mult_iff
% 0.29/0.53  thf(fact_2514_even__add,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_add
% 0.29/0.53  thf(fact_2515_even__add,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_add
% 0.29/0.53  thf(fact_2516_even__add,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.29/0.53        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_add
% 0.29/0.53  thf(fact_2517_odd__add,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.29/0.53        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.53         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_add
% 0.29/0.53  thf(fact_2518_odd__add,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.29/0.53        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.53         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_add
% 0.29/0.53  thf(fact_2519_odd__add,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.29/0.53        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.53         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_add
% 0.29/0.53  thf(fact_2520_even__mod__2__iff,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.53        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mod_2_iff
% 0.29/0.53  thf(fact_2521_even__mod__2__iff,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.29/0.53        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mod_2_iff
% 0.29/0.53  thf(fact_2522_even__mod__2__iff,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.29/0.53        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_mod_2_iff
% 0.29/0.53  thf(fact_2523_even__Suc__Suc__iff,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 0.29/0.53        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_Suc_Suc_iff
% 0.29/0.53  thf(fact_2524_even__Suc,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_Suc
% 0.29/0.53  thf(fact_2525_odd__of__bool__self,axiom,
% 0.29/0.53      ! [P2: $o] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 0.29/0.53        = P2 ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_of_bool_self
% 0.29/0.53  thf(fact_2526_odd__of__bool__self,axiom,
% 0.29/0.53      ! [P2: $o] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 0.29/0.53        = P2 ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_of_bool_self
% 0.29/0.53  thf(fact_2527_odd__of__bool__self,axiom,
% 0.29/0.53      ! [P2: $o] :
% 0.29/0.53        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 0.29/0.53        = P2 ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_of_bool_self
% 0.29/0.53  thf(fact_2528_even__plus__one__iff,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.29/0.53        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_plus_one_iff
% 0.29/0.53  thf(fact_2529_even__plus__one__iff,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_plus_one_iff
% 0.29/0.53  thf(fact_2530_even__plus__one__iff,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.29/0.53        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_plus_one_iff
% 0.29/0.53  thf(fact_2531_of__bool__half__eq__0,axiom,
% 0.29/0.53      ! [B: $o] :
% 0.29/0.53        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53        = zero_zero_nat ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_half_eq_0
% 0.29/0.53  thf(fact_2532_of__bool__half__eq__0,axiom,
% 0.29/0.53      ! [B: $o] :
% 0.29/0.53        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.53        = zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_half_eq_0
% 0.29/0.53  thf(fact_2533_of__bool__half__eq__0,axiom,
% 0.29/0.53      ! [B: $o] :
% 0.29/0.53        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.53        = zero_z3403309356797280102nteger ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_half_eq_0
% 0.29/0.53  thf(fact_2534_even__Suc__div__two,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.53       => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_Suc_div_two
% 0.29/0.53  thf(fact_2535_odd__Suc__div__two,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.53       => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_Suc_div_two
% 0.29/0.53  thf(fact_2536_even__succ__div__2,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_2
% 0.29/0.53  thf(fact_2537_even__succ__div__2,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_2
% 0.29/0.53  thf(fact_2538_even__succ__div__2,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_2
% 0.29/0.53  thf(fact_2539_even__succ__div__two,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_two
% 0.29/0.53  thf(fact_2540_even__succ__div__two,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_two
% 0.29/0.53  thf(fact_2541_even__succ__div__two,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_succ_div_two
% 0.29/0.53  thf(fact_2542_odd__succ__div__two,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_succ_div_two
% 0.29/0.53  thf(fact_2543_odd__succ__div__two,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_succ_div_two
% 0.29/0.53  thf(fact_2544_odd__succ__div__two,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.53          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_succ_div_two
% 0.29/0.53  thf(fact_2545_zero__le__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: real,W: num] :
% 0.29/0.53        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_power_eq_numeral
% 0.29/0.53  thf(fact_2546_zero__le__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: rat,W: num] :
% 0.29/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_power_eq_numeral
% 0.29/0.53  thf(fact_2547_zero__le__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: int,W: num] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_le_power_eq_numeral
% 0.29/0.53  thf(fact_2548_even__power,axiom,
% 0.29/0.53      ! [A: code_integer,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.29/0.53        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_power
% 0.29/0.53  thf(fact_2549_even__power,axiom,
% 0.29/0.53      ! [A: nat,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 0.29/0.53        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_power
% 0.29/0.53  thf(fact_2550_even__power,axiom,
% 0.29/0.53      ! [A: int,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 0.29/0.53        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % even_power
% 0.29/0.53  thf(fact_2551_power__less__zero__eq__numeral,axiom,
% 0.29/0.53      ! [A: real,W: num] :
% 0.29/0.53        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq_numeral
% 0.29/0.53  thf(fact_2552_power__less__zero__eq__numeral,axiom,
% 0.29/0.53      ! [A: rat,W: num] :
% 0.29/0.53        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq_numeral
% 0.29/0.53  thf(fact_2553_power__less__zero__eq__numeral,axiom,
% 0.29/0.53      ! [A: int,W: num] :
% 0.29/0.53        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq_numeral
% 0.29/0.53  thf(fact_2554_power__less__zero__eq,axiom,
% 0.29/0.53      ! [A: real,N2: nat] :
% 0.29/0.53        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.53          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq
% 0.29/0.53  thf(fact_2555_power__less__zero__eq,axiom,
% 0.29/0.53      ! [A: rat,N2: nat] :
% 0.29/0.53        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.53          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq
% 0.29/0.53  thf(fact_2556_power__less__zero__eq,axiom,
% 0.29/0.53      ! [A: int,N2: nat] :
% 0.29/0.53        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 0.29/0.53        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.53          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % power_less_zero_eq
% 0.29/0.53  thf(fact_2557_odd__two__times__div__two__succ,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.29/0.53          = A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_two_times_div_two_succ
% 0.29/0.53  thf(fact_2558_odd__two__times__div__two__succ,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.29/0.53          = A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_two_times_div_two_succ
% 0.29/0.53  thf(fact_2559_odd__two__times__div__two__succ,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.53       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.29/0.53          = A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_two_times_div_two_succ
% 0.29/0.53  thf(fact_2560_zero__less__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: real,W: num] :
% 0.29/0.53        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( ( numeral_numeral_nat @ W )
% 0.29/0.53            = zero_zero_nat )
% 0.29/0.53          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( A != zero_zero_real ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_power_eq_numeral
% 0.29/0.53  thf(fact_2561_zero__less__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: rat,W: num] :
% 0.29/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( ( numeral_numeral_nat @ W )
% 0.29/0.53            = zero_zero_nat )
% 0.29/0.53          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( A != zero_zero_rat ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_power_eq_numeral
% 0.29/0.53  thf(fact_2562_zero__less__power__eq__numeral,axiom,
% 0.29/0.53      ! [A: int,W: num] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.29/0.53        = ( ( ( numeral_numeral_nat @ W )
% 0.29/0.53            = zero_zero_nat )
% 0.29/0.53          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( A != zero_zero_int ) )
% 0.29/0.53          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.53            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zero_less_power_eq_numeral
% 0.29/0.53  thf(fact_2563_one__div__2__pow__eq,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % one_div_2_pow_eq
% 0.29/0.53  thf(fact_2564_one__div__2__pow__eq,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % one_div_2_pow_eq
% 0.29/0.53  thf(fact_2565_one__div__2__pow__eq,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % one_div_2_pow_eq
% 0.29/0.53  thf(fact_2566_bits__1__div__exp,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_1_div_exp
% 0.29/0.53  thf(fact_2567_bits__1__div__exp,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_1_div_exp
% 0.29/0.53  thf(fact_2568_bits__1__div__exp,axiom,
% 0.29/0.53      ! [N2: nat] :
% 0.29/0.53        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.53        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bits_1_div_exp
% 0.29/0.53  thf(fact_2569_add1__zle__eq,axiom,
% 0.29/0.53      ! [W: int,Z: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.29/0.53        = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.53  
% 0.29/0.53  % add1_zle_eq
% 0.29/0.53  thf(fact_2570_zdvd__imp__le,axiom,
% 0.29/0.53      ! [Z: int,N2: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ Z @ N2 )
% 0.29/0.53       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 0.29/0.53         => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zdvd_imp_le
% 0.29/0.53  thf(fact_2571_int__gr__induct,axiom,
% 0.29/0.53      ! [K: int,I2: int,P: int > $o] :
% 0.29/0.53        ( ( ord_less_int @ K @ I2 )
% 0.29/0.53       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.29/0.53         => ( ! [I4: int] :
% 0.29/0.53                ( ( ord_less_int @ K @ I4 )
% 0.29/0.53               => ( ( P @ I4 )
% 0.29/0.53                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.53           => ( P @ I2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % int_gr_induct
% 0.29/0.53  thf(fact_2572_le__imp__0__less,axiom,
% 0.29/0.53      ! [Z: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.53       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % le_imp_0_less
% 0.29/0.53  thf(fact_2573_zless__add1__eq,axiom,
% 0.29/0.53      ! [W: int,Z: int] :
% 0.29/0.53        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.29/0.53        = ( ( ord_less_int @ W @ Z )
% 0.29/0.53          | ( W = Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zless_add1_eq
% 0.29/0.53  thf(fact_2574_split__zmod,axiom,
% 0.29/0.53      ! [P: int > $o,N2: int,K: int] :
% 0.29/0.53        ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 0.29/0.53        = ( ( ( K = zero_zero_int )
% 0.29/0.53           => ( P @ N2 ) )
% 0.29/0.53          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.53           => ! [I3: int,J3: int] :
% 0.29/0.53                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.29/0.53                  & ( ord_less_int @ J3 @ K )
% 0.29/0.53                  & ( N2
% 0.29/0.53                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.53               => ( P @ J3 ) ) )
% 0.29/0.53          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.53           => ! [I3: int,J3: int] :
% 0.29/0.53                ( ( ( ord_less_int @ K @ J3 )
% 0.29/0.53                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.29/0.53                  & ( N2
% 0.29/0.53                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.53               => ( P @ J3 ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % split_zmod
% 0.29/0.53  thf(fact_2575_odd__less__0__iff,axiom,
% 0.29/0.53      ! [Z: int] :
% 0.29/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.29/0.53        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % odd_less_0_iff
% 0.29/0.53  thf(fact_2576_q__pos__lemma,axiom,
% 0.29/0.53      ! [B4: int,Q4: int,R4: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 0.29/0.53       => ( ( ord_less_int @ R4 @ B4 )
% 0.29/0.53         => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.29/0.53           => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % q_pos_lemma
% 0.29/0.53  thf(fact_2577_neg__mod__conj,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.53       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.29/0.53          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % neg_mod_conj
% 0.29/0.53  thf(fact_2578_pos__mod__conj,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.53          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pos_mod_conj
% 0.29/0.53  thf(fact_2579_int__mod__neg__eq,axiom,
% 0.29/0.53      ! [A: int,B: int,Q3: int,R3: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.29/0.53         => ( ( ord_less_int @ B @ R3 )
% 0.29/0.53           => ( ( modulo_modulo_int @ A @ B )
% 0.29/0.53              = R3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % int_mod_neg_eq
% 0.29/0.53  thf(fact_2580_int__mod__pos__eq,axiom,
% 0.29/0.53      ! [A: int,B: int,Q3: int,R3: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.29/0.53         => ( ( ord_less_int @ R3 @ B )
% 0.29/0.53           => ( ( modulo_modulo_int @ A @ B )
% 0.29/0.53              = R3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % int_mod_pos_eq
% 0.29/0.53  thf(fact_2581_pos__zmult__eq__1__iff,axiom,
% 0.29/0.53      ! [M: int,N2: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ M )
% 0.29/0.53       => ( ( ( times_times_int @ M @ N2 )
% 0.29/0.53            = one_one_int )
% 0.29/0.53          = ( ( M = one_one_int )
% 0.29/0.53            & ( N2 = one_one_int ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % pos_zmult_eq_1_iff
% 0.29/0.53  thf(fact_2582_zless__imp__add1__zle,axiom,
% 0.29/0.53      ! [W: int,Z: int] :
% 0.29/0.53        ( ( ord_less_int @ W @ Z )
% 0.29/0.53       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zless_imp_add1_zle
% 0.29/0.53  thf(fact_2583_mod__int__pos__iff,axiom,
% 0.29/0.53      ! [K: int,L: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 0.29/0.53        = ( ( dvd_dvd_int @ L @ K )
% 0.29/0.53          | ( ( L = zero_zero_int )
% 0.29/0.53            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.29/0.53          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_int_pos_iff
% 0.29/0.53  thf(fact_2584_zdiv__mono2__lemma,axiom,
% 0.29/0.53      ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 0.29/0.53        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 0.29/0.53          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 0.29/0.53         => ( ( ord_less_int @ R4 @ B4 )
% 0.29/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.29/0.53             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.29/0.53               => ( ( ord_less_eq_int @ B4 @ B )
% 0.29/0.53                 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zdiv_mono2_lemma
% 0.29/0.53  thf(fact_2585_zmod__trivial__iff,axiom,
% 0.29/0.53      ! [I2: int,K: int] :
% 0.29/0.53        ( ( ( modulo_modulo_int @ I2 @ K )
% 0.29/0.53          = I2 )
% 0.29/0.53        = ( ( K = zero_zero_int )
% 0.29/0.53          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.29/0.53            & ( ord_less_int @ I2 @ K ) )
% 0.29/0.53          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.29/0.53            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmod_trivial_iff
% 0.29/0.53  thf(fact_2586_zdiv__mono2__neg__lemma,axiom,
% 0.29/0.53      ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 0.29/0.53        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 0.29/0.53          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 0.29/0.53       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) @ zero_zero_int )
% 0.29/0.53         => ( ( ord_less_int @ R3 @ B )
% 0.29/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.29/0.53             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.29/0.53               => ( ( ord_less_eq_int @ B4 @ B )
% 0.29/0.53                 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zdiv_mono2_neg_lemma
% 0.29/0.53  thf(fact_2587_int__one__le__iff__zero__less,axiom,
% 0.29/0.53      ! [Z: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.29/0.53        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.53  
% 0.29/0.53  % int_one_le_iff_zero_less
% 0.29/0.53  thf(fact_2588_unique__quotient__lemma,axiom,
% 0.29/0.53      ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.29/0.53         => ( ( ord_less_int @ R4 @ B )
% 0.29/0.53           => ( ( ord_less_int @ R3 @ B )
% 0.29/0.53             => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unique_quotient_lemma
% 0.29/0.53  thf(fact_2589_neg__mod__sign,axiom,
% 0.29/0.53      ! [L: int,K: int] :
% 0.29/0.53        ( ( ord_less_int @ L @ zero_zero_int )
% 0.29/0.53       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % neg_mod_sign
% 0.29/0.53  thf(fact_2590_Euclidean__Division_Opos__mod__sign,axiom,
% 0.29/0.53      ! [L: int,K: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.53       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Euclidean_Division.pos_mod_sign
% 0.29/0.53  thf(fact_2591_unique__quotient__lemma__neg,axiom,
% 0.29/0.53      ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.29/0.53         => ( ( ord_less_int @ B @ R3 )
% 0.29/0.53           => ( ( ord_less_int @ B @ R4 )
% 0.29/0.53             => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unique_quotient_lemma_neg
% 0.29/0.53  thf(fact_2592_mod__pos__neg__trivial,axiom,
% 0.29/0.53      ! [K: int,L: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.53       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.29/0.53         => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.53            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_pos_neg_trivial
% 0.29/0.53  thf(fact_2593_zmod__le__nonneg__dividend,axiom,
% 0.29/0.53      ! [M: int,K: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.29/0.53       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmod_le_nonneg_dividend
% 0.29/0.53  thf(fact_2594_zdvd__antisym__nonneg,axiom,
% 0.29/0.53      ! [M: int,N2: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.29/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.29/0.53         => ( ( dvd_dvd_int @ M @ N2 )
% 0.29/0.53           => ( ( dvd_dvd_int @ N2 @ M )
% 0.29/0.53             => ( M = N2 ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zdvd_antisym_nonneg
% 0.29/0.53  thf(fact_2595_verit__la__generic,axiom,
% 0.29/0.53      ! [A: int,X4: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ X4 )
% 0.29/0.53        | ( A = X4 )
% 0.29/0.53        | ( ord_less_eq_int @ X4 @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % verit_la_generic
% 0.29/0.53  thf(fact_2596_less__eq__int__code_I1_J,axiom,
% 0.29/0.53      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.29/0.53  
% 0.29/0.53  % less_eq_int_code(1)
% 0.29/0.53  thf(fact_2597_zmod__eq__0D,axiom,
% 0.29/0.53      ! [M: int,D: int] :
% 0.29/0.53        ( ( ( modulo_modulo_int @ M @ D )
% 0.29/0.53          = zero_zero_int )
% 0.29/0.53       => ? [Q2: int] :
% 0.29/0.53            ( M
% 0.29/0.53            = ( times_times_int @ D @ Q2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmod_eq_0D
% 0.29/0.53  thf(fact_2598_zmod__eq__0__iff,axiom,
% 0.29/0.53      ! [M: int,D: int] :
% 0.29/0.53        ( ( ( modulo_modulo_int @ M @ D )
% 0.29/0.53          = zero_zero_int )
% 0.29/0.53        = ( ? [Q5: int] :
% 0.29/0.53              ( M
% 0.29/0.53              = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmod_eq_0_iff
% 0.29/0.53  thf(fact_2599_Euclidean__Division_Opos__mod__bound,axiom,
% 0.29/0.53      ! [L: int,K: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.53       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Euclidean_Division.pos_mod_bound
% 0.29/0.53  thf(fact_2600_neg__mod__bound,axiom,
% 0.29/0.53      ! [L: int,K: int] :
% 0.29/0.53        ( ( ord_less_int @ L @ zero_zero_int )
% 0.29/0.53       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % neg_mod_bound
% 0.29/0.53  thf(fact_2601_zmult__zless__mono2,axiom,
% 0.29/0.53      ! [I2: int,J: int,K: int] :
% 0.29/0.53        ( ( ord_less_int @ I2 @ J )
% 0.29/0.53       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.53         => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zmult_zless_mono2
% 0.29/0.53  thf(fact_2602_zdvd__not__zless,axiom,
% 0.29/0.53      ! [M: int,N2: int] :
% 0.29/0.53        ( ( ord_less_int @ zero_zero_int @ M )
% 0.29/0.53       => ( ( ord_less_int @ M @ N2 )
% 0.29/0.53         => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % zdvd_not_zless
% 0.29/0.53  thf(fact_2603_less__int__code_I1_J,axiom,
% 0.29/0.53      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.29/0.53  
% 0.29/0.53  % less_int_code(1)
% 0.29/0.53  thf(fact_2604_iadd__is__0,axiom,
% 0.29/0.53      ! [M: extended_enat,N2: extended_enat] :
% 0.29/0.53        ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 0.29/0.53          = zero_z5237406670263579293d_enat )
% 0.29/0.53        = ( ( M = zero_z5237406670263579293d_enat )
% 0.29/0.53          & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % iadd_is_0
% 0.29/0.53  thf(fact_2605_imult__is__0,axiom,
% 0.29/0.53      ! [M: extended_enat,N2: extended_enat] :
% 0.29/0.53        ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 0.29/0.53          = zero_z5237406670263579293d_enat )
% 0.29/0.53        = ( ( M = zero_z5237406670263579293d_enat )
% 0.29/0.53          | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % imult_is_0
% 0.29/0.53  thf(fact_2606_zero__one__enat__neq_I1_J,axiom,
% 0.29/0.53      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 0.29/0.53  
% 0.29/0.53  % zero_one_enat_neq(1)
% 0.29/0.53  thf(fact_2607_int__ge__induct,axiom,
% 0.29/0.53      ! [K: int,I2: int,P: int > $o] :
% 0.29/0.53        ( ( ord_less_eq_int @ K @ I2 )
% 0.29/0.53       => ( ( P @ K )
% 0.29/0.53         => ( ! [I4: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ K @ I4 )
% 0.29/0.53               => ( ( P @ I4 )
% 0.29/0.53                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.53           => ( P @ I2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % int_ge_induct
% 0.29/0.53  thf(fact_2608_is__unit__mult__iff,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.29/0.53        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_mult_iff
% 0.29/0.53  thf(fact_2609_is__unit__mult__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.29/0.53        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_mult_iff
% 0.29/0.53  thf(fact_2610_is__unit__mult__iff,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.29/0.53        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_mult_iff
% 0.29/0.53  thf(fact_2611_dvd__mult__unit__iff,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff
% 0.29/0.53  thf(fact_2612_dvd__mult__unit__iff,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff
% 0.29/0.53  thf(fact_2613_dvd__mult__unit__iff,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.29/0.53          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff
% 0.29/0.53  thf(fact_2614_mult__unit__dvd__iff,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff
% 0.29/0.53  thf(fact_2615_mult__unit__dvd__iff,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff
% 0.29/0.53  thf(fact_2616_mult__unit__dvd__iff,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff
% 0.29/0.53  thf(fact_2617_dvd__mult__unit__iff_H,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff'
% 0.29/0.53  thf(fact_2618_dvd__mult__unit__iff_H,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff'
% 0.29/0.53  thf(fact_2619_dvd__mult__unit__iff_H,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_unit_iff'
% 0.29/0.53  thf(fact_2620_mult__unit__dvd__iff_H,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff'
% 0.29/0.53  thf(fact_2621_mult__unit__dvd__iff_H,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff'
% 0.29/0.53  thf(fact_2622_mult__unit__dvd__iff_H,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_unit_dvd_iff'
% 0.29/0.53  thf(fact_2623_unit__mult__left__cancel,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.53            = ( times_3573771949741848930nteger @ A @ C ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_left_cancel
% 0.29/0.53  thf(fact_2624_unit__mult__left__cancel,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ( ( ( times_times_nat @ A @ B )
% 0.29/0.53            = ( times_times_nat @ A @ C ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_left_cancel
% 0.29/0.53  thf(fact_2625_unit__mult__left__cancel,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ( ( ( times_times_int @ A @ B )
% 0.29/0.53            = ( times_times_int @ A @ C ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_left_cancel
% 0.29/0.53  thf(fact_2626_unit__mult__right__cancel,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.29/0.53            = ( times_3573771949741848930nteger @ C @ A ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_right_cancel
% 0.29/0.53  thf(fact_2627_unit__mult__right__cancel,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ( ( ( times_times_nat @ B @ A )
% 0.29/0.53            = ( times_times_nat @ C @ A ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_right_cancel
% 0.29/0.53  thf(fact_2628_unit__mult__right__cancel,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ( ( ( times_times_int @ B @ A )
% 0.29/0.53            = ( times_times_int @ C @ A ) )
% 0.29/0.53          = ( B = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_mult_right_cancel
% 0.29/0.53  thf(fact_2629_dvd__div__mult,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 0.29/0.53          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult
% 0.29/0.53  thf(fact_2630_dvd__div__mult,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 0.29/0.53          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult
% 0.29/0.53  thf(fact_2631_dvd__div__mult,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 0.29/0.53          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult
% 0.29/0.53  thf(fact_2632_div__mult__swap,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.29/0.53          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_swap
% 0.29/0.53  thf(fact_2633_div__mult__swap,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.29/0.53          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_swap
% 0.29/0.53  thf(fact_2634_div__mult__swap,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_swap
% 0.29/0.53  thf(fact_2635_div__div__eq__right,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.29/0.53            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_eq_right
% 0.29/0.53  thf(fact_2636_div__div__eq__right,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.29/0.53            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_eq_right
% 0.29/0.53  thf(fact_2637_div__div__eq__right,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_eq_right
% 0.29/0.53  thf(fact_2638_dvd__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: nat,C: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 0.29/0.53       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.53          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult2_eq
% 0.29/0.53  thf(fact_2639_dvd__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: int,C: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 0.29/0.53       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.53          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult2_eq
% 0.29/0.53  thf(fact_2640_dvd__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 0.29/0.53       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_mult2_eq
% 0.29/0.53  thf(fact_2641_dvd__mult__imp__div,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 0.29/0.53       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_imp_div
% 0.29/0.53  thf(fact_2642_dvd__mult__imp__div,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 0.29/0.53       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_imp_div
% 0.29/0.53  thf(fact_2643_dvd__mult__imp__div,axiom,
% 0.29/0.53      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_imp_div
% 0.29/0.53  thf(fact_2644_div__mult__div__if__dvd,axiom,
% 0.29/0.53      ! [B: nat,A: nat,D: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53       => ( ( dvd_dvd_nat @ D @ C )
% 0.29/0.53         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 0.29/0.53            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_div_if_dvd
% 0.29/0.53  thf(fact_2645_div__mult__div__if__dvd,axiom,
% 0.29/0.53      ! [B: int,A: int,D: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53       => ( ( dvd_dvd_int @ D @ C )
% 0.29/0.53         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 0.29/0.53            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_div_if_dvd
% 0.29/0.53  thf(fact_2646_div__mult__div__if__dvd,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ D @ C )
% 0.29/0.53         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 0.29/0.53            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_div_if_dvd
% 0.29/0.53  thf(fact_2647_dvd__antisym,axiom,
% 0.29/0.53      ! [M: nat,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ M @ N2 )
% 0.29/0.53       => ( ( dvd_dvd_nat @ N2 @ M )
% 0.29/0.53         => ( M = N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_antisym
% 0.29/0.53  thf(fact_2648_bezout__lemma__nat,axiom,
% 0.29/0.53      ! [D: nat,A: nat,B: nat,X4: nat,Y: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ D @ A )
% 0.29/0.53       => ( ( dvd_dvd_nat @ D @ B )
% 0.29/0.53         => ( ( ( ( times_times_nat @ A @ X4 )
% 0.29/0.53                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 0.29/0.53              | ( ( times_times_nat @ B @ X4 )
% 0.29/0.53                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 0.29/0.53           => ? [X5: nat,Y3: nat] :
% 0.29/0.53                ( ( dvd_dvd_nat @ D @ A )
% 0.29/0.53                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.53                & ( ( ( times_times_nat @ A @ X5 )
% 0.29/0.53                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 0.29/0.53                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 0.29/0.53                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bezout_lemma_nat
% 0.29/0.53  thf(fact_2649_bezout__add__nat,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53      ? [D3: nat,X5: nat,Y3: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ D3 @ A )
% 0.29/0.53        & ( dvd_dvd_nat @ D3 @ B )
% 0.29/0.53        & ( ( ( times_times_nat @ A @ X5 )
% 0.29/0.53            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 0.29/0.53          | ( ( times_times_nat @ B @ X5 )
% 0.29/0.53            = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bezout_add_nat
% 0.29/0.53  thf(fact_2650_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.53  thf(fact_2651_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.53  thf(fact_2652_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.53  thf(fact_2653_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.53  thf(fact_2654_dvdE,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53       => ~ ! [K2: code_integer] :
% 0.29/0.53              ( A
% 0.29/0.53             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdE
% 0.29/0.53  thf(fact_2655_dvdE,axiom,
% 0.29/0.53      ! [B: complex,A: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ B @ A )
% 0.29/0.53       => ~ ! [K2: complex] :
% 0.29/0.53              ( A
% 0.29/0.53             != ( times_times_complex @ B @ K2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdE
% 0.29/0.53  thf(fact_2656_dvdE,axiom,
% 0.29/0.53      ! [B: real,A: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ B @ A )
% 0.29/0.53       => ~ ! [K2: real] :
% 0.29/0.53              ( A
% 0.29/0.53             != ( times_times_real @ B @ K2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdE
% 0.29/0.53  thf(fact_2657_dvdE,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53       => ~ ! [K2: nat] :
% 0.29/0.53              ( A
% 0.29/0.53             != ( times_times_nat @ B @ K2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdE
% 0.29/0.53  thf(fact_2658_dvdE,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53       => ~ ! [K2: int] :
% 0.29/0.53              ( A
% 0.29/0.53             != ( times_times_int @ B @ K2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdE
% 0.29/0.53  thf(fact_2659_dvdI,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,K: code_integer] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( times_3573771949741848930nteger @ B @ K ) )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdI
% 0.29/0.53  thf(fact_2660_dvdI,axiom,
% 0.29/0.53      ! [A: complex,B: complex,K: complex] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( times_times_complex @ B @ K ) )
% 0.29/0.53       => ( dvd_dvd_complex @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdI
% 0.29/0.53  thf(fact_2661_dvdI,axiom,
% 0.29/0.53      ! [A: real,B: real,K: real] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( times_times_real @ B @ K ) )
% 0.29/0.53       => ( dvd_dvd_real @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdI
% 0.29/0.53  thf(fact_2662_dvdI,axiom,
% 0.29/0.53      ! [A: nat,B: nat,K: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( times_times_nat @ B @ K ) )
% 0.29/0.53       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdI
% 0.29/0.53  thf(fact_2663_dvdI,axiom,
% 0.29/0.53      ! [A: int,B: int,K: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( times_times_int @ B @ K ) )
% 0.29/0.53       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvdI
% 0.29/0.53  thf(fact_2664_dvd__def,axiom,
% 0.29/0.53      ( dvd_dvd_Code_integer
% 0.29/0.53      = ( ^ [B2: code_integer,A3: code_integer] :
% 0.29/0.53          ? [K3: code_integer] :
% 0.29/0.53            ( A3
% 0.29/0.53            = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_def
% 0.29/0.53  thf(fact_2665_dvd__def,axiom,
% 0.29/0.53      ( dvd_dvd_complex
% 0.29/0.53      = ( ^ [B2: complex,A3: complex] :
% 0.29/0.53          ? [K3: complex] :
% 0.29/0.53            ( A3
% 0.29/0.53            = ( times_times_complex @ B2 @ K3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_def
% 0.29/0.53  thf(fact_2666_dvd__def,axiom,
% 0.29/0.53      ( dvd_dvd_real
% 0.29/0.53      = ( ^ [B2: real,A3: real] :
% 0.29/0.53          ? [K3: real] :
% 0.29/0.53            ( A3
% 0.29/0.53            = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_def
% 0.29/0.53  thf(fact_2667_dvd__def,axiom,
% 0.29/0.53      ( dvd_dvd_nat
% 0.29/0.53      = ( ^ [B2: nat,A3: nat] :
% 0.29/0.53          ? [K3: nat] :
% 0.29/0.53            ( A3
% 0.29/0.53            = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_def
% 0.29/0.53  thf(fact_2668_dvd__def,axiom,
% 0.29/0.53      ( dvd_dvd_int
% 0.29/0.53      = ( ^ [B2: int,A3: int] :
% 0.29/0.53          ? [K3: int] :
% 0.29/0.53            ( A3
% 0.29/0.53            = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_def
% 0.29/0.53  thf(fact_2669_of__bool__conj,axiom,
% 0.29/0.53      ! [P: $o,Q: $o] :
% 0.29/0.53        ( ( zero_n1201886186963655149omplex
% 0.29/0.53          @ ( P
% 0.29/0.53            & Q ) )
% 0.29/0.53        = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_conj
% 0.29/0.53  thf(fact_2670_of__bool__conj,axiom,
% 0.29/0.53      ! [P: $o,Q: $o] :
% 0.29/0.53        ( ( zero_n3304061248610475627l_real
% 0.29/0.53          @ ( P
% 0.29/0.53            & Q ) )
% 0.29/0.53        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_conj
% 0.29/0.53  thf(fact_2671_of__bool__conj,axiom,
% 0.29/0.53      ! [P: $o,Q: $o] :
% 0.29/0.53        ( ( zero_n2687167440665602831ol_nat
% 0.29/0.53          @ ( P
% 0.29/0.53            & Q ) )
% 0.29/0.53        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_conj
% 0.29/0.53  thf(fact_2672_of__bool__conj,axiom,
% 0.29/0.53      ! [P: $o,Q: $o] :
% 0.29/0.53        ( ( zero_n2684676970156552555ol_int
% 0.29/0.53          @ ( P
% 0.29/0.53            & Q ) )
% 0.29/0.53        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_conj
% 0.29/0.53  thf(fact_2673_of__bool__conj,axiom,
% 0.29/0.53      ! [P: $o,Q: $o] :
% 0.29/0.53        ( ( zero_n356916108424825756nteger
% 0.29/0.53          @ ( P
% 0.29/0.53            & Q ) )
% 0.29/0.53        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_conj
% 0.29/0.53  thf(fact_2674_dvd__mult,axiom,
% 0.29/0.53      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult
% 0.29/0.53  thf(fact_2675_dvd__mult,axiom,
% 0.29/0.53      ! [A: complex,C: complex,B: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ A @ C )
% 0.29/0.53       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult
% 0.29/0.53  thf(fact_2676_dvd__mult,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ C )
% 0.29/0.53       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult
% 0.29/0.53  thf(fact_2677_dvd__mult,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ C )
% 0.29/0.53       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult
% 0.29/0.53  thf(fact_2678_dvd__mult,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ C )
% 0.29/0.53       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult
% 0.29/0.53  thf(fact_2679_dvd__refl,axiom,
% 0.29/0.53      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_refl
% 0.29/0.53  thf(fact_2680_dvd__refl,axiom,
% 0.29/0.53      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_refl
% 0.29/0.53  thf(fact_2681_dvd__refl,axiom,
% 0.29/0.53      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_refl
% 0.29/0.53  thf(fact_2682_mult_Oassoc,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.assoc
% 0.29/0.53  thf(fact_2683_mult_Oassoc,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.assoc
% 0.29/0.53  thf(fact_2684_mult_Oassoc,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.assoc
% 0.29/0.53  thf(fact_2685_mult_Oassoc,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.assoc
% 0.29/0.53  thf(fact_2686_dvd__mult2,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult2
% 0.29/0.53  thf(fact_2687_dvd__mult2,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ A @ B )
% 0.29/0.53       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult2
% 0.29/0.53  thf(fact_2688_dvd__mult2,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ B )
% 0.29/0.53       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult2
% 0.29/0.53  thf(fact_2689_dvd__mult2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult2
% 0.29/0.53  thf(fact_2690_dvd__mult2,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult2
% 0.29/0.53  thf(fact_2691_dvd__trans,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ C )
% 0.29/0.53         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_trans
% 0.29/0.53  thf(fact_2692_dvd__trans,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ C )
% 0.29/0.53         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_trans
% 0.29/0.53  thf(fact_2693_dvd__trans,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ C )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_trans
% 0.29/0.53  thf(fact_2694_of__bool__eq__iff,axiom,
% 0.29/0.53      ! [P2: $o,Q3: $o] :
% 0.29/0.53        ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 0.29/0.53          = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 0.29/0.53        = ( P2 = Q3 ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_eq_iff
% 0.29/0.53  thf(fact_2695_of__bool__eq__iff,axiom,
% 0.29/0.53      ! [P2: $o,Q3: $o] :
% 0.29/0.53        ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 0.29/0.53          = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 0.29/0.53        = ( P2 = Q3 ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_eq_iff
% 0.29/0.53  thf(fact_2696_of__bool__eq__iff,axiom,
% 0.29/0.53      ! [P2: $o,Q3: $o] :
% 0.29/0.53        ( ( ( zero_n356916108424825756nteger @ P2 )
% 0.29/0.53          = ( zero_n356916108424825756nteger @ Q3 ) )
% 0.29/0.53        = ( P2 = Q3 ) ) ).
% 0.29/0.53  
% 0.29/0.53  % of_bool_eq_iff
% 0.29/0.53  thf(fact_2697_dvd__mult__left,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_left
% 0.29/0.53  thf(fact_2698_dvd__mult__left,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_complex @ A @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_left
% 0.29/0.53  thf(fact_2699_dvd__mult__left,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_real @ A @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_left
% 0.29/0.53  thf(fact_2700_dvd__mult__left,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_nat @ A @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_left
% 0.29/0.53  thf(fact_2701_dvd__mult__left,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_int @ A @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_left
% 0.29/0.53  thf(fact_2702_dvd__triv__left,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_left
% 0.29/0.53  thf(fact_2703_dvd__triv__left,axiom,
% 0.29/0.53      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_left
% 0.29/0.53  thf(fact_2704_dvd__triv__left,axiom,
% 0.29/0.53      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_left
% 0.29/0.53  thf(fact_2705_dvd__triv__left,axiom,
% 0.29/0.53      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_left
% 0.29/0.53  thf(fact_2706_dvd__triv__left,axiom,
% 0.29/0.53      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_left
% 0.29/0.53  thf(fact_2707_mult__dvd__mono,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ D )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_dvd_mono
% 0.29/0.53  thf(fact_2708_mult__dvd__mono,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex,D: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_complex @ C @ D )
% 0.29/0.53         => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_dvd_mono
% 0.29/0.53  thf(fact_2709_mult__dvd__mono,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_real @ C @ D )
% 0.29/0.53         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_dvd_mono
% 0.29/0.53  thf(fact_2710_mult__dvd__mono,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ D )
% 0.29/0.53         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_dvd_mono
% 0.29/0.53  thf(fact_2711_mult__dvd__mono,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ D )
% 0.29/0.53         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_dvd_mono
% 0.29/0.53  thf(fact_2712_mult_Ocommute,axiom,
% 0.29/0.53      ( times_times_complex
% 0.29/0.53      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ B2 @ A3 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.commute
% 0.29/0.53  thf(fact_2713_mult_Ocommute,axiom,
% 0.29/0.53      ( times_times_real
% 0.29/0.53      = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.commute
% 0.29/0.53  thf(fact_2714_mult_Ocommute,axiom,
% 0.29/0.53      ( times_times_nat
% 0.29/0.53      = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.commute
% 0.29/0.53  thf(fact_2715_mult_Ocommute,axiom,
% 0.29/0.53      ( times_times_int
% 0.29/0.53      = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.commute
% 0.29/0.53  thf(fact_2716_dvd__mult__right,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_right
% 0.29/0.53  thf(fact_2717_dvd__mult__right,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_complex @ B @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_right
% 0.29/0.53  thf(fact_2718_dvd__mult__right,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_real @ B @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_right
% 0.29/0.53  thf(fact_2719_dvd__mult__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_nat @ B @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_right
% 0.29/0.53  thf(fact_2720_dvd__mult__right,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.53       => ( dvd_dvd_int @ B @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_right
% 0.29/0.53  thf(fact_2721_dvd__triv__right,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_right
% 0.29/0.53  thf(fact_2722_dvd__triv__right,axiom,
% 0.29/0.53      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_right
% 0.29/0.53  thf(fact_2723_dvd__triv__right,axiom,
% 0.29/0.53      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_right
% 0.29/0.53  thf(fact_2724_dvd__triv__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_right
% 0.29/0.53  thf(fact_2725_dvd__triv__right,axiom,
% 0.29/0.53      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_triv_right
% 0.29/0.53  thf(fact_2726_mult_Oleft__commute,axiom,
% 0.29/0.53      ! [B: complex,A: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 0.29/0.53        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.left_commute
% 0.29/0.53  thf(fact_2727_mult_Oleft__commute,axiom,
% 0.29/0.53      ! [B: real,A: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.29/0.53        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.left_commute
% 0.29/0.53  thf(fact_2728_mult_Oleft__commute,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.29/0.53        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.left_commute
% 0.29/0.53  thf(fact_2729_mult_Oleft__commute,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.29/0.53        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.left_commute
% 0.29/0.53  thf(fact_2730_bezout__add__strong__nat,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( A != zero_zero_nat )
% 0.29/0.53       => ? [D3: nat,X5: nat,Y3: nat] :
% 0.29/0.53            ( ( dvd_dvd_nat @ D3 @ A )
% 0.29/0.53            & ( dvd_dvd_nat @ D3 @ B )
% 0.29/0.53            & ( ( times_times_nat @ A @ X5 )
% 0.29/0.53              = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % bezout_add_strong_nat
% 0.29/0.53  thf(fact_2731_unit__dvdE,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.53       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.53           => ! [C3: code_integer] :
% 0.29/0.53                ( B
% 0.29/0.53               != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_dvdE
% 0.29/0.53  thf(fact_2732_unit__dvdE,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.53       => ~ ( ( A != zero_zero_nat )
% 0.29/0.53           => ! [C3: nat] :
% 0.29/0.53                ( B
% 0.29/0.53               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_dvdE
% 0.29/0.53  thf(fact_2733_unit__dvdE,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.53       => ~ ( ( A != zero_zero_int )
% 0.29/0.53           => ! [C3: int] :
% 0.29/0.53                ( B
% 0.29/0.53               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_dvdE
% 0.29/0.53  thf(fact_2734_dvd__div__eq__mult,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( A != zero_zero_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53         => ( ( ( divide_divide_nat @ B @ A )
% 0.29/0.53              = C )
% 0.29/0.53            = ( B
% 0.29/0.53              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_mult
% 0.29/0.53  thf(fact_2735_dvd__div__eq__mult,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( A != zero_zero_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53         => ( ( ( divide_divide_int @ B @ A )
% 0.29/0.53              = C )
% 0.29/0.53            = ( B
% 0.29/0.53              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_mult
% 0.29/0.53  thf(fact_2736_dvd__div__eq__mult,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.29/0.53              = C )
% 0.29/0.53            = ( B
% 0.29/0.53              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_mult
% 0.29/0.53  thf(fact_2737_div__dvd__iff__mult,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( B != zero_zero_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.29/0.53            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_dvd_iff_mult
% 0.29/0.53  thf(fact_2738_div__dvd__iff__mult,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( B != zero_zero_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.29/0.53            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_dvd_iff_mult
% 0.29/0.53  thf(fact_2739_div__dvd__iff__mult,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.29/0.53            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_dvd_iff_mult
% 0.29/0.53  thf(fact_2740_dvd__div__iff__mult,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( C != zero_zero_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.29/0.53            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_iff_mult
% 0.29/0.53  thf(fact_2741_dvd__div__iff__mult,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( C != zero_zero_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.29/0.53            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_iff_mult
% 0.29/0.53  thf(fact_2742_dvd__div__iff__mult,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_iff_mult
% 0.29/0.53  thf(fact_2743_dvd__div__div__eq__mult,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat,D: nat] :
% 0.29/0.53        ( ( A != zero_zero_nat )
% 0.29/0.53       => ( ( C != zero_zero_nat )
% 0.29/0.53         => ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53           => ( ( dvd_dvd_nat @ C @ D )
% 0.29/0.53             => ( ( ( divide_divide_nat @ B @ A )
% 0.29/0.53                  = ( divide_divide_nat @ D @ C ) )
% 0.29/0.53                = ( ( times_times_nat @ B @ C )
% 0.29/0.53                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_div_eq_mult
% 0.29/0.53  thf(fact_2744_dvd__div__div__eq__mult,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int,D: int] :
% 0.29/0.53        ( ( A != zero_zero_int )
% 0.29/0.53       => ( ( C != zero_zero_int )
% 0.29/0.53         => ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53           => ( ( dvd_dvd_int @ C @ D )
% 0.29/0.53             => ( ( ( divide_divide_int @ B @ A )
% 0.29/0.53                  = ( divide_divide_int @ D @ C ) )
% 0.29/0.53                = ( ( times_times_int @ B @ C )
% 0.29/0.53                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_div_eq_mult
% 0.29/0.53  thf(fact_2745_dvd__div__div__eq__mult,axiom,
% 0.29/0.53      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.29/0.53        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.53       => ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.53         => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53           => ( ( dvd_dvd_Code_integer @ C @ D )
% 0.29/0.53             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.29/0.53                  = ( divide6298287555418463151nteger @ D @ C ) )
% 0.29/0.53                = ( ( times_3573771949741848930nteger @ B @ C )
% 0.29/0.53                  = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_div_eq_mult
% 0.29/0.53  thf(fact_2746_is__unit__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: nat,C: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.29/0.53         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.53            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_div_mult2_eq
% 0.29/0.53  thf(fact_2747_is__unit__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: int,C: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.29/0.53         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.53            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_div_mult2_eq
% 0.29/0.53  thf(fact_2748_is__unit__div__mult2__eq,axiom,
% 0.29/0.53      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.29/0.53         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.53            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % is_unit_div_mult2_eq
% 0.29/0.53  thf(fact_2749_unit__div__mult__swap,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.29/0.53       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.29/0.53          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_swap
% 0.29/0.53  thf(fact_2750_unit__div__mult__swap,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.29/0.53       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.29/0.53          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_swap
% 0.29/0.53  thf(fact_2751_unit__div__mult__swap,axiom,
% 0.29/0.53      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_mult_swap
% 0.29/0.53  thf(fact_2752_unit__div__commute,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.29/0.53          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_commute
% 0.29/0.53  thf(fact_2753_unit__div__commute,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.29/0.53          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_commute
% 0.29/0.53  thf(fact_2754_unit__div__commute,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.29/0.53          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_div_commute
% 0.29/0.53  thf(fact_2755_div__mult__unit2,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.53            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_unit2
% 0.29/0.53  thf(fact_2756_div__mult__unit2,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.53            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_unit2
% 0.29/0.53  thf(fact_2757_div__mult__unit2,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.53            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_mult_unit2
% 0.29/0.53  thf(fact_2758_unit__eq__div2,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( A
% 0.29/0.53            = ( divide_divide_nat @ C @ B ) )
% 0.29/0.53          = ( ( times_times_nat @ A @ B )
% 0.29/0.53            = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div2
% 0.29/0.53  thf(fact_2759_unit__eq__div2,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( A
% 0.29/0.53            = ( divide_divide_int @ C @ B ) )
% 0.29/0.53          = ( ( times_times_int @ A @ B )
% 0.29/0.53            = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div2
% 0.29/0.53  thf(fact_2760_unit__eq__div2,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( A
% 0.29/0.53            = ( divide6298287555418463151nteger @ C @ B ) )
% 0.29/0.53          = ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.53            = C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div2
% 0.29/0.53  thf(fact_2761_unit__eq__div1,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( ( ( divide_divide_nat @ A @ B )
% 0.29/0.53            = C )
% 0.29/0.53          = ( A
% 0.29/0.53            = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div1
% 0.29/0.53  thf(fact_2762_unit__eq__div1,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( ( ( divide_divide_int @ A @ B )
% 0.29/0.53            = C )
% 0.29/0.53          = ( A
% 0.29/0.53            = ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div1
% 0.29/0.53  thf(fact_2763_unit__eq__div1,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.29/0.53            = C )
% 0.29/0.53          = ( A
% 0.29/0.53            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_eq_div1
% 0.29/0.53  thf(fact_2764_nat__mult__dvd__cancel1,axiom,
% 0.29/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.53       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.53          = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % nat_mult_dvd_cancel1
% 0.29/0.53  thf(fact_2765_dvd__mult__cancel,axiom,
% 0.29/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.53         => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mult_cancel
% 0.29/0.53  thf(fact_2766_dvd__field__iff,axiom,
% 0.29/0.53      ( dvd_dvd_complex
% 0.29/0.53      = ( ^ [A3: complex,B2: complex] :
% 0.29/0.53            ( ( A3 = zero_zero_complex )
% 0.29/0.53           => ( B2 = zero_zero_complex ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_field_iff
% 0.29/0.53  thf(fact_2767_dvd__field__iff,axiom,
% 0.29/0.53      ( dvd_dvd_real
% 0.29/0.53      = ( ^ [A3: real,B2: real] :
% 0.29/0.53            ( ( A3 = zero_zero_real )
% 0.29/0.53           => ( B2 = zero_zero_real ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_field_iff
% 0.29/0.53  thf(fact_2768_dvd__field__iff,axiom,
% 0.29/0.53      ( dvd_dvd_rat
% 0.29/0.53      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.53            ( ( A3 = zero_zero_rat )
% 0.29/0.53           => ( B2 = zero_zero_rat ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_field_iff
% 0.29/0.53  thf(fact_2769_dvd__0__left,axiom,
% 0.29/0.53      ! [A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.29/0.53       => ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2770_dvd__0__left,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.29/0.53       => ( A = zero_zero_complex ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2771_dvd__0__left,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.29/0.53       => ( A = zero_zero_real ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2772_dvd__0__left,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.29/0.53       => ( A = zero_zero_rat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2773_dvd__0__left,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.29/0.53       => ( A = zero_zero_nat ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2774_dvd__0__left,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.29/0.53       => ( A = zero_zero_int ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_0_left
% 0.29/0.53  thf(fact_2775_dvd__unit__imp__unit,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_unit_imp_unit
% 0.29/0.53  thf(fact_2776_dvd__unit__imp__unit,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_unit_imp_unit
% 0.29/0.53  thf(fact_2777_dvd__unit__imp__unit,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_unit_imp_unit
% 0.29/0.53  thf(fact_2778_unit__imp__dvd,axiom,
% 0.29/0.53      ! [B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_imp_dvd
% 0.29/0.53  thf(fact_2779_unit__imp__dvd,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.53       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_imp_dvd
% 0.29/0.53  thf(fact_2780_unit__imp__dvd,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.53       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % unit_imp_dvd
% 0.29/0.53  thf(fact_2781_one__dvd,axiom,
% 0.29/0.53      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2782_one__dvd,axiom,
% 0.29/0.53      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2783_one__dvd,axiom,
% 0.29/0.53      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2784_one__dvd,axiom,
% 0.29/0.53      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2785_one__dvd,axiom,
% 0.29/0.53      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2786_one__dvd,axiom,
% 0.29/0.53      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % one_dvd
% 0.29/0.53  thf(fact_2787_dvd__add__right__iff,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_right_iff
% 0.29/0.53  thf(fact_2788_dvd__add__right__iff,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_right_iff
% 0.29/0.53  thf(fact_2789_dvd__add__right__iff,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( dvd_dvd_rat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_right_iff
% 0.29/0.53  thf(fact_2790_dvd__add__right__iff,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_right_iff
% 0.29/0.53  thf(fact_2791_dvd__add__right__iff,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_right_iff
% 0.29/0.53  thf(fact_2792_dvd__add__left__iff,axiom,
% 0.29/0.53      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_left_iff
% 0.29/0.53  thf(fact_2793_dvd__add__left__iff,axiom,
% 0.29/0.53      ! [A: real,C: real,B: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ C )
% 0.29/0.53       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_left_iff
% 0.29/0.53  thf(fact_2794_dvd__add__left__iff,axiom,
% 0.29/0.53      ! [A: rat,C: rat,B: rat] :
% 0.29/0.53        ( ( dvd_dvd_rat @ A @ C )
% 0.29/0.53       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_left_iff
% 0.29/0.53  thf(fact_2795_dvd__add__left__iff,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ C )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_left_iff
% 0.29/0.53  thf(fact_2796_dvd__add__left__iff,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ C )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.53          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add_left_iff
% 0.29/0.53  thf(fact_2797_dvd__add,axiom,
% 0.29/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add
% 0.29/0.53  thf(fact_2798_dvd__add,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_real @ A @ C )
% 0.29/0.53         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add
% 0.29/0.53  thf(fact_2799_dvd__add,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( dvd_dvd_rat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_rat @ A @ C )
% 0.29/0.53         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add
% 0.29/0.53  thf(fact_2800_dvd__add,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ A @ C )
% 0.29/0.53         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add
% 0.29/0.53  thf(fact_2801_dvd__add,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ A @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ A @ C )
% 0.29/0.53         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_add
% 0.29/0.53  thf(fact_2802_div__div__div__same,axiom,
% 0.29/0.53      ! [D: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ D @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.53         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 0.29/0.53            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_div_same
% 0.29/0.53  thf(fact_2803_div__div__div__same,axiom,
% 0.29/0.53      ! [D: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ D @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ B @ A )
% 0.29/0.53         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 0.29/0.53            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_div_same
% 0.29/0.53  thf(fact_2804_div__div__div__same,axiom,
% 0.29/0.53      ! [D: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ D @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.53         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 0.29/0.53            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % div_div_div_same
% 0.29/0.53  thf(fact_2805_dvd__div__eq__cancel,axiom,
% 0.29/0.53      ! [A: nat,C: nat,B: nat] :
% 0.29/0.53        ( ( ( divide_divide_nat @ A @ C )
% 0.29/0.53          = ( divide_divide_nat @ B @ C ) )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ A )
% 0.29/0.53         => ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53           => ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_cancel
% 0.29/0.53  thf(fact_2806_dvd__div__eq__cancel,axiom,
% 0.29/0.53      ! [A: int,C: int,B: int] :
% 0.29/0.53        ( ( ( divide_divide_int @ A @ C )
% 0.29/0.53          = ( divide_divide_int @ B @ C ) )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ A )
% 0.29/0.53         => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53           => ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_cancel
% 0.29/0.53  thf(fact_2807_dvd__div__eq__cancel,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       => ( ( dvd_dvd_real @ C @ A )
% 0.29/0.53         => ( ( dvd_dvd_real @ C @ B )
% 0.29/0.53           => ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_cancel
% 0.29/0.53  thf(fact_2808_dvd__div__eq__cancel,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       => ( ( dvd_dvd_complex @ C @ A )
% 0.29/0.53         => ( ( dvd_dvd_complex @ C @ B )
% 0.29/0.53           => ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_cancel
% 0.29/0.53  thf(fact_2809_dvd__div__eq__cancel,axiom,
% 0.29/0.53      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.53        ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.29/0.53          = ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ A )
% 0.29/0.53         => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53           => ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_cancel
% 0.29/0.53  thf(fact_2810_dvd__div__eq__iff,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ A )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53         => ( ( ( divide_divide_nat @ A @ C )
% 0.29/0.53              = ( divide_divide_nat @ B @ C ) )
% 0.29/0.53            = ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_iff
% 0.29/0.53  thf(fact_2811_dvd__div__eq__iff,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ A )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53         => ( ( ( divide_divide_int @ A @ C )
% 0.29/0.53              = ( divide_divide_int @ B @ C ) )
% 0.29/0.53            = ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_iff
% 0.29/0.53  thf(fact_2812_dvd__div__eq__iff,axiom,
% 0.29/0.53      ! [C: real,A: real,B: real] :
% 0.29/0.53        ( ( dvd_dvd_real @ C @ A )
% 0.29/0.53       => ( ( dvd_dvd_real @ C @ B )
% 0.29/0.53         => ( ( ( divide_divide_real @ A @ C )
% 0.29/0.53              = ( divide_divide_real @ B @ C ) )
% 0.29/0.53            = ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_iff
% 0.29/0.53  thf(fact_2813_dvd__div__eq__iff,axiom,
% 0.29/0.53      ! [C: complex,A: complex,B: complex] :
% 0.29/0.53        ( ( dvd_dvd_complex @ C @ A )
% 0.29/0.53       => ( ( dvd_dvd_complex @ C @ B )
% 0.29/0.53         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.29/0.53              = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.53            = ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_iff
% 0.29/0.53  thf(fact_2814_dvd__div__eq__iff,axiom,
% 0.29/0.53      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.29/0.53              = ( divide6298287555418463151nteger @ B @ C ) )
% 0.29/0.53            = ( A = B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_div_eq_iff
% 0.29/0.53  thf(fact_2815_dvd__power__same,axiom,
% 0.29/0.53      ! [X4: code_integer,Y: code_integer,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 0.29/0.53       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_power_same
% 0.29/0.53  thf(fact_2816_dvd__power__same,axiom,
% 0.29/0.53      ! [X4: nat,Y: nat,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ X4 @ Y )
% 0.29/0.53       => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_power_same
% 0.29/0.53  thf(fact_2817_dvd__power__same,axiom,
% 0.29/0.53      ! [X4: real,Y: real,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_real @ X4 @ Y )
% 0.29/0.53       => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_power_same
% 0.29/0.53  thf(fact_2818_dvd__power__same,axiom,
% 0.29/0.53      ! [X4: int,Y: int,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_int @ X4 @ Y )
% 0.29/0.53       => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_power_same
% 0.29/0.53  thf(fact_2819_dvd__power__same,axiom,
% 0.29/0.53      ! [X4: complex,Y: complex,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_complex @ X4 @ Y )
% 0.29/0.53       => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_power_same
% 0.29/0.53  thf(fact_2820_mult__not__zero,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_not_zero
% 0.29/0.53  thf(fact_2821_mult__not__zero,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_not_zero
% 0.29/0.53  thf(fact_2822_mult__not__zero,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_not_zero
% 0.29/0.53  thf(fact_2823_mult__not__zero,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_not_zero
% 0.29/0.53  thf(fact_2824_mult__not__zero,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_not_zero
% 0.29/0.53  thf(fact_2825_divisors__zero,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  % divisors_zero
% 0.29/0.53  thf(fact_2826_divisors__zero,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  % divisors_zero
% 0.29/0.53  thf(fact_2827_divisors__zero,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  % divisors_zero
% 0.29/0.53  thf(fact_2828_divisors__zero,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  % divisors_zero
% 0.29/0.53  thf(fact_2829_divisors__zero,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  % divisors_zero
% 0.29/0.53  thf(fact_2830_no__zero__divisors,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( A != zero_zero_rat )
% 0.29/0.53       => ( ( B != zero_zero_rat )
% 0.29/0.53         => ( ( times_times_rat @ A @ B )
% 0.29/0.53           != zero_zero_rat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % no_zero_divisors
% 0.29/0.53  thf(fact_2831_no__zero__divisors,axiom,
% 0.29/0.53      ! [A: complex,B: complex] :
% 0.29/0.53        ( ( A != zero_zero_complex )
% 0.29/0.53       => ( ( B != zero_zero_complex )
% 0.29/0.53         => ( ( times_times_complex @ A @ B )
% 0.29/0.53           != zero_zero_complex ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % no_zero_divisors
% 0.29/0.53  thf(fact_2832_no__zero__divisors,axiom,
% 0.29/0.53      ! [A: real,B: real] :
% 0.29/0.53        ( ( A != zero_zero_real )
% 0.29/0.53       => ( ( B != zero_zero_real )
% 0.29/0.53         => ( ( times_times_real @ A @ B )
% 0.29/0.53           != zero_zero_real ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % no_zero_divisors
% 0.29/0.53  thf(fact_2833_no__zero__divisors,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( A != zero_zero_nat )
% 0.29/0.53       => ( ( B != zero_zero_nat )
% 0.29/0.53         => ( ( times_times_nat @ A @ B )
% 0.29/0.53           != zero_zero_nat ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % no_zero_divisors
% 0.29/0.53  thf(fact_2834_no__zero__divisors,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( A != zero_zero_int )
% 0.29/0.53       => ( ( B != zero_zero_int )
% 0.29/0.53         => ( ( times_times_int @ A @ B )
% 0.29/0.53           != zero_zero_int ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % no_zero_divisors
% 0.29/0.53  thf(fact_2835_mult__left__cancel,axiom,
% 0.29/0.53      ! [C: rat,A: rat,B: rat] :
% 0.29/0.53        ( ( C != zero_zero_rat )
% 0.29/0.53       => ( ( ( times_times_rat @ C @ A )
% 0.29/0.53            = ( times_times_rat @ C @ B ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_left_cancel
% 0.29/0.53  thf(fact_2836_mult__left__cancel,axiom,
% 0.29/0.53      ! [C: complex,A: complex,B: complex] :
% 0.29/0.53        ( ( C != zero_zero_complex )
% 0.29/0.53       => ( ( ( times_times_complex @ C @ A )
% 0.29/0.53            = ( times_times_complex @ C @ B ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_left_cancel
% 0.29/0.53  thf(fact_2837_mult__left__cancel,axiom,
% 0.29/0.53      ! [C: real,A: real,B: real] :
% 0.29/0.53        ( ( C != zero_zero_real )
% 0.29/0.53       => ( ( ( times_times_real @ C @ A )
% 0.29/0.53            = ( times_times_real @ C @ B ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_left_cancel
% 0.29/0.53  thf(fact_2838_mult__left__cancel,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( C != zero_zero_nat )
% 0.29/0.53       => ( ( ( times_times_nat @ C @ A )
% 0.29/0.53            = ( times_times_nat @ C @ B ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_left_cancel
% 0.29/0.53  thf(fact_2839_mult__left__cancel,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( C != zero_zero_int )
% 0.29/0.53       => ( ( ( times_times_int @ C @ A )
% 0.29/0.53            = ( times_times_int @ C @ B ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_left_cancel
% 0.29/0.53  thf(fact_2840_mult__right__cancel,axiom,
% 0.29/0.53      ! [C: rat,A: rat,B: rat] :
% 0.29/0.53        ( ( C != zero_zero_rat )
% 0.29/0.53       => ( ( ( times_times_rat @ A @ C )
% 0.29/0.53            = ( times_times_rat @ B @ C ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_right_cancel
% 0.29/0.53  thf(fact_2841_mult__right__cancel,axiom,
% 0.29/0.53      ! [C: complex,A: complex,B: complex] :
% 0.29/0.53        ( ( C != zero_zero_complex )
% 0.29/0.53       => ( ( ( times_times_complex @ A @ C )
% 0.29/0.53            = ( times_times_complex @ B @ C ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_right_cancel
% 0.29/0.53  thf(fact_2842_mult__right__cancel,axiom,
% 0.29/0.53      ! [C: real,A: real,B: real] :
% 0.29/0.53        ( ( C != zero_zero_real )
% 0.29/0.53       => ( ( ( times_times_real @ A @ C )
% 0.29/0.53            = ( times_times_real @ B @ C ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_right_cancel
% 0.29/0.53  thf(fact_2843_mult__right__cancel,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( C != zero_zero_nat )
% 0.29/0.53       => ( ( ( times_times_nat @ A @ C )
% 0.29/0.53            = ( times_times_nat @ B @ C ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_right_cancel
% 0.29/0.53  thf(fact_2844_mult__right__cancel,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( C != zero_zero_int )
% 0.29/0.53       => ( ( ( times_times_int @ A @ C )
% 0.29/0.53            = ( times_times_int @ B @ C ) )
% 0.29/0.53          = ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mult_right_cancel
% 0.29/0.53  thf(fact_2845_mult_Ocomm__neutral,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.comm_neutral
% 0.29/0.53  thf(fact_2846_mult_Ocomm__neutral,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( times_times_complex @ A @ one_one_complex )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.comm_neutral
% 0.29/0.53  thf(fact_2847_mult_Ocomm__neutral,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( times_times_real @ A @ one_one_real )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.comm_neutral
% 0.29/0.53  thf(fact_2848_mult_Ocomm__neutral,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.comm_neutral
% 0.29/0.53  thf(fact_2849_mult_Ocomm__neutral,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( times_times_int @ A @ one_one_int )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % mult.comm_neutral
% 0.29/0.53  thf(fact_2850_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_monoid_mult_class.mult_1
% 0.29/0.53  thf(fact_2851_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.53      ! [A: complex] :
% 0.29/0.53        ( ( times_times_complex @ one_one_complex @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_monoid_mult_class.mult_1
% 0.29/0.53  thf(fact_2852_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.53      ! [A: real] :
% 0.29/0.53        ( ( times_times_real @ one_one_real @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_monoid_mult_class.mult_1
% 0.29/0.53  thf(fact_2853_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_monoid_mult_class.mult_1
% 0.29/0.53  thf(fact_2854_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ( ( times_times_int @ one_one_int @ A )
% 0.29/0.53        = A ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_monoid_mult_class.mult_1
% 0.29/0.53  thf(fact_2855_combine__common__factor,axiom,
% 0.29/0.53      ! [A: rat,E2: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % combine_common_factor
% 0.29/0.53  thf(fact_2856_combine__common__factor,axiom,
% 0.29/0.53      ! [A: complex,E2: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ C ) )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E2 ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % combine_common_factor
% 0.29/0.53  thf(fact_2857_combine__common__factor,axiom,
% 0.29/0.53      ! [A: real,E2: real,B: real,C: real] :
% 0.29/0.53        ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % combine_common_factor
% 0.29/0.53  thf(fact_2858_combine__common__factor,axiom,
% 0.29/0.53      ! [A: nat,E2: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 0.29/0.53        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % combine_common_factor
% 0.29/0.53  thf(fact_2859_combine__common__factor,axiom,
% 0.29/0.53      ! [A: int,E2: int,B: int,C: int] :
% 0.29/0.53        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 0.29/0.53  
% 0.29/0.53  % combine_common_factor
% 0.29/0.53  thf(fact_2860_distrib__right,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_right
% 0.29/0.53  thf(fact_2861_distrib__right,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_right
% 0.29/0.53  thf(fact_2862_distrib__right,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_right
% 0.29/0.53  thf(fact_2863_distrib__right,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_right
% 0.29/0.53  thf(fact_2864_distrib__right,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_right
% 0.29/0.53  thf(fact_2865_distrib__left,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_left
% 0.29/0.53  thf(fact_2866_distrib__left,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_left
% 0.29/0.53  thf(fact_2867_distrib__left,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_left
% 0.29/0.53  thf(fact_2868_distrib__left,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.53        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_left
% 0.29/0.53  thf(fact_2869_distrib__left,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % distrib_left
% 0.29/0.53  thf(fact_2870_comm__semiring__class_Odistrib,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_semiring_class.distrib
% 0.29/0.53  thf(fact_2871_comm__semiring__class_Odistrib,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_semiring_class.distrib
% 0.29/0.53  thf(fact_2872_comm__semiring__class_Odistrib,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_semiring_class.distrib
% 0.29/0.53  thf(fact_2873_comm__semiring__class_Odistrib,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_semiring_class.distrib
% 0.29/0.53  thf(fact_2874_comm__semiring__class_Odistrib,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % comm_semiring_class.distrib
% 0.29/0.53  thf(fact_2875_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(1)
% 0.29/0.53  thf(fact_2876_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(1)
% 0.29/0.53  thf(fact_2877_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(1)
% 0.29/0.53  thf(fact_2878_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(1)
% 0.29/0.53  thf(fact_2879_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(2)
% 0.29/0.53  thf(fact_2880_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(2)
% 0.29/0.53  thf(fact_2881_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(2)
% 0.29/0.53  thf(fact_2882_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.53        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ring_class.ring_distribs(2)
% 0.29/0.53  thf(fact_2883_dvd__mod,axiom,
% 0.29/0.53      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ K @ M )
% 0.29/0.53       => ( ( dvd_dvd_nat @ K @ N2 )
% 0.29/0.53         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod
% 0.29/0.53  thf(fact_2884_dvd__mod,axiom,
% 0.29/0.53      ! [K: int,M: int,N2: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ K @ M )
% 0.29/0.53       => ( ( dvd_dvd_int @ K @ N2 )
% 0.29/0.53         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod
% 0.29/0.53  thf(fact_2885_dvd__mod,axiom,
% 0.29/0.53      ! [K: code_integer,M: code_integer,N2: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ K @ M )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod
% 0.29/0.53  thf(fact_2886_mod__mod__cancel,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 0.29/0.53          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_mod_cancel
% 0.29/0.53  thf(fact_2887_mod__mod__cancel,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 0.29/0.53          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_mod_cancel
% 0.29/0.53  thf(fact_2888_mod__mod__cancel,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 0.29/0.53          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % mod_mod_cancel
% 0.29/0.53  thf(fact_2889_dvd__mod__iff,axiom,
% 0.29/0.53      ! [C: nat,B: nat,A: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.53          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_iff
% 0.29/0.53  thf(fact_2890_dvd__mod__iff,axiom,
% 0.29/0.53      ! [C: int,B: int,A: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.53          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_iff
% 0.29/0.53  thf(fact_2891_dvd__mod__iff,axiom,
% 0.29/0.53      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.53          = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_iff
% 0.29/0.53  thf(fact_2892_dvd__mod__imp__dvd,axiom,
% 0.29/0.53      ! [C: nat,A: nat,B: nat] :
% 0.29/0.53        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.53       => ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.53         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_imp_dvd
% 0.29/0.53  thf(fact_2893_dvd__mod__imp__dvd,axiom,
% 0.29/0.53      ! [C: int,A: int,B: int] :
% 0.29/0.53        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.53       => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.53         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_imp_dvd
% 0.29/0.53  thf(fact_2894_dvd__mod__imp__dvd,axiom,
% 0.29/0.53      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.53        ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.53       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.53         => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dvd_mod_imp_dvd
% 0.29/0.53  thf(fact_2895_divide__divide__eq__left_H,axiom,
% 0.29/0.53      ! [A: real,B: real,C: real] :
% 0.29/0.53        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.29/0.53        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % divide_divide_eq_left'
% 0.29/0.53  thf(fact_2896_divide__divide__eq__left_H,axiom,
% 0.29/0.53      ! [A: complex,B: complex,C: complex] :
% 0.29/0.53        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 0.29/0.53        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.54  % divide_divide_eq_left'
% 0.29/0.54  thf(fact_2897_divide__divide__times__eq,axiom,
% 0.29/0.54      ! [X4: real,Y: real,Z: real,W: real] :
% 0.29/0.54        ( ( divide_divide_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 0.29/0.54        = ( divide_divide_real @ ( times_times_real @ X4 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_divide_times_eq
% 0.29/0.54  thf(fact_2898_divide__divide__times__eq,axiom,
% 0.29/0.54      ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 0.29/0.54        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.29/0.54        = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_divide_times_eq
% 0.29/0.54  thf(fact_2899_times__divide__times__eq,axiom,
% 0.29/0.54      ! [X4: real,Y: real,Z: real,W: real] :
% 0.29/0.54        ( ( times_times_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 0.29/0.54        = ( divide_divide_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % times_divide_times_eq
% 0.29/0.54  thf(fact_2900_times__divide__times__eq,axiom,
% 0.29/0.54      ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 0.29/0.54        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.29/0.54        = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % times_divide_times_eq
% 0.29/0.54  thf(fact_2901_power__commuting__commutes,axiom,
% 0.29/0.54      ! [X4: complex,Y: complex,N2: nat] :
% 0.29/0.54        ( ( ( times_times_complex @ X4 @ Y )
% 0.29/0.54          = ( times_times_complex @ Y @ X4 ) )
% 0.29/0.54       => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ Y )
% 0.29/0.54          = ( times_times_complex @ Y @ ( power_power_complex @ X4 @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commuting_commutes
% 0.29/0.54  thf(fact_2902_power__commuting__commutes,axiom,
% 0.29/0.54      ! [X4: real,Y: real,N2: nat] :
% 0.29/0.54        ( ( ( times_times_real @ X4 @ Y )
% 0.29/0.54          = ( times_times_real @ Y @ X4 ) )
% 0.29/0.54       => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ Y )
% 0.29/0.54          = ( times_times_real @ Y @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commuting_commutes
% 0.29/0.54  thf(fact_2903_power__commuting__commutes,axiom,
% 0.29/0.54      ! [X4: nat,Y: nat,N2: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ X4 @ Y )
% 0.29/0.54          = ( times_times_nat @ Y @ X4 ) )
% 0.29/0.54       => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ Y )
% 0.29/0.54          = ( times_times_nat @ Y @ ( power_power_nat @ X4 @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commuting_commutes
% 0.29/0.54  thf(fact_2904_power__commuting__commutes,axiom,
% 0.29/0.54      ! [X4: int,Y: int,N2: nat] :
% 0.29/0.54        ( ( ( times_times_int @ X4 @ Y )
% 0.29/0.54          = ( times_times_int @ Y @ X4 ) )
% 0.29/0.54       => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ Y )
% 0.29/0.54          = ( times_times_int @ Y @ ( power_power_int @ X4 @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commuting_commutes
% 0.29/0.54  thf(fact_2905_power__mult__distrib,axiom,
% 0.29/0.54      ! [A: complex,B: complex,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 0.29/0.54        = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult_distrib
% 0.29/0.54  thf(fact_2906_power__mult__distrib,axiom,
% 0.29/0.54      ! [A: real,B: real,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 0.29/0.54        = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult_distrib
% 0.29/0.54  thf(fact_2907_power__mult__distrib,axiom,
% 0.29/0.54      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 0.29/0.54        = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult_distrib
% 0.29/0.54  thf(fact_2908_power__mult__distrib,axiom,
% 0.29/0.54      ! [A: int,B: int,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 0.29/0.54        = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult_distrib
% 0.29/0.54  thf(fact_2909_power__commutes,axiom,
% 0.29/0.54      ! [A: complex,N2: nat] :
% 0.29/0.54        ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 0.29/0.54        = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commutes
% 0.29/0.54  thf(fact_2910_power__commutes,axiom,
% 0.29/0.54      ! [A: real,N2: nat] :
% 0.29/0.54        ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 0.29/0.54        = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commutes
% 0.29/0.54  thf(fact_2911_power__commutes,axiom,
% 0.29/0.54      ! [A: nat,N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 0.29/0.54        = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commutes
% 0.29/0.54  thf(fact_2912_power__commutes,axiom,
% 0.29/0.54      ! [A: int,N2: nat] :
% 0.29/0.54        ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 0.29/0.54        = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_commutes
% 0.29/0.54  thf(fact_2913_Suc__mult__cancel1,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.29/0.54          = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.29/0.54        = ( M = N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_mult_cancel1
% 0.29/0.54  thf(fact_2914_power__mult,axiom,
% 0.29/0.54      ! [A: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.54        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult
% 0.29/0.54  thf(fact_2915_power__mult,axiom,
% 0.29/0.54      ! [A: real,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.54        = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult
% 0.29/0.54  thf(fact_2916_power__mult,axiom,
% 0.29/0.54      ! [A: int,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.54        = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult
% 0.29/0.54  thf(fact_2917_power__mult,axiom,
% 0.29/0.54      ! [A: complex,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.54        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_mult
% 0.29/0.54  thf(fact_2918_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.29/0.54      ! [X4: produc3368934014287244435at_num] :
% 0.29/0.54        ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 0.29/0.54            ( X4
% 0.29/0.54           != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % fold_atLeastAtMost_nat.cases
% 0.29/0.54  thf(fact_2919_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.29/0.54      ! [X4: produc4471711990508489141at_nat] :
% 0.29/0.54        ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 0.29/0.54            ( X4
% 0.29/0.54           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % fold_atLeastAtMost_nat.cases
% 0.29/0.54  thf(fact_2920_mult__0,axiom,
% 0.29/0.54      ! [N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ zero_zero_nat @ N2 )
% 0.29/0.54        = zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_0
% 0.29/0.54  thf(fact_2921_nat__mult__eq__cancel__disj,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ K @ M )
% 0.29/0.54          = ( times_times_nat @ K @ N2 ) )
% 0.29/0.54        = ( ( K = zero_zero_nat )
% 0.29/0.54          | ( M = N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_eq_cancel_disj
% 0.29/0.54  thf(fact_2922_mult__le__mono2,axiom,
% 0.29/0.54      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.54       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_mono2
% 0.29/0.54  thf(fact_2923_mult__le__mono1,axiom,
% 0.29/0.54      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.54       => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_mono1
% 0.29/0.54  thf(fact_2924_mult__le__mono,axiom,
% 0.29/0.54      ! [I2: nat,J: nat,K: nat,L: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.54       => ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_mono
% 0.29/0.54  thf(fact_2925_le__square,axiom,
% 0.29/0.54      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_square
% 0.29/0.54  thf(fact_2926_le__cube,axiom,
% 0.29/0.54      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_cube
% 0.29/0.54  thf(fact_2927_mod__mult__eq,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_eq
% 0.29/0.54  thf(fact_2928_mod__mult__eq,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_eq
% 0.29/0.54  thf(fact_2929_mod__mult__eq,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_eq
% 0.29/0.54  thf(fact_2930_mod__mult__cong,axiom,
% 0.29/0.54      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 0.29/0.54        ( ( ( modulo_modulo_nat @ A @ C )
% 0.29/0.54          = ( modulo_modulo_nat @ A4 @ C ) )
% 0.29/0.54       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.29/0.54            = ( modulo_modulo_nat @ B4 @ C ) )
% 0.29/0.54         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.54            = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_cong
% 0.29/0.54  thf(fact_2931_mod__mult__cong,axiom,
% 0.29/0.54      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.29/0.54        ( ( ( modulo_modulo_int @ A @ C )
% 0.29/0.54          = ( modulo_modulo_int @ A4 @ C ) )
% 0.29/0.54       => ( ( ( modulo_modulo_int @ B @ C )
% 0.29/0.54            = ( modulo_modulo_int @ B4 @ C ) )
% 0.29/0.54         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.54            = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_cong
% 0.29/0.54  thf(fact_2932_mod__mult__cong,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.29/0.54        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.29/0.54          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.29/0.54       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.29/0.54            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.29/0.54         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.54            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_cong
% 0.29/0.54  thf(fact_2933_mod__mult__mult2,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.54        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_mult2
% 0.29/0.54  thf(fact_2934_mod__mult__mult2,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_mult2
% 0.29/0.54  thf(fact_2935_mod__mult__mult2,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_mult2
% 0.29/0.54  thf(fact_2936_mult__mod__right,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.54        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mod_right
% 0.29/0.54  thf(fact_2937_mult__mod__right,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.54        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mod_right
% 0.29/0.54  thf(fact_2938_mult__mod__right,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.54        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mod_right
% 0.29/0.54  thf(fact_2939_mod__mult__left__eq,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.29/0.54        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_left_eq
% 0.29/0.54  thf(fact_2940_mod__mult__left__eq,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.29/0.54        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_left_eq
% 0.29/0.54  thf(fact_2941_mod__mult__left__eq,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.29/0.54        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_left_eq
% 0.29/0.54  thf(fact_2942_mod__mult__right__eq,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_right_eq
% 0.29/0.54  thf(fact_2943_mod__mult__right__eq,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_right_eq
% 0.29/0.54  thf(fact_2944_mod__mult__right__eq,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.29/0.54        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_mult_right_eq
% 0.29/0.54  thf(fact_2945_left__add__mult__distrib,axiom,
% 0.29/0.54      ! [I2: nat,U: nat,J: nat,K: nat] :
% 0.29/0.54        ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.29/0.54        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_add_mult_distrib
% 0.29/0.54  thf(fact_2946_add__mult__distrib2,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.54        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % add_mult_distrib2
% 0.29/0.54  thf(fact_2947_add__mult__distrib,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,K: nat] :
% 0.29/0.54        ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 0.29/0.54        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % add_mult_distrib
% 0.29/0.54  thf(fact_2948_nat__mult__1__right,axiom,
% 0.29/0.54      ! [N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ N2 @ one_one_nat )
% 0.29/0.54        = N2 ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_1_right
% 0.29/0.54  thf(fact_2949_nat__mult__1,axiom,
% 0.29/0.54      ! [N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ one_one_nat @ N2 )
% 0.29/0.54        = N2 ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_1
% 0.29/0.54  thf(fact_2950_div__mult2__eq,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.54        ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 0.29/0.54        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult2_eq
% 0.29/0.54  thf(fact_2951_div__mod__decomp__int,axiom,
% 0.29/0.54      ! [A2: int,N2: int] :
% 0.29/0.54        ( A2
% 0.29/0.54        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mod_decomp_int
% 0.29/0.54  thf(fact_2952_split__zdiv,axiom,
% 0.29/0.54      ! [P: int > $o,N2: int,K: int] :
% 0.29/0.54        ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 0.29/0.54        = ( ( ( K = zero_zero_int )
% 0.29/0.54           => ( P @ zero_zero_int ) )
% 0.29/0.54          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.54           => ! [I3: int,J3: int] :
% 0.29/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.29/0.54                  & ( ord_less_int @ J3 @ K )
% 0.29/0.54                  & ( N2
% 0.29/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.54               => ( P @ I3 ) ) )
% 0.29/0.54          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.54           => ! [I3: int,J3: int] :
% 0.29/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.29/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.29/0.54                  & ( N2
% 0.29/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.54               => ( P @ I3 ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_zdiv
% 0.29/0.54  thf(fact_2953_int__div__neg__eq,axiom,
% 0.29/0.54      ! [A: int,B: int,Q3: int,R3: int] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.29/0.54         => ( ( ord_less_int @ B @ R3 )
% 0.29/0.54           => ( ( divide_divide_int @ A @ B )
% 0.29/0.54              = Q3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % int_div_neg_eq
% 0.29/0.54  thf(fact_2954_int__div__pos__eq,axiom,
% 0.29/0.54      ! [A: int,B: int,Q3: int,R3: int] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.29/0.54         => ( ( ord_less_int @ R3 @ B )
% 0.29/0.54           => ( ( divide_divide_int @ A @ B )
% 0.29/0.54              = Q3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % int_div_pos_eq
% 0.29/0.54  thf(fact_2955_split__neg__lemma,axiom,
% 0.29/0.54      ! [K: int,P: int > int > $o,N2: int] :
% 0.29/0.54        ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.54       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.29/0.54          = ( ! [I3: int,J3: int] :
% 0.29/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.29/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.29/0.54                  & ( N2
% 0.29/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.54               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_neg_lemma
% 0.29/0.54  thf(fact_2956_split__pos__lemma,axiom,
% 0.29/0.54      ! [K: int,P: int > int > $o,N2: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.54       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 0.29/0.54          = ( ! [I3: int,J3: int] :
% 0.29/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.29/0.54                  & ( ord_less_int @ J3 @ K )
% 0.29/0.54                  & ( N2
% 0.29/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.29/0.54               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_pos_lemma
% 0.29/0.54  thf(fact_2957_zdiv__zmult2__eq,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.54          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zdiv_zmult2_eq
% 0.29/0.54  thf(fact_2958_zmod__zmult2__eq,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.54          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zmod_zmult2_eq
% 0.29/0.54  thf(fact_2959_dvd__pos__nat,axiom,
% 0.29/0.54      ! [N2: nat,M: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.54       => ( ( dvd_dvd_nat @ M @ N2 )
% 0.29/0.54         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_pos_nat
% 0.29/0.54  thf(fact_2960_enat__0__less__mult__iff,axiom,
% 0.29/0.54      ! [M: extended_enat,N2: extended_enat] :
% 0.29/0.54        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 0.29/0.54        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.29/0.54          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % enat_0_less_mult_iff
% 0.29/0.54  thf(fact_2961_is__unit__div__mult__cancel__right,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.29/0.54            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_right
% 0.29/0.54  thf(fact_2962_is__unit__div__mult__cancel__right,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.29/0.54            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_right
% 0.29/0.54  thf(fact_2963_is__unit__div__mult__cancel__right,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.54       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.29/0.54            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_right
% 0.29/0.54  thf(fact_2964_is__unit__div__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( A != zero_zero_nat )
% 0.29/0.54       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.29/0.54            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_left
% 0.29/0.54  thf(fact_2965_is__unit__div__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( A != zero_zero_int )
% 0.29/0.54       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.29/0.54            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_left
% 0.29/0.54  thf(fact_2966_is__unit__div__mult__cancel__left,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.54       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.29/0.54            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_div_mult_cancel_left
% 0.29/0.54  thf(fact_2967_is__unitE,axiom,
% 0.29/0.54      ! [A: nat,C: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.54       => ~ ( ( A != zero_zero_nat )
% 0.29/0.54           => ! [B5: nat] :
% 0.29/0.54                ( ( B5 != zero_zero_nat )
% 0.29/0.54               => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 0.29/0.54                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.29/0.54                      = B5 )
% 0.29/0.54                   => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 0.29/0.54                        = A )
% 0.29/0.54                     => ( ( ( times_times_nat @ A @ B5 )
% 0.29/0.54                          = one_one_nat )
% 0.29/0.54                       => ( ( divide_divide_nat @ C @ A )
% 0.29/0.54                         != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unitE
% 0.29/0.54  thf(fact_2968_is__unitE,axiom,
% 0.29/0.54      ! [A: int,C: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.54       => ~ ( ( A != zero_zero_int )
% 0.29/0.54           => ! [B5: int] :
% 0.29/0.54                ( ( B5 != zero_zero_int )
% 0.29/0.54               => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 0.29/0.54                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.29/0.54                      = B5 )
% 0.29/0.54                   => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 0.29/0.54                        = A )
% 0.29/0.54                     => ( ( ( times_times_int @ A @ B5 )
% 0.29/0.54                          = one_one_int )
% 0.29/0.54                       => ( ( divide_divide_int @ C @ A )
% 0.29/0.54                         != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unitE
% 0.29/0.54  thf(fact_2969_is__unitE,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.54       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.54           => ! [B5: code_integer] :
% 0.29/0.54                ( ( B5 != zero_z3403309356797280102nteger )
% 0.29/0.54               => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 0.29/0.54                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.29/0.54                      = B5 )
% 0.29/0.54                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 0.29/0.54                        = A )
% 0.29/0.54                     => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 0.29/0.54                          = one_one_Code_integer )
% 0.29/0.54                       => ( ( divide6298287555418463151nteger @ C @ A )
% 0.29/0.54                         != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unitE
% 0.29/0.54  thf(fact_2970_evenE,axiom,
% 0.29/0.54      ! [A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: code_integer] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % evenE
% 0.29/0.54  thf(fact_2971_evenE,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: nat] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % evenE
% 0.29/0.54  thf(fact_2972_evenE,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: int] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % evenE
% 0.29/0.54  thf(fact_2973_dvd__mult__cancel2,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 0.29/0.54          = ( N2 = one_one_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_mult_cancel2
% 0.29/0.54  thf(fact_2974_dvd__mult__cancel1,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.54       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 0.29/0.54          = ( N2 = one_one_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_mult_cancel1
% 0.29/0.54  thf(fact_2975_of__bool__odd__eq__mod__2,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( zero_n2687167440665602831ol_nat
% 0.29/0.54          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.54        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_odd_eq_mod_2
% 0.29/0.54  thf(fact_2976_of__bool__odd__eq__mod__2,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( zero_n2684676970156552555ol_int
% 0.29/0.54          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.54        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_odd_eq_mod_2
% 0.29/0.54  thf(fact_2977_of__bool__odd__eq__mod__2,axiom,
% 0.29/0.54      ! [A: code_integer] :
% 0.29/0.54        ( ( zero_n356916108424825756nteger
% 0.29/0.54          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.54        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_odd_eq_mod_2
% 0.29/0.54  thf(fact_2978_even__two__times__div__two,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_two_times_div_two
% 0.29/0.54  thf(fact_2979_even__two__times__div__two,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_two_times_div_two
% 0.29/0.54  thf(fact_2980_even__two__times__div__two,axiom,
% 0.29/0.54      ! [A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_two_times_div_two
% 0.29/0.54  thf(fact_2981_zero__less__eq__of__bool,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_eq_of_bool
% 0.29/0.54  thf(fact_2982_zero__less__eq__of__bool,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_eq_of_bool
% 0.29/0.54  thf(fact_2983_zero__less__eq__of__bool,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_eq_of_bool
% 0.29/0.54  thf(fact_2984_zero__less__eq__of__bool,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_eq_of_bool
% 0.29/0.54  thf(fact_2985_zero__less__eq__of__bool,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_eq_of_bool
% 0.29/0.54  thf(fact_2986_of__bool__less__eq__one,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_less_eq_one
% 0.29/0.54  thf(fact_2987_of__bool__less__eq__one,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_less_eq_one
% 0.29/0.54  thf(fact_2988_of__bool__less__eq__one,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_less_eq_one
% 0.29/0.54  thf(fact_2989_of__bool__less__eq__one,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_less_eq_one
% 0.29/0.54  thf(fact_2990_of__bool__less__eq__one,axiom,
% 0.29/0.54      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_less_eq_one
% 0.29/0.54  thf(fact_2991_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: complex > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_complex ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2992_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: real > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_real ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2993_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: rat > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_rat ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2994_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: nat > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_nat ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2995_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: int > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_int ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2996_split__of__bool__asm,axiom,
% 0.29/0.54      ! [P: code_integer > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 0.29/0.54        = ( ~ ( ( P2
% 0.29/0.54                & ~ ( P @ one_one_Code_integer ) )
% 0.29/0.54              | ( ~ P2
% 0.29/0.54                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool_asm
% 0.29/0.54  thf(fact_2997_split__of__bool,axiom,
% 0.29/0.54      ! [P: complex > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_complex ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_zero_complex ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_2998_split__of__bool,axiom,
% 0.29/0.54      ! [P: real > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_real ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_2999_split__of__bool,axiom,
% 0.29/0.54      ! [P: rat > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_rat ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_3000_split__of__bool,axiom,
% 0.29/0.54      ! [P: nat > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_nat ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_3001_split__of__bool,axiom,
% 0.29/0.54      ! [P: int > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_int ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_zero_int ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_3002_split__of__bool,axiom,
% 0.29/0.54      ! [P: code_integer > $o,P2: $o] :
% 0.29/0.54        ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 0.29/0.54        = ( ( P2
% 0.29/0.54           => ( P @ one_one_Code_integer ) )
% 0.29/0.54          & ( ~ P2
% 0.29/0.54           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_of_bool
% 0.29/0.54  thf(fact_3003_of__bool__def,axiom,
% 0.29/0.54      ( zero_n1201886186963655149omplex
% 0.29/0.54      = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3004_of__bool__def,axiom,
% 0.29/0.54      ( zero_n3304061248610475627l_real
% 0.29/0.54      = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3005_of__bool__def,axiom,
% 0.29/0.54      ( zero_n2052037380579107095ol_rat
% 0.29/0.54      = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3006_of__bool__def,axiom,
% 0.29/0.54      ( zero_n2687167440665602831ol_nat
% 0.29/0.54      = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3007_of__bool__def,axiom,
% 0.29/0.54      ( zero_n2684676970156552555ol_int
% 0.29/0.54      = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3008_of__bool__def,axiom,
% 0.29/0.54      ( zero_n356916108424825756nteger
% 0.29/0.54      = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % of_bool_def
% 0.29/0.54  thf(fact_3009_not__is__unit__0,axiom,
% 0.29/0.54      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.29/0.54  
% 0.29/0.54  % not_is_unit_0
% 0.29/0.54  thf(fact_3010_not__is__unit__0,axiom,
% 0.29/0.54      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_is_unit_0
% 0.29/0.54  thf(fact_3011_not__is__unit__0,axiom,
% 0.29/0.54      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.29/0.54  
% 0.29/0.54  % not_is_unit_0
% 0.29/0.54  thf(fact_3012_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( dvd_dvd_rat @ B @ A )
% 0.29/0.54       => ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.54            = zero_zero_rat )
% 0.29/0.54          = ( A = zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3013_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.54       => ( ( ( divide_divide_nat @ A @ B )
% 0.29/0.54            = zero_zero_nat )
% 0.29/0.54          = ( A = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3014_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.54       => ( ( ( divide_divide_int @ A @ B )
% 0.29/0.54            = zero_zero_int )
% 0.29/0.54          = ( A = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3015_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( dvd_dvd_real @ B @ A )
% 0.29/0.54       => ( ( ( divide_divide_real @ A @ B )
% 0.29/0.54            = zero_zero_real )
% 0.29/0.54          = ( A = zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3016_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: complex,A: complex] :
% 0.29/0.54        ( ( dvd_dvd_complex @ B @ A )
% 0.29/0.54       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.54            = zero_zero_complex )
% 0.29/0.54          = ( A = zero_zero_complex ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3017_dvd__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.54       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.29/0.54            = zero_z3403309356797280102nteger )
% 0.29/0.54          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_eq_0_iff
% 0.29/0.54  thf(fact_3018_dvd__div__unit__iff,axiom,
% 0.29/0.54      ! [B: nat,A: nat,C: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.29/0.54          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_unit_iff
% 0.29/0.54  thf(fact_3019_dvd__div__unit__iff,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.29/0.54          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_unit_iff
% 0.29/0.54  thf(fact_3020_dvd__div__unit__iff,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 0.29/0.54          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_div_unit_iff
% 0.29/0.54  thf(fact_3021_div__unit__dvd__iff,axiom,
% 0.29/0.54      ! [B: nat,A: nat,C: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.29/0.54          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_unit_dvd_iff
% 0.29/0.54  thf(fact_3022_div__unit__dvd__iff,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.29/0.54          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_unit_dvd_iff
% 0.29/0.54  thf(fact_3023_div__unit__dvd__iff,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.29/0.54          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_unit_dvd_iff
% 0.29/0.54  thf(fact_3024_unit__div__cancel,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.54       => ( ( ( divide_divide_nat @ B @ A )
% 0.29/0.54            = ( divide_divide_nat @ C @ A ) )
% 0.29/0.54          = ( B = C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_cancel
% 0.29/0.54  thf(fact_3025_unit__div__cancel,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.54       => ( ( ( divide_divide_int @ B @ A )
% 0.29/0.54            = ( divide_divide_int @ C @ A ) )
% 0.29/0.54          = ( B = C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_cancel
% 0.29/0.54  thf(fact_3026_unit__div__cancel,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.54       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.29/0.54            = ( divide6298287555418463151nteger @ C @ A ) )
% 0.29/0.54          = ( B = C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_cancel
% 0.29/0.54  thf(fact_3027_div__plus__div__distrib__dvd__right,axiom,
% 0.29/0.54      ! [C: nat,B: nat,A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ C @ B )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.54          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_right
% 0.29/0.54  thf(fact_3028_div__plus__div__distrib__dvd__right,axiom,
% 0.29/0.54      ! [C: int,B: int,A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ C @ B )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.54          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_right
% 0.29/0.54  thf(fact_3029_div__plus__div__distrib__dvd__right,axiom,
% 0.29/0.54      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.54       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.29/0.54          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_right
% 0.29/0.54  thf(fact_3030_div__plus__div__distrib__dvd__left,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ C @ A )
% 0.29/0.54       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.54          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_left
% 0.29/0.54  thf(fact_3031_div__plus__div__distrib__dvd__left,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ C @ A )
% 0.29/0.54       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.29/0.54          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_left
% 0.29/0.54  thf(fact_3032_div__plus__div__distrib__dvd__left,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.29/0.54       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.29/0.54          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_plus_div_distrib_dvd_left
% 0.29/0.54  thf(fact_3033_div__power,axiom,
% 0.29/0.54      ! [B: nat,A: nat,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ A )
% 0.29/0.54       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 0.29/0.54          = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_power
% 0.29/0.54  thf(fact_3034_div__power,axiom,
% 0.29/0.54      ! [B: int,A: int,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.54       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 0.29/0.54          = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_power
% 0.29/0.54  thf(fact_3035_div__power,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.54       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 0.29/0.54          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_power
% 0.29/0.54  thf(fact_3036_mod__0__imp__dvd,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ( modulo_modulo_nat @ A @ B )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_0_imp_dvd
% 0.29/0.54  thf(fact_3037_mod__0__imp__dvd,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_0_imp_dvd
% 0.29/0.54  thf(fact_3038_mod__0__imp__dvd,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.54          = zero_z3403309356797280102nteger )
% 0.29/0.54       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_0_imp_dvd
% 0.29/0.54  thf(fact_3039_dvd__eq__mod__eq__0,axiom,
% 0.29/0.54      ( dvd_dvd_nat
% 0.29/0.54      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.54            ( ( modulo_modulo_nat @ B2 @ A3 )
% 0.29/0.54            = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_eq_mod_eq_0
% 0.29/0.54  thf(fact_3040_dvd__eq__mod__eq__0,axiom,
% 0.29/0.54      ( dvd_dvd_int
% 0.29/0.54      = ( ^ [A3: int,B2: int] :
% 0.29/0.54            ( ( modulo_modulo_int @ B2 @ A3 )
% 0.29/0.54            = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_eq_mod_eq_0
% 0.29/0.54  thf(fact_3041_dvd__eq__mod__eq__0,axiom,
% 0.29/0.54      ( dvd_dvd_Code_integer
% 0.29/0.54      = ( ^ [A3: code_integer,B2: code_integer] :
% 0.29/0.54            ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 0.29/0.54            = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_eq_mod_eq_0
% 0.29/0.54  thf(fact_3042_mod__eq__0__iff__dvd,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ( modulo_modulo_nat @ A @ B )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54        = ( dvd_dvd_nat @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eq_0_iff_dvd
% 0.29/0.54  thf(fact_3043_mod__eq__0__iff__dvd,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.54          = zero_zero_int )
% 0.29/0.54        = ( dvd_dvd_int @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eq_0_iff_dvd
% 0.29/0.54  thf(fact_3044_mod__eq__0__iff__dvd,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.54          = zero_z3403309356797280102nteger )
% 0.29/0.54        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eq_0_iff_dvd
% 0.29/0.54  thf(fact_3045_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.54  thf(fact_3046_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.54  thf(fact_3047_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.54  thf(fact_3048_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.29/0.54  thf(fact_3049_zero__le__mult__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 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_eq_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_mult_iff
% 0.29/0.54  thf(fact_3050_zero__le__mult__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 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_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_mult_iff
% 0.29/0.54  thf(fact_3051_zero__le__mult__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 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_eq_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_mult_iff
% 0.29/0.54  thf(fact_3052_mult__nonneg__nonpos2,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos2
% 0.29/0.54  thf(fact_3053_mult__nonneg__nonpos2,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos2
% 0.29/0.54  thf(fact_3054_mult__nonneg__nonpos2,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos2
% 0.29/0.54  thf(fact_3055_mult__nonneg__nonpos2,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos2
% 0.29/0.54  thf(fact_3056_mult__nonpos__nonneg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonneg
% 0.29/0.54  thf(fact_3057_mult__nonpos__nonneg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonneg
% 0.29/0.54  thf(fact_3058_mult__nonpos__nonneg,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonneg
% 0.29/0.54  thf(fact_3059_mult__nonpos__nonneg,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonneg
% 0.29/0.54  thf(fact_3060_mult__nonneg__nonpos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos
% 0.29/0.54  thf(fact_3061_mult__nonneg__nonpos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos
% 0.29/0.54  thf(fact_3062_mult__nonneg__nonpos,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos
% 0.29/0.54  thf(fact_3063_mult__nonneg__nonpos,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonpos
% 0.29/0.54  thf(fact_3064_mult__nonneg__nonneg,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 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_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonneg
% 0.29/0.54  thf(fact_3065_mult__nonneg__nonneg,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 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_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonneg
% 0.29/0.54  thf(fact_3066_mult__nonneg__nonneg,axiom,
% 0.29/0.54      ! [A: nat,B: 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_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonneg
% 0.29/0.54  thf(fact_3067_mult__nonneg__nonneg,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 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_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonneg_nonneg
% 0.29/0.54  thf(fact_3068_split__mult__neg__le,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.54          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.29/0.54       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_neg_le
% 0.29/0.54  thf(fact_3069_split__mult__neg__le,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.54          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.29/0.54       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_neg_le
% 0.29/0.54  thf(fact_3070_split__mult__neg__le,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.29/0.54          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.54            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.29/0.54       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_neg_le
% 0.29/0.54  thf(fact_3071_split__mult__neg__le,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.29/0.54          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.29/0.54       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_neg_le
% 0.29/0.54  thf(fact_3072_mult__le__0__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.54          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_0_iff
% 0.29/0.54  thf(fact_3073_mult__le__0__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.29/0.54          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_0_iff
% 0.29/0.54  thf(fact_3074_mult__le__0__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.29/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.29/0.54          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_0_iff
% 0.29/0.54  thf(fact_3075_mult__right__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ 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 @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono
% 0.29/0.54  thf(fact_3076_mult__right__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ 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 @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono
% 0.29/0.54  thf(fact_3077_mult__right__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ 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 @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono
% 0.29/0.54  thf(fact_3078_mult__right__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ 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 @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono
% 0.29/0.54  thf(fact_3079_mult__right__mono__neg,axiom,
% 0.29/0.54      ! [B: real,A: real,C: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono_neg
% 0.29/0.54  thf(fact_3080_mult__right__mono__neg,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono_neg
% 0.29/0.54  thf(fact_3081_mult__right__mono__neg,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_mono_neg
% 0.29/0.54  thf(fact_3082_mult__left__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono
% 0.29/0.54  thf(fact_3083_mult__left__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono
% 0.29/0.54  thf(fact_3084_mult__left__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono
% 0.29/0.54  thf(fact_3085_mult__left__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono
% 0.29/0.54  thf(fact_3086_mult__nonpos__nonpos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonpos
% 0.29/0.54  thf(fact_3087_mult__nonpos__nonpos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonpos
% 0.29/0.54  thf(fact_3088_mult__nonpos__nonpos,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_nonpos_nonpos
% 0.29/0.54  thf(fact_3089_mult__left__mono__neg,axiom,
% 0.29/0.54      ! [B: real,A: real,C: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.54         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono_neg
% 0.29/0.54  thf(fact_3090_mult__left__mono__neg,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono_neg
% 0.29/0.54  thf(fact_3091_mult__left__mono__neg,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_mono_neg
% 0.29/0.54  thf(fact_3092_split__mult__pos__le,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 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_eq_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.29/0.54       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_pos_le
% 0.29/0.54  thf(fact_3093_split__mult__pos__le,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 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_eq_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.29/0.54       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_pos_le
% 0.29/0.54  thf(fact_3094_split__mult__pos__le,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 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_eq_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.29/0.54       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % split_mult_pos_le
% 0.29/0.54  thf(fact_3095_zero__le__square,axiom,
% 0.29/0.54      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_square
% 0.29/0.54  thf(fact_3096_zero__le__square,axiom,
% 0.29/0.54      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_square
% 0.29/0.54  thf(fact_3097_zero__le__square,axiom,
% 0.29/0.54      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le_square
% 0.29/0.54  thf(fact_3098_mult__mono_H,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono'
% 0.29/0.54  thf(fact_3099_mult__mono_H,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono'
% 0.29/0.54  thf(fact_3100_mult__mono_H,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono'
% 0.29/0.54  thf(fact_3101_mult__mono_H,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono'
% 0.29/0.54  thf(fact_3102_mult__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_real @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_3103_mult__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_3104_mult__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_3105_mult__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_mono
% 0.29/0.54  thf(fact_3106_mult__neg__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 @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_neg
% 0.29/0.54  thf(fact_3107_mult__neg__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 @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_neg
% 0.29/0.54  thf(fact_3108_mult__neg__neg,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_neg
% 0.29/0.54  thf(fact_3109_not__square__less__zero,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.29/0.54  
% 0.29/0.54  % not_square_less_zero
% 0.29/0.54  thf(fact_3110_not__square__less__zero,axiom,
% 0.29/0.54      ! [A: rat] :
% 0.29/0.54        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_square_less_zero
% 0.29/0.54  thf(fact_3111_not__square__less__zero,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.29/0.54  
% 0.29/0.54  % not_square_less_zero
% 0.29/0.54  thf(fact_3112_mult__less__0__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.29/0.54          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_0_iff
% 0.29/0.54  thf(fact_3113_mult__less__0__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.29/0.54          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_0_iff
% 0.29/0.54  thf(fact_3114_mult__less__0__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.29/0.54          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_0_iff
% 0.29/0.54  thf(fact_3115_mult__neg__pos,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 @ zero_zero_real @ B )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_pos
% 0.29/0.54  thf(fact_3116_mult__neg__pos,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 @ zero_zero_rat @ B )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_pos
% 0.29/0.54  thf(fact_3117_mult__neg__pos,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_pos
% 0.29/0.54  thf(fact_3118_mult__neg__pos,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_neg_pos
% 0.29/0.54  thf(fact_3119_mult__pos__neg,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 @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg
% 0.29/0.54  thf(fact_3120_mult__pos__neg,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 @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg
% 0.29/0.54  thf(fact_3121_mult__pos__neg,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg
% 0.29/0.54  thf(fact_3122_mult__pos__neg,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg
% 0.29/0.54  thf(fact_3123_mult__pos__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 @ zero_zero_real @ B )
% 0.29/0.54         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_pos
% 0.29/0.54  thf(fact_3124_mult__pos__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 @ zero_zero_rat @ B )
% 0.29/0.54         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_pos
% 0.29/0.54  thf(fact_3125_mult__pos__pos,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_pos
% 0.29/0.54  thf(fact_3126_mult__pos__pos,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_pos
% 0.29/0.54  thf(fact_3127_mult__pos__neg2,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 @ B @ zero_zero_real )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg2
% 0.29/0.54  thf(fact_3128_mult__pos__neg2,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 @ B @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg2
% 0.29/0.54  thf(fact_3129_mult__pos__neg2,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg2
% 0.29/0.54  thf(fact_3130_mult__pos__neg2,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_pos_neg2
% 0.29/0.54  thf(fact_3131_zero__less__mult__iff,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.29/0.54          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.54            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_iff
% 0.29/0.54  thf(fact_3132_zero__less__mult__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.29/0.54          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_iff
% 0.29/0.54  thf(fact_3133_zero__less__mult__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.29/0.54          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.54            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_iff
% 0.29/0.54  thf(fact_3134_zero__less__mult__pos,axiom,
% 0.29/0.54      ! [A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos
% 0.29/0.54  thf(fact_3135_zero__less__mult__pos,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos
% 0.29/0.54  thf(fact_3136_zero__less__mult__pos,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos
% 0.29/0.54  thf(fact_3137_zero__less__mult__pos,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos
% 0.29/0.54  thf(fact_3138_zero__less__mult__pos2,axiom,
% 0.29/0.54      ! [B: real,A: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.54         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos2
% 0.29/0.54  thf(fact_3139_zero__less__mult__pos2,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos2
% 0.29/0.54  thf(fact_3140_zero__less__mult__pos2,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos2
% 0.29/0.54  thf(fact_3141_zero__less__mult__pos2,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_mult_pos2
% 0.29/0.54  thf(fact_3142_mult__less__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_neg
% 0.29/0.54  thf(fact_3143_mult__less__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_neg
% 0.29/0.54  thf(fact_3144_mult__less__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( ord_less_int @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_neg
% 0.29/0.54  thf(fact_3145_mult__less__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_pos
% 0.29/0.54  thf(fact_3146_mult__less__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_pos
% 0.29/0.54  thf(fact_3147_mult__less__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_pos
% 0.29/0.54  thf(fact_3148_mult__strict__left__mono__neg,axiom,
% 0.29/0.54      ! [B: real,A: real,C: real] :
% 0.29/0.54        ( ( ord_less_real @ B @ A )
% 0.29/0.54       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono_neg
% 0.29/0.54  thf(fact_3149_mult__strict__left__mono__neg,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ A )
% 0.29/0.54       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono_neg
% 0.29/0.54  thf(fact_3150_mult__strict__left__mono__neg,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ A )
% 0.29/0.54       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono_neg
% 0.29/0.54  thf(fact_3151_mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono
% 0.29/0.54  thf(fact_3152_mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono
% 0.29/0.54  thf(fact_3153_mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono
% 0.29/0.54  thf(fact_3154_mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_left_mono
% 0.29/0.54  thf(fact_3155_mult__less__cancel__left__disj,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54            & ( ord_less_real @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_disj
% 0.29/0.54  thf(fact_3156_mult__less__cancel__left__disj,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54            & ( ord_less_rat @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_disj
% 0.29/0.54  thf(fact_3157_mult__less__cancel__left__disj,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54            & ( ord_less_int @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left_disj
% 0.29/0.54  thf(fact_3158_mult__strict__right__mono__neg,axiom,
% 0.29/0.54      ! [B: real,A: real,C: real] :
% 0.29/0.54        ( ( ord_less_real @ B @ A )
% 0.29/0.54       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono_neg
% 0.29/0.54  thf(fact_3159_mult__strict__right__mono__neg,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ A )
% 0.29/0.54       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono_neg
% 0.29/0.54  thf(fact_3160_mult__strict__right__mono__neg,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ A )
% 0.29/0.54       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono_neg
% 0.29/0.54  thf(fact_3161_mult__strict__right__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono
% 0.29/0.54  thf(fact_3162_mult__strict__right__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono
% 0.29/0.54  thf(fact_3163_mult__strict__right__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono
% 0.29/0.54  thf(fact_3164_mult__strict__right__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_right_mono
% 0.29/0.54  thf(fact_3165_mult__less__cancel__right__disj,axiom,
% 0.29/0.54      ! [A: real,C: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54            & ( ord_less_real @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right_disj
% 0.29/0.54  thf(fact_3166_mult__less__cancel__right__disj,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54            & ( ord_less_rat @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right_disj
% 0.29/0.54  thf(fact_3167_mult__less__cancel__right__disj,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54            & ( ord_less_int @ A @ B ) )
% 0.29/0.54          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right_disj
% 0.29/0.54  thf(fact_3168_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.54  thf(fact_3169_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.54  thf(fact_3170_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.54  thf(fact_3171_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.54  thf(fact_3172_dvd__power__le,axiom,
% 0.29/0.54      ! [X4: code_integer,Y: code_integer,N2: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.54         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_power_le
% 0.29/0.54  thf(fact_3173_dvd__power__le,axiom,
% 0.29/0.54      ! [X4: nat,Y: nat,N2: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ X4 @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.54         => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_power_le
% 0.29/0.54  thf(fact_3174_dvd__power__le,axiom,
% 0.29/0.54      ! [X4: real,Y: real,N2: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_real @ X4 @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.54         => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_power_le
% 0.29/0.54  thf(fact_3175_dvd__power__le,axiom,
% 0.29/0.54      ! [X4: int,Y: int,N2: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_int @ X4 @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.54         => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_power_le
% 0.29/0.54  thf(fact_3176_dvd__power__le,axiom,
% 0.29/0.54      ! [X4: complex,Y: complex,N2: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_complex @ X4 @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.54         => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dvd_power_le
% 0.29/0.54  thf(fact_3177_power__le__dvd,axiom,
% 0.29/0.54      ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_le_dvd
% 0.29/0.54  thf(fact_3178_power__le__dvd,axiom,
% 0.29/0.54      ! [A: nat,N2: nat,B: nat,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_le_dvd
% 0.29/0.54  thf(fact_3179_power__le__dvd,axiom,
% 0.29/0.54      ! [A: real,N2: nat,B: real,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_le_dvd
% 0.29/0.54  thf(fact_3180_power__le__dvd,axiom,
% 0.29/0.54      ! [A: int,N2: nat,B: int,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_le_dvd
% 0.29/0.54  thf(fact_3181_power__le__dvd,axiom,
% 0.29/0.54      ! [A: complex,N2: nat,B: complex,M: nat] :
% 0.29/0.54        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_le_dvd
% 0.29/0.54  thf(fact_3182_le__imp__power__dvd,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,A: code_integer] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_power_dvd
% 0.29/0.54  thf(fact_3183_le__imp__power__dvd,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_power_dvd
% 0.29/0.54  thf(fact_3184_le__imp__power__dvd,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,A: real] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_power_dvd
% 0.29/0.54  thf(fact_3185_le__imp__power__dvd,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,A: int] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_power_dvd
% 0.29/0.54  thf(fact_3186_le__imp__power__dvd,axiom,
% 0.29/0.54      ! [M: nat,N2: nat,A: complex] :
% 0.29/0.54        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.54       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_power_dvd
% 0.29/0.54  thf(fact_3187_less__1__mult,axiom,
% 0.29/0.54      ! [M: real,N2: real] :
% 0.29/0.54        ( ( ord_less_real @ one_one_real @ M )
% 0.29/0.54       => ( ( ord_less_real @ one_one_real @ N2 )
% 0.29/0.54         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_1_mult
% 0.29/0.54  thf(fact_3188_less__1__mult,axiom,
% 0.29/0.54      ! [M: rat,N2: rat] :
% 0.29/0.54        ( ( ord_less_rat @ one_one_rat @ M )
% 0.29/0.54       => ( ( ord_less_rat @ one_one_rat @ N2 )
% 0.29/0.54         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_1_mult
% 0.29/0.54  thf(fact_3189_less__1__mult,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ one_one_nat @ M )
% 0.29/0.54       => ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.29/0.54         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_1_mult
% 0.29/0.54  thf(fact_3190_less__1__mult,axiom,
% 0.29/0.54      ! [M: int,N2: int] :
% 0.29/0.54        ( ( ord_less_int @ one_one_int @ M )
% 0.29/0.54       => ( ( ord_less_int @ one_one_int @ N2 )
% 0.29/0.54         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_1_mult
% 0.29/0.54  thf(fact_3191_nonzero__eq__divide__eq,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( A
% 0.29/0.54            = ( divide_divide_rat @ B @ C ) )
% 0.29/0.54          = ( ( times_times_rat @ A @ C )
% 0.29/0.54            = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_eq_divide_eq
% 0.29/0.54  thf(fact_3192_nonzero__eq__divide__eq,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( A
% 0.29/0.54            = ( divide_divide_real @ B @ C ) )
% 0.29/0.54          = ( ( times_times_real @ A @ C )
% 0.29/0.54            = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_eq_divide_eq
% 0.29/0.54  thf(fact_3193_nonzero__eq__divide__eq,axiom,
% 0.29/0.54      ! [C: complex,A: complex,B: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( A
% 0.29/0.54            = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.54          = ( ( times_times_complex @ A @ C )
% 0.29/0.54            = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_eq_divide_eq
% 0.29/0.54  thf(fact_3194_nonzero__divide__eq__eq,axiom,
% 0.29/0.54      ! [C: rat,B: rat,A: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.54            = A )
% 0.29/0.54          = ( B
% 0.29/0.54            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_eq_eq
% 0.29/0.54  thf(fact_3195_nonzero__divide__eq__eq,axiom,
% 0.29/0.54      ! [C: real,B: real,A: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( ( divide_divide_real @ B @ C )
% 0.29/0.54            = A )
% 0.29/0.54          = ( B
% 0.29/0.54            = ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_eq_eq
% 0.29/0.54  thf(fact_3196_nonzero__divide__eq__eq,axiom,
% 0.29/0.54      ! [C: complex,B: complex,A: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.54            = A )
% 0.29/0.54          = ( B
% 0.29/0.54            = ( times_times_complex @ A @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nonzero_divide_eq_eq
% 0.29/0.54  thf(fact_3197_eq__divide__imp,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            = B )
% 0.29/0.54         => ( A
% 0.29/0.54            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_imp
% 0.29/0.54  thf(fact_3198_eq__divide__imp,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            = B )
% 0.29/0.54         => ( A
% 0.29/0.54            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_imp
% 0.29/0.54  thf(fact_3199_eq__divide__imp,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            = B )
% 0.29/0.54         => ( A
% 0.29/0.54            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_imp
% 0.29/0.54  thf(fact_3200_divide__eq__imp,axiom,
% 0.29/0.54      ! [C: rat,B: rat,A: rat] :
% 0.29/0.54        ( ( C != zero_zero_rat )
% 0.29/0.54       => ( ( B
% 0.29/0.54            = ( times_times_rat @ A @ C ) )
% 0.29/0.54         => ( ( divide_divide_rat @ B @ C )
% 0.29/0.54            = A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_imp
% 0.29/0.54  thf(fact_3201_divide__eq__imp,axiom,
% 0.29/0.54      ! [C: real,B: real,A: real] :
% 0.29/0.54        ( ( C != zero_zero_real )
% 0.29/0.54       => ( ( B
% 0.29/0.54            = ( times_times_real @ A @ C ) )
% 0.29/0.54         => ( ( divide_divide_real @ B @ C )
% 0.29/0.54            = A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_imp
% 0.29/0.54  thf(fact_3202_divide__eq__imp,axiom,
% 0.29/0.54      ! [C: complex,B: complex,A: complex] :
% 0.29/0.54        ( ( C != zero_zero_complex )
% 0.29/0.54       => ( ( B
% 0.29/0.54            = ( times_times_complex @ A @ C ) )
% 0.29/0.54         => ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.54            = A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_imp
% 0.29/0.54  thf(fact_3203_eq__divide__eq,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( C != zero_zero_rat )
% 0.29/0.54           => ( ( times_times_rat @ A @ C )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( C = zero_zero_rat )
% 0.29/0.54           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq
% 0.29/0.54  thf(fact_3204_eq__divide__eq,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide_divide_real @ B @ C ) )
% 0.29/0.54        = ( ( ( C != zero_zero_real )
% 0.29/0.54           => ( ( times_times_real @ A @ C )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( C = zero_zero_real )
% 0.29/0.54           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq
% 0.29/0.54  thf(fact_3205_eq__divide__eq,axiom,
% 0.29/0.54      ! [A: complex,B: complex,C: complex] :
% 0.29/0.54        ( ( A
% 0.29/0.54          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.54        = ( ( ( C != zero_zero_complex )
% 0.29/0.54           => ( ( times_times_complex @ A @ C )
% 0.29/0.54              = B ) )
% 0.29/0.54          & ( ( C = zero_zero_complex )
% 0.29/0.54           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % eq_divide_eq
% 0.29/0.54  thf(fact_3206_divide__eq__eq,axiom,
% 0.29/0.54      ! [B: rat,C: rat,A: rat] :
% 0.29/0.54        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( C != zero_zero_rat )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_rat @ A @ C ) ) )
% 0.29/0.54          & ( ( C = zero_zero_rat )
% 0.29/0.54           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq
% 0.29/0.54  thf(fact_3207_divide__eq__eq,axiom,
% 0.29/0.54      ! [B: real,C: real,A: real] :
% 0.29/0.54        ( ( ( divide_divide_real @ B @ C )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( C != zero_zero_real )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_real @ A @ C ) ) )
% 0.29/0.54          & ( ( C = zero_zero_real )
% 0.29/0.54           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq
% 0.29/0.54  thf(fact_3208_divide__eq__eq,axiom,
% 0.29/0.54      ! [B: complex,C: complex,A: complex] :
% 0.29/0.54        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.54          = A )
% 0.29/0.54        = ( ( ( C != zero_zero_complex )
% 0.29/0.54           => ( B
% 0.29/0.54              = ( times_times_complex @ A @ C ) ) )
% 0.29/0.54          & ( ( C = zero_zero_complex )
% 0.29/0.54           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % divide_eq_eq
% 0.29/0.54  thf(fact_3209_frac__eq__eq,axiom,
% 0.29/0.54      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 0.29/0.54        ( ( Y != zero_zero_rat )
% 0.29/0.54       => ( ( Z != zero_zero_rat )
% 0.29/0.54         => ( ( ( divide_divide_rat @ X4 @ Y )
% 0.29/0.54              = ( divide_divide_rat @ W @ Z ) )
% 0.29/0.54            = ( ( times_times_rat @ X4 @ Z )
% 0.29/0.54              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % frac_eq_eq
% 0.29/0.54  thf(fact_3210_frac__eq__eq,axiom,
% 0.29/0.54      ! [Y: real,Z: real,X4: real,W: real] :
% 0.29/0.54        ( ( Y != zero_zero_real )
% 0.29/0.54       => ( ( Z != zero_zero_real )
% 0.29/0.54         => ( ( ( divide_divide_real @ X4 @ Y )
% 0.29/0.54              = ( divide_divide_real @ W @ Z ) )
% 0.29/0.54            = ( ( times_times_real @ X4 @ Z )
% 0.29/0.54              = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % frac_eq_eq
% 0.29/0.54  thf(fact_3211_frac__eq__eq,axiom,
% 0.29/0.54      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 0.29/0.54        ( ( Y != zero_zero_complex )
% 0.29/0.54       => ( ( Z != zero_zero_complex )
% 0.29/0.54         => ( ( ( divide1717551699836669952omplex @ X4 @ Y )
% 0.29/0.54              = ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.54            = ( ( times_times_complex @ X4 @ Z )
% 0.29/0.54              = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % frac_eq_eq
% 0.29/0.54  thf(fact_3212_mult__numeral__1__right,axiom,
% 0.29/0.54      ! [A: extended_enat] :
% 0.29/0.54        ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1_right
% 0.29/0.54  thf(fact_3213_mult__numeral__1__right,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1_right
% 0.29/0.54  thf(fact_3214_mult__numeral__1__right,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1_right
% 0.29/0.54  thf(fact_3215_mult__numeral__1__right,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1_right
% 0.29/0.54  thf(fact_3216_mult__numeral__1__right,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1_right
% 0.29/0.54  thf(fact_3217_mult__numeral__1,axiom,
% 0.29/0.54      ! [A: extended_enat] :
% 0.29/0.54        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1
% 0.29/0.54  thf(fact_3218_mult__numeral__1,axiom,
% 0.29/0.54      ! [A: complex] :
% 0.29/0.54        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1
% 0.29/0.54  thf(fact_3219_mult__numeral__1,axiom,
% 0.29/0.54      ! [A: real] :
% 0.29/0.54        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1
% 0.29/0.54  thf(fact_3220_mult__numeral__1,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1
% 0.29/0.54  thf(fact_3221_mult__numeral__1,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.29/0.54        = A ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_numeral_1
% 0.29/0.54  thf(fact_3222_nat__dvd__not__less,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.54       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.54         => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_dvd_not_less
% 0.29/0.54  thf(fact_3223_div__mult2__numeral__eq,axiom,
% 0.29/0.54      ! [A: nat,K: num,L: num] :
% 0.29/0.54        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 0.29/0.54        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult2_numeral_eq
% 0.29/0.54  thf(fact_3224_div__mult2__numeral__eq,axiom,
% 0.29/0.54      ! [A: int,K: num,L: num] :
% 0.29/0.54        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 0.29/0.54        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult2_numeral_eq
% 0.29/0.54  thf(fact_3225_div__mult2__numeral__eq,axiom,
% 0.29/0.54      ! [A: code_integer,K: num,L: num] :
% 0.29/0.54        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ L ) )
% 0.29/0.54        = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( times_times_num @ K @ L ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % div_mult2_numeral_eq
% 0.29/0.54  thf(fact_3226_left__right__inverse__power,axiom,
% 0.29/0.54      ! [X4: rat,Y: rat,N2: nat] :
% 0.29/0.54        ( ( ( times_times_rat @ X4 @ Y )
% 0.29/0.54          = one_one_rat )
% 0.29/0.54       => ( ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 0.29/0.54          = one_one_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_right_inverse_power
% 0.29/0.54  thf(fact_3227_left__right__inverse__power,axiom,
% 0.29/0.54      ! [X4: complex,Y: complex,N2: nat] :
% 0.29/0.54        ( ( ( times_times_complex @ X4 @ Y )
% 0.29/0.54          = one_one_complex )
% 0.29/0.54       => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 0.29/0.54          = one_one_complex ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_right_inverse_power
% 0.29/0.54  thf(fact_3228_left__right__inverse__power,axiom,
% 0.29/0.54      ! [X4: real,Y: real,N2: nat] :
% 0.29/0.54        ( ( ( times_times_real @ X4 @ Y )
% 0.29/0.54          = one_one_real )
% 0.29/0.54       => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 0.29/0.54          = one_one_real ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_right_inverse_power
% 0.29/0.54  thf(fact_3229_left__right__inverse__power,axiom,
% 0.29/0.54      ! [X4: nat,Y: nat,N2: nat] :
% 0.29/0.54        ( ( ( times_times_nat @ X4 @ Y )
% 0.29/0.54          = one_one_nat )
% 0.29/0.54       => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 0.29/0.54          = one_one_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_right_inverse_power
% 0.29/0.54  thf(fact_3230_left__right__inverse__power,axiom,
% 0.29/0.54      ! [X4: int,Y: int,N2: nat] :
% 0.29/0.54        ( ( ( times_times_int @ X4 @ Y )
% 0.29/0.54          = one_one_int )
% 0.29/0.54       => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 0.29/0.54          = one_one_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % left_right_inverse_power
% 0.29/0.54  thf(fact_3231_power__Suc,axiom,
% 0.29/0.54      ! [A: complex,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc
% 0.29/0.54  thf(fact_3232_power__Suc,axiom,
% 0.29/0.54      ! [A: real,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc
% 0.29/0.54  thf(fact_3233_power__Suc,axiom,
% 0.29/0.54      ! [A: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc
% 0.29/0.54  thf(fact_3234_power__Suc,axiom,
% 0.29/0.54      ! [A: int,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc
% 0.29/0.54  thf(fact_3235_power__Suc2,axiom,
% 0.29/0.54      ! [A: complex,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc2
% 0.29/0.54  thf(fact_3236_power__Suc2,axiom,
% 0.29/0.54      ! [A: real,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc2
% 0.29/0.54  thf(fact_3237_power__Suc2,axiom,
% 0.29/0.54      ! [A: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc2
% 0.29/0.54  thf(fact_3238_power__Suc2,axiom,
% 0.29/0.54      ! [A: int,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ A @ ( suc @ N2 ) )
% 0.29/0.54        = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_Suc2
% 0.29/0.54  thf(fact_3239_mod__eqE,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ( modulo_modulo_int @ A @ C )
% 0.29/0.54          = ( modulo_modulo_int @ B @ C ) )
% 0.29/0.54       => ~ ! [D3: int] :
% 0.29/0.54              ( B
% 0.29/0.54             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eqE
% 0.29/0.54  thf(fact_3240_mod__eqE,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.29/0.54          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.29/0.54       => ~ ! [D3: code_integer] :
% 0.29/0.54              ( B
% 0.29/0.54             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eqE
% 0.29/0.54  thf(fact_3241_Suc__mult__less__cancel1,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.29/0.54        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_mult_less_cancel1
% 0.29/0.54  thf(fact_3242_power__add,axiom,
% 0.29/0.54      ! [A: complex,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.54        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_add
% 0.29/0.54  thf(fact_3243_power__add,axiom,
% 0.29/0.54      ! [A: real,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.54        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_add
% 0.29/0.54  thf(fact_3244_power__add,axiom,
% 0.29/0.54      ! [A: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.54        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_add
% 0.29/0.54  thf(fact_3245_power__add,axiom,
% 0.29/0.54      ! [A: int,M: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.54        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_add
% 0.29/0.54  thf(fact_3246_nat__mult__less__cancel1,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.54          = ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_less_cancel1
% 0.29/0.54  thf(fact_3247_nat__mult__eq__cancel1,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54       => ( ( ( times_times_nat @ K @ M )
% 0.29/0.54            = ( times_times_nat @ K @ N2 ) )
% 0.29/0.54          = ( M = N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mult_eq_cancel1
% 0.29/0.54  thf(fact_3248_mult__less__mono2,axiom,
% 0.29/0.54      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.54        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_mono2
% 0.29/0.54  thf(fact_3249_mult__less__mono1,axiom,
% 0.29/0.54      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.54        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.54         => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_mono1
% 0.29/0.54  thf(fact_3250_Suc__mult__le__cancel1,axiom,
% 0.29/0.54      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 0.29/0.54        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % Suc_mult_le_cancel1
% 0.29/0.54  thf(fact_3251_mult__Suc,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 0.29/0.54        = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_Suc
% 0.29/0.54  thf(fact_3252_mult__eq__self__implies__10,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( M
% 0.29/0.54          = ( times_times_nat @ M @ N2 ) )
% 0.29/0.54       => ( ( N2 = one_one_nat )
% 0.29/0.54          | ( M = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_eq_self_implies_10
% 0.29/0.54  thf(fact_3253_less__mult__imp__div__less,axiom,
% 0.29/0.54      ! [M: nat,I2: nat,N2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 0.29/0.54       => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_mult_imp_div_less
% 0.29/0.54  thf(fact_3254_div__times__less__eq__dividend,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 0.29/0.54  
% 0.29/0.54  % div_times_less_eq_dividend
% 0.29/0.54  thf(fact_3255_times__div__less__eq__dividend,axiom,
% 0.29/0.54      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 0.29/0.54  
% 0.29/0.54  % times_div_less_eq_dividend
% 0.29/0.54  thf(fact_3256_mod__eq__0D,axiom,
% 0.29/0.54      ! [M: nat,D: nat] :
% 0.29/0.54        ( ( ( modulo_modulo_nat @ M @ D )
% 0.29/0.54          = zero_zero_nat )
% 0.29/0.54       => ? [Q2: nat] :
% 0.29/0.54            ( M
% 0.29/0.54            = ( times_times_nat @ D @ Q2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mod_eq_0D
% 0.29/0.54  thf(fact_3257_nat__mod__eq__iff,axiom,
% 0.29/0.54      ! [X4: nat,N2: nat,Y: nat] :
% 0.29/0.54        ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 0.29/0.54          = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.29/0.54        = ( ? [Q1: nat,Q22: nat] :
% 0.29/0.54              ( ( plus_plus_nat @ X4 @ ( times_times_nat @ N2 @ Q1 ) )
% 0.29/0.54              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nat_mod_eq_iff
% 0.29/0.54  thf(fact_3258_bits__induct,axiom,
% 0.29/0.54      ! [P: nat > $o,A: nat] :
% 0.29/0.54        ( ! [A5: nat] :
% 0.29/0.54            ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54              = A5 )
% 0.29/0.54           => ( P @ A5 ) )
% 0.29/0.54       => ( ! [A5: nat,B5: $o] :
% 0.29/0.54              ( ( P @ A5 )
% 0.29/0.54             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.54                  = A5 )
% 0.29/0.54               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.29/0.54         => ( P @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bits_induct
% 0.29/0.54  thf(fact_3259_bits__induct,axiom,
% 0.29/0.54      ! [P: int > $o,A: int] :
% 0.29/0.54        ( ! [A5: int] :
% 0.29/0.54            ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.54              = A5 )
% 0.29/0.54           => ( P @ A5 ) )
% 0.29/0.54       => ( ! [A5: int,B5: $o] :
% 0.29/0.54              ( ( P @ A5 )
% 0.29/0.54             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.54                  = A5 )
% 0.29/0.54               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.29/0.54         => ( P @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bits_induct
% 0.29/0.54  thf(fact_3260_bits__induct,axiom,
% 0.29/0.54      ! [P: code_integer > $o,A: code_integer] :
% 0.29/0.54        ( ! [A5: code_integer] :
% 0.29/0.54            ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.54              = A5 )
% 0.29/0.54           => ( P @ A5 ) )
% 0.29/0.54       => ( ! [A5: code_integer,B5: $o] :
% 0.29/0.54              ( ( P @ A5 )
% 0.29/0.54             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.54                  = A5 )
% 0.29/0.54               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.29/0.54         => ( P @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bits_induct
% 0.29/0.54  thf(fact_3261_oddE,axiom,
% 0.29/0.54      ! [A: code_integer] :
% 0.29/0.54        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: code_integer] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % oddE
% 0.29/0.54  thf(fact_3262_oddE,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: nat] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % oddE
% 0.29/0.54  thf(fact_3263_oddE,axiom,
% 0.29/0.54      ! [A: int] :
% 0.29/0.54        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.54       => ~ ! [B5: int] :
% 0.29/0.54              ( A
% 0.29/0.54             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % oddE
% 0.29/0.54  thf(fact_3264_VEBT__internal_Ovalid_H_Ocases,axiom,
% 0.29/0.54      ! [X4: produc9072475918466114483BT_nat] :
% 0.29/0.54        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 0.29/0.54            ( X4
% 0.29/0.54           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 0.29/0.54       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Deg3: nat] :
% 0.29/0.54              ( X4
% 0.29/0.54             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Deg3 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % VEBT_internal.valid'.cases
% 0.29/0.54  thf(fact_3265_power__odd__eq,axiom,
% 0.29/0.54      ! [A: complex,N2: nat] :
% 0.29/0.54        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.54        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_odd_eq
% 0.29/0.54  thf(fact_3266_power__odd__eq,axiom,
% 0.29/0.54      ! [A: real,N2: nat] :
% 0.29/0.54        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.54        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_odd_eq
% 0.29/0.54  thf(fact_3267_power__odd__eq,axiom,
% 0.29/0.54      ! [A: nat,N2: nat] :
% 0.29/0.54        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.54        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_odd_eq
% 0.29/0.54  thf(fact_3268_power__odd__eq,axiom,
% 0.29/0.54      ! [A: int,N2: nat] :
% 0.29/0.54        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.54        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % power_odd_eq
% 0.29/0.54  thf(fact_3269_exp__mod__exp,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.54        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % exp_mod_exp
% 0.29/0.54  thf(fact_3270_exp__mod__exp,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.54        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % exp_mod_exp
% 0.29/0.54  thf(fact_3271_exp__mod__exp,axiom,
% 0.29/0.54      ! [M: nat,N2: nat] :
% 0.29/0.54        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.54        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % exp_mod_exp
% 0.29/0.54  thf(fact_3272_unit__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54       => ( ( ( divide_divide_nat @ A @ B )
% 0.29/0.54            = zero_zero_nat )
% 0.29/0.54          = ( A = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_eq_0_iff
% 0.29/0.54  thf(fact_3273_unit__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54       => ( ( ( divide_divide_int @ A @ B )
% 0.29/0.54            = zero_zero_int )
% 0.29/0.54          = ( A = zero_zero_int ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_eq_0_iff
% 0.29/0.54  thf(fact_3274_unit__div__eq__0__iff,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.29/0.54            = zero_z3403309356797280102nteger )
% 0.29/0.54          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_div_eq_0_iff
% 0.29/0.54  thf(fact_3275_even__numeral,axiom,
% 0.29/0.54      ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_numeral
% 0.29/0.54  thf(fact_3276_even__numeral,axiom,
% 0.29/0.54      ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_numeral
% 0.29/0.54  thf(fact_3277_even__numeral,axiom,
% 0.29/0.54      ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % even_numeral
% 0.29/0.54  thf(fact_3278_unit__imp__mod__eq__0,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.29/0.54       => ( ( modulo_modulo_nat @ A @ B )
% 0.29/0.54          = zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_imp_mod_eq_0
% 0.29/0.54  thf(fact_3279_unit__imp__mod__eq__0,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.29/0.54       => ( ( modulo_modulo_int @ A @ B )
% 0.29/0.54          = zero_zero_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_imp_mod_eq_0
% 0.29/0.54  thf(fact_3280_unit__imp__mod__eq__0,axiom,
% 0.29/0.54      ! [B: code_integer,A: code_integer] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.29/0.54       => ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.54          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.54  
% 0.29/0.54  % unit_imp_mod_eq_0
% 0.29/0.54  thf(fact_3281_is__unit__power__iff,axiom,
% 0.29/0.54      ! [A: code_integer,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 0.29/0.54        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.29/0.54          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_power_iff
% 0.29/0.54  thf(fact_3282_is__unit__power__iff,axiom,
% 0.29/0.54      ! [A: nat,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 0.29/0.54        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.29/0.54          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_power_iff
% 0.29/0.54  thf(fact_3283_is__unit__power__iff,axiom,
% 0.29/0.54      ! [A: int,N2: nat] :
% 0.29/0.54        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 0.29/0.54        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.29/0.54          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % is_unit_power_iff
% 0.29/0.54  thf(fact_3284_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_3285_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_3286_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_3287_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: real,C: real,B: real] :
% 0.29/0.54        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.54           => ( ord_less_eq_real @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_3288_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_3289_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_3290_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_3291_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_3292_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_3293_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_3294_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_real @ C @ D )
% 0.29/0.54         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_3295_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ C @ D )
% 0.29/0.54         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_3296_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ C @ D )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_3297_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ C @ D )
% 0.29/0.54         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_3298_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54           => ( ord_less_real @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.54           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_3299_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_3300_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_3301_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: real,C: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_3302_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_3303_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_3304_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_3305_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.54        ( ( ord_less_real @ A @ B )
% 0.29/0.54       => ( ( ord_less_real @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_3306_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ C @ D )
% 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_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_3307_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_3308_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ C @ D )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_3309_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: real,C: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.54           => ( ord_less_real @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.54           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_3310_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_3311_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_3312_mult__le__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: real,A: real,B: real] :
% 0.29/0.54        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.54       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.29/0.54          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_neg
% 0.29/0.54  thf(fact_3313_mult__le__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54       => ( ( 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_3314_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_3315_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_3316_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_3317_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_3318_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_3319_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_3320_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_3321_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_3322_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_3323_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_3324_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_3325_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_3326_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_real @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_3327_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_rat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_3328_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_nat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_3329_mult__le__less__imp__less,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_int @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_less_imp_less
% 0.29/0.55  thf(fact_3330_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_real @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_3331_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_3332_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.55        ( ( ord_less_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_3333_mult__less__le__imp__less,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.55        ( ( ord_less_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ D )
% 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 @ D ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_le_imp_less
% 0.29/0.55  thf(fact_3334_mult__left__le__one__le,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.55         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.55           => ( ord_less_eq_real @ ( times_times_real @ Y @ X4 ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_one_le
% 0.29/0.55  thf(fact_3335_mult__left__le__one__le,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.55         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X4 ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_one_le
% 0.29/0.55  thf(fact_3336_mult__left__le__one__le,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.55         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.29/0.55           => ( ord_less_eq_int @ ( times_times_int @ Y @ X4 ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le_one_le
% 0.29/0.55  thf(fact_3337_mult__right__le__one__le,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.55         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.55           => ( ord_less_eq_real @ ( times_times_real @ X4 @ Y ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_one_le
% 0.29/0.55  thf(fact_3338_mult__right__le__one__le,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.55         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Y ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_one_le
% 0.29/0.55  thf(fact_3339_mult__right__le__one__le,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.55         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.29/0.55           => ( ord_less_eq_int @ ( times_times_int @ X4 @ Y ) @ X4 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_right_le_one_le
% 0.29/0.55  thf(fact_3340_mult__le__one,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.55         => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.29/0.55           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_one
% 0.29/0.55  thf(fact_3341_mult__le__one,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.55         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_one
% 0.29/0.55  thf(fact_3342_mult__le__one,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.29/0.55         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.29/0.55           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_one
% 0.29/0.55  thf(fact_3343_mult__le__one,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.55         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.29/0.55           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_one
% 0.29/0.55  thf(fact_3344_mult__left__le,axiom,
% 0.29/0.55      ! [C: real,A: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ C @ one_one_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.55         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le
% 0.29/0.55  thf(fact_3345_mult__left__le,axiom,
% 0.29/0.55      ! [C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le
% 0.29/0.55  thf(fact_3346_mult__left__le,axiom,
% 0.29/0.55      ! [C: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le
% 0.29/0.55  thf(fact_3347_mult__left__le,axiom,
% 0.29/0.55      ! [C: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_left_le
% 0.29/0.55  thf(fact_3348_sum__squares__ge__zero,axiom,
% 0.29/0.55      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_ge_zero
% 0.29/0.55  thf(fact_3349_sum__squares__ge__zero,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_ge_zero
% 0.29/0.55  thf(fact_3350_sum__squares__ge__zero,axiom,
% 0.29/0.55      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_ge_zero
% 0.29/0.55  thf(fact_3351_sum__squares__le__zero__iff,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 0.29/0.55        = ( ( X4 = zero_zero_real )
% 0.29/0.55          & ( Y = zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_le_zero_iff
% 0.29/0.55  thf(fact_3352_sum__squares__le__zero__iff,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.29/0.55        = ( ( X4 = zero_zero_rat )
% 0.29/0.55          & ( Y = zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_le_zero_iff
% 0.29/0.55  thf(fact_3353_sum__squares__le__zero__iff,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.29/0.55        = ( ( X4 = zero_zero_int )
% 0.29/0.55          & ( Y = zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_le_zero_iff
% 0.29/0.55  thf(fact_3354_not__sum__squares__lt__zero,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 0.29/0.55  
% 0.29/0.55  % not_sum_squares_lt_zero
% 0.29/0.55  thf(fact_3355_not__sum__squares__lt__zero,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.29/0.55  
% 0.29/0.55  % not_sum_squares_lt_zero
% 0.29/0.55  thf(fact_3356_not__sum__squares__lt__zero,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.29/0.55  
% 0.29/0.55  % not_sum_squares_lt_zero
% 0.29/0.55  thf(fact_3357_sum__squares__gt__zero__iff,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) )
% 0.29/0.55        = ( ( X4 != zero_zero_real )
% 0.29/0.55          | ( Y != zero_zero_real ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_gt_zero_iff
% 0.29/0.55  thf(fact_3358_sum__squares__gt__zero__iff,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.29/0.55        = ( ( X4 != zero_zero_rat )
% 0.29/0.55          | ( Y != zero_zero_rat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_gt_zero_iff
% 0.29/0.55  thf(fact_3359_sum__squares__gt__zero__iff,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) )
% 0.29/0.55        = ( ( X4 != zero_zero_int )
% 0.29/0.55          | ( Y != zero_zero_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_gt_zero_iff
% 0.29/0.55  thf(fact_3360_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.29/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.55       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.55          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.29/0.55  thf(fact_3361_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.29/0.55      ! [C: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.55          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.29/0.55  thf(fact_3362_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.55          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.29/0.55  thf(fact_3363_divide__strict__left__mono__neg,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 @ C @ zero_zero_rat )
% 0.29/0.55         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_left_mono_neg
% 0.29/0.55  thf(fact_3364_divide__strict__left__mono__neg,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 @ C @ zero_zero_real )
% 0.29/0.55         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_left_mono_neg
% 0.29/0.55  thf(fact_3365_divide__strict__left__mono,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 @ zero_zero_rat @ C )
% 0.29/0.55         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_left_mono
% 0.29/0.55  thf(fact_3366_divide__strict__left__mono,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 @ zero_zero_real @ C )
% 0.29/0.55         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_strict_left_mono
% 0.29/0.55  thf(fact_3367_mult__imp__less__div__pos,axiom,
% 0.29/0.55      ! [Y: rat,Z: rat,X4: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.55       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 0.29/0.55         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_less_div_pos
% 0.29/0.55  thf(fact_3368_mult__imp__less__div__pos,axiom,
% 0.29/0.55      ! [Y: real,Z: real,X4: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.55       => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 0.29/0.55         => ( ord_less_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_less_div_pos
% 0.29/0.55  thf(fact_3369_mult__imp__div__pos__less,axiom,
% 0.29/0.55      ! [Y: rat,X4: rat,Z: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.55       => ( ( ord_less_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 0.29/0.55         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_div_pos_less
% 0.29/0.55  thf(fact_3370_mult__imp__div__pos__less,axiom,
% 0.29/0.55      ! [Y: real,X4: real,Z: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.55       => ( ( ord_less_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 0.29/0.55         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_div_pos_less
% 0.29/0.55  thf(fact_3371_pos__less__divide__eq,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 @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_less_divide_eq
% 0.29/0.55  thf(fact_3372_pos__less__divide__eq,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 @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_less_divide_eq
% 0.29/0.55  thf(fact_3373_pos__divide__less__eq,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_divide_less_eq
% 0.29/0.55  thf(fact_3374_pos__divide__less__eq,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_divide_less_eq
% 0.29/0.55  thf(fact_3375_neg__less__divide__eq,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 @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_less_divide_eq
% 0.29/0.55  thf(fact_3376_neg__less__divide__eq,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 @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_less_divide_eq
% 0.29/0.55  thf(fact_3377_neg__divide__less__eq,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_divide_less_eq
% 0.29/0.55  thf(fact_3378_neg__divide__less__eq,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_divide_less_eq
% 0.29/0.55  thf(fact_3379_less__divide__eq,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_divide_eq
% 0.29/0.55  thf(fact_3380_less__divide__eq,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_divide_eq
% 0.29/0.55  thf(fact_3381_divide__less__eq,axiom,
% 0.29/0.55      ! [B: rat,C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_eq
% 0.29/0.55  thf(fact_3382_divide__less__eq,axiom,
% 0.29/0.55      ! [B: real,C: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_eq
% 0.29/0.55  thf(fact_3383_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: rat,C: rat] :
% 0.29/0.55        ( ( ( numeral_numeral_rat @ W )
% 0.29/0.55          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_rat )
% 0.29/0.55           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_rat )
% 0.29/0.55           => ( ( numeral_numeral_rat @ W )
% 0.29/0.55              = zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3384_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: real,C: real] :
% 0.29/0.55        ( ( ( numeral_numeral_real @ W )
% 0.29/0.55          = ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_real )
% 0.29/0.55           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_real )
% 0.29/0.55           => ( ( numeral_numeral_real @ W )
% 0.29/0.55              = zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3385_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: complex,C: complex] :
% 0.29/0.55        ( ( ( numera6690914467698888265omplex @ W )
% 0.29/0.55          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.55        = ( ( ( C != zero_zero_complex )
% 0.29/0.55           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 0.29/0.55              = B ) )
% 0.29/0.55          & ( ( C = zero_zero_complex )
% 0.29/0.55           => ( ( numera6690914467698888265omplex @ W )
% 0.29/0.55              = zero_zero_complex ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % eq_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3386_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: rat,C: rat,W: num] :
% 0.29/0.55        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.55          = ( numeral_numeral_rat @ W ) )
% 0.29/0.55        = ( ( ( C != zero_zero_rat )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_rat )
% 0.29/0.55           => ( ( numeral_numeral_rat @ W )
% 0.29/0.55              = zero_zero_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq_numeral(1)
% 0.29/0.55  thf(fact_3387_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: real,C: real,W: num] :
% 0.29/0.55        ( ( ( divide_divide_real @ B @ C )
% 0.29/0.55          = ( numeral_numeral_real @ W ) )
% 0.29/0.55        = ( ( ( C != zero_zero_real )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_real )
% 0.29/0.55           => ( ( numeral_numeral_real @ W )
% 0.29/0.55              = zero_zero_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq_numeral(1)
% 0.29/0.55  thf(fact_3388_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: complex,C: complex,W: num] :
% 0.29/0.55        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.55          = ( numera6690914467698888265omplex @ W ) )
% 0.29/0.55        = ( ( ( C != zero_zero_complex )
% 0.29/0.55           => ( B
% 0.29/0.55              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 0.29/0.55          & ( ( C = zero_zero_complex )
% 0.29/0.55           => ( ( numera6690914467698888265omplex @ W )
% 0.29/0.55              = zero_zero_complex ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_eq_eq_numeral(1)
% 0.29/0.55  thf(fact_3389_divide__add__eq__iff,axiom,
% 0.29/0.55      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.55        ( ( Z != zero_zero_rat )
% 0.29/0.55       => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 0.29/0.55          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_add_eq_iff
% 0.29/0.55  thf(fact_3390_divide__add__eq__iff,axiom,
% 0.29/0.55      ! [Z: real,X4: real,Y: real] :
% 0.29/0.55        ( ( Z != zero_zero_real )
% 0.29/0.55       => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 0.29/0.55          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_add_eq_iff
% 0.29/0.55  thf(fact_3391_divide__add__eq__iff,axiom,
% 0.29/0.55      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.55        ( ( Z != zero_zero_complex )
% 0.29/0.55       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 0.29/0.55          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_add_eq_iff
% 0.29/0.55  thf(fact_3392_add__divide__eq__iff,axiom,
% 0.29/0.55      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.55        ( ( Z != zero_zero_rat )
% 0.29/0.55       => ( ( plus_plus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 0.29/0.55          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_iff
% 0.29/0.55  thf(fact_3393_add__divide__eq__iff,axiom,
% 0.29/0.55      ! [Z: real,X4: real,Y: real] :
% 0.29/0.55        ( ( Z != zero_zero_real )
% 0.29/0.55       => ( ( plus_plus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 0.29/0.55          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_iff
% 0.29/0.55  thf(fact_3394_add__divide__eq__iff,axiom,
% 0.29/0.55      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.55        ( ( Z != zero_zero_complex )
% 0.29/0.55       => ( ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 0.29/0.55          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_iff
% 0.29/0.55  thf(fact_3395_add__num__frac,axiom,
% 0.29/0.55      ! [Y: rat,Z: rat,X4: rat] :
% 0.29/0.55        ( ( Y != zero_zero_rat )
% 0.29/0.55       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) )
% 0.29/0.55          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_num_frac
% 0.29/0.55  thf(fact_3396_add__num__frac,axiom,
% 0.29/0.55      ! [Y: real,Z: real,X4: real] :
% 0.29/0.55        ( ( Y != zero_zero_real )
% 0.29/0.55       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.55          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_num_frac
% 0.29/0.55  thf(fact_3397_add__num__frac,axiom,
% 0.29/0.55      ! [Y: complex,Z: complex,X4: complex] :
% 0.29/0.55        ( ( Y != zero_zero_complex )
% 0.29/0.55       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 0.29/0.55          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_num_frac
% 0.29/0.55  thf(fact_3398_add__frac__num,axiom,
% 0.29/0.55      ! [Y: rat,X4: rat,Z: rat] :
% 0.29/0.55        ( ( Y != zero_zero_rat )
% 0.29/0.55       => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z )
% 0.29/0.55          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_num
% 0.29/0.55  thf(fact_3399_add__frac__num,axiom,
% 0.29/0.55      ! [Y: real,X4: real,Z: real] :
% 0.29/0.55        ( ( Y != zero_zero_real )
% 0.29/0.55       => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ Z )
% 0.29/0.55          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_num
% 0.29/0.55  thf(fact_3400_add__frac__num,axiom,
% 0.29/0.55      ! [Y: complex,X4: complex,Z: complex] :
% 0.29/0.55        ( ( Y != zero_zero_complex )
% 0.29/0.55       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ Z )
% 0.29/0.55          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_num
% 0.29/0.55  thf(fact_3401_add__frac__eq,axiom,
% 0.29/0.55      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 0.29/0.55        ( ( Y != zero_zero_rat )
% 0.29/0.55       => ( ( Z != zero_zero_rat )
% 0.29/0.55         => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.55            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_eq
% 0.29/0.55  thf(fact_3402_add__frac__eq,axiom,
% 0.29/0.55      ! [Y: real,Z: real,X4: real,W: real] :
% 0.29/0.55        ( ( Y != zero_zero_real )
% 0.29/0.55       => ( ( Z != zero_zero_real )
% 0.29/0.55         => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.55            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_eq
% 0.29/0.55  thf(fact_3403_add__frac__eq,axiom,
% 0.29/0.55      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 0.29/0.55        ( ( Y != zero_zero_complex )
% 0.29/0.55       => ( ( Z != zero_zero_complex )
% 0.29/0.55         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.55            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_frac_eq
% 0.29/0.55  thf(fact_3404_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.55      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ( Z = zero_zero_rat )
% 0.29/0.55         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.55            = A ) )
% 0.29/0.55        & ( ( Z != zero_zero_rat )
% 0.29/0.55         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.55            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(1)
% 0.29/0.55  thf(fact_3405_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.55      ! [Z: real,A: real,B: real] :
% 0.29/0.55        ( ( ( Z = zero_zero_real )
% 0.29/0.55         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.55            = A ) )
% 0.29/0.55        & ( ( Z != zero_zero_real )
% 0.29/0.55         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.55            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(1)
% 0.29/0.55  thf(fact_3406_add__divide__eq__if__simps_I1_J,axiom,
% 0.29/0.55      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.55        ( ( ( Z = zero_zero_complex )
% 0.29/0.55         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.55            = A ) )
% 0.29/0.55        & ( ( Z != zero_zero_complex )
% 0.29/0.55         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.55            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(1)
% 0.29/0.55  thf(fact_3407_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.55      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ( Z = zero_zero_rat )
% 0.29/0.55         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.55            = B ) )
% 0.29/0.55        & ( ( Z != zero_zero_rat )
% 0.29/0.55         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.55            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(2)
% 0.29/0.55  thf(fact_3408_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.55      ! [Z: real,A: real,B: real] :
% 0.29/0.55        ( ( ( Z = zero_zero_real )
% 0.29/0.55         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.55            = B ) )
% 0.29/0.55        & ( ( Z != zero_zero_real )
% 0.29/0.55         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.55            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(2)
% 0.29/0.55  thf(fact_3409_add__divide__eq__if__simps_I2_J,axiom,
% 0.29/0.55      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.55        ( ( ( Z = zero_zero_complex )
% 0.29/0.55         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.55            = B ) )
% 0.29/0.55        & ( ( Z != zero_zero_complex )
% 0.29/0.55         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.55            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % add_divide_eq_if_simps(2)
% 0.29/0.55  thf(fact_3410_power__less__power__Suc,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.55       => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_less_power_Suc
% 0.29/0.55  thf(fact_3411_power__less__power__Suc,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.55       => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_less_power_Suc
% 0.29/0.55  thf(fact_3412_power__less__power__Suc,axiom,
% 0.29/0.55      ! [A: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.55       => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_less_power_Suc
% 0.29/0.55  thf(fact_3413_power__less__power__Suc,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.55       => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_less_power_Suc
% 0.29/0.55  thf(fact_3414_power__gt1__lemma,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.55       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_gt1_lemma
% 0.29/0.55  thf(fact_3415_power__gt1__lemma,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_rat @ one_one_rat @ A )
% 0.29/0.55       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_gt1_lemma
% 0.29/0.55  thf(fact_3416_power__gt1__lemma,axiom,
% 0.29/0.55      ! [A: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ one_one_nat @ A )
% 0.29/0.55       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_gt1_lemma
% 0.29/0.55  thf(fact_3417_power__gt1__lemma,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_int @ one_one_int @ A )
% 0.29/0.55       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_gt1_lemma
% 0.29/0.55  thf(fact_3418_dvd__imp__le,axiom,
% 0.29/0.55      ! [K: nat,N2: nat] :
% 0.29/0.55        ( ( dvd_dvd_nat @ K @ N2 )
% 0.29/0.55       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55         => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_imp_le
% 0.29/0.55  thf(fact_3419_mult__div__mod__eq,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_div_mod_eq
% 0.29/0.55  thf(fact_3420_mult__div__mod__eq,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_div_mod_eq
% 0.29/0.55  thf(fact_3421_mult__div__mod__eq,axiom,
% 0.29/0.55      ! [B: code_integer,A: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_div_mod_eq
% 0.29/0.55  thf(fact_3422_mod__mult__div__eq,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_mult_div_eq
% 0.29/0.55  thf(fact_3423_mod__mult__div__eq,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_mult_div_eq
% 0.29/0.55  thf(fact_3424_mod__mult__div__eq,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_mult_div_eq
% 0.29/0.55  thf(fact_3425_mod__div__mult__eq,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_mult_eq
% 0.29/0.55  thf(fact_3426_mod__div__mult__eq,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_mult_eq
% 0.29/0.55  thf(fact_3427_mod__div__mult__eq,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_mult_eq
% 0.29/0.55  thf(fact_3428_div__mult__mod__eq,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult_mod_eq
% 0.29/0.55  thf(fact_3429_div__mult__mod__eq,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult_mod_eq
% 0.29/0.55  thf(fact_3430_div__mult__mod__eq,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.55        = A ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult_mod_eq
% 0.29/0.55  thf(fact_3431_mod__div__decomp,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( A
% 0.29/0.55        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_decomp
% 0.29/0.55  thf(fact_3432_mod__div__decomp,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( A
% 0.29/0.55        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_decomp
% 0.29/0.55  thf(fact_3433_mod__div__decomp,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer] :
% 0.29/0.55        ( A
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_div_decomp
% 0.29/0.55  thf(fact_3434_cancel__div__mod__rules_I1_J,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_plus_nat @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(1)
% 0.29/0.55  thf(fact_3435_cancel__div__mod__rules_I1_J,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_plus_int @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(1)
% 0.29/0.55  thf(fact_3436_cancel__div__mod__rules_I1_J,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(1)
% 0.29/0.55  thf(fact_3437_cancel__div__mod__rules_I2_J,axiom,
% 0.29/0.55      ! [B: nat,A: nat,C: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_plus_nat @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(2)
% 0.29/0.55  thf(fact_3438_cancel__div__mod__rules_I2_J,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_plus_int @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(2)
% 0.29/0.55  thf(fact_3439_cancel__div__mod__rules_I2_J,axiom,
% 0.29/0.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.55        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % cancel_div_mod_rules(2)
% 0.29/0.55  thf(fact_3440_div__mult1__eq,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.55        = ( 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 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult1_eq
% 0.29/0.55  thf(fact_3441_div__mult1__eq,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.55        = ( 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 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult1_eq
% 0.29/0.55  thf(fact_3442_div__mult1__eq,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.55        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mult1_eq
% 0.29/0.55  thf(fact_3443_pos__zmod__mult__2,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       => ( ( 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 ) )
% 0.29/0.55          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_zmod_mult_2
% 0.29/0.55  thf(fact_3444_one__less__mult,axiom,
% 0.29/0.55      ! [N2: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.55         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % one_less_mult
% 0.29/0.55  thf(fact_3445_n__less__m__mult__n,axiom,
% 0.29/0.55      ! [N2: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.55         => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % n_less_m_mult_n
% 0.29/0.55  thf(fact_3446_n__less__n__mult__m,axiom,
% 0.29/0.55      ! [N2: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.55         => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % n_less_n_mult_m
% 0.29/0.55  thf(fact_3447_mod__greater__zero__iff__not__dvd,axiom,
% 0.29/0.55      ! [M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.55        = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_greater_zero_iff_not_dvd
% 0.29/0.55  thf(fact_3448_nat__mult__le__cancel1,axiom,
% 0.29/0.55      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.55          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_mult_le_cancel1
% 0.29/0.55  thf(fact_3449_div__less__iff__less__mult,axiom,
% 0.29/0.55      ! [Q3: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.29/0.55       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N2 )
% 0.29/0.55          = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_less_iff_less_mult
% 0.29/0.55  thf(fact_3450_nat__mult__div__cancel1,axiom,
% 0.29/0.55      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.55       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 0.29/0.55          = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_mult_div_cancel1
% 0.29/0.55  thf(fact_3451_mod__eq__nat1E,axiom,
% 0.29/0.55      ! [M: nat,Q3: nat,N2: nat] :
% 0.29/0.55        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.29/0.55          = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 0.29/0.55       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.55         => ~ ! [S3: nat] :
% 0.29/0.55                ( M
% 0.29/0.55               != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_eq_nat1E
% 0.29/0.55  thf(fact_3452_mod__eq__nat2E,axiom,
% 0.29/0.55      ! [M: nat,Q3: nat,N2: nat] :
% 0.29/0.55        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.29/0.55          = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 0.29/0.55       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.55         => ~ ! [S3: nat] :
% 0.29/0.55                ( N2
% 0.29/0.55               != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_eq_nat2E
% 0.29/0.55  thf(fact_3453_nat__mod__eq__lemma,axiom,
% 0.29/0.55      ! [X4: nat,N2: nat,Y: nat] :
% 0.29/0.55        ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 0.29/0.55          = ( modulo_modulo_nat @ Y @ N2 ) )
% 0.29/0.55       => ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.55         => ? [Q2: nat] :
% 0.29/0.55              ( X4
% 0.29/0.55              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_mod_eq_lemma
% 0.29/0.55  thf(fact_3454_div__mod__decomp,axiom,
% 0.29/0.55      ! [A2: nat,N2: nat] :
% 0.29/0.55        ( A2
% 0.29/0.55        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_mod_decomp
% 0.29/0.55  thf(fact_3455_mod__mult2__eq,axiom,
% 0.29/0.55      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.55        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 0.29/0.55        = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_mult2_eq
% 0.29/0.55  thf(fact_3456_even__zero,axiom,
% 0.29/0.55      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 0.29/0.55  
% 0.29/0.55  % even_zero
% 0.29/0.55  thf(fact_3457_even__zero,axiom,
% 0.29/0.55      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.29/0.55  
% 0.29/0.55  % even_zero
% 0.29/0.55  thf(fact_3458_even__zero,axiom,
% 0.29/0.55      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.29/0.55  
% 0.29/0.55  % even_zero
% 0.29/0.55  thf(fact_3459_odd__one,axiom,
% 0.29/0.55      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_one
% 0.29/0.55  thf(fact_3460_odd__one,axiom,
% 0.29/0.55      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_one
% 0.29/0.55  thf(fact_3461_odd__one,axiom,
% 0.29/0.55      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_one
% 0.29/0.55  thf(fact_3462_odd__even__add,axiom,
% 0.29/0.55      ! [A: code_integer,B: code_integer] :
% 0.29/0.55        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.29/0.55         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_even_add
% 0.29/0.55  thf(fact_3463_odd__even__add,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.55         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_even_add
% 0.29/0.55  thf(fact_3464_odd__even__add,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.29/0.55         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_even_add
% 0.29/0.55  thf(fact_3465_bit__eq__rec,axiom,
% 0.29/0.55      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.55      = ( ^ [A3: nat,B2: nat] :
% 0.29/0.55            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 0.29/0.55              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 0.29/0.55            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55              = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % bit_eq_rec
% 0.29/0.55  thf(fact_3466_bit__eq__rec,axiom,
% 0.29/0.55      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.55      = ( ^ [A3: int,B2: int] :
% 0.29/0.55            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 0.29/0.55              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 0.29/0.55            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55              = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % bit_eq_rec
% 0.29/0.55  thf(fact_3467_bit__eq__rec,axiom,
% 0.29/0.55      ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 0.29/0.55      = ( ^ [A3: code_integer,B2: code_integer] :
% 0.29/0.55            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 0.29/0.55              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 0.29/0.55            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55              = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % bit_eq_rec
% 0.29/0.55  thf(fact_3468_dvd__power__iff,axiom,
% 0.29/0.55      ! [X4: code_integer,M: nat,N2: nat] :
% 0.29/0.55        ( ( X4 != zero_z3403309356797280102nteger )
% 0.29/0.55       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ M ) @ ( power_8256067586552552935nteger @ X4 @ N2 ) )
% 0.29/0.55          = ( ( dvd_dvd_Code_integer @ X4 @ one_one_Code_integer )
% 0.29/0.55            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power_iff
% 0.29/0.55  thf(fact_3469_dvd__power__iff,axiom,
% 0.29/0.55      ! [X4: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( X4 != zero_zero_nat )
% 0.29/0.55       => ( ( dvd_dvd_nat @ ( power_power_nat @ X4 @ M ) @ ( power_power_nat @ X4 @ N2 ) )
% 0.29/0.55          = ( ( dvd_dvd_nat @ X4 @ one_one_nat )
% 0.29/0.55            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power_iff
% 0.29/0.55  thf(fact_3470_dvd__power__iff,axiom,
% 0.29/0.55      ! [X4: int,M: nat,N2: nat] :
% 0.29/0.55        ( ( X4 != zero_zero_int )
% 0.29/0.55       => ( ( dvd_dvd_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ N2 ) )
% 0.29/0.55          = ( ( dvd_dvd_int @ X4 @ one_one_int )
% 0.29/0.55            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power_iff
% 0.29/0.55  thf(fact_3471_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: code_integer] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_Code_integer ) )
% 0.29/0.55       => ( dvd_dvd_Code_integer @ X4 @ ( power_8256067586552552935nteger @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3472_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: rat] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_rat ) )
% 0.29/0.55       => ( dvd_dvd_rat @ X4 @ ( power_power_rat @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3473_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: nat] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_nat ) )
% 0.29/0.55       => ( dvd_dvd_nat @ X4 @ ( power_power_nat @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3474_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: real] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_real ) )
% 0.29/0.55       => ( dvd_dvd_real @ X4 @ ( power_power_real @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3475_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: int] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_int ) )
% 0.29/0.55       => ( dvd_dvd_int @ X4 @ ( power_power_int @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3476_dvd__power,axiom,
% 0.29/0.55      ! [N2: nat,X4: complex] :
% 0.29/0.55        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          | ( X4 = one_one_complex ) )
% 0.29/0.55       => ( dvd_dvd_complex @ X4 @ ( power_power_complex @ X4 @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power
% 0.29/0.55  thf(fact_3477_field__le__mult__one__interval,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ! [Z2: real] :
% 0.29/0.55            ( ( ord_less_real @ zero_zero_real @ Z2 )
% 0.29/0.55           => ( ( ord_less_real @ Z2 @ one_one_real )
% 0.29/0.55             => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X4 ) @ Y ) ) )
% 0.29/0.55       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % field_le_mult_one_interval
% 0.29/0.55  thf(fact_3478_field__le__mult__one__interval,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ! [Z2: rat] :
% 0.29/0.55            ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.29/0.55           => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 0.29/0.55             => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X4 ) @ Y ) ) )
% 0.29/0.55       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % field_le_mult_one_interval
% 0.29/0.55  thf(fact_3479_mult__less__cancel__right2,axiom,
% 0.29/0.55      ! [A: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ A @ one_one_real ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right2
% 0.29/0.55  thf(fact_3480_mult__less__cancel__right2,axiom,
% 0.29/0.55      ! [A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right2
% 0.29/0.55  thf(fact_3481_mult__less__cancel__right2,axiom,
% 0.29/0.55      ! [A: int,C: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right2
% 0.29/0.55  thf(fact_3482_mult__less__cancel__right1,axiom,
% 0.29/0.55      ! [C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ 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 @ one_one_real @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right1
% 0.29/0.55  thf(fact_3483_mult__less__cancel__right1,axiom,
% 0.29/0.55      ! [C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ 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 @ one_one_rat @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right1
% 0.29/0.55  thf(fact_3484_mult__less__cancel__right1,axiom,
% 0.29/0.55      ! [C: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ 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 @ one_one_int @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_right1
% 0.29/0.55  thf(fact_3485_mult__less__cancel__left2,axiom,
% 0.29/0.55      ! [C: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ A @ one_one_real ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left2
% 0.29/0.55  thf(fact_3486_mult__less__cancel__left2,axiom,
% 0.29/0.55      ! [C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left2
% 0.29/0.55  thf(fact_3487_mult__less__cancel__left2,axiom,
% 0.29/0.55      ! [C: int,A: int] :
% 0.29/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left2
% 0.29/0.55  thf(fact_3488_mult__less__cancel__left1,axiom,
% 0.29/0.55      ! [C: real,B: real] :
% 0.29/0.55        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ one_one_real @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left1
% 0.29/0.55  thf(fact_3489_mult__less__cancel__left1,axiom,
% 0.29/0.55      ! [C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left1
% 0.29/0.55  thf(fact_3490_mult__less__cancel__left1,axiom,
% 0.29/0.55      ! [C: int,B: int] :
% 0.29/0.55        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_int @ one_one_int @ B ) )
% 0.29/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_less_cancel_left1
% 0.29/0.55  thf(fact_3491_mult__le__cancel__right2,axiom,
% 0.29/0.55      ! [A: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right2
% 0.29/0.55  thf(fact_3492_mult__le__cancel__right2,axiom,
% 0.29/0.55      ! [A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right2
% 0.29/0.55  thf(fact_3493_mult__le__cancel__right2,axiom,
% 0.29/0.55      ! [A: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right2
% 0.29/0.55  thf(fact_3494_mult__le__cancel__right1,axiom,
% 0.29/0.55      ! [C: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ 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 @ one_one_real @ B ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right1
% 0.29/0.55  thf(fact_3495_mult__le__cancel__right1,axiom,
% 0.29/0.55      ! [C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ 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 @ one_one_rat @ B ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right1
% 0.29/0.55  thf(fact_3496_mult__le__cancel__right1,axiom,
% 0.29/0.55      ! [C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ 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 @ one_one_int @ B ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_right1
% 0.29/0.55  thf(fact_3497_mult__le__cancel__left2,axiom,
% 0.29/0.55      ! [C: real,A: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left2
% 0.29/0.55  thf(fact_3498_mult__le__cancel__left2,axiom,
% 0.29/0.55      ! [C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left2
% 0.29/0.55  thf(fact_3499_mult__le__cancel__left2,axiom,
% 0.29/0.55      ! [C: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left2
% 0.29/0.55  thf(fact_3500_mult__le__cancel__left1,axiom,
% 0.29/0.55      ! [C: real,B: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.29/0.55          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left1
% 0.29/0.55  thf(fact_3501_mult__le__cancel__left1,axiom,
% 0.29/0.55      ! [C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.29/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left1
% 0.29/0.55  thf(fact_3502_mult__le__cancel__left1,axiom,
% 0.29/0.55      ! [C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.29/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.55           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.29/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_le_cancel_left1
% 0.29/0.55  thf(fact_3503_divide__left__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_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_left_mono_neg
% 0.29/0.55  thf(fact_3504_divide__left__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_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_left_mono_neg
% 0.29/0.55  thf(fact_3505_mult__imp__le__div__pos,axiom,
% 0.29/0.55      ! [Y: real,Z: real,X4: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.55       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 0.29/0.55         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_le_div_pos
% 0.29/0.55  thf(fact_3506_mult__imp__le__div__pos,axiom,
% 0.29/0.55      ! [Y: rat,Z: rat,X4: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 0.29/0.55         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_le_div_pos
% 0.29/0.55  thf(fact_3507_mult__imp__div__pos__le,axiom,
% 0.29/0.55      ! [Y: real,X4: real,Z: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.55       => ( ( ord_less_eq_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 0.29/0.55         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_div_pos_le
% 0.29/0.55  thf(fact_3508_mult__imp__div__pos__le,axiom,
% 0.29/0.55      ! [Y: rat,X4: rat,Z: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.55       => ( ( ord_less_eq_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 0.29/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_imp_div_pos_le
% 0.29/0.55  thf(fact_3509_pos__le__divide__eq,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 @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_le_divide_eq
% 0.29/0.55  thf(fact_3510_pos__le__divide__eq,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 @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_le_divide_eq
% 0.29/0.55  thf(fact_3511_pos__divide__le__eq,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_divide_le_eq
% 0.29/0.55  thf(fact_3512_pos__divide__le__eq,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_divide_le_eq
% 0.29/0.55  thf(fact_3513_neg__le__divide__eq,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 @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_le_divide_eq
% 0.29/0.55  thf(fact_3514_neg__le__divide__eq,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 @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_le_divide_eq
% 0.29/0.55  thf(fact_3515_neg__divide__le__eq,axiom,
% 0.29/0.55      ! [C: real,B: real,A: real] :
% 0.29/0.55        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_divide_le_eq
% 0.29/0.55  thf(fact_3516_neg__divide__le__eq,axiom,
% 0.29/0.55      ! [C: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_divide_le_eq
% 0.29/0.55  thf(fact_3517_divide__left__mono,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 @ zero_zero_real @ C )
% 0.29/0.55         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.55           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_left_mono
% 0.29/0.55  thf(fact_3518_divide__left__mono,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 @ zero_zero_rat @ C )
% 0.29/0.55         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.55           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_left_mono
% 0.29/0.55  thf(fact_3519_le__divide__eq,axiom,
% 0.29/0.55      ! [A: real,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_divide_eq
% 0.29/0.55  thf(fact_3520_le__divide__eq,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_divide_eq
% 0.29/0.55  thf(fact_3521_divide__le__eq,axiom,
% 0.29/0.55      ! [B: real,C: real,A: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_eq
% 0.29/0.55  thf(fact_3522_divide__le__eq,axiom,
% 0.29/0.55      ! [B: rat,C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_eq
% 0.29/0.55  thf(fact_3523_convex__bound__le,axiom,
% 0.29/0.55      ! [X4: real,A: real,Y: real,U: real,V: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_eq_real @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.29/0.55           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.29/0.55             => ( ( ( plus_plus_real @ U @ V )
% 0.29/0.55                  = one_one_real )
% 0.29/0.55               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_le
% 0.29/0.55  thf(fact_3524_convex__bound__le,axiom,
% 0.29/0.55      ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.29/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.29/0.55             => ( ( ( plus_plus_rat @ U @ V )
% 0.29/0.55                  = one_one_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_le
% 0.29/0.55  thf(fact_3525_convex__bound__le,axiom,
% 0.29/0.55      ! [X4: int,A: int,Y: int,U: int,V: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.29/0.55             => ( ( ( plus_plus_int @ U @ V )
% 0.29/0.55                  = one_one_int )
% 0.29/0.55               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_le
% 0.29/0.55  thf(fact_3526_less__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3527_less__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3528_divide__less__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: rat,C: rat,W: num] :
% 0.29/0.55        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_eq_numeral(1)
% 0.29/0.55  thf(fact_3529_divide__less__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: real,C: real,W: num] :
% 0.29/0.55        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_less_eq_numeral(1)
% 0.29/0.55  thf(fact_3530_power__Suc__less,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.55       => ( ( ord_less_real @ A @ one_one_real )
% 0.29/0.55         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_Suc_less
% 0.29/0.55  thf(fact_3531_power__Suc__less,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.55       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.29/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_Suc_less
% 0.29/0.55  thf(fact_3532_power__Suc__less,axiom,
% 0.29/0.55      ! [A: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.55       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.29/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_Suc_less
% 0.29/0.55  thf(fact_3533_power__Suc__less,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.55       => ( ( ord_less_int @ A @ one_one_int )
% 0.29/0.55         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_Suc_less
% 0.29/0.55  thf(fact_3534_left__add__twice,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.55        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3535_left__add__twice,axiom,
% 0.29/0.55      ! [A: extended_enat,B: extended_enat] :
% 0.29/0.55        ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 0.29/0.55        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3536_left__add__twice,axiom,
% 0.29/0.55      ! [A: complex,B: complex] :
% 0.29/0.55        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.55        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3537_left__add__twice,axiom,
% 0.29/0.55      ! [A: real,B: real] :
% 0.29/0.55        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.55        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3538_left__add__twice,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.55        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3539_left__add__twice,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.29/0.55        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % left_add_twice
% 0.29/0.55  thf(fact_3540_mult__2__right,axiom,
% 0.29/0.55      ! [Z: rat] :
% 0.29/0.55        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3541_mult__2__right,axiom,
% 0.29/0.55      ! [Z: extended_enat] :
% 0.29/0.55        ( ( times_7803423173614009249d_enat @ Z @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3542_mult__2__right,axiom,
% 0.29/0.55      ! [Z: complex] :
% 0.29/0.55        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3543_mult__2__right,axiom,
% 0.29/0.55      ! [Z: real] :
% 0.29/0.55        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3544_mult__2__right,axiom,
% 0.29/0.55      ! [Z: nat] :
% 0.29/0.55        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3545_mult__2__right,axiom,
% 0.29/0.55      ! [Z: int] :
% 0.29/0.55        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2_right
% 0.29/0.55  thf(fact_3546_mult__2,axiom,
% 0.29/0.55      ! [Z: rat] :
% 0.29/0.55        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3547_mult__2,axiom,
% 0.29/0.55      ! [Z: extended_enat] :
% 0.29/0.55        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3548_mult__2,axiom,
% 0.29/0.55      ! [Z: complex] :
% 0.29/0.55        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3549_mult__2,axiom,
% 0.29/0.55      ! [Z: real] :
% 0.29/0.55        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3550_mult__2,axiom,
% 0.29/0.55      ! [Z: nat] :
% 0.29/0.55        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3551_mult__2,axiom,
% 0.29/0.55      ! [Z: int] :
% 0.29/0.55        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.29/0.55        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mult_2
% 0.29/0.55  thf(fact_3552_power2__eq__square,axiom,
% 0.29/0.55      ! [A: complex] :
% 0.29/0.55        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( times_times_complex @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_eq_square
% 0.29/0.55  thf(fact_3553_power2__eq__square,axiom,
% 0.29/0.55      ! [A: real] :
% 0.29/0.55        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( times_times_real @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_eq_square
% 0.29/0.55  thf(fact_3554_power2__eq__square,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( times_times_nat @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_eq_square
% 0.29/0.55  thf(fact_3555_power2__eq__square,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( times_times_int @ A @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_eq_square
% 0.29/0.55  thf(fact_3556_power4__eq__xxxx,axiom,
% 0.29/0.55      ! [X4: complex] :
% 0.29/0.55        ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.55        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power4_eq_xxxx
% 0.29/0.55  thf(fact_3557_power4__eq__xxxx,axiom,
% 0.29/0.55      ! [X4: real] :
% 0.29/0.55        ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.55        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power4_eq_xxxx
% 0.29/0.55  thf(fact_3558_power4__eq__xxxx,axiom,
% 0.29/0.55      ! [X4: nat] :
% 0.29/0.55        ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.55        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power4_eq_xxxx
% 0.29/0.55  thf(fact_3559_power4__eq__xxxx,axiom,
% 0.29/0.55      ! [X4: int] :
% 0.29/0.55        ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.55        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power4_eq_xxxx
% 0.29/0.55  thf(fact_3560_double__not__eq__Suc__double,axiom,
% 0.29/0.55      ! [M: nat,N2: nat] :
% 0.29/0.55        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.29/0.55       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % double_not_eq_Suc_double
% 0.29/0.55  thf(fact_3561_Suc__double__not__eq__double,axiom,
% 0.29/0.55      ! [M: nat,N2: nat] :
% 0.29/0.55        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % Suc_double_not_eq_double
% 0.29/0.55  thf(fact_3562_power__even__eq,axiom,
% 0.29/0.55      ! [A: nat,N2: nat] :
% 0.29/0.55        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.55        = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_even_eq
% 0.29/0.55  thf(fact_3563_power__even__eq,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.55        = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_even_eq
% 0.29/0.55  thf(fact_3564_power__even__eq,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.55        = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_even_eq
% 0.29/0.55  thf(fact_3565_power__even__eq,axiom,
% 0.29/0.55      ! [A: complex,N2: nat] :
% 0.29/0.55        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.55        = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_even_eq
% 0.29/0.55  thf(fact_3566_power__dvd__imp__le,axiom,
% 0.29/0.55      ! [I2: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 0.29/0.55       => ( ( ord_less_nat @ one_one_nat @ I2 )
% 0.29/0.55         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_dvd_imp_le
% 0.29/0.55  thf(fact_3567_neg__zdiv__mult__2,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       => ( ( 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 ) )
% 0.29/0.55          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % neg_zdiv_mult_2
% 0.29/0.55  thf(fact_3568_pos__zdiv__mult__2,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       => ( ( 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 ) )
% 0.29/0.55          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % pos_zdiv_mult_2
% 0.29/0.55  thf(fact_3569_div__nat__eqI,axiom,
% 0.29/0.55      ! [N2: nat,Q3: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q3 ) @ M )
% 0.29/0.55       => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q3 ) ) )
% 0.29/0.55         => ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.55            = Q3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div_nat_eqI
% 0.29/0.55  thf(fact_3570_less__eq__div__iff__mult__less__eq,axiom,
% 0.29/0.55      ! [Q3: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.29/0.55       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q3 ) )
% 0.29/0.55          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % less_eq_div_iff_mult_less_eq
% 0.29/0.55  thf(fact_3571_dividend__less__times__div,axiom,
% 0.29/0.55      ! [N2: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dividend_less_times_div
% 0.29/0.55  thf(fact_3572_dividend__less__div__times,axiom,
% 0.29/0.55      ! [N2: nat,M: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dividend_less_div_times
% 0.29/0.55  thf(fact_3573_split__div,axiom,
% 0.29/0.55      ! [P: nat > $o,M: nat,N2: nat] :
% 0.29/0.55        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.55        = ( ( ( N2 = zero_zero_nat )
% 0.29/0.55           => ( P @ zero_zero_nat ) )
% 0.29/0.55          & ( ( N2 != zero_zero_nat )
% 0.29/0.55           => ! [I3: nat,J3: nat] :
% 0.29/0.55                ( ( ord_less_nat @ J3 @ N2 )
% 0.29/0.55               => ( ( M
% 0.29/0.55                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 0.29/0.55                 => ( P @ I3 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_div
% 0.29/0.55  thf(fact_3574_split__mod,axiom,
% 0.29/0.55      ! [P: nat > $o,M: nat,N2: nat] :
% 0.29/0.55        ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.55        = ( ( ( N2 = zero_zero_nat )
% 0.29/0.55           => ( P @ M ) )
% 0.29/0.55          & ( ( N2 != zero_zero_nat )
% 0.29/0.55           => ! [I3: nat,J3: nat] :
% 0.29/0.55                ( ( ord_less_nat @ J3 @ N2 )
% 0.29/0.55               => ( ( M
% 0.29/0.55                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 0.29/0.55                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_mod
% 0.29/0.55  thf(fact_3575_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.29/0.55      ! [X4: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [A5: $o,B5: $o,X5: nat] :
% 0.29/0.55            ( X4
% 0.29/0.55           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 0.29/0.55       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.29/0.55              ( X4
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 0.29/0.55         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 0.29/0.55                ( X4
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X5 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % VEBT_internal.naive_member.cases
% 0.29/0.55  thf(fact_3576_even__iff__mod__2__eq__zero,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55          = zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % even_iff_mod_2_eq_zero
% 0.29/0.55  thf(fact_3577_even__iff__mod__2__eq__zero,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55          = zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % even_iff_mod_2_eq_zero
% 0.29/0.55  thf(fact_3578_even__iff__mod__2__eq__zero,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.55  
% 0.29/0.55  % even_iff_mod_2_eq_zero
% 0.29/0.55  thf(fact_3579_odd__iff__mod__2__eq__one,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.55        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55          = one_one_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_iff_mod_2_eq_one
% 0.29/0.55  thf(fact_3580_odd__iff__mod__2__eq__one,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.55        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55          = one_one_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_iff_mod_2_eq_one
% 0.29/0.55  thf(fact_3581_odd__iff__mod__2__eq__one,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.55        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55          = one_one_Code_integer ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_iff_mod_2_eq_one
% 0.29/0.55  thf(fact_3582_power__mono__odd,axiom,
% 0.29/0.55      ! [N2: nat,A: real,B: real] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono_odd
% 0.29/0.55  thf(fact_3583_power__mono__odd,axiom,
% 0.29/0.55      ! [N2: nat,A: rat,B: rat] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono_odd
% 0.29/0.55  thf(fact_3584_power__mono__odd,axiom,
% 0.29/0.55      ! [N2: nat,A: int,B: int] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_mono_odd
% 0.29/0.55  thf(fact_3585_convex__bound__lt,axiom,
% 0.29/0.55      ! [X4: real,A: real,Y: real,U: real,V: real] :
% 0.29/0.55        ( ( ord_less_real @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_real @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.29/0.55           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.29/0.55             => ( ( ( plus_plus_real @ U @ V )
% 0.29/0.55                  = one_one_real )
% 0.29/0.55               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_lt
% 0.29/0.55  thf(fact_3586_convex__bound__lt,axiom,
% 0.29/0.55      ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_rat @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.29/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.29/0.55             => ( ( ( plus_plus_rat @ U @ V )
% 0.29/0.55                  = one_one_rat )
% 0.29/0.55               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_lt
% 0.29/0.55  thf(fact_3587_convex__bound__lt,axiom,
% 0.29/0.55      ! [X4: int,A: int,Y: int,U: int,V: int] :
% 0.29/0.55        ( ( ord_less_int @ X4 @ A )
% 0.29/0.55       => ( ( ord_less_int @ Y @ A )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.29/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.29/0.55             => ( ( ( plus_plus_int @ U @ V )
% 0.29/0.55                  = one_one_int )
% 0.29/0.55               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % convex_bound_lt
% 0.29/0.55  thf(fact_3588_le__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: real,C: real] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3589_le__divide__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [W: num,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_divide_eq_numeral(1)
% 0.29/0.55  thf(fact_3590_divide__le__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: real,C: real,W: num] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.29/0.55        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.55           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.55               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_eq_numeral(1)
% 0.29/0.55  thf(fact_3591_divide__le__eq__numeral_I1_J,axiom,
% 0.29/0.55      ! [B: rat,C: rat,W: num] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.29/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.29/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.55               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divide_le_eq_numeral(1)
% 0.29/0.55  thf(fact_3592_odd__pos,axiom,
% 0.29/0.55      ! [N2: nat] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_pos
% 0.29/0.55  thf(fact_3593_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.29/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.55       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.55          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.29/0.55  thf(fact_3594_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.29/0.55      ! [C: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.55       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.29/0.55          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.29/0.55  thf(fact_3595_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.29/0.55      ! [C: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.55       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.29/0.55          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.29/0.55  thf(fact_3596_dvd__power__iff__le,axiom,
% 0.29/0.55      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.55       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 0.29/0.55          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % dvd_power_iff_le
% 0.29/0.55  thf(fact_3597_num_Osize__gen_I1_J,axiom,
% 0.29/0.55      ( ( size_num @ one )
% 0.29/0.55      = zero_zero_nat ) ).
% 0.29/0.55  
% 0.29/0.55  % num.size_gen(1)
% 0.29/0.55  thf(fact_3598_four__x__squared,axiom,
% 0.29/0.55      ! [X4: real] :
% 0.29/0.55        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.55        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % four_x_squared
% 0.29/0.55  thf(fact_3599_split__div_H,axiom,
% 0.29/0.55      ! [P: nat > $o,M: nat,N2: nat] :
% 0.29/0.55        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.55        = ( ( ( N2 = zero_zero_nat )
% 0.29/0.55            & ( P @ zero_zero_nat ) )
% 0.29/0.55          | ? [Q5: nat] :
% 0.29/0.55              ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M )
% 0.29/0.55              & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 0.29/0.55              & ( P @ Q5 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % split_div'
% 0.29/0.55  thf(fact_3600_Suc__times__mod__eq,axiom,
% 0.29/0.55      ! [M: nat,N2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.29/0.55       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 0.29/0.55          = one_one_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % Suc_times_mod_eq
% 0.29/0.55  thf(fact_3601_parity__cases,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55           != zero_zero_nat ) )
% 0.29/0.55       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55             != one_one_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % parity_cases
% 0.29/0.55  thf(fact_3602_parity__cases,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55           != zero_zero_int ) )
% 0.29/0.55       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55             != one_one_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % parity_cases
% 0.29/0.55  thf(fact_3603_parity__cases,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55           != zero_z3403309356797280102nteger ) )
% 0.29/0.55       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55             != one_one_Code_integer ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % parity_cases
% 0.29/0.55  thf(fact_3604_mod2__eq__if,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55            = zero_zero_nat ) )
% 0.29/0.55        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55            = one_one_nat ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod2_eq_if
% 0.29/0.55  thf(fact_3605_mod2__eq__if,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55            = zero_zero_int ) )
% 0.29/0.55        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.55            = one_one_int ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod2_eq_if
% 0.29/0.55  thf(fact_3606_mod2__eq__if,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55            = zero_z3403309356797280102nteger ) )
% 0.29/0.55        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.55         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.55            = one_one_Code_integer ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod2_eq_if
% 0.29/0.55  thf(fact_3607_zero__le__even__power,axiom,
% 0.29/0.55      ! [N2: nat,A: real] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power
% 0.29/0.55  thf(fact_3608_zero__le__even__power,axiom,
% 0.29/0.55      ! [N2: nat,A: rat] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power
% 0.29/0.55  thf(fact_3609_zero__le__even__power,axiom,
% 0.29/0.55      ! [N2: nat,A: int] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power
% 0.29/0.55  thf(fact_3610_zero__le__odd__power,axiom,
% 0.29/0.55      ! [N2: nat,A: real] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.29/0.55          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_odd_power
% 0.29/0.55  thf(fact_3611_zero__le__odd__power,axiom,
% 0.29/0.55      ! [N2: nat,A: rat] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.29/0.55          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_odd_power
% 0.29/0.55  thf(fact_3612_zero__le__odd__power,axiom,
% 0.29/0.55      ! [N2: nat,A: int] :
% 0.29/0.55        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.29/0.55          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_odd_power
% 0.29/0.55  thf(fact_3613_zero__le__power__eq,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.29/0.55        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power_eq
% 0.29/0.55  thf(fact_3614_zero__le__power__eq,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.29/0.55        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power_eq
% 0.29/0.55  thf(fact_3615_zero__le__power__eq,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.29/0.55        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_power_eq
% 0.29/0.55  thf(fact_3616_divmod__digit__0_I2_J,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.29/0.55            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(2)
% 0.29/0.55  thf(fact_3617_divmod__digit__0_I2_J,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.29/0.55            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(2)
% 0.29/0.55  thf(fact_3618_divmod__digit__0_I2_J,axiom,
% 0.29/0.55      ! [B: code_integer,A: code_integer] :
% 0.29/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.55       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 0.29/0.55            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(2)
% 0.29/0.55  thf(fact_3619_power2__sum,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] :
% 0.29/0.55        ( ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3620_power2__sum,axiom,
% 0.29/0.55      ! [X4: extended_enat,Y: extended_enat] :
% 0.29/0.55        ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3621_power2__sum,axiom,
% 0.29/0.55      ! [X4: complex,Y: complex] :
% 0.29/0.55        ( ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3622_power2__sum,axiom,
% 0.29/0.55      ! [X4: real,Y: real] :
% 0.29/0.55        ( ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3623_power2__sum,axiom,
% 0.29/0.55      ! [X4: nat,Y: nat] :
% 0.29/0.55        ( ( power_power_nat @ ( plus_plus_nat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3624_power2__sum,axiom,
% 0.29/0.55      ! [X4: int,Y: int] :
% 0.29/0.55        ( ( power_power_int @ ( plus_plus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power2_sum
% 0.29/0.55  thf(fact_3625_zero__le__even__power_H,axiom,
% 0.29/0.55      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power'
% 0.29/0.55  thf(fact_3626_zero__le__even__power_H,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power'
% 0.29/0.55  thf(fact_3627_zero__le__even__power_H,axiom,
% 0.29/0.55      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_le_even_power'
% 0.29/0.55  thf(fact_3628_nat__bit__induct,axiom,
% 0.29/0.55      ! [P: nat > $o,N2: nat] :
% 0.29/0.55        ( ( P @ zero_zero_nat )
% 0.29/0.55       => ( ! [N3: nat] :
% 0.29/0.55              ( ( P @ N3 )
% 0.29/0.55             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.55               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.29/0.55         => ( ! [N3: nat] :
% 0.29/0.55                ( ( P @ N3 )
% 0.29/0.55               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.29/0.55           => ( P @ N2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % nat_bit_induct
% 0.29/0.55  thf(fact_3629_L2__set__mult__ineq__lemma,axiom,
% 0.29/0.55      ! [A: real,C: real,B: real,D: 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 @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % L2_set_mult_ineq_lemma
% 0.29/0.55  thf(fact_3630_zero__less__power__eq,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 0.29/0.55        = ( ( N2 = zero_zero_nat )
% 0.29/0.55          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( A != zero_zero_real ) )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power_eq
% 0.29/0.55  thf(fact_3631_zero__less__power__eq,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 0.29/0.55        = ( ( N2 = zero_zero_nat )
% 0.29/0.55          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( A != zero_zero_rat ) )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power_eq
% 0.29/0.55  thf(fact_3632_zero__less__power__eq,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 0.29/0.55        = ( ( N2 = zero_zero_nat )
% 0.29/0.55          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( A != zero_zero_int ) )
% 0.29/0.55          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % zero_less_power_eq
% 0.29/0.55  thf(fact_3633_Euclid__induct,axiom,
% 0.29/0.55      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.55        ( ! [A5: nat,B5: nat] :
% 0.29/0.55            ( ( P @ A5 @ B5 )
% 0.29/0.55            = ( P @ B5 @ A5 ) )
% 0.29/0.55       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 0.29/0.55         => ( ! [A5: nat,B5: nat] :
% 0.29/0.55                ( ( P @ A5 @ B5 )
% 0.29/0.55               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 0.29/0.55           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % Euclid_induct
% 0.29/0.55  thf(fact_3634_sum__squares__bound,axiom,
% 0.29/0.55      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_bound
% 0.29/0.55  thf(fact_3635_sum__squares__bound,axiom,
% 0.29/0.55      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sum_squares_bound
% 0.29/0.55  thf(fact_3636_divmod__digit__0_I1_J,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.55       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.55            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(1)
% 0.29/0.55  thf(fact_3637_divmod__digit__0_I1_J,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.55       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.55            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(1)
% 0.29/0.55  thf(fact_3638_divmod__digit__0_I1_J,axiom,
% 0.29/0.55      ! [B: code_integer,A: code_integer] :
% 0.29/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.55       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.55         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.55            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % divmod_digit_0(1)
% 0.29/0.55  thf(fact_3639_odd__0__le__power__imp__0__le,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.55       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_0_le_power_imp_0_le
% 0.29/0.55  thf(fact_3640_odd__0__le__power__imp__0__le,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_0_le_power_imp_0_le
% 0.29/0.55  thf(fact_3641_odd__0__le__power__imp__0__le,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.55       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_0_le_power_imp_0_le
% 0.29/0.55  thf(fact_3642_odd__power__less__zero,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.55       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_power_less_zero
% 0.29/0.55  thf(fact_3643_odd__power__less__zero,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.55       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_power_less_zero
% 0.29/0.55  thf(fact_3644_odd__power__less__zero,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.55       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % odd_power_less_zero
% 0.29/0.55  thf(fact_3645_VEBT__internal_Omembermima_Ocases,axiom,
% 0.29/0.55      ! [X4: produc9072475918466114483BT_nat] :
% 0.29/0.55        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 0.29/0.55            ( X4
% 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              ( X4
% 0.29/0.55             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 0.29/0.55         => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 0.29/0.55                ( X4
% 0.29/0.55               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 0.29/0.55           => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT,X5: nat] :
% 0.29/0.55                  ( X4
% 0.29/0.55                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ X5 ) )
% 0.29/0.55             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 0.29/0.55                    ( X4
% 0.29/0.55                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % VEBT_internal.membermima.cases
% 0.29/0.55  thf(fact_3646_power__le__zero__eq,axiom,
% 0.29/0.55      ! [A: real,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 0.29/0.55        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.29/0.55            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_le_zero_eq
% 0.29/0.55  thf(fact_3647_power__le__zero__eq,axiom,
% 0.29/0.55      ! [A: rat,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 0.29/0.55        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.29/0.55            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_le_zero_eq
% 0.29/0.55  thf(fact_3648_power__le__zero__eq,axiom,
% 0.29/0.55      ! [A: int,N2: nat] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 0.29/0.55        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.29/0.55            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % power_le_zero_eq
% 0.29/0.55  thf(fact_3649_mod__double__modulus,axiom,
% 0.29/0.55      ! [M: code_integer,X4: code_integer] :
% 0.29/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 0.29/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 0.29/0.55         => ( ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( modulo364778990260209775nteger @ X4 @ M ) )
% 0.29/0.55            | ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X4 @ M ) @ M ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_double_modulus
% 0.29/0.55  thf(fact_3650_mod__double__modulus,axiom,
% 0.29/0.55      ! [M: nat,X4: nat] :
% 0.29/0.55        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 0.29/0.55         => ( ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( modulo_modulo_nat @ X4 @ M ) )
% 0.29/0.55            | ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( plus_plus_nat @ ( modulo_modulo_nat @ X4 @ M ) @ M ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_double_modulus
% 0.29/0.55  thf(fact_3651_mod__double__modulus,axiom,
% 0.29/0.55      ! [M: int,X4: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ M )
% 0.29/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.55         => ( ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( modulo_modulo_int @ X4 @ M ) )
% 0.29/0.55            | ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.29/0.55              = ( plus_plus_int @ ( modulo_modulo_int @ X4 @ M ) @ M ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % mod_double_modulus
% 0.29/0.55  thf(fact_3652_option_Osize__gen_I1_J,axiom,
% 0.29/0.55      ! [X4: product_prod_nat_nat > nat] :
% 0.29/0.55        ( ( size_o8335143837870341156at_nat @ X4 @ none_P5556105721700978146at_nat )
% 0.29/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size_gen(1)
% 0.29/0.55  thf(fact_3653_option_Osize__gen_I1_J,axiom,
% 0.29/0.55      ! [X4: num > nat] :
% 0.29/0.55        ( ( size_option_num @ X4 @ none_num )
% 0.29/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55  
% 0.29/0.55  % option.size_gen(1)
% 0.29/0.55  thf(fact_3654_flip__bit__0,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_0
% 0.29/0.55  thf(fact_3655_flip__bit__0,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.29/0.55        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_0
% 0.29/0.55  thf(fact_3656_flip__bit__0,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.29/0.55        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_0
% 0.29/0.55  thf(fact_3657_set__bit__0,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_0
% 0.29/0.55  thf(fact_3658_set__bit__0,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.29/0.55        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_0
% 0.29/0.55  thf(fact_3659_set__bit__0,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.29/0.55        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_0
% 0.29/0.55  thf(fact_3660_even__even__mod__4__iff,axiom,
% 0.29/0.55      ! [N2: nat] :
% 0.29/0.55        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.55        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % even_even_mod_4_iff
% 0.29/0.55  thf(fact_3661_div2__even__ext__nat,axiom,
% 0.29/0.55      ! [X4: nat,Y: nat] :
% 0.29/0.55        ( ( ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.55          = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.55       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.55            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 0.29/0.55         => ( X4 = Y ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % div2_even_ext_nat
% 0.29/0.55  thf(fact_3662_unset__bit__0,axiom,
% 0.29/0.55      ! [A: code_integer] :
% 0.29/0.55        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 0.29/0.55        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_0
% 0.29/0.55  thf(fact_3663_unset__bit__0,axiom,
% 0.29/0.55      ! [A: int] :
% 0.29/0.55        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.29/0.55        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_0
% 0.29/0.55  thf(fact_3664_unset__bit__0,axiom,
% 0.29/0.55      ! [A: nat] :
% 0.29/0.55        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.29/0.55        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_0
% 0.29/0.55  thf(fact_3665_incr__mult__lemma,axiom,
% 0.29/0.55      ! [D: int,P: int > $o,K: int] :
% 0.29/0.55        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.55       => ( ! [X5: int] :
% 0.29/0.55              ( ( P @ X5 )
% 0.29/0.55             => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 0.29/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.55           => ! [X2: int] :
% 0.29/0.55                ( ( P @ X2 )
% 0.29/0.55               => ( P @ ( plus_plus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % incr_mult_lemma
% 0.29/0.55  thf(fact_3666_unset__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: code_integer] :
% 0.29/0.55        ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_Suc
% 0.29/0.55  thf(fact_3667_unset__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: int] :
% 0.29/0.55        ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_Suc
% 0.29/0.55  thf(fact_3668_unset__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: nat] :
% 0.29/0.55        ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_Suc
% 0.29/0.55  thf(fact_3669_flip__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: code_integer] :
% 0.29/0.55        ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_Suc
% 0.29/0.55  thf(fact_3670_flip__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: int] :
% 0.29/0.55        ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_Suc
% 0.29/0.55  thf(fact_3671_flip__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: nat] :
% 0.29/0.55        ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_Suc
% 0.29/0.55  thf(fact_3672_set__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: code_integer] :
% 0.29/0.55        ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_Suc
% 0.29/0.55  thf(fact_3673_set__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: int] :
% 0.29/0.55        ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_Suc
% 0.29/0.55  thf(fact_3674_set__bit__Suc,axiom,
% 0.29/0.55      ! [N2: nat,A: nat] :
% 0.29/0.55        ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 0.29/0.55        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_Suc
% 0.29/0.55  thf(fact_3675_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: code_integer > $o,L: code_integer] :
% 0.29/0.55        ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: code_integer] :
% 0.29/0.55              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3676_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: rat > $o,L: rat] :
% 0.29/0.55        ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: rat] :
% 0.29/0.55              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3677_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: complex > $o,L: complex] :
% 0.29/0.55        ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: complex] :
% 0.29/0.55              ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3678_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: real > $o,L: real] :
% 0.29/0.55        ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: real] :
% 0.29/0.55              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3679_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: nat > $o,L: nat] :
% 0.29/0.55        ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: nat] :
% 0.29/0.55              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3680_unity__coeff__ex,axiom,
% 0.29/0.55      ! [P: int > $o,L: int] :
% 0.29/0.55        ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 0.29/0.55        = ( ? [X: int] :
% 0.29/0.55              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 0.29/0.55              & ( P @ X ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unity_coeff_ex
% 0.29/0.55  thf(fact_3681_unset__bit__nonnegative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 0.29/0.55        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_nonnegative_int_iff
% 0.29/0.55  thf(fact_3682_set__bit__nonnegative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 0.29/0.55        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_nonnegative_int_iff
% 0.29/0.55  thf(fact_3683_flip__bit__nonnegative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 0.29/0.55        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_nonnegative_int_iff
% 0.29/0.55  thf(fact_3684_unset__bit__negative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.55        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_negative_int_iff
% 0.29/0.55  thf(fact_3685_set__bit__negative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.55        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_negative_int_iff
% 0.29/0.55  thf(fact_3686_flip__bit__negative__int__iff,axiom,
% 0.29/0.55      ! [N2: nat,K: int] :
% 0.29/0.55        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.55        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.55  
% 0.29/0.55  % flip_bit_negative_int_iff
% 0.29/0.55  thf(fact_3687_unset__bit__less__eq,axiom,
% 0.29/0.55      ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 0.29/0.55  
% 0.29/0.55  % unset_bit_less_eq
% 0.29/0.55  thf(fact_3688_set__bit__greater__eq,axiom,
% 0.29/0.55      ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 0.29/0.55  
% 0.29/0.55  % set_bit_greater_eq
% 0.29/0.55  thf(fact_3689_minf_I7_J,axiom,
% 0.29/0.55      ! [T2: real] :
% 0.29/0.55      ? [Z2: real] :
% 0.29/0.55      ! [X2: real] :
% 0.29/0.55        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.55       => ~ ( ord_less_real @ T2 @ X2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(7)
% 0.29/0.55  thf(fact_3690_minf_I7_J,axiom,
% 0.29/0.55      ! [T2: rat] :
% 0.29/0.55      ? [Z2: rat] :
% 0.29/0.55      ! [X2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.55       => ~ ( ord_less_rat @ T2 @ X2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(7)
% 0.29/0.55  thf(fact_3691_minf_I7_J,axiom,
% 0.29/0.55      ! [T2: num] :
% 0.29/0.55      ? [Z2: num] :
% 0.29/0.55      ! [X2: num] :
% 0.29/0.55        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.55       => ~ ( ord_less_num @ T2 @ X2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(7)
% 0.29/0.55  thf(fact_3692_minf_I7_J,axiom,
% 0.29/0.55      ! [T2: nat] :
% 0.29/0.55      ? [Z2: nat] :
% 0.29/0.55      ! [X2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.55       => ~ ( ord_less_nat @ T2 @ X2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(7)
% 0.29/0.55  thf(fact_3693_minf_I7_J,axiom,
% 0.29/0.55      ! [T2: int] :
% 0.29/0.55      ? [Z2: int] :
% 0.29/0.55      ! [X2: int] :
% 0.29/0.55        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.55       => ~ ( ord_less_int @ T2 @ X2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(7)
% 0.29/0.55  thf(fact_3694_minf_I5_J,axiom,
% 0.29/0.55      ! [T2: real] :
% 0.29/0.55      ? [Z2: real] :
% 0.29/0.55      ! [X2: real] :
% 0.29/0.55        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.55       => ( ord_less_real @ X2 @ T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(5)
% 0.29/0.55  thf(fact_3695_minf_I5_J,axiom,
% 0.29/0.55      ! [T2: rat] :
% 0.29/0.55      ? [Z2: rat] :
% 0.29/0.55      ! [X2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.55       => ( ord_less_rat @ X2 @ T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(5)
% 0.29/0.55  thf(fact_3696_minf_I5_J,axiom,
% 0.29/0.55      ! [T2: num] :
% 0.29/0.55      ? [Z2: num] :
% 0.29/0.55      ! [X2: num] :
% 0.29/0.55        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.55       => ( ord_less_num @ X2 @ T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(5)
% 0.29/0.55  thf(fact_3697_minf_I5_J,axiom,
% 0.29/0.55      ! [T2: nat] :
% 0.29/0.55      ? [Z2: nat] :
% 0.29/0.55      ! [X2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.55       => ( ord_less_nat @ X2 @ T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(5)
% 0.29/0.55  thf(fact_3698_minf_I5_J,axiom,
% 0.29/0.55      ! [T2: int] :
% 0.29/0.55      ? [Z2: int] :
% 0.29/0.55      ! [X2: int] :
% 0.29/0.55        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.55       => ( ord_less_int @ X2 @ T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(5)
% 0.29/0.55  thf(fact_3699_minf_I4_J,axiom,
% 0.29/0.55      ! [T2: real] :
% 0.29/0.55      ? [Z2: real] :
% 0.29/0.55      ! [X2: real] :
% 0.29/0.55        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.55       => ( X2 != T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(4)
% 0.29/0.55  thf(fact_3700_minf_I4_J,axiom,
% 0.29/0.55      ! [T2: rat] :
% 0.29/0.55      ? [Z2: rat] :
% 0.29/0.55      ! [X2: rat] :
% 0.29/0.55        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.55       => ( X2 != T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(4)
% 0.29/0.55  thf(fact_3701_minf_I4_J,axiom,
% 0.29/0.55      ! [T2: num] :
% 0.29/0.55      ? [Z2: num] :
% 0.29/0.55      ! [X2: num] :
% 0.29/0.55        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.55       => ( X2 != T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(4)
% 0.29/0.55  thf(fact_3702_minf_I4_J,axiom,
% 0.29/0.55      ! [T2: nat] :
% 0.29/0.55      ? [Z2: nat] :
% 0.29/0.55      ! [X2: nat] :
% 0.29/0.55        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.55       => ( X2 != T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(4)
% 0.29/0.55  thf(fact_3703_minf_I4_J,axiom,
% 0.29/0.55      ! [T2: int] :
% 0.29/0.55      ? [Z2: int] :
% 0.29/0.55      ! [X2: int] :
% 0.29/0.55        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.55       => ( X2 != T2 ) ) ).
% 0.29/0.55  
% 0.29/0.55  % minf(4)
% 0.29/0.55  thf(fact_3704_minf_I3_J,axiom,
% 0.29/0.55      ! [T2: real] :
% 0.29/0.55      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(3)
% 0.29/0.56  thf(fact_3705_minf_I3_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(3)
% 0.29/0.56  thf(fact_3706_minf_I3_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(3)
% 0.29/0.56  thf(fact_3707_minf_I3_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(3)
% 0.29/0.56  thf(fact_3708_minf_I3_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(3)
% 0.29/0.56  thf(fact_3709_minf_I2_J,axiom,
% 0.29/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.29/0.56        ( ? [Z3: real] :
% 0.29/0.56          ! [X5: real] :
% 0.29/0.56            ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: real] :
% 0.29/0.56            ! [X5: real] :
% 0.29/0.56              ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: real] :
% 0.29/0.56            ! [X2: real] :
% 0.29/0.56              ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(2)
% 0.29/0.56  thf(fact_3710_minf_I2_J,axiom,
% 0.29/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.29/0.56        ( ? [Z3: rat] :
% 0.29/0.56          ! [X5: rat] :
% 0.29/0.56            ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: rat] :
% 0.29/0.56            ! [X5: rat] :
% 0.29/0.56              ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: rat] :
% 0.29/0.56            ! [X2: rat] :
% 0.29/0.56              ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(2)
% 0.29/0.56  thf(fact_3711_minf_I2_J,axiom,
% 0.29/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.29/0.56        ( ? [Z3: num] :
% 0.29/0.56          ! [X5: num] :
% 0.29/0.56            ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: num] :
% 0.29/0.56            ! [X5: num] :
% 0.29/0.56              ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: num] :
% 0.29/0.56            ! [X2: num] :
% 0.29/0.56              ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(2)
% 0.29/0.56  thf(fact_3712_minf_I2_J,axiom,
% 0.29/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.29/0.56        ( ? [Z3: nat] :
% 0.29/0.56          ! [X5: nat] :
% 0.29/0.56            ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: nat] :
% 0.29/0.56            ! [X5: nat] :
% 0.29/0.56              ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: nat] :
% 0.29/0.56            ! [X2: nat] :
% 0.29/0.56              ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(2)
% 0.29/0.56  thf(fact_3713_minf_I2_J,axiom,
% 0.29/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.29/0.56        ( ? [Z3: int] :
% 0.29/0.56          ! [X5: int] :
% 0.29/0.56            ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: int] :
% 0.29/0.56            ! [X5: int] :
% 0.29/0.56              ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: int] :
% 0.29/0.56            ! [X2: int] :
% 0.29/0.56              ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(2)
% 0.29/0.56  thf(fact_3714_minf_I1_J,axiom,
% 0.29/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.29/0.56        ( ? [Z3: real] :
% 0.29/0.56          ! [X5: real] :
% 0.29/0.56            ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: real] :
% 0.29/0.56            ! [X5: real] :
% 0.29/0.56              ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: real] :
% 0.29/0.56            ! [X2: real] :
% 0.29/0.56              ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(1)
% 0.29/0.56  thf(fact_3715_minf_I1_J,axiom,
% 0.29/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.29/0.56        ( ? [Z3: rat] :
% 0.29/0.56          ! [X5: rat] :
% 0.29/0.56            ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: rat] :
% 0.29/0.56            ! [X5: rat] :
% 0.29/0.56              ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: rat] :
% 0.29/0.56            ! [X2: rat] :
% 0.29/0.56              ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(1)
% 0.29/0.56  thf(fact_3716_minf_I1_J,axiom,
% 0.29/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.29/0.56        ( ? [Z3: num] :
% 0.29/0.56          ! [X5: num] :
% 0.29/0.56            ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: num] :
% 0.29/0.56            ! [X5: num] :
% 0.29/0.56              ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: num] :
% 0.29/0.56            ! [X2: num] :
% 0.29/0.56              ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(1)
% 0.29/0.56  thf(fact_3717_minf_I1_J,axiom,
% 0.29/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.29/0.56        ( ? [Z3: nat] :
% 0.29/0.56          ! [X5: nat] :
% 0.29/0.56            ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: nat] :
% 0.29/0.56            ! [X5: nat] :
% 0.29/0.56              ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: nat] :
% 0.29/0.56            ! [X2: nat] :
% 0.29/0.56              ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(1)
% 0.29/0.56  thf(fact_3718_minf_I1_J,axiom,
% 0.29/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.29/0.56        ( ? [Z3: int] :
% 0.29/0.56          ! [X5: int] :
% 0.29/0.56            ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: int] :
% 0.29/0.56            ! [X5: int] :
% 0.29/0.56              ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: int] :
% 0.29/0.56            ! [X2: int] :
% 0.29/0.56              ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(1)
% 0.29/0.56  thf(fact_3719_pinf_I7_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_real @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(7)
% 0.29/0.56  thf(fact_3720_pinf_I7_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_rat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(7)
% 0.29/0.56  thf(fact_3721_pinf_I7_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_num @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(7)
% 0.29/0.56  thf(fact_3722_pinf_I7_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_nat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(7)
% 0.29/0.56  thf(fact_3723_pinf_I7_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_int @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(7)
% 0.29/0.56  thf(fact_3724_pinf_I5_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_real @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(5)
% 0.29/0.56  thf(fact_3725_pinf_I5_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_rat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(5)
% 0.29/0.56  thf(fact_3726_pinf_I5_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_num @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(5)
% 0.29/0.56  thf(fact_3727_pinf_I5_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_nat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(5)
% 0.29/0.56  thf(fact_3728_pinf_I5_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_int @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(5)
% 0.29/0.56  thf(fact_3729_pinf_I4_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(4)
% 0.29/0.56  thf(fact_3730_pinf_I4_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(4)
% 0.29/0.56  thf(fact_3731_pinf_I4_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(4)
% 0.29/0.56  thf(fact_3732_pinf_I4_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(4)
% 0.29/0.56  thf(fact_3733_pinf_I4_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(4)
% 0.29/0.56  thf(fact_3734_pinf_I3_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(3)
% 0.29/0.56  thf(fact_3735_pinf_I3_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(3)
% 0.29/0.56  thf(fact_3736_pinf_I3_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(3)
% 0.29/0.56  thf(fact_3737_pinf_I3_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(3)
% 0.29/0.56  thf(fact_3738_pinf_I3_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( X2 != T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(3)
% 0.29/0.56  thf(fact_3739_pinf_I2_J,axiom,
% 0.29/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.29/0.56        ( ? [Z3: real] :
% 0.29/0.56          ! [X5: real] :
% 0.29/0.56            ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: real] :
% 0.29/0.56            ! [X5: real] :
% 0.29/0.56              ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: real] :
% 0.29/0.56            ! [X2: real] :
% 0.29/0.56              ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(2)
% 0.29/0.56  thf(fact_3740_pinf_I2_J,axiom,
% 0.29/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.29/0.56        ( ? [Z3: rat] :
% 0.29/0.56          ! [X5: rat] :
% 0.29/0.56            ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: rat] :
% 0.29/0.56            ! [X5: rat] :
% 0.29/0.56              ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: rat] :
% 0.29/0.56            ! [X2: rat] :
% 0.29/0.56              ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(2)
% 0.29/0.56  thf(fact_3741_pinf_I2_J,axiom,
% 0.29/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.29/0.56        ( ? [Z3: num] :
% 0.29/0.56          ! [X5: num] :
% 0.29/0.56            ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: num] :
% 0.29/0.56            ! [X5: num] :
% 0.29/0.56              ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: num] :
% 0.29/0.56            ! [X2: num] :
% 0.29/0.56              ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(2)
% 0.29/0.56  thf(fact_3742_pinf_I2_J,axiom,
% 0.29/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.29/0.56        ( ? [Z3: nat] :
% 0.29/0.56          ! [X5: nat] :
% 0.29/0.56            ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: nat] :
% 0.29/0.56            ! [X5: nat] :
% 0.29/0.56              ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: nat] :
% 0.29/0.56            ! [X2: nat] :
% 0.29/0.56              ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(2)
% 0.29/0.56  thf(fact_3743_pinf_I2_J,axiom,
% 0.29/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.29/0.56        ( ? [Z3: int] :
% 0.29/0.56          ! [X5: int] :
% 0.29/0.56            ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: int] :
% 0.29/0.56            ! [X5: int] :
% 0.29/0.56              ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: int] :
% 0.29/0.56            ! [X2: int] :
% 0.29/0.56              ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  | ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(2)
% 0.29/0.56  thf(fact_3744_pinf_I1_J,axiom,
% 0.29/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.29/0.56        ( ? [Z3: real] :
% 0.29/0.56          ! [X5: real] :
% 0.29/0.56            ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: real] :
% 0.29/0.56            ! [X5: real] :
% 0.29/0.56              ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: real] :
% 0.29/0.56            ! [X2: real] :
% 0.29/0.56              ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(1)
% 0.29/0.56  thf(fact_3745_pinf_I1_J,axiom,
% 0.29/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.29/0.56        ( ? [Z3: rat] :
% 0.29/0.56          ! [X5: rat] :
% 0.29/0.56            ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: rat] :
% 0.29/0.56            ! [X5: rat] :
% 0.29/0.56              ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: rat] :
% 0.29/0.56            ! [X2: rat] :
% 0.29/0.56              ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(1)
% 0.29/0.56  thf(fact_3746_pinf_I1_J,axiom,
% 0.29/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.29/0.56        ( ? [Z3: num] :
% 0.29/0.56          ! [X5: num] :
% 0.29/0.56            ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: num] :
% 0.29/0.56            ! [X5: num] :
% 0.29/0.56              ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: num] :
% 0.29/0.56            ! [X2: num] :
% 0.29/0.56              ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(1)
% 0.29/0.56  thf(fact_3747_pinf_I1_J,axiom,
% 0.29/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.29/0.56        ( ? [Z3: nat] :
% 0.29/0.56          ! [X5: nat] :
% 0.29/0.56            ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: nat] :
% 0.29/0.56            ! [X5: nat] :
% 0.29/0.56              ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: nat] :
% 0.29/0.56            ! [X2: nat] :
% 0.29/0.56              ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(1)
% 0.29/0.56  thf(fact_3748_pinf_I1_J,axiom,
% 0.29/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.29/0.56        ( ? [Z3: int] :
% 0.29/0.56          ! [X5: int] :
% 0.29/0.56            ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.56           => ( ( P @ X5 )
% 0.29/0.56              = ( P6 @ X5 ) ) )
% 0.29/0.56       => ( ? [Z3: int] :
% 0.29/0.56            ! [X5: int] :
% 0.29/0.56              ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.56             => ( ( Q @ X5 )
% 0.29/0.56                = ( Q6 @ X5 ) ) )
% 0.29/0.56         => ? [Z2: int] :
% 0.29/0.56            ! [X2: int] :
% 0.29/0.56              ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56             => ( ( ( P @ X2 )
% 0.29/0.56                  & ( Q @ X2 ) )
% 0.29/0.56                = ( ( P6 @ X2 )
% 0.29/0.56                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(1)
% 0.29/0.56  thf(fact_3749_minf_I8_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56       => ~ ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(8)
% 0.29/0.56  thf(fact_3750_minf_I8_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56       => ~ ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(8)
% 0.29/0.56  thf(fact_3751_minf_I8_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.56       => ~ ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(8)
% 0.29/0.56  thf(fact_3752_minf_I8_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56       => ~ ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(8)
% 0.29/0.56  thf(fact_3753_minf_I8_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56       => ~ ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(8)
% 0.29/0.56  thf(fact_3754_minf_I6_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56       => ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(6)
% 0.29/0.56  thf(fact_3755_minf_I6_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56       => ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(6)
% 0.29/0.56  thf(fact_3756_minf_I6_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ X2 @ Z2 )
% 0.29/0.56       => ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(6)
% 0.29/0.56  thf(fact_3757_minf_I6_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56       => ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(6)
% 0.29/0.56  thf(fact_3758_minf_I6_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56       => ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(6)
% 0.29/0.56  thf(fact_3759_pinf_I8_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(8)
% 0.29/0.56  thf(fact_3760_pinf_I8_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(8)
% 0.29/0.56  thf(fact_3761_pinf_I8_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(8)
% 0.29/0.56  thf(fact_3762_pinf_I8_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(8)
% 0.29/0.56  thf(fact_3763_pinf_I8_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(8)
% 0.29/0.56  thf(fact_3764_pinf_I6_J,axiom,
% 0.29/0.56      ! [T2: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(6)
% 0.29/0.56  thf(fact_3765_pinf_I6_J,axiom,
% 0.29/0.56      ! [T2: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(6)
% 0.29/0.56  thf(fact_3766_pinf_I6_J,axiom,
% 0.29/0.56      ! [T2: num] :
% 0.29/0.56      ? [Z2: num] :
% 0.29/0.56      ! [X2: num] :
% 0.29/0.56        ( ( ord_less_num @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(6)
% 0.29/0.56  thf(fact_3767_pinf_I6_J,axiom,
% 0.29/0.56      ! [T2: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(6)
% 0.29/0.56  thf(fact_3768_pinf_I6_J,axiom,
% 0.29/0.56      ! [T2: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ~ ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(6)
% 0.29/0.56  thf(fact_3769_list__decode_Ocases,axiom,
% 0.29/0.56      ! [X4: nat] :
% 0.29/0.56        ( ( X4 != zero_zero_nat )
% 0.29/0.56       => ~ ! [N3: nat] :
% 0.29/0.56              ( X4
% 0.29/0.56             != ( suc @ N3 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % list_decode.cases
% 0.29/0.56  thf(fact_3770_imp__le__cong,axiom,
% 0.29/0.56      ! [X4: int,X7: int,P: $o,P6: $o] :
% 0.29/0.56        ( ( X4 = X7 )
% 0.29/0.56       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.29/0.56           => ( P = P6 ) )
% 0.29/0.56         => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.56             => P )
% 0.29/0.56            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.29/0.56             => P6 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % imp_le_cong
% 0.29/0.56  thf(fact_3771_conj__le__cong,axiom,
% 0.29/0.56      ! [X4: int,X7: int,P: $o,P6: $o] :
% 0.29/0.56        ( ( X4 = X7 )
% 0.29/0.56       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.29/0.56           => ( P = P6 ) )
% 0.29/0.56         => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.56              & P )
% 0.29/0.56            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 0.29/0.56              & P6 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % conj_le_cong
% 0.29/0.56  thf(fact_3772_even__set__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          & ( M != zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_set_bit_iff
% 0.29/0.56  thf(fact_3773_even__set__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          & ( M != zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_set_bit_iff
% 0.29/0.56  thf(fact_3774_even__set__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          & ( M != zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_set_bit_iff
% 0.29/0.56  thf(fact_3775_even__flip__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.56         != ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_flip_bit_iff
% 0.29/0.56  thf(fact_3776_even__flip__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.56         != ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_flip_bit_iff
% 0.29/0.56  thf(fact_3777_even__flip__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.56         != ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_flip_bit_iff
% 0.29/0.56  thf(fact_3778_even__unset__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          | ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_unset_bit_iff
% 0.29/0.56  thf(fact_3779_even__unset__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          | ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_unset_bit_iff
% 0.29/0.56  thf(fact_3780_even__unset__bit__iff,axiom,
% 0.29/0.56      ! [M: nat,A: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.29/0.56        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.56          | ( M = zero_zero_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_unset_bit_iff
% 0.29/0.56  thf(fact_3781_minf_I10_J,axiom,
% 0.29/0.56      ! [D: code_integer,S: code_integer] :
% 0.29/0.56      ? [Z2: code_integer] :
% 0.29/0.56      ! [X2: code_integer] :
% 0.29/0.56        ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(10)
% 0.29/0.56  thf(fact_3782_minf_I10_J,axiom,
% 0.29/0.56      ! [D: real,S: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(10)
% 0.29/0.56  thf(fact_3783_minf_I10_J,axiom,
% 0.29/0.56      ! [D: rat,S: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(10)
% 0.29/0.56  thf(fact_3784_minf_I10_J,axiom,
% 0.29/0.56      ! [D: nat,S: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(10)
% 0.29/0.56  thf(fact_3785_minf_I10_J,axiom,
% 0.29/0.56      ! [D: int,S: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(10)
% 0.29/0.56  thf(fact_3786_minf_I9_J,axiom,
% 0.29/0.56      ! [D: code_integer,S: code_integer] :
% 0.29/0.56      ? [Z2: code_integer] :
% 0.29/0.56      ! [X2: code_integer] :
% 0.29/0.56        ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 0.29/0.56       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(9)
% 0.29/0.56  thf(fact_3787_minf_I9_J,axiom,
% 0.29/0.56      ! [D: real,S: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ X2 @ Z2 )
% 0.29/0.56       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(9)
% 0.29/0.56  thf(fact_3788_minf_I9_J,axiom,
% 0.29/0.56      ! [D: rat,S: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ X2 @ Z2 )
% 0.29/0.56       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(9)
% 0.29/0.56  thf(fact_3789_minf_I9_J,axiom,
% 0.29/0.56      ! [D: nat,S: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.56       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(9)
% 0.29/0.56  thf(fact_3790_minf_I9_J,axiom,
% 0.29/0.56      ! [D: int,S: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ X2 @ Z2 )
% 0.29/0.56       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minf(9)
% 0.29/0.56  thf(fact_3791_pinf_I10_J,axiom,
% 0.29/0.56      ! [D: code_integer,S: code_integer] :
% 0.29/0.56      ? [Z2: code_integer] :
% 0.29/0.56      ! [X2: code_integer] :
% 0.29/0.56        ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(10)
% 0.29/0.56  thf(fact_3792_pinf_I10_J,axiom,
% 0.29/0.56      ! [D: real,S: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(10)
% 0.29/0.56  thf(fact_3793_pinf_I10_J,axiom,
% 0.29/0.56      ! [D: rat,S: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(10)
% 0.29/0.56  thf(fact_3794_pinf_I10_J,axiom,
% 0.29/0.56      ! [D: nat,S: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(10)
% 0.29/0.56  thf(fact_3795_pinf_I10_J,axiom,
% 0.29/0.56      ! [D: int,S: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 0.29/0.56          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(10)
% 0.29/0.56  thf(fact_3796_pinf_I9_J,axiom,
% 0.29/0.56      ! [D: code_integer,S: code_integer] :
% 0.29/0.56      ? [Z2: code_integer] :
% 0.29/0.56      ! [X2: code_integer] :
% 0.29/0.56        ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 0.29/0.56       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(9)
% 0.29/0.56  thf(fact_3797_pinf_I9_J,axiom,
% 0.29/0.56      ! [D: real,S: real] :
% 0.29/0.56      ? [Z2: real] :
% 0.29/0.56      ! [X2: real] :
% 0.29/0.56        ( ( ord_less_real @ Z2 @ X2 )
% 0.29/0.56       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(9)
% 0.29/0.56  thf(fact_3798_pinf_I9_J,axiom,
% 0.29/0.56      ! [D: rat,S: rat] :
% 0.29/0.56      ? [Z2: rat] :
% 0.29/0.56      ! [X2: rat] :
% 0.29/0.56        ( ( ord_less_rat @ Z2 @ X2 )
% 0.29/0.56       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(9)
% 0.29/0.56  thf(fact_3799_pinf_I9_J,axiom,
% 0.29/0.56      ! [D: nat,S: nat] :
% 0.29/0.56      ? [Z2: nat] :
% 0.29/0.56      ! [X2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.56       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(9)
% 0.29/0.56  thf(fact_3800_pinf_I9_J,axiom,
% 0.29/0.56      ! [D: int,S: int] :
% 0.29/0.56      ? [Z2: int] :
% 0.29/0.56      ! [X2: int] :
% 0.29/0.56        ( ( ord_less_int @ Z2 @ X2 )
% 0.29/0.56       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 0.29/0.56          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pinf(9)
% 0.29/0.56  thf(fact_3801_length__mul__elem,axiom,
% 0.29/0.56      ! [Xs: list_list_VEBT_VEBT,N2: nat] :
% 0.29/0.56        ( ! [X5: list_VEBT_VEBT] :
% 0.29/0.56            ( ( member2936631157270082147T_VEBT @ X5 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 0.29/0.56           => ( ( size_s6755466524823107622T_VEBT @ X5 )
% 0.29/0.56              = N2 ) )
% 0.29/0.56       => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 0.29/0.56          = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_mul_elem
% 0.29/0.56  thf(fact_3802_length__mul__elem,axiom,
% 0.29/0.56      ! [Xs: list_list_o,N2: nat] :
% 0.29/0.56        ( ! [X5: list_o] :
% 0.29/0.56            ( ( member_list_o @ X5 @ ( set_list_o2 @ Xs ) )
% 0.29/0.56           => ( ( size_size_list_o @ X5 )
% 0.29/0.56              = N2 ) )
% 0.29/0.56       => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 0.29/0.56          = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_mul_elem
% 0.29/0.56  thf(fact_3803_length__mul__elem,axiom,
% 0.29/0.56      ! [Xs: list_list_nat,N2: nat] :
% 0.29/0.56        ( ! [X5: list_nat] :
% 0.29/0.56            ( ( member_list_nat @ X5 @ ( set_list_nat2 @ Xs ) )
% 0.29/0.56           => ( ( size_size_list_nat @ X5 )
% 0.29/0.56              = N2 ) )
% 0.29/0.56       => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 0.29/0.56          = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_mul_elem
% 0.29/0.56  thf(fact_3804_length__mul__elem,axiom,
% 0.29/0.56      ! [Xs: list_list_int,N2: nat] :
% 0.29/0.56        ( ! [X5: list_int] :
% 0.29/0.56            ( ( member_list_int @ X5 @ ( set_list_int2 @ Xs ) )
% 0.29/0.56           => ( ( size_size_list_int @ X5 )
% 0.29/0.56              = N2 ) )
% 0.29/0.56       => ( ( size_size_list_int @ ( concat_int @ Xs ) )
% 0.29/0.56          = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs ) @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_mul_elem
% 0.29/0.56  thf(fact_3805_mult__le__cancel__iff2,axiom,
% 0.29/0.56      ! [Z: real,X4: real,Y: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.29/0.56       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X4 ) @ ( times_times_real @ Z @ Y ) )
% 0.29/0.56          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff2
% 0.29/0.56  thf(fact_3806_mult__le__cancel__iff2,axiom,
% 0.29/0.56      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.29/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X4 ) @ ( times_times_rat @ Z @ Y ) )
% 0.29/0.56          = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff2
% 0.29/0.56  thf(fact_3807_mult__le__cancel__iff2,axiom,
% 0.29/0.56      ! [Z: int,X4: int,Y: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.56       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X4 ) @ ( times_times_int @ Z @ Y ) )
% 0.29/0.56          = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff2
% 0.29/0.56  thf(fact_3808_mult__le__cancel__iff1,axiom,
% 0.29/0.56      ! [Z: real,X4: real,Y: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.29/0.56       => ( ( ord_less_eq_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff1
% 0.29/0.56  thf(fact_3809_mult__le__cancel__iff1,axiom,
% 0.29/0.56      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.29/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff1
% 0.29/0.56  thf(fact_3810_mult__le__cancel__iff1,axiom,
% 0.29/0.56      ! [Z: int,X4: int,Y: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.56       => ( ( ord_less_eq_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_le_cancel_iff1
% 0.29/0.56  thf(fact_3811_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_num,Ys: list_num] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3812_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3813_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3814_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3815_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3816_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3817_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3818_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_o,Ys: list_o] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3819_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3820_product__nth,axiom,
% 0.29/0.56      ! [N2: nat,Xs: list_o,Ys: list_int] :
% 0.29/0.56        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.29/0.56       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 0.29/0.56          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % product_nth
% 0.29/0.56  thf(fact_3821_triangle__def,axiom,
% 0.29/0.56      ( nat_triangle
% 0.29/0.56      = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % triangle_def
% 0.29/0.56  thf(fact_3822_pos__eucl__rel__int__mult__2,axiom,
% 0.29/0.56      ! [B: int,A: int,Q3: int,R3: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.56       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56         => ( 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 @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % pos_eucl_rel_int_mult_2
% 0.29/0.56  thf(fact_3823_length__product,axiom,
% 0.29/0.56      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.29/0.56        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3824_length__product,axiom,
% 0.29/0.56      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.29/0.56        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3825_length__product,axiom,
% 0.29/0.56      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.29/0.56        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3826_length__product,axiom,
% 0.29/0.56      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.29/0.56        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3827_length__product,axiom,
% 0.29/0.56      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.29/0.56        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3828_length__product,axiom,
% 0.29/0.56      ! [Xs: list_o,Ys: list_o] :
% 0.29/0.56        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3829_length__product,axiom,
% 0.29/0.56      ! [Xs: list_o,Ys: list_nat] :
% 0.29/0.56        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3830_length__product,axiom,
% 0.29/0.56      ! [Xs: list_o,Ys: list_int] :
% 0.29/0.56        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3831_length__product,axiom,
% 0.29/0.56      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 0.29/0.56        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3832_length__product,axiom,
% 0.29/0.56      ! [Xs: list_nat,Ys: list_o] :
% 0.29/0.56        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 0.29/0.56        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % length_product
% 0.29/0.56  thf(fact_3833_triangle__Suc,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( nat_triangle @ ( suc @ N2 ) )
% 0.29/0.56        = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % triangle_Suc
% 0.29/0.56  thf(fact_3834_unique__remainder,axiom,
% 0.29/0.56      ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 0.29/0.56        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 0.29/0.56         => ( R3 = R4 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_remainder
% 0.29/0.56  thf(fact_3835_unique__quotient,axiom,
% 0.29/0.56      ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 0.29/0.56        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 0.29/0.56         => ( Q3 = Q4 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % unique_quotient
% 0.29/0.56  thf(fact_3836_eucl__rel__int__by0,axiom,
% 0.29/0.56      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eucl_rel_int_by0
% 0.29/0.56  thf(fact_3837_div__int__unique,axiom,
% 0.29/0.56      ! [K: int,L: int,Q3: int,R3: int] :
% 0.29/0.56        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56       => ( ( divide_divide_int @ K @ L )
% 0.29/0.56          = Q3 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_int_unique
% 0.29/0.56  thf(fact_3838_mod__int__unique,axiom,
% 0.29/0.56      ! [K: int,L: int,Q3: int,R3: int] :
% 0.29/0.56        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56       => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.56          = R3 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_int_unique
% 0.29/0.56  thf(fact_3839_eucl__rel__int__dividesI,axiom,
% 0.29/0.56      ! [L: int,K: int,Q3: int] :
% 0.29/0.56        ( ( L != zero_zero_int )
% 0.29/0.56       => ( ( K
% 0.29/0.56            = ( times_times_int @ Q3 @ L ) )
% 0.29/0.56         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eucl_rel_int_dividesI
% 0.29/0.56  thf(fact_3840_eucl__rel__int,axiom,
% 0.29/0.56      ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eucl_rel_int
% 0.29/0.56  thf(fact_3841_eucl__rel__int__iff,axiom,
% 0.29/0.56      ! [K: int,L: int,Q3: int,R3: int] :
% 0.29/0.56        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56        = ( ( K
% 0.29/0.56            = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R3 ) )
% 0.29/0.56          & ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.56           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.29/0.56              & ( ord_less_int @ R3 @ L ) ) )
% 0.29/0.56          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.56           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.29/0.56               => ( ( ord_less_int @ L @ R3 )
% 0.29/0.56                  & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 0.29/0.56              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.29/0.56               => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eucl_rel_int_iff
% 0.29/0.56  thf(fact_3842_mult__less__iff1,axiom,
% 0.29/0.56      ! [Z: real,X4: real,Y: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.29/0.56       => ( ( ord_less_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_real @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_less_iff1
% 0.29/0.56  thf(fact_3843_mult__less__iff1,axiom,
% 0.29/0.56      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.29/0.56       => ( ( ord_less_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_rat @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_less_iff1
% 0.29/0.56  thf(fact_3844_mult__less__iff1,axiom,
% 0.29/0.56      ! [Z: int,X4: int,Y: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.56       => ( ( ord_less_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.29/0.56          = ( ord_less_int @ X4 @ Y ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mult_less_iff1
% 0.29/0.56  thf(fact_3845_Divides_Oadjust__div__eq,axiom,
% 0.29/0.56      ! [Q3: int,R3: int] :
% 0.29/0.56        ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56        = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Divides.adjust_div_eq
% 0.29/0.56  thf(fact_3846_concat__bit__Suc,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 0.29/0.56        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % concat_bit_Suc
% 0.29/0.56  thf(fact_3847_neg__eucl__rel__int__mult__2,axiom,
% 0.29/0.56      ! [B: int,A: int,Q3: int,R3: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.29/0.56       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.56         => ( 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 @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % neg_eucl_rel_int_mult_2
% 0.29/0.56  thf(fact_3848_signed__take__bit__Suc,axiom,
% 0.29/0.56      ! [N2: nat,A: code_integer] :
% 0.29/0.56        ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 0.29/0.56        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_Suc
% 0.29/0.56  thf(fact_3849_signed__take__bit__Suc,axiom,
% 0.29/0.56      ! [N2: nat,A: int] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 0.29/0.56        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_Suc
% 0.29/0.56  thf(fact_3850_set__decode__Suc,axiom,
% 0.29/0.56      ! [N2: nat,X4: nat] :
% 0.29/0.56        ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X4 ) )
% 0.29/0.56        = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % set_decode_Suc
% 0.29/0.56  thf(fact_3851_set__decode__0,axiom,
% 0.29/0.56      ! [X4: nat] :
% 0.29/0.56        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X4 ) )
% 0.29/0.56        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % set_decode_0
% 0.29/0.56  thf(fact_3852_add__scale__eq__noteq,axiom,
% 0.29/0.56      ! [R3: rat,A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.56        ( ( R3 != zero_zero_rat )
% 0.29/0.56       => ( ( ( A = B )
% 0.29/0.56            & ( C != D ) )
% 0.29/0.56         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 0.29/0.56           != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_scale_eq_noteq
% 0.29/0.56  thf(fact_3853_add__scale__eq__noteq,axiom,
% 0.29/0.56      ! [R3: complex,A: complex,B: complex,C: complex,D: complex] :
% 0.29/0.56        ( ( R3 != zero_zero_complex )
% 0.29/0.56       => ( ( ( A = B )
% 0.29/0.56            & ( C != D ) )
% 0.29/0.56         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C ) )
% 0.29/0.56           != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_scale_eq_noteq
% 0.29/0.56  thf(fact_3854_add__scale__eq__noteq,axiom,
% 0.29/0.56      ! [R3: real,A: real,B: real,C: real,D: real] :
% 0.29/0.56        ( ( R3 != zero_zero_real )
% 0.29/0.56       => ( ( ( A = B )
% 0.29/0.56            & ( C != D ) )
% 0.29/0.56         => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C ) )
% 0.29/0.56           != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_scale_eq_noteq
% 0.29/0.56  thf(fact_3855_add__scale__eq__noteq,axiom,
% 0.29/0.56      ! [R3: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.56        ( ( R3 != zero_zero_nat )
% 0.29/0.56       => ( ( ( A = B )
% 0.29/0.56            & ( C != D ) )
% 0.29/0.56         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 0.29/0.56           != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_scale_eq_noteq
% 0.29/0.56  thf(fact_3856_add__scale__eq__noteq,axiom,
% 0.29/0.56      ! [R3: int,A: int,B: int,C: int,D: int] :
% 0.29/0.56        ( ( R3 != zero_zero_int )
% 0.29/0.56       => ( ( ( A = B )
% 0.29/0.56            & ( C != D ) )
% 0.29/0.56         => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 0.29/0.56           != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_scale_eq_noteq
% 0.29/0.56  thf(fact_3857_even__mult__exp__div__exp__iff,axiom,
% 0.29/0.56      ! [A: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.56        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.56          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.56            = zero_zero_nat )
% 0.29/0.56          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_mult_exp_div_exp_iff
% 0.29/0.56  thf(fact_3858_even__mult__exp__div__exp__iff,axiom,
% 0.29/0.56      ! [A: int,M: nat,N2: nat] :
% 0.29/0.56        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.56        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.56          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.56            = zero_zero_int )
% 0.29/0.56          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_mult_exp_div_exp_iff
% 0.29/0.56  thf(fact_3859_even__mult__exp__div__exp__iff,axiom,
% 0.29/0.56      ! [A: code_integer,M: nat,N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.56        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.56          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.56            = zero_z3403309356797280102nteger )
% 0.29/0.56          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_mult_exp_div_exp_iff
% 0.29/0.56  thf(fact_3860_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.56      ! [A: complex] :
% 0.29/0.56        ( ( minus_minus_complex @ A @ A )
% 0.29/0.56        = zero_zero_complex ) ).
% 0.29/0.56  
% 0.29/0.56  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.56  thf(fact_3861_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.56      ! [A: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ A )
% 0.29/0.56        = zero_zero_real ) ).
% 0.29/0.56  
% 0.29/0.56  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.56  thf(fact_3862_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.56      ! [A: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ A )
% 0.29/0.56        = zero_zero_rat ) ).
% 0.29/0.56  
% 0.29/0.56  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.56  thf(fact_3863_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.56      ! [A: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ A @ A )
% 0.29/0.56        = zero_zero_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.56  thf(fact_3864_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.56      ! [A: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ A )
% 0.29/0.56        = zero_zero_int ) ).
% 0.29/0.56  
% 0.29/0.56  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.56  thf(fact_3865_diff__zero,axiom,
% 0.29/0.56      ! [A: complex] :
% 0.29/0.56        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_zero
% 0.29/0.56  thf(fact_3866_diff__zero,axiom,
% 0.29/0.56      ! [A: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_zero
% 0.29/0.56  thf(fact_3867_diff__zero,axiom,
% 0.29/0.56      ! [A: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_zero
% 0.29/0.56  thf(fact_3868_diff__zero,axiom,
% 0.29/0.56      ! [A: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_zero
% 0.29/0.56  thf(fact_3869_diff__zero,axiom,
% 0.29/0.56      ! [A: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_zero
% 0.29/0.56  thf(fact_3870_zero__diff,axiom,
% 0.29/0.56      ! [A: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/0.56        = zero_zero_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_diff
% 0.29/0.56  thf(fact_3871_diff__0__right,axiom,
% 0.29/0.56      ! [A: complex] :
% 0.29/0.56        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_0_right
% 0.29/0.56  thf(fact_3872_diff__0__right,axiom,
% 0.29/0.56      ! [A: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_0_right
% 0.29/0.56  thf(fact_3873_diff__0__right,axiom,
% 0.29/0.56      ! [A: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_0_right
% 0.29/0.56  thf(fact_3874_diff__0__right,axiom,
% 0.29/0.56      ! [A: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_0_right
% 0.29/0.56  thf(fact_3875_diff__self,axiom,
% 0.29/0.56      ! [A: complex] :
% 0.29/0.56        ( ( minus_minus_complex @ A @ A )
% 0.29/0.56        = zero_zero_complex ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_self
% 0.29/0.56  thf(fact_3876_diff__self,axiom,
% 0.29/0.56      ! [A: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ A )
% 0.29/0.56        = zero_zero_real ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_self
% 0.29/0.56  thf(fact_3877_diff__self,axiom,
% 0.29/0.56      ! [A: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ A )
% 0.29/0.56        = zero_zero_rat ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_self
% 0.29/0.56  thf(fact_3878_diff__self,axiom,
% 0.29/0.56      ! [A: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ A )
% 0.29/0.56        = zero_zero_int ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_self
% 0.29/0.56  thf(fact_3879_add__diff__cancel,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel
% 0.29/0.56  thf(fact_3880_add__diff__cancel,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel
% 0.29/0.56  thf(fact_3881_add__diff__cancel,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel
% 0.29/0.56  thf(fact_3882_diff__add__cancel,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_cancel
% 0.29/0.56  thf(fact_3883_diff__add__cancel,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_cancel
% 0.29/0.56  thf(fact_3884_diff__add__cancel,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_cancel
% 0.29/0.56  thf(fact_3885_add__diff__cancel__left,axiom,
% 0.29/0.56      ! [C: real,A: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.56        = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left
% 0.29/0.56  thf(fact_3886_add__diff__cancel__left,axiom,
% 0.29/0.56      ! [C: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.29/0.56        = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left
% 0.29/0.56  thf(fact_3887_add__diff__cancel__left,axiom,
% 0.29/0.56      ! [C: nat,A: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.56        = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left
% 0.29/0.56  thf(fact_3888_add__diff__cancel__left,axiom,
% 0.29/0.56      ! [C: int,A: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.29/0.56        = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left
% 0.29/0.56  thf(fact_3889_add__diff__cancel__left_H,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.29/0.56        = B ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left'
% 0.29/0.56  thf(fact_3890_add__diff__cancel__left_H,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.29/0.56        = B ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left'
% 0.29/0.56  thf(fact_3891_add__diff__cancel__left_H,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.29/0.56        = B ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left'
% 0.29/0.56  thf(fact_3892_add__diff__cancel__left_H,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.29/0.56        = B ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_left'
% 0.29/0.56  thf(fact_3893_add__diff__cancel__right,axiom,
% 0.29/0.56      ! [A: real,C: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right
% 0.29/0.56  thf(fact_3894_add__diff__cancel__right,axiom,
% 0.29/0.56      ! [A: rat,C: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right
% 0.29/0.56  thf(fact_3895_add__diff__cancel__right,axiom,
% 0.29/0.56      ! [A: nat,C: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right
% 0.29/0.56  thf(fact_3896_add__diff__cancel__right,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right
% 0.29/0.56  thf(fact_3897_add__diff__cancel__right_H,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right'
% 0.29/0.56  thf(fact_3898_add__diff__cancel__right_H,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right'
% 0.29/0.56  thf(fact_3899_add__diff__cancel__right_H,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right'
% 0.29/0.56  thf(fact_3900_add__diff__cancel__right_H,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.29/0.56        = A ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_cancel_right'
% 0.29/0.56  thf(fact_3901_minus__mod__self2,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.56        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minus_mod_self2
% 0.29/0.56  thf(fact_3902_minus__mod__self2,axiom,
% 0.29/0.56      ! [A: code_integer,B: code_integer] :
% 0.29/0.56        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.29/0.56        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % minus_mod_self2
% 0.29/0.56  thf(fact_3903_diff__Suc__Suc,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/0.56        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_Suc_Suc
% 0.29/0.56  thf(fact_3904_Suc__diff__diff,axiom,
% 0.29/0.56      ! [M: nat,N2: nat,K: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.29/0.56        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Suc_diff_diff
% 0.29/0.56  thf(fact_3905_diff__self__eq__0,axiom,
% 0.29/0.56      ! [M: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ M @ M )
% 0.29/0.56        = zero_zero_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_self_eq_0
% 0.29/0.56  thf(fact_3906_diff__0__eq__0,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 0.29/0.56        = zero_zero_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_0_eq_0
% 0.29/0.56  thf(fact_3907_diff__diff__cancel,axiom,
% 0.29/0.56      ! [I2: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ I2 @ N2 )
% 0.29/0.56       => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 0.29/0.56          = I2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_cancel
% 0.29/0.56  thf(fact_3908_diff__diff__left,axiom,
% 0.29/0.56      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 0.29/0.56        = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_left
% 0.29/0.56  thf(fact_3909_signed__take__bit__of__0,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 0.29/0.56        = zero_zero_int ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_of_0
% 0.29/0.56  thf(fact_3910_concat__bit__0,axiom,
% 0.29/0.56      ! [K: int,L: int] :
% 0.29/0.56        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 0.29/0.56        = L ) ).
% 0.29/0.56  
% 0.29/0.56  % concat_bit_0
% 0.29/0.56  thf(fact_3911_diff__ge__0__iff__ge,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.56        = ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_ge_0_iff_ge
% 0.29/0.56  thf(fact_3912_diff__ge__0__iff__ge,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.56        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_ge_0_iff_ge
% 0.29/0.56  thf(fact_3913_diff__ge__0__iff__ge,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.56        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_ge_0_iff_ge
% 0.29/0.56  thf(fact_3914_diff__gt__0__iff__gt,axiom,
% 0.29/0.56      ! [A: real,B: real] :
% 0.29/0.56        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.56        = ( ord_less_real @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_gt_0_iff_gt
% 0.29/0.56  thf(fact_3915_diff__gt__0__iff__gt,axiom,
% 0.29/0.56      ! [A: rat,B: rat] :
% 0.29/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.56        = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_gt_0_iff_gt
% 0.29/0.56  thf(fact_3916_diff__gt__0__iff__gt,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.56        = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_gt_0_iff_gt
% 0.29/0.56  thf(fact_3917_le__add__diff__inverse2,axiom,
% 0.29/0.56      ! [B: real,A: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.56       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse2
% 0.29/0.56  thf(fact_3918_le__add__diff__inverse2,axiom,
% 0.29/0.56      ! [B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.56       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse2
% 0.29/0.56  thf(fact_3919_le__add__diff__inverse2,axiom,
% 0.29/0.56      ! [B: nat,A: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.56       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse2
% 0.29/0.56  thf(fact_3920_le__add__diff__inverse2,axiom,
% 0.29/0.56      ! [B: int,A: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.56       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse2
% 0.29/0.56  thf(fact_3921_le__add__diff__inverse,axiom,
% 0.29/0.56      ! [B: real,A: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.56       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse
% 0.29/0.56  thf(fact_3922_le__add__diff__inverse,axiom,
% 0.29/0.56      ! [B: rat,A: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.56       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse
% 0.29/0.56  thf(fact_3923_le__add__diff__inverse,axiom,
% 0.29/0.56      ! [B: nat,A: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.56       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse
% 0.29/0.56  thf(fact_3924_le__add__diff__inverse,axiom,
% 0.29/0.56      ! [B: int,A: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.56       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.29/0.56          = A ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_add_diff_inverse
% 0.29/0.56  thf(fact_3925_diff__numeral__special_I9_J,axiom,
% 0.29/0.56      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.29/0.56      = zero_zero_complex ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_numeral_special(9)
% 0.29/0.56  thf(fact_3926_diff__numeral__special_I9_J,axiom,
% 0.29/0.56      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.29/0.56      = zero_zero_real ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_numeral_special(9)
% 0.29/0.56  thf(fact_3927_diff__numeral__special_I9_J,axiom,
% 0.29/0.56      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.56      = zero_zero_rat ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_numeral_special(9)
% 0.29/0.56  thf(fact_3928_diff__numeral__special_I9_J,axiom,
% 0.29/0.56      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.29/0.56      = zero_zero_int ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_numeral_special(9)
% 0.29/0.56  thf(fact_3929_diff__add__zero,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.56        = zero_zero_nat ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_zero
% 0.29/0.56  thf(fact_3930_right__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [V: num,B: rat,C: rat] :
% 0.29/0.56        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib_numeral
% 0.29/0.56  thf(fact_3931_right__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [V: num,B: complex,C: complex] :
% 0.29/0.56        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib_numeral
% 0.29/0.56  thf(fact_3932_right__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [V: num,B: real,C: real] :
% 0.29/0.56        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib_numeral
% 0.29/0.56  thf(fact_3933_right__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [V: num,B: int,C: int] :
% 0.29/0.56        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib_numeral
% 0.29/0.56  thf(fact_3934_left__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [A: rat,B: rat,V: num] :
% 0.29/0.56        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib_numeral
% 0.29/0.56  thf(fact_3935_left__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [A: complex,B: complex,V: num] :
% 0.29/0.56        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib_numeral
% 0.29/0.56  thf(fact_3936_left__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [A: real,B: real,V: num] :
% 0.29/0.56        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib_numeral
% 0.29/0.56  thf(fact_3937_left__diff__distrib__numeral,axiom,
% 0.29/0.56      ! [A: int,B: int,V: num] :
% 0.29/0.56        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib_numeral
% 0.29/0.56  thf(fact_3938_div__diff,axiom,
% 0.29/0.56      ! [C: int,A: int,B: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ C @ A )
% 0.29/0.56       => ( ( dvd_dvd_int @ C @ B )
% 0.29/0.56         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.56            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_diff
% 0.29/0.56  thf(fact_3939_div__diff,axiom,
% 0.29/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.29/0.56       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.29/0.56         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.56            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % div_diff
% 0.29/0.56  thf(fact_3940_zero__less__diff,axiom,
% 0.29/0.56      ! [N2: nat,M: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.56        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_less_diff
% 0.29/0.56  thf(fact_3941_diff__is__0__eq_H,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56       => ( ( minus_minus_nat @ M @ N2 )
% 0.29/0.56          = zero_zero_nat ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_is_0_eq'
% 0.29/0.56  thf(fact_3942_diff__is__0__eq,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( ( minus_minus_nat @ M @ N2 )
% 0.29/0.56          = zero_zero_nat )
% 0.29/0.56        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_is_0_eq
% 0.29/0.56  thf(fact_3943_of__bool__not__iff,axiom,
% 0.29/0.56      ! [P: $o] :
% 0.29/0.56        ( ( zero_n1201886186963655149omplex @ ~ P )
% 0.29/0.56        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % of_bool_not_iff
% 0.29/0.56  thf(fact_3944_of__bool__not__iff,axiom,
% 0.29/0.56      ! [P: $o] :
% 0.29/0.56        ( ( zero_n3304061248610475627l_real @ ~ P )
% 0.29/0.56        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % of_bool_not_iff
% 0.29/0.56  thf(fact_3945_of__bool__not__iff,axiom,
% 0.29/0.56      ! [P: $o] :
% 0.29/0.56        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.29/0.56        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % of_bool_not_iff
% 0.29/0.56  thf(fact_3946_of__bool__not__iff,axiom,
% 0.29/0.56      ! [P: $o] :
% 0.29/0.56        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.29/0.56        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % of_bool_not_iff
% 0.29/0.56  thf(fact_3947_of__bool__not__iff,axiom,
% 0.29/0.56      ! [P: $o] :
% 0.29/0.56        ( ( zero_n356916108424825756nteger @ ~ P )
% 0.29/0.56        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % of_bool_not_iff
% 0.29/0.56  thf(fact_3948_Nat_Odiff__diff__right,axiom,
% 0.29/0.56      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.56       => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Nat.diff_diff_right
% 0.29/0.56  thf(fact_3949_Nat_Oadd__diff__assoc2,axiom,
% 0.29/0.56      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.56       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Nat.add_diff_assoc2
% 0.29/0.56  thf(fact_3950_Nat_Oadd__diff__assoc,axiom,
% 0.29/0.56      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.56       => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Nat.add_diff_assoc
% 0.29/0.56  thf(fact_3951_diff__Suc__1,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.29/0.56        = N2 ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_Suc_1
% 0.29/0.56  thf(fact_3952_signed__take__bit__Suc__1,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 0.29/0.56        = one_one_int ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_Suc_1
% 0.29/0.56  thf(fact_3953_signed__take__bit__numeral__of__1,axiom,
% 0.29/0.56      ! [K: num] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.29/0.56        = one_one_int ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_numeral_of_1
% 0.29/0.56  thf(fact_3954_concat__bit__nonnegative__iff,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 0.29/0.56        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 0.29/0.56  
% 0.29/0.56  % concat_bit_nonnegative_iff
% 0.29/0.56  thf(fact_3955_concat__bit__negative__iff,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 0.29/0.56        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 0.29/0.56  
% 0.29/0.56  % concat_bit_negative_iff
% 0.29/0.56  thf(fact_3956_Suc__pred,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.56       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.56          = N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Suc_pred
% 0.29/0.56  thf(fact_3957_diff__Suc__diff__eq2,axiom,
% 0.29/0.56      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.56       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 0.29/0.56          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_Suc_diff_eq2
% 0.29/0.56  thf(fact_3958_diff__Suc__diff__eq1,axiom,
% 0.29/0.56      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.56       => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_Suc_diff_eq1
% 0.29/0.56  thf(fact_3959_zle__diff1__eq,axiom,
% 0.29/0.56      ! [W: int,Z: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.29/0.56        = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.56  
% 0.29/0.56  % zle_diff1_eq
% 0.29/0.56  thf(fact_3960_signed__take__bit__Suc__bit0,axiom,
% 0.29/0.56      ! [N2: nat,K: num] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.29/0.56        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_Suc_bit0
% 0.29/0.56  thf(fact_3961_Suc__diff__1,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.56       => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.29/0.56          = N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Suc_diff_1
% 0.29/0.56  thf(fact_3962_even__diff,axiom,
% 0.29/0.56      ! [A: code_integer,B: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.56        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_diff
% 0.29/0.56  thf(fact_3963_even__diff,axiom,
% 0.29/0.56      ! [A: int,B: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.29/0.56        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_diff
% 0.29/0.56  thf(fact_3964_odd__Suc__minus__one,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.56       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.56          = N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % odd_Suc_minus_one
% 0.29/0.56  thf(fact_3965_even__diff__nat,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.56        = ( ( ord_less_nat @ M @ N2 )
% 0.29/0.56          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % even_diff_nat
% 0.29/0.56  thf(fact_3966_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 0.29/0.56        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.56  
% 0.29/0.56  % semiring_parity_class.even_mask_iff
% 0.29/0.56  thf(fact_3967_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 0.29/0.56        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.56  
% 0.29/0.56  % semiring_parity_class.even_mask_iff
% 0.29/0.56  thf(fact_3968_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 0.29/0.56        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.56  
% 0.29/0.56  % semiring_parity_class.even_mask_iff
% 0.29/0.56  thf(fact_3969_odd__two__times__div__two__nat,axiom,
% 0.29/0.56      ! [N2: nat] :
% 0.29/0.56        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.56       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.56          = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % odd_two_times_div_two_nat
% 0.29/0.56  thf(fact_3970_diff__right__commute,axiom,
% 0.29/0.56      ! [A: real,C: real,B: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.29/0.56        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_commute
% 0.29/0.56  thf(fact_3971_diff__right__commute,axiom,
% 0.29/0.56      ! [A: rat,C: rat,B: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.29/0.56        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_commute
% 0.29/0.56  thf(fact_3972_diff__right__commute,axiom,
% 0.29/0.56      ! [A: nat,C: nat,B: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/0.56        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_commute
% 0.29/0.56  thf(fact_3973_diff__right__commute,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.29/0.56        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_commute
% 0.29/0.56  thf(fact_3974_diff__eq__diff__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.56        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.56          = ( minus_minus_real @ C @ D ) )
% 0.29/0.56       => ( ( A = B )
% 0.29/0.56          = ( C = D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_eq
% 0.29/0.56  thf(fact_3975_diff__eq__diff__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.56        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.56          = ( minus_minus_rat @ C @ D ) )
% 0.29/0.56       => ( ( A = B )
% 0.29/0.56          = ( C = D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_eq
% 0.29/0.56  thf(fact_3976_diff__eq__diff__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.56        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.56          = ( minus_minus_int @ C @ D ) )
% 0.29/0.56       => ( ( A = B )
% 0.29/0.56          = ( C = D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_eq
% 0.29/0.56  thf(fact_3977_signed__take__bit__diff,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 0.29/0.56        = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_diff
% 0.29/0.56  thf(fact_3978_diff__commute,axiom,
% 0.29/0.56      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 0.29/0.56        = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_commute
% 0.29/0.56  thf(fact_3979_diff__mono,axiom,
% 0.29/0.56      ! [A: real,B: real,D: real,C: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.56       => ( ( ord_less_eq_real @ D @ C )
% 0.29/0.56         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_mono
% 0.29/0.56  thf(fact_3980_diff__mono,axiom,
% 0.29/0.56      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.56       => ( ( ord_less_eq_rat @ D @ C )
% 0.29/0.56         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_mono
% 0.29/0.56  thf(fact_3981_diff__mono,axiom,
% 0.29/0.56      ! [A: int,B: int,D: int,C: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.56       => ( ( ord_less_eq_int @ D @ C )
% 0.29/0.56         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_mono
% 0.29/0.56  thf(fact_3982_diff__left__mono,axiom,
% 0.29/0.56      ! [B: real,A: real,C: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.56       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_left_mono
% 0.29/0.56  thf(fact_3983_diff__left__mono,axiom,
% 0.29/0.56      ! [B: rat,A: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.56       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_left_mono
% 0.29/0.56  thf(fact_3984_diff__left__mono,axiom,
% 0.29/0.56      ! [B: int,A: int,C: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.56       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_left_mono
% 0.29/0.56  thf(fact_3985_diff__right__mono,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.56       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_mono
% 0.29/0.56  thf(fact_3986_diff__right__mono,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.56       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_mono
% 0.29/0.56  thf(fact_3987_diff__right__mono,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.56       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_right_mono
% 0.29/0.56  thf(fact_3988_diff__eq__diff__less__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.56        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.56          = ( minus_minus_real @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.56          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less_eq
% 0.29/0.56  thf(fact_3989_diff__eq__diff__less__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.56        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.56          = ( minus_minus_rat @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.56          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less_eq
% 0.29/0.56  thf(fact_3990_diff__eq__diff__less__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.56        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.56          = ( minus_minus_int @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.56          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less_eq
% 0.29/0.56  thf(fact_3991_eq__iff__diff__eq__0,axiom,
% 0.29/0.56      ( ( ^ [Y6: complex,Z4: complex] : ( Y6 = Z4 ) )
% 0.29/0.56      = ( ^ [A3: complex,B2: complex] :
% 0.29/0.56            ( ( minus_minus_complex @ A3 @ B2 )
% 0.29/0.56            = zero_zero_complex ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_iff_diff_eq_0
% 0.29/0.56  thf(fact_3992_eq__iff__diff__eq__0,axiom,
% 0.29/0.56      ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 0.29/0.56      = ( ^ [A3: real,B2: real] :
% 0.29/0.56            ( ( minus_minus_real @ A3 @ B2 )
% 0.29/0.56            = zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_iff_diff_eq_0
% 0.29/0.56  thf(fact_3993_eq__iff__diff__eq__0,axiom,
% 0.29/0.56      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.56      = ( ^ [A3: rat,B2: rat] :
% 0.29/0.56            ( ( minus_minus_rat @ A3 @ B2 )
% 0.29/0.56            = zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_iff_diff_eq_0
% 0.29/0.56  thf(fact_3994_eq__iff__diff__eq__0,axiom,
% 0.29/0.56      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.56      = ( ^ [A3: int,B2: int] :
% 0.29/0.56            ( ( minus_minus_int @ A3 @ B2 )
% 0.29/0.56            = zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_iff_diff_eq_0
% 0.29/0.56  thf(fact_3995_diff__strict__mono,axiom,
% 0.29/0.56      ! [A: real,B: real,D: real,C: real] :
% 0.29/0.56        ( ( ord_less_real @ A @ B )
% 0.29/0.56       => ( ( ord_less_real @ D @ C )
% 0.29/0.56         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_mono
% 0.29/0.56  thf(fact_3996_diff__strict__mono,axiom,
% 0.29/0.56      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.29/0.56        ( ( ord_less_rat @ A @ B )
% 0.29/0.56       => ( ( ord_less_rat @ D @ C )
% 0.29/0.56         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_mono
% 0.29/0.56  thf(fact_3997_diff__strict__mono,axiom,
% 0.29/0.56      ! [A: int,B: int,D: int,C: int] :
% 0.29/0.56        ( ( ord_less_int @ A @ B )
% 0.29/0.56       => ( ( ord_less_int @ D @ C )
% 0.29/0.56         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_mono
% 0.29/0.56  thf(fact_3998_diff__eq__diff__less,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.56        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.56          = ( minus_minus_real @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_real @ A @ B )
% 0.29/0.56          = ( ord_less_real @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less
% 0.29/0.56  thf(fact_3999_diff__eq__diff__less,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.56        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.56          = ( minus_minus_rat @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_rat @ A @ B )
% 0.29/0.56          = ( ord_less_rat @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less
% 0.29/0.56  thf(fact_4000_diff__eq__diff__less,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.56        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.56          = ( minus_minus_int @ C @ D ) )
% 0.29/0.56       => ( ( ord_less_int @ A @ B )
% 0.29/0.56          = ( ord_less_int @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_diff_less
% 0.29/0.56  thf(fact_4001_diff__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 @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_left_mono
% 0.29/0.56  thf(fact_4002_diff__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 @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_left_mono
% 0.29/0.56  thf(fact_4003_diff__strict__left__mono,axiom,
% 0.29/0.56      ! [B: int,A: int,C: int] :
% 0.29/0.56        ( ( ord_less_int @ B @ A )
% 0.29/0.56       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_left_mono
% 0.29/0.56  thf(fact_4004_diff__strict__right__mono,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 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_right_mono
% 0.29/0.56  thf(fact_4005_diff__strict__right__mono,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 @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_right_mono
% 0.29/0.56  thf(fact_4006_diff__strict__right__mono,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( ord_less_int @ A @ B )
% 0.29/0.56       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_strict_right_mono
% 0.29/0.56  thf(fact_4007_right__diff__distrib_H,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib'
% 0.29/0.56  thf(fact_4008_right__diff__distrib_H,axiom,
% 0.29/0.56      ! [A: complex,B: complex,C: complex] :
% 0.29/0.56        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib'
% 0.29/0.56  thf(fact_4009_right__diff__distrib_H,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib'
% 0.29/0.56  thf(fact_4010_right__diff__distrib_H,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib'
% 0.29/0.56  thf(fact_4011_right__diff__distrib_H,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib'
% 0.29/0.56  thf(fact_4012_left__diff__distrib_H,axiom,
% 0.29/0.56      ! [B: rat,C: rat,A: rat] :
% 0.29/0.56        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib'
% 0.29/0.56  thf(fact_4013_left__diff__distrib_H,axiom,
% 0.29/0.56      ! [B: complex,C: complex,A: complex] :
% 0.29/0.56        ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib'
% 0.29/0.56  thf(fact_4014_left__diff__distrib_H,axiom,
% 0.29/0.56      ! [B: real,C: real,A: real] :
% 0.29/0.56        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib'
% 0.29/0.56  thf(fact_4015_left__diff__distrib_H,axiom,
% 0.29/0.56      ! [B: nat,C: nat,A: nat] :
% 0.29/0.56        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.29/0.56        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib'
% 0.29/0.56  thf(fact_4016_left__diff__distrib_H,axiom,
% 0.29/0.56      ! [B: int,C: int,A: int] :
% 0.29/0.56        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib'
% 0.29/0.56  thf(fact_4017_right__diff__distrib,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib
% 0.29/0.56  thf(fact_4018_right__diff__distrib,axiom,
% 0.29/0.56      ! [A: complex,B: complex,C: complex] :
% 0.29/0.56        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib
% 0.29/0.56  thf(fact_4019_right__diff__distrib,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib
% 0.29/0.56  thf(fact_4020_right__diff__distrib,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % right_diff_distrib
% 0.29/0.56  thf(fact_4021_left__diff__distrib,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib
% 0.29/0.56  thf(fact_4022_left__diff__distrib,axiom,
% 0.29/0.56      ! [A: complex,B: complex,C: complex] :
% 0.29/0.56        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib
% 0.29/0.56  thf(fact_4023_left__diff__distrib,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib
% 0.29/0.56  thf(fact_4024_left__diff__distrib,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % left_diff_distrib
% 0.29/0.56  thf(fact_4025_add__diff__add,axiom,
% 0.29/0.56      ! [A: real,C: real,B: real,D: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 0.29/0.56        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_add
% 0.29/0.56  thf(fact_4026_add__diff__add,axiom,
% 0.29/0.56      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 0.29/0.56        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_add
% 0.29/0.56  thf(fact_4027_add__diff__add,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int,D: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 0.29/0.56        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_add
% 0.29/0.56  thf(fact_4028_group__cancel_Osub1,axiom,
% 0.29/0.56      ! [A2: real,K: real,A: real,B: real] :
% 0.29/0.56        ( ( A2
% 0.29/0.56          = ( plus_plus_real @ K @ A ) )
% 0.29/0.56       => ( ( minus_minus_real @ A2 @ B )
% 0.29/0.56          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % group_cancel.sub1
% 0.29/0.56  thf(fact_4029_group__cancel_Osub1,axiom,
% 0.29/0.56      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.29/0.56        ( ( A2
% 0.29/0.56          = ( plus_plus_rat @ K @ A ) )
% 0.29/0.56       => ( ( minus_minus_rat @ A2 @ B )
% 0.29/0.56          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % group_cancel.sub1
% 0.29/0.56  thf(fact_4030_group__cancel_Osub1,axiom,
% 0.29/0.56      ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.56        ( ( A2
% 0.29/0.56          = ( plus_plus_int @ K @ A ) )
% 0.29/0.56       => ( ( minus_minus_int @ A2 @ B )
% 0.29/0.56          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % group_cancel.sub1
% 0.29/0.56  thf(fact_4031_diff__eq__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( ( minus_minus_real @ A @ B )
% 0.29/0.56          = C )
% 0.29/0.56        = ( A
% 0.29/0.56          = ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_eq
% 0.29/0.56  thf(fact_4032_diff__eq__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.56          = C )
% 0.29/0.56        = ( A
% 0.29/0.56          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_eq
% 0.29/0.56  thf(fact_4033_diff__eq__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.56          = C )
% 0.29/0.56        = ( A
% 0.29/0.56          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_eq_eq
% 0.29/0.56  thf(fact_4034_eq__diff__eq,axiom,
% 0.29/0.56      ! [A: real,C: real,B: real] :
% 0.29/0.56        ( ( A
% 0.29/0.56          = ( minus_minus_real @ C @ B ) )
% 0.29/0.56        = ( ( plus_plus_real @ A @ B )
% 0.29/0.56          = C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_diff_eq
% 0.29/0.56  thf(fact_4035_eq__diff__eq,axiom,
% 0.29/0.56      ! [A: rat,C: rat,B: rat] :
% 0.29/0.56        ( ( A
% 0.29/0.56          = ( minus_minus_rat @ C @ B ) )
% 0.29/0.56        = ( ( plus_plus_rat @ A @ B )
% 0.29/0.56          = C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_diff_eq
% 0.29/0.56  thf(fact_4036_eq__diff__eq,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( A
% 0.29/0.56          = ( minus_minus_int @ C @ B ) )
% 0.29/0.56        = ( ( plus_plus_int @ A @ B )
% 0.29/0.56          = C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_diff_eq
% 0.29/0.56  thf(fact_4037_add__diff__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_eq
% 0.29/0.56  thf(fact_4038_add__diff__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_eq
% 0.29/0.56  thf(fact_4039_add__diff__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_diff_eq
% 0.29/0.56  thf(fact_4040_diff__diff__eq2,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq2
% 0.29/0.56  thf(fact_4041_diff__diff__eq2,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq2
% 0.29/0.56  thf(fact_4042_diff__diff__eq2,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq2
% 0.29/0.56  thf(fact_4043_diff__add__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq
% 0.29/0.56  thf(fact_4044_diff__add__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq
% 0.29/0.56  thf(fact_4045_diff__add__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq
% 0.29/0.56  thf(fact_4046_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.56        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq_diff_diff_swap
% 0.29/0.56  thf(fact_4047_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.29/0.56        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq_diff_diff_swap
% 0.29/0.56  thf(fact_4048_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.29/0.56        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_eq_diff_diff_swap
% 0.29/0.56  thf(fact_4049_add__implies__diff,axiom,
% 0.29/0.56      ! [C: real,B: real,A: real] :
% 0.29/0.56        ( ( ( plus_plus_real @ C @ B )
% 0.29/0.56          = A )
% 0.29/0.56       => ( C
% 0.29/0.56          = ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_implies_diff
% 0.29/0.56  thf(fact_4050_add__implies__diff,axiom,
% 0.29/0.56      ! [C: rat,B: rat,A: rat] :
% 0.29/0.56        ( ( ( plus_plus_rat @ C @ B )
% 0.29/0.56          = A )
% 0.29/0.56       => ( C
% 0.29/0.56          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_implies_diff
% 0.29/0.56  thf(fact_4051_add__implies__diff,axiom,
% 0.29/0.56      ! [C: nat,B: nat,A: nat] :
% 0.29/0.56        ( ( ( plus_plus_nat @ C @ B )
% 0.29/0.56          = A )
% 0.29/0.56       => ( C
% 0.29/0.56          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_implies_diff
% 0.29/0.56  thf(fact_4052_add__implies__diff,axiom,
% 0.29/0.56      ! [C: int,B: int,A: int] :
% 0.29/0.56        ( ( ( plus_plus_int @ C @ B )
% 0.29/0.56          = A )
% 0.29/0.56       => ( C
% 0.29/0.56          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % add_implies_diff
% 0.29/0.56  thf(fact_4053_diff__diff__eq,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq
% 0.29/0.56  thf(fact_4054_diff__diff__eq,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq
% 0.29/0.56  thf(fact_4055_diff__diff__eq,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq
% 0.29/0.56  thf(fact_4056_diff__diff__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_diff_eq
% 0.29/0.56  thf(fact_4057_diff__divide__distrib,axiom,
% 0.29/0.56      ! [A: rat,B: rat,C: rat] :
% 0.29/0.56        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_distrib
% 0.29/0.56  thf(fact_4058_diff__divide__distrib,axiom,
% 0.29/0.56      ! [A: real,B: real,C: real] :
% 0.29/0.56        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_distrib
% 0.29/0.56  thf(fact_4059_diff__divide__distrib,axiom,
% 0.29/0.56      ! [A: complex,B: complex,C: complex] :
% 0.29/0.56        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.29/0.56        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_divide_distrib
% 0.29/0.56  thf(fact_4060_dvd__diff,axiom,
% 0.29/0.56      ! [X4: code_integer,Y: code_integer,Z: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 0.29/0.56       => ( ( dvd_dvd_Code_integer @ X4 @ Z )
% 0.29/0.56         => ( dvd_dvd_Code_integer @ X4 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff
% 0.29/0.56  thf(fact_4061_dvd__diff,axiom,
% 0.29/0.56      ! [X4: real,Y: real,Z: real] :
% 0.29/0.56        ( ( dvd_dvd_real @ X4 @ Y )
% 0.29/0.56       => ( ( dvd_dvd_real @ X4 @ Z )
% 0.29/0.56         => ( dvd_dvd_real @ X4 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff
% 0.29/0.56  thf(fact_4062_dvd__diff,axiom,
% 0.29/0.56      ! [X4: rat,Y: rat,Z: rat] :
% 0.29/0.56        ( ( dvd_dvd_rat @ X4 @ Y )
% 0.29/0.56       => ( ( dvd_dvd_rat @ X4 @ Z )
% 0.29/0.56         => ( dvd_dvd_rat @ X4 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff
% 0.29/0.56  thf(fact_4063_dvd__diff,axiom,
% 0.29/0.56      ! [X4: int,Y: int,Z: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ X4 @ Y )
% 0.29/0.56       => ( ( dvd_dvd_int @ X4 @ Z )
% 0.29/0.56         => ( dvd_dvd_int @ X4 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff
% 0.29/0.56  thf(fact_4064_dvd__diff__commute,axiom,
% 0.29/0.56      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.56        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.29/0.56        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff_commute
% 0.29/0.56  thf(fact_4065_dvd__diff__commute,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.29/0.56        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff_commute
% 0.29/0.56  thf(fact_4066_zero__induct__lemma,axiom,
% 0.29/0.56      ! [P: nat > $o,K: nat,I2: nat] :
% 0.29/0.56        ( ( P @ K )
% 0.29/0.56       => ( ! [N3: nat] :
% 0.29/0.56              ( ( P @ ( suc @ N3 ) )
% 0.29/0.56             => ( P @ N3 ) )
% 0.29/0.56         => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % zero_induct_lemma
% 0.29/0.56  thf(fact_4067_diffs0__imp__equal,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( ( minus_minus_nat @ M @ N2 )
% 0.29/0.56          = zero_zero_nat )
% 0.29/0.56       => ( ( ( minus_minus_nat @ N2 @ M )
% 0.29/0.56            = zero_zero_nat )
% 0.29/0.56         => ( M = N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diffs0_imp_equal
% 0.29/0.56  thf(fact_4068_minus__nat_Odiff__0,axiom,
% 0.29/0.56      ! [M: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/0.56        = M ) ).
% 0.29/0.56  
% 0.29/0.56  % minus_nat.diff_0
% 0.29/0.56  thf(fact_4069_mod__diff__right__eq,axiom,
% 0.29/0.56      ! [A: int,B: int,C: int] :
% 0.29/0.56        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.29/0.56        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_right_eq
% 0.29/0.56  thf(fact_4070_mod__diff__right__eq,axiom,
% 0.29/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.56        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.29/0.56        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_right_eq
% 0.29/0.56  thf(fact_4071_mod__diff__left__eq,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.29/0.56        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_left_eq
% 0.29/0.56  thf(fact_4072_mod__diff__left__eq,axiom,
% 0.29/0.56      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.56        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.29/0.56        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_left_eq
% 0.29/0.56  thf(fact_4073_mod__diff__cong,axiom,
% 0.29/0.56      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.29/0.56        ( ( ( modulo_modulo_int @ A @ C )
% 0.29/0.56          = ( modulo_modulo_int @ A4 @ C ) )
% 0.29/0.56       => ( ( ( modulo_modulo_int @ B @ C )
% 0.29/0.56            = ( modulo_modulo_int @ B4 @ C ) )
% 0.29/0.56         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.56            = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_cong
% 0.29/0.56  thf(fact_4074_mod__diff__cong,axiom,
% 0.29/0.56      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.29/0.56        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.29/0.56          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.29/0.56       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.29/0.56            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.29/0.56         => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.56            = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_cong
% 0.29/0.56  thf(fact_4075_mod__diff__eq,axiom,
% 0.29/0.56      ! [A: int,C: int,B: int] :
% 0.29/0.56        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.29/0.56        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_eq
% 0.29/0.56  thf(fact_4076_mod__diff__eq,axiom,
% 0.29/0.56      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.56        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.29/0.56        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.29/0.56  
% 0.29/0.56  % mod_diff_eq
% 0.29/0.56  thf(fact_4077_diff__less__mono2,axiom,
% 0.29/0.56      ! [M: nat,N2: nat,L: nat] :
% 0.29/0.56        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.56       => ( ( ord_less_nat @ M @ L )
% 0.29/0.56         => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_less_mono2
% 0.29/0.56  thf(fact_4078_less__imp__diff__less,axiom,
% 0.29/0.56      ! [J: nat,K: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_nat @ J @ K )
% 0.29/0.56       => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_imp_diff_less
% 0.29/0.56  thf(fact_4079_signed__take__bit__mult,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 0.29/0.56        = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_mult
% 0.29/0.56  thf(fact_4080_eq__diff__iff,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.56       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.56         => ( ( ( minus_minus_nat @ M @ K )
% 0.29/0.56              = ( minus_minus_nat @ N2 @ K ) )
% 0.29/0.56            = ( M = N2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % eq_diff_iff
% 0.29/0.56  thf(fact_4081_le__diff__iff,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.56       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.56         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/0.56            = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_diff_iff
% 0.29/0.56  thf(fact_4082_Nat_Odiff__diff__eq,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.56       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.56         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/0.56            = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Nat.diff_diff_eq
% 0.29/0.56  thf(fact_4083_diff__le__mono,axiom,
% 0.29/0.56      ! [M: nat,N2: nat,L: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_le_mono
% 0.29/0.56  thf(fact_4084_diff__le__self,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_le_self
% 0.29/0.56  thf(fact_4085_le__diff__iff_H,axiom,
% 0.29/0.56      ! [A: nat,C: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.56       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.56         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.29/0.56            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_diff_iff'
% 0.29/0.56  thf(fact_4086_diff__le__mono2,axiom,
% 0.29/0.56      ! [M: nat,N2: nat,L: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.56       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_le_mono2
% 0.29/0.56  thf(fact_4087_signed__take__bit__add,axiom,
% 0.29/0.56      ! [N2: nat,K: int,L: int] :
% 0.29/0.56        ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 0.29/0.56        = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % signed_take_bit_add
% 0.29/0.56  thf(fact_4088_Nat_Odiff__cancel,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 0.29/0.56        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % Nat.diff_cancel
% 0.29/0.56  thf(fact_4089_diff__cancel2,axiom,
% 0.29/0.56      ! [M: nat,K: nat,N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.56        = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_cancel2
% 0.29/0.56  thf(fact_4090_diff__add__inverse,axiom,
% 0.29/0.56      ! [N2: nat,M: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 0.29/0.56        = M ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_inverse
% 0.29/0.56  thf(fact_4091_diff__add__inverse2,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 0.29/0.56        = M ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_add_inverse2
% 0.29/0.56  thf(fact_4092_diff__mult__distrib,axiom,
% 0.29/0.56      ! [M: nat,N2: nat,K: nat] :
% 0.29/0.56        ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 0.29/0.56        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_mult_distrib
% 0.29/0.56  thf(fact_4093_diff__mult__distrib2,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.56        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % diff_mult_distrib2
% 0.29/0.56  thf(fact_4094_dvd__diff__nat,axiom,
% 0.29/0.56      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.56        ( ( dvd_dvd_nat @ K @ M )
% 0.29/0.56       => ( ( dvd_dvd_nat @ K @ N2 )
% 0.29/0.56         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % dvd_diff_nat
% 0.29/0.56  thf(fact_4095_concat__bit__assoc,axiom,
% 0.29/0.56      ! [N2: nat,K: int,M: nat,L: int,R3: int] :
% 0.29/0.56        ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L @ R3 ) )
% 0.29/0.56        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % concat_bit_assoc
% 0.29/0.56  thf(fact_4096_subset__decode__imp__le,axiom,
% 0.29/0.56      ! [M: nat,N2: nat] :
% 0.29/0.56        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 0.29/0.56       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.56  
% 0.29/0.56  % subset_decode_imp_le
% 0.29/0.56  thf(fact_4097_le__iff__diff__le__0,axiom,
% 0.29/0.56      ( ord_less_eq_real
% 0.29/0.56      = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_iff_diff_le_0
% 0.29/0.56  thf(fact_4098_le__iff__diff__le__0,axiom,
% 0.29/0.56      ( ord_less_eq_rat
% 0.29/0.56      = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_iff_diff_le_0
% 0.29/0.56  thf(fact_4099_le__iff__diff__le__0,axiom,
% 0.29/0.56      ( ord_less_eq_int
% 0.29/0.56      = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % le_iff_diff_le_0
% 0.29/0.56  thf(fact_4100_less__iff__diff__less__0,axiom,
% 0.29/0.56      ( ord_less_real
% 0.29/0.56      = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_iff_diff_less_0
% 0.29/0.56  thf(fact_4101_less__iff__diff__less__0,axiom,
% 0.29/0.56      ( ord_less_rat
% 0.29/0.56      = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_iff_diff_less_0
% 0.29/0.56  thf(fact_4102_less__iff__diff__less__0,axiom,
% 0.29/0.56      ( ord_less_int
% 0.29/0.56      = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % less_iff_diff_less_0
% 0.29/0.56  thf(fact_4103_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56         => ( ( ( minus_minus_nat @ B @ A )
% 0.29/0.56              = C )
% 0.29/0.56            = ( B
% 0.29/0.56              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.29/0.56  thf(fact_4104_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.29/0.56      ! [A: nat,B: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.56          = B ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.29/0.56  thf(fact_4105_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.29/0.56  thf(fact_4106_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.29/0.56          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.29/0.56  thf(fact_4107_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.29/0.56      ! [A: nat,B: nat,C: nat] :
% 0.29/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.56       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.29/0.56          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.56  
% 0.29/0.56  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.29/0.56  thf(fact_4108_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.29/0.57          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.29/0.57  thf(fact_4109_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.57       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.57          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.29/0.57  thf(fact_4110_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.57       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.57          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.29/0.57  thf(fact_4111_le__add__diff,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.57       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_add_diff
% 0.29/0.57  thf(fact_4112_add__le__add__imp__diff__le,axiom,
% 0.29/0.57      ! [I2: real,K: real,N2: real,J: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 0.29/0.57         => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 0.29/0.57           => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 0.29/0.57             => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_add_imp_diff_le
% 0.29/0.57  thf(fact_4113_add__le__add__imp__diff__le,axiom,
% 0.29/0.57      ! [I2: rat,K: rat,N2: rat,J: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.29/0.57         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 0.29/0.57           => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 0.29/0.57             => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_add_imp_diff_le
% 0.29/0.57  thf(fact_4114_add__le__add__imp__diff__le,axiom,
% 0.29/0.57      ! [I2: nat,K: nat,N2: nat,J: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.57         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 0.29/0.57           => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.57             => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_add_imp_diff_le
% 0.29/0.57  thf(fact_4115_add__le__add__imp__diff__le,axiom,
% 0.29/0.57      ! [I2: int,K: int,N2: int,J: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.29/0.57         => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 0.29/0.57           => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 0.29/0.57             => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_add_imp_diff_le
% 0.29/0.57  thf(fact_4116_diff__add,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.57       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.29/0.57          = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_add
% 0.29/0.57  thf(fact_4117_add__le__imp__le__diff,axiom,
% 0.29/0.57      ! [I2: real,K: real,N2: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_imp_le_diff
% 0.29/0.57  thf(fact_4118_add__le__imp__le__diff,axiom,
% 0.29/0.57      ! [I2: rat,K: rat,N2: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_imp_le_diff
% 0.29/0.57  thf(fact_4119_add__le__imp__le__diff,axiom,
% 0.29/0.57      ! [I2: nat,K: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_imp_le_diff
% 0.29/0.57  thf(fact_4120_add__le__imp__le__diff,axiom,
% 0.29/0.57      ! [I2: int,K: int,N2: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 0.29/0.57       => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_le_imp_le_diff
% 0.29/0.57  thf(fact_4121_le__diff__eq,axiom,
% 0.29/0.57      ! [A: real,C: real,B: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.29/0.57        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_diff_eq
% 0.29/0.57  thf(fact_4122_le__diff__eq,axiom,
% 0.29/0.57      ! [A: rat,C: rat,B: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.29/0.57        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_diff_eq
% 0.29/0.57  thf(fact_4123_le__diff__eq,axiom,
% 0.29/0.57      ! [A: int,C: int,B: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.29/0.57        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_diff_eq
% 0.29/0.57  thf(fact_4124_diff__le__eq,axiom,
% 0.29/0.57      ! [A: real,B: real,C: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_le_eq
% 0.29/0.57  thf(fact_4125_diff__le__eq,axiom,
% 0.29/0.57      ! [A: rat,B: rat,C: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_le_eq
% 0.29/0.57  thf(fact_4126_diff__le__eq,axiom,
% 0.29/0.57      ! [A: int,B: int,C: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_le_eq
% 0.29/0.57  thf(fact_4127_diff__less__eq,axiom,
% 0.29/0.57      ! [A: real,B: real,C: real] :
% 0.29/0.57        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less_eq
% 0.29/0.57  thf(fact_4128_diff__less__eq,axiom,
% 0.29/0.57      ! [A: rat,B: rat,C: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less_eq
% 0.29/0.57  thf(fact_4129_diff__less__eq,axiom,
% 0.29/0.57      ! [A: int,B: int,C: int] :
% 0.29/0.57        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.57        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less_eq
% 0.29/0.57  thf(fact_4130_less__diff__eq,axiom,
% 0.29/0.57      ! [A: real,C: real,B: real] :
% 0.29/0.57        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.29/0.57        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_eq
% 0.29/0.57  thf(fact_4131_less__diff__eq,axiom,
% 0.29/0.57      ! [A: rat,C: rat,B: rat] :
% 0.29/0.57        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.29/0.57        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_eq
% 0.29/0.57  thf(fact_4132_less__diff__eq,axiom,
% 0.29/0.57      ! [A: int,C: int,B: int] :
% 0.29/0.57        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.29/0.57        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_eq
% 0.29/0.57  thf(fact_4133_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ~ ( ord_less_real @ A @ B )
% 0.29/0.57       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.29/0.57          = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % linordered_semidom_class.add_diff_inverse
% 0.29/0.57  thf(fact_4134_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ~ ( ord_less_rat @ A @ B )
% 0.29/0.57       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.57          = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % linordered_semidom_class.add_diff_inverse
% 0.29/0.57  thf(fact_4135_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ~ ( ord_less_nat @ A @ B )
% 0.29/0.57       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.57          = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % linordered_semidom_class.add_diff_inverse
% 0.29/0.57  thf(fact_4136_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ~ ( ord_less_int @ A @ B )
% 0.29/0.57       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.29/0.57          = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % linordered_semidom_class.add_diff_inverse
% 0.29/0.57  thf(fact_4137_square__diff__square__factored,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat] :
% 0.29/0.57        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 0.29/0.57        = ( times_times_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_rat @ X4 @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_square_factored
% 0.29/0.57  thf(fact_4138_square__diff__square__factored,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex] :
% 0.29/0.57        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ ( times_times_complex @ Y @ Y ) )
% 0.29/0.57        = ( times_times_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_complex @ X4 @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_square_factored
% 0.29/0.57  thf(fact_4139_square__diff__square__factored,axiom,
% 0.29/0.57      ! [X4: real,Y: real] :
% 0.29/0.57        ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 0.29/0.57        = ( times_times_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ X4 @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_square_factored
% 0.29/0.57  thf(fact_4140_square__diff__square__factored,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 0.29/0.57        = ( times_times_int @ ( plus_plus_int @ X4 @ Y ) @ ( minus_minus_int @ X4 @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_square_factored
% 0.29/0.57  thf(fact_4141_eq__add__iff2,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( C
% 0.29/0.57          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff2
% 0.29/0.57  thf(fact_4142_eq__add__iff2,axiom,
% 0.29/0.57      ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 0.29/0.57        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( C
% 0.29/0.57          = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff2
% 0.29/0.57  thf(fact_4143_eq__add__iff2,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( C
% 0.29/0.57          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff2
% 0.29/0.57  thf(fact_4144_eq__add__iff2,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( C
% 0.29/0.57          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff2
% 0.29/0.57  thf(fact_4145_eq__add__iff1,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 0.29/0.57          = D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff1
% 0.29/0.57  thf(fact_4146_eq__add__iff1,axiom,
% 0.29/0.57      ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 0.29/0.57        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E2 ) @ C )
% 0.29/0.57          = D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff1
% 0.29/0.57  thf(fact_4147_eq__add__iff1,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 0.29/0.57          = D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff1
% 0.29/0.57  thf(fact_4148_eq__add__iff1,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.29/0.57          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 0.29/0.57          = D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % eq_add_iff1
% 0.29/0.57  thf(fact_4149_mult__diff__mult,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat,A: rat,B: rat] :
% 0.29/0.57        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ Y ) @ ( times_times_rat @ A @ B ) )
% 0.29/0.57        = ( plus_plus_rat @ ( times_times_rat @ X4 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X4 @ A ) @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_diff_mult
% 0.29/0.57  thf(fact_4150_mult__diff__mult,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex,A: complex,B: complex] :
% 0.29/0.57        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ Y ) @ ( times_times_complex @ A @ B ) )
% 0.29/0.57        = ( plus_plus_complex @ ( times_times_complex @ X4 @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X4 @ A ) @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_diff_mult
% 0.29/0.57  thf(fact_4151_mult__diff__mult,axiom,
% 0.29/0.57      ! [X4: real,Y: real,A: real,B: real] :
% 0.29/0.57        ( ( minus_minus_real @ ( times_times_real @ X4 @ Y ) @ ( times_times_real @ A @ B ) )
% 0.29/0.57        = ( plus_plus_real @ ( times_times_real @ X4 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X4 @ A ) @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_diff_mult
% 0.29/0.57  thf(fact_4152_mult__diff__mult,axiom,
% 0.29/0.57      ! [X4: int,Y: int,A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ ( times_times_int @ X4 @ Y ) @ ( times_times_int @ A @ B ) )
% 0.29/0.57        = ( plus_plus_int @ ( times_times_int @ X4 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X4 @ A ) @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_diff_mult
% 0.29/0.57  thf(fact_4153_mod__eq__dvd__iff,axiom,
% 0.29/0.57      ! [A: int,C: int,B: int] :
% 0.29/0.57        ( ( ( modulo_modulo_int @ A @ C )
% 0.29/0.57          = ( modulo_modulo_int @ B @ C ) )
% 0.29/0.57        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_eq_dvd_iff
% 0.29/0.57  thf(fact_4154_mod__eq__dvd__iff,axiom,
% 0.29/0.57      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.57        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.29/0.57          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.29/0.57        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_eq_dvd_iff
% 0.29/0.57  thf(fact_4155_dvd__minus__mod,axiom,
% 0.29/0.57      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_mod
% 0.29/0.57  thf(fact_4156_dvd__minus__mod,axiom,
% 0.29/0.57      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_mod
% 0.29/0.57  thf(fact_4157_dvd__minus__mod,axiom,
% 0.29/0.57      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_mod
% 0.29/0.57  thf(fact_4158_diff__less__Suc,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less_Suc
% 0.29/0.57  thf(fact_4159_Suc__diff__Suc,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ N2 @ M )
% 0.29/0.57       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.57          = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Suc_diff_Suc
% 0.29/0.57  thf(fact_4160_diff__less,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.57         => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less
% 0.29/0.57  thf(fact_4161_Suc__diff__le,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.29/0.57          = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Suc_diff_le
% 0.29/0.57  thf(fact_4162_diff__less__mono,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat] :
% 0.29/0.57        ( ( ord_less_nat @ A @ B )
% 0.29/0.57       => ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.57         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_less_mono
% 0.29/0.57  thf(fact_4163_less__diff__iff,axiom,
% 0.29/0.57      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.57       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.57         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/0.57            = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_iff
% 0.29/0.57  thf(fact_4164_diff__add__0,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.57        = zero_zero_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_add_0
% 0.29/0.57  thf(fact_4165_less__diff__conv,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.57        ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.57        = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_conv
% 0.29/0.57  thf(fact_4166_add__diff__inverse__nat,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ~ ( ord_less_nat @ M @ N2 )
% 0.29/0.57       => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57          = M ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_diff_inverse_nat
% 0.29/0.57  thf(fact_4167_Nat_Ole__imp__diff__is__add,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.57       => ( ( ( minus_minus_nat @ J @ I2 )
% 0.29/0.57            = K )
% 0.29/0.57          = ( J
% 0.29/0.57            = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Nat.le_imp_diff_is_add
% 0.29/0.57  thf(fact_4168_Nat_Odiff__add__assoc2,axiom,
% 0.29/0.57      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 0.29/0.57          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Nat.diff_add_assoc2
% 0.29/0.57  thf(fact_4169_Nat_Odiff__add__assoc,axiom,
% 0.29/0.57      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 0.29/0.57          = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Nat.diff_add_assoc
% 0.29/0.57  thf(fact_4170_Nat_Ole__diff__conv2,axiom,
% 0.29/0.57      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.57       => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.57          = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Nat.le_diff_conv2
% 0.29/0.57  thf(fact_4171_le__diff__conv,axiom,
% 0.29/0.57      ! [J: nat,K: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.57        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_diff_conv
% 0.29/0.57  thf(fact_4172_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.29/0.57        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_Suc_eq_diff_pred
% 0.29/0.57  thf(fact_4173_int__le__induct,axiom,
% 0.29/0.57      ! [I2: int,K: int,P: int > $o] :
% 0.29/0.57        ( ( ord_less_eq_int @ I2 @ K )
% 0.29/0.57       => ( ( P @ K )
% 0.29/0.57         => ( ! [I4: int] :
% 0.29/0.57                ( ( ord_less_eq_int @ I4 @ K )
% 0.29/0.57               => ( ( P @ I4 )
% 0.29/0.57                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.57           => ( P @ I2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % int_le_induct
% 0.29/0.57  thf(fact_4174_dvd__minus__self,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.57        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.57          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_self
% 0.29/0.57  thf(fact_4175_int__less__induct,axiom,
% 0.29/0.57      ! [I2: int,K: int,P: int > $o] :
% 0.29/0.57        ( ( ord_less_int @ I2 @ K )
% 0.29/0.57       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.29/0.57         => ( ! [I4: int] :
% 0.29/0.57                ( ( ord_less_int @ I4 @ K )
% 0.29/0.57               => ( ( P @ I4 )
% 0.29/0.57                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.57           => ( P @ I2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % int_less_induct
% 0.29/0.57  thf(fact_4176_dvd__diffD,axiom,
% 0.29/0.57      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57       => ( ( dvd_dvd_nat @ K @ N2 )
% 0.29/0.57         => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_diffD
% 0.29/0.57  thf(fact_4177_dvd__diffD1,axiom,
% 0.29/0.57      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57       => ( ( dvd_dvd_nat @ K @ M )
% 0.29/0.57         => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_diffD1
% 0.29/0.57  thf(fact_4178_less__eq__dvd__minus,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.57       => ( ( dvd_dvd_nat @ M @ N2 )
% 0.29/0.57          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_eq_dvd_minus
% 0.29/0.57  thf(fact_4179_mod__geq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ~ ( ord_less_nat @ M @ N2 )
% 0.29/0.57       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.29/0.57          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_geq
% 0.29/0.57  thf(fact_4180_mod__if,axiom,
% 0.29/0.57      ( modulo_modulo_nat
% 0.29/0.57      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_if
% 0.29/0.57  thf(fact_4181_le__mod__geq,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57       => ( ( modulo_modulo_nat @ M @ N2 )
% 0.29/0.57          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_mod_geq
% 0.29/0.57  thf(fact_4182_signed__take__bit__int__less__eq,axiom,
% 0.29/0.57      ! [N2: nat,K: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 0.29/0.57       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_int_less_eq
% 0.29/0.57  thf(fact_4183_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff2
% 0.29/0.57  thf(fact_4184_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff2
% 0.29/0.57  thf(fact_4185_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff2
% 0.29/0.57  thf(fact_4186_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff1
% 0.29/0.57  thf(fact_4187_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff1
% 0.29/0.57  thf(fact_4188_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % ordered_ring_class.le_add_iff1
% 0.29/0.57  thf(fact_4189_less__add__iff1,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff1
% 0.29/0.57  thf(fact_4190_less__add__iff1,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff1
% 0.29/0.57  thf(fact_4191_less__add__iff1,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff1
% 0.29/0.57  thf(fact_4192_less__add__iff2,axiom,
% 0.29/0.57      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.57        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff2
% 0.29/0.57  thf(fact_4193_less__add__iff2,axiom,
% 0.29/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff2
% 0.29/0.57  thf(fact_4194_less__add__iff2,axiom,
% 0.29/0.57      ! [A: int,E2: int,C: int,B: int,D: int] :
% 0.29/0.57        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.29/0.57        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_add_iff2
% 0.29/0.57  thf(fact_4195_divide__diff__eq__iff,axiom,
% 0.29/0.57      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.57        ( ( Z != zero_zero_rat )
% 0.29/0.57       => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 0.29/0.57          = ( divide_divide_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_diff_eq_iff
% 0.29/0.57  thf(fact_4196_divide__diff__eq__iff,axiom,
% 0.29/0.57      ! [Z: real,X4: real,Y: real] :
% 0.29/0.57        ( ( Z != zero_zero_real )
% 0.29/0.57       => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 0.29/0.57          = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_diff_eq_iff
% 0.29/0.57  thf(fact_4197_divide__diff__eq__iff,axiom,
% 0.29/0.57      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.57        ( ( Z != zero_zero_complex )
% 0.29/0.57       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 0.29/0.57          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_diff_eq_iff
% 0.29/0.57  thf(fact_4198_diff__divide__eq__iff,axiom,
% 0.29/0.57      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.57        ( ( Z != zero_zero_rat )
% 0.29/0.57       => ( ( minus_minus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 0.29/0.57          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_divide_eq_iff
% 0.29/0.57  thf(fact_4199_diff__divide__eq__iff,axiom,
% 0.29/0.57      ! [Z: real,X4: real,Y: real] :
% 0.29/0.57        ( ( Z != zero_zero_real )
% 0.29/0.57       => ( ( minus_minus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 0.29/0.57          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_divide_eq_iff
% 0.29/0.57  thf(fact_4200_diff__divide__eq__iff,axiom,
% 0.29/0.57      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.57        ( ( Z != zero_zero_complex )
% 0.29/0.57       => ( ( minus_minus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 0.29/0.57          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_divide_eq_iff
% 0.29/0.57  thf(fact_4201_diff__frac__eq,axiom,
% 0.29/0.57      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 0.29/0.57        ( ( Y != zero_zero_rat )
% 0.29/0.57       => ( ( Z != zero_zero_rat )
% 0.29/0.57         => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.57            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_frac_eq
% 0.29/0.57  thf(fact_4202_diff__frac__eq,axiom,
% 0.29/0.57      ! [Y: real,Z: real,X4: real,W: real] :
% 0.29/0.57        ( ( Y != zero_zero_real )
% 0.29/0.57       => ( ( Z != zero_zero_real )
% 0.29/0.57         => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.57            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_frac_eq
% 0.29/0.57  thf(fact_4203_diff__frac__eq,axiom,
% 0.29/0.57      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 0.29/0.57        ( ( Y != zero_zero_complex )
% 0.29/0.57       => ( ( Z != zero_zero_complex )
% 0.29/0.57         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.29/0.57            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_frac_eq
% 0.29/0.57  thf(fact_4204_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.57      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.57        ( ( ( Z = zero_zero_rat )
% 0.29/0.57         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.57            = A ) )
% 0.29/0.57        & ( ( Z != zero_zero_rat )
% 0.29/0.57         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.57            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_divide_eq_if_simps(4)
% 0.29/0.57  thf(fact_4205_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.57      ! [Z: real,A: real,B: real] :
% 0.29/0.57        ( ( ( Z = zero_zero_real )
% 0.29/0.57         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.57            = A ) )
% 0.29/0.57        & ( ( Z != zero_zero_real )
% 0.29/0.57         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.29/0.57            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_divide_eq_if_simps(4)
% 0.29/0.57  thf(fact_4206_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.57      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.57        ( ( ( Z = zero_zero_complex )
% 0.29/0.57         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.57            = A ) )
% 0.29/0.57        & ( ( Z != zero_zero_complex )
% 0.29/0.57         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.29/0.57            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_divide_eq_if_simps(4)
% 0.29/0.57  thf(fact_4207_square__diff__one__factored,axiom,
% 0.29/0.57      ! [X4: rat] :
% 0.29/0.57        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ one_one_rat )
% 0.29/0.57        = ( times_times_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_one_factored
% 0.29/0.57  thf(fact_4208_square__diff__one__factored,axiom,
% 0.29/0.57      ! [X4: complex] :
% 0.29/0.57        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ one_one_complex )
% 0.29/0.57        = ( times_times_complex @ ( plus_plus_complex @ X4 @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_one_factored
% 0.29/0.57  thf(fact_4209_square__diff__one__factored,axiom,
% 0.29/0.57      ! [X4: real] :
% 0.29/0.57        ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ one_one_real )
% 0.29/0.57        = ( times_times_real @ ( plus_plus_real @ X4 @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_one_factored
% 0.29/0.57  thf(fact_4210_square__diff__one__factored,axiom,
% 0.29/0.57      ! [X4: int] :
% 0.29/0.57        ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ one_one_int )
% 0.29/0.57        = ( times_times_int @ ( plus_plus_int @ X4 @ one_one_int ) @ ( minus_minus_int @ X4 @ one_one_int ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % square_diff_one_factored
% 0.29/0.57  thf(fact_4211_inf__period_I4_J,axiom,
% 0.29/0.57      ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 0.29/0.57        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 0.29/0.57       => ! [X2: code_integer,K4: code_integer] :
% 0.29/0.57            ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) ) )
% 0.29/0.57            = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(4)
% 0.29/0.57  thf(fact_4212_inf__period_I4_J,axiom,
% 0.29/0.57      ! [D: rat,D4: rat,T2: rat] :
% 0.29/0.57        ( ( dvd_dvd_rat @ D @ D4 )
% 0.29/0.57       => ! [X2: rat,K4: rat] :
% 0.29/0.57            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) ) )
% 0.29/0.57            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(4)
% 0.29/0.57  thf(fact_4213_inf__period_I4_J,axiom,
% 0.29/0.57      ! [D: complex,D4: complex,T2: complex] :
% 0.29/0.57        ( ( dvd_dvd_complex @ D @ D4 )
% 0.29/0.57       => ! [X2: complex,K4: complex] :
% 0.29/0.57            ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) ) )
% 0.29/0.57            = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(4)
% 0.29/0.57  thf(fact_4214_inf__period_I4_J,axiom,
% 0.29/0.57      ! [D: real,D4: real,T2: real] :
% 0.29/0.57        ( ( dvd_dvd_real @ D @ D4 )
% 0.29/0.57       => ! [X2: real,K4: real] :
% 0.29/0.57            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) ) )
% 0.29/0.57            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(4)
% 0.29/0.57  thf(fact_4215_inf__period_I4_J,axiom,
% 0.29/0.57      ! [D: int,D4: int,T2: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ D @ D4 )
% 0.29/0.57       => ! [X2: int,K4: int] :
% 0.29/0.57            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) ) )
% 0.29/0.57            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(4)
% 0.29/0.57  thf(fact_4216_inf__period_I3_J,axiom,
% 0.29/0.57      ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 0.29/0.57        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 0.29/0.57       => ! [X2: code_integer,K4: code_integer] :
% 0.29/0.57            ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) )
% 0.29/0.57            = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(3)
% 0.29/0.57  thf(fact_4217_inf__period_I3_J,axiom,
% 0.29/0.57      ! [D: rat,D4: rat,T2: rat] :
% 0.29/0.57        ( ( dvd_dvd_rat @ D @ D4 )
% 0.29/0.57       => ! [X2: rat,K4: rat] :
% 0.29/0.57            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) )
% 0.29/0.57            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(3)
% 0.29/0.57  thf(fact_4218_inf__period_I3_J,axiom,
% 0.29/0.57      ! [D: complex,D4: complex,T2: complex] :
% 0.29/0.57        ( ( dvd_dvd_complex @ D @ D4 )
% 0.29/0.57       => ! [X2: complex,K4: complex] :
% 0.29/0.57            ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) )
% 0.29/0.57            = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(3)
% 0.29/0.57  thf(fact_4219_inf__period_I3_J,axiom,
% 0.29/0.57      ! [D: real,D4: real,T2: real] :
% 0.29/0.57        ( ( dvd_dvd_real @ D @ D4 )
% 0.29/0.57       => ! [X2: real,K4: real] :
% 0.29/0.57            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) )
% 0.29/0.57            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(3)
% 0.29/0.57  thf(fact_4220_inf__period_I3_J,axiom,
% 0.29/0.57      ! [D: int,D4: int,T2: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ D @ D4 )
% 0.29/0.57       => ! [X2: int,K4: int] :
% 0.29/0.57            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) )
% 0.29/0.57            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % inf_period(3)
% 0.29/0.57  thf(fact_4221_minus__mult__div__eq__mod,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.29/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_div_eq_mod
% 0.29/0.57  thf(fact_4222_minus__mult__div__eq__mod,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.29/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_div_eq_mod
% 0.29/0.57  thf(fact_4223_minus__mult__div__eq__mod,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.29/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_div_eq_mod
% 0.29/0.57  thf(fact_4224_minus__mod__eq__mult__div,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.57        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_mult_div
% 0.29/0.57  thf(fact_4225_minus__mod__eq__mult__div,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.57        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_mult_div
% 0.29/0.57  thf(fact_4226_minus__mod__eq__mult__div,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.57        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_mult_div
% 0.29/0.57  thf(fact_4227_minus__mod__eq__div__mult,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.57        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_div_mult
% 0.29/0.57  thf(fact_4228_minus__mod__eq__div__mult,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.29/0.57        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_div_mult
% 0.29/0.57  thf(fact_4229_minus__mod__eq__div__mult,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.29/0.57        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_eq_div_mult
% 0.29/0.57  thf(fact_4230_minus__div__mult__eq__mod,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.29/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_div_mult_eq_mod
% 0.29/0.57  thf(fact_4231_minus__div__mult__eq__mod,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.29/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_div_mult_eq_mod
% 0.29/0.57  thf(fact_4232_minus__div__mult__eq__mod,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.29/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_div_mult_eq_mod
% 0.29/0.57  thf(fact_4233_diff__Suc__less,axiom,
% 0.29/0.57      ! [N2: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_Suc_less
% 0.29/0.57  thf(fact_4234_nat__diff__split,axiom,
% 0.29/0.57      ! [P: nat > $o,A: nat,B: nat] :
% 0.29/0.57        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.57        = ( ( ( ord_less_nat @ A @ B )
% 0.29/0.57           => ( P @ zero_zero_nat ) )
% 0.29/0.57          & ! [D5: nat] :
% 0.29/0.57              ( ( A
% 0.29/0.57                = ( plus_plus_nat @ B @ D5 ) )
% 0.29/0.57             => ( P @ D5 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_diff_split
% 0.29/0.57  thf(fact_4235_nat__diff__split__asm,axiom,
% 0.29/0.57      ! [P: nat > $o,A: nat,B: nat] :
% 0.29/0.57        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.57        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.29/0.57                & ~ ( P @ zero_zero_nat ) )
% 0.29/0.57              | ? [D5: nat] :
% 0.29/0.57                  ( ( A
% 0.29/0.57                    = ( plus_plus_nat @ B @ D5 ) )
% 0.29/0.57                  & ~ ( P @ D5 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_diff_split_asm
% 0.29/0.57  thf(fact_4236_less__diff__conv2,axiom,
% 0.29/0.57      ! [K: nat,J: nat,I2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.57       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 0.29/0.57          = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_diff_conv2
% 0.29/0.57  thf(fact_4237_nat__diff__add__eq2,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_diff_add_eq2
% 0.29/0.57  thf(fact_4238_nat__diff__add__eq1,axiom,
% 0.29/0.57      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_diff_add_eq1
% 0.29/0.57  thf(fact_4239_nat__le__add__iff2,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.57       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_le_add_iff2
% 0.29/0.57  thf(fact_4240_nat__le__add__iff1,axiom,
% 0.29/0.57      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.57       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_le_add_iff1
% 0.29/0.57  thf(fact_4241_nat__eq__add__iff2,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.57       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 0.29/0.57            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( M
% 0.29/0.57            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_eq_add_iff2
% 0.29/0.57  thf(fact_4242_nat__eq__add__iff1,axiom,
% 0.29/0.57      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.57       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 0.29/0.57            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 0.29/0.57            = N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_eq_add_iff1
% 0.29/0.57  thf(fact_4243_plusinfinity,axiom,
% 0.29/0.57      ! [D: int,P6: int > $o,P: int > $o] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.57       => ( ! [X5: int,K2: int] :
% 0.29/0.57              ( ( P6 @ X5 )
% 0.29/0.57              = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.29/0.57         => ( ? [Z3: int] :
% 0.29/0.57              ! [X5: int] :
% 0.29/0.57                ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.57               => ( ( P @ X5 )
% 0.29/0.57                  = ( P6 @ X5 ) ) )
% 0.29/0.57           => ( ? [X_1: int] : ( P6 @ X_1 )
% 0.29/0.57             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % plusinfinity
% 0.29/0.57  thf(fact_4244_minusinfinity,axiom,
% 0.29/0.57      ! [D: int,P1: int > $o,P: int > $o] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.57       => ( ! [X5: int,K2: int] :
% 0.29/0.57              ( ( P1 @ X5 )
% 0.29/0.57              = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.29/0.57         => ( ? [Z3: int] :
% 0.29/0.57              ! [X5: int] :
% 0.29/0.57                ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.57               => ( ( P @ X5 )
% 0.29/0.57                  = ( P1 @ X5 ) ) )
% 0.29/0.57           => ( ? [X_1: int] : ( P1 @ X_1 )
% 0.29/0.57             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minusinfinity
% 0.29/0.57  thf(fact_4245_int__induct,axiom,
% 0.29/0.57      ! [P: int > $o,K: int,I2: int] :
% 0.29/0.57        ( ( P @ K )
% 0.29/0.57       => ( ! [I4: int] :
% 0.29/0.57              ( ( ord_less_eq_int @ K @ I4 )
% 0.29/0.57             => ( ( P @ I4 )
% 0.29/0.57               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.57         => ( ! [I4: int] :
% 0.29/0.57                ( ( ord_less_eq_int @ I4 @ K )
% 0.29/0.57               => ( ( P @ I4 )
% 0.29/0.57                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.29/0.57           => ( P @ I2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % int_induct
% 0.29/0.57  thf(fact_4246_mod__eq__dvd__iff__nat,axiom,
% 0.29/0.57      ! [N2: nat,M: nat,Q3: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57       => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.29/0.57            = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 0.29/0.57          = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_eq_dvd_iff_nat
% 0.29/0.57  thf(fact_4247_modulo__nat__def,axiom,
% 0.29/0.57      ( modulo_modulo_nat
% 0.29/0.57      = ( ^ [M6: nat,N: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N ) @ N ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % modulo_nat_def
% 0.29/0.57  thf(fact_4248_frac__le__eq,axiom,
% 0.29/0.57      ! [Y: real,Z: real,X4: real,W: real] :
% 0.29/0.57        ( ( Y != zero_zero_real )
% 0.29/0.57       => ( ( Z != zero_zero_real )
% 0.29/0.57         => ( ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.57            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % frac_le_eq
% 0.29/0.57  thf(fact_4249_frac__le__eq,axiom,
% 0.29/0.57      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 0.29/0.57        ( ( Y != zero_zero_rat )
% 0.29/0.57       => ( ( Z != zero_zero_rat )
% 0.29/0.57         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.57            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % frac_le_eq
% 0.29/0.57  thf(fact_4250_frac__less__eq,axiom,
% 0.29/0.57      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 0.29/0.57        ( ( Y != zero_zero_rat )
% 0.29/0.57       => ( ( Z != zero_zero_rat )
% 0.29/0.57         => ( ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.57            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % frac_less_eq
% 0.29/0.57  thf(fact_4251_frac__less__eq,axiom,
% 0.29/0.57      ! [Y: real,Z: real,X4: real,W: real] :
% 0.29/0.57        ( ( Y != zero_zero_real )
% 0.29/0.57       => ( ( Z != zero_zero_real )
% 0.29/0.57         => ( ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.29/0.57            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % frac_less_eq
% 0.29/0.57  thf(fact_4252_power2__commute,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex] :
% 0.29/0.57        ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( power_power_complex @ ( minus_minus_complex @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_commute
% 0.29/0.57  thf(fact_4253_power2__commute,axiom,
% 0.29/0.57      ! [X4: real,Y: real] :
% 0.29/0.57        ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( power_power_real @ ( minus_minus_real @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_commute
% 0.29/0.57  thf(fact_4254_power2__commute,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat] :
% 0.29/0.57        ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( power_power_rat @ ( minus_minus_rat @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_commute
% 0.29/0.57  thf(fact_4255_power2__commute,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( power_power_int @ ( minus_minus_int @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_commute
% 0.29/0.57  thf(fact_4256_power__diff,axiom,
% 0.29/0.57      ! [A: rat,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_rat )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4257_power__diff,axiom,
% 0.29/0.57      ! [A: nat,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_nat )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4258_power__diff,axiom,
% 0.29/0.57      ! [A: int,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_int )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4259_power__diff,axiom,
% 0.29/0.57      ! [A: real,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_real )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4260_power__diff,axiom,
% 0.29/0.57      ! [A: complex,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_complex )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4261_power__diff,axiom,
% 0.29/0.57      ! [A: code_integer,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.57            = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff
% 0.29/0.57  thf(fact_4262_Suc__pred_H,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( N2
% 0.29/0.57          = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Suc_pred'
% 0.29/0.57  thf(fact_4263_Suc__diff__eq__diff__pred,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.29/0.57          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Suc_diff_eq_diff_pred
% 0.29/0.57  thf(fact_4264_div__geq,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ~ ( ord_less_nat @ M @ N2 )
% 0.29/0.57         => ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.57            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_geq
% 0.29/0.57  thf(fact_4265_div__if,axiom,
% 0.29/0.57      ( divide_divide_nat
% 0.29/0.57      = ( ^ [M6: nat,N: nat] :
% 0.29/0.57            ( if_nat
% 0.29/0.57            @ ( ( ord_less_nat @ M6 @ N )
% 0.29/0.57              | ( N = zero_zero_nat ) )
% 0.29/0.57            @ zero_zero_nat
% 0.29/0.57            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_if
% 0.29/0.57  thf(fact_4266_add__eq__if,axiom,
% 0.29/0.57      ( plus_plus_nat
% 0.29/0.57      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_eq_if
% 0.29/0.57  thf(fact_4267_nat__less__add__iff1,axiom,
% 0.29/0.57      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.57       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_less_add_iff1
% 0.29/0.57  thf(fact_4268_nat__less__add__iff2,axiom,
% 0.29/0.57      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.57       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 0.29/0.57          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % nat_less_add_iff2
% 0.29/0.57  thf(fact_4269_mult__eq__if,axiom,
% 0.29/0.57      ( times_times_nat
% 0.29/0.57      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_eq_if
% 0.29/0.57  thf(fact_4270_decr__mult__lemma,axiom,
% 0.29/0.57      ! [D: int,P: int > $o,K: int] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.57       => ( ! [X5: int] :
% 0.29/0.57              ( ( P @ X5 )
% 0.29/0.57             => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 0.29/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.57           => ! [X2: int] :
% 0.29/0.57                ( ( P @ X2 )
% 0.29/0.57               => ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % decr_mult_lemma
% 0.29/0.57  thf(fact_4271_dvd__minus__add,axiom,
% 0.29/0.57      ! [Q3: nat,N2: nat,R3: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ Q3 @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R3 @ M ) )
% 0.29/0.57         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q3 ) )
% 0.29/0.57            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M ) @ Q3 ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_add
% 0.29/0.57  thf(fact_4272_mod__nat__eqI,axiom,
% 0.29/0.57      ! [R3: nat,N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ R3 @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_nat @ R3 @ M )
% 0.29/0.57         => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R3 ) )
% 0.29/0.57           => ( ( modulo_modulo_nat @ M @ N2 )
% 0.29/0.57              = R3 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_nat_eqI
% 0.29/0.57  thf(fact_4273_mod__pos__geq,axiom,
% 0.29/0.57      ! [L: int,K: int] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.57       => ( ( ord_less_eq_int @ L @ K )
% 0.29/0.57         => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.57            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_pos_geq
% 0.29/0.57  thf(fact_4274_scaling__mono,axiom,
% 0.29/0.57      ! [U: real,V: real,R3: real,S: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ U @ V )
% 0.29/0.57       => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 0.29/0.57         => ( ( ord_less_eq_real @ R3 @ S )
% 0.29/0.57           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % scaling_mono
% 0.29/0.57  thf(fact_4275_scaling__mono,axiom,
% 0.29/0.57      ! [U: rat,V: rat,R3: rat,S: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ U @ V )
% 0.29/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 0.29/0.57         => ( ( ord_less_eq_rat @ R3 @ S )
% 0.29/0.57           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % scaling_mono
% 0.29/0.57  thf(fact_4276_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57         != zero_zero_nat )
% 0.29/0.57       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.57         != zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % exp_not_zero_imp_exp_diff_not_zero
% 0.29/0.57  thf(fact_4277_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57         != zero_zero_int )
% 0.29/0.57       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.57         != zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % exp_not_zero_imp_exp_diff_not_zero
% 0.29/0.57  thf(fact_4278_power__diff__power__eq,axiom,
% 0.29/0.57      ! [A: nat,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_nat )
% 0.29/0.57       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.29/0.57              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 0.29/0.57          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 0.29/0.57              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff_power_eq
% 0.29/0.57  thf(fact_4279_power__diff__power__eq,axiom,
% 0.29/0.57      ! [A: int,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_zero_int )
% 0.29/0.57       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.29/0.57              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 0.29/0.57          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 0.29/0.57              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff_power_eq
% 0.29/0.57  thf(fact_4280_power__diff__power__eq,axiom,
% 0.29/0.57      ! [A: code_integer,N2: nat,M: nat] :
% 0.29/0.57        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.57       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.29/0.57              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 0.29/0.57          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.29/0.57              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_diff_power_eq
% 0.29/0.57  thf(fact_4281_signed__take__bit__int__less__exp,axiom,
% 0.29/0.57      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_int_less_exp
% 0.29/0.57  thf(fact_4282_power__eq__if,axiom,
% 0.29/0.57      ( power_power_rat
% 0.29/0.57      = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_eq_if
% 0.29/0.57  thf(fact_4283_power__eq__if,axiom,
% 0.29/0.57      ( power_power_complex
% 0.29/0.57      = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_eq_if
% 0.29/0.57  thf(fact_4284_power__eq__if,axiom,
% 0.29/0.57      ( power_power_real
% 0.29/0.57      = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_eq_if
% 0.29/0.57  thf(fact_4285_power__eq__if,axiom,
% 0.29/0.57      ( power_power_nat
% 0.29/0.57      = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_eq_if
% 0.29/0.57  thf(fact_4286_power__eq__if,axiom,
% 0.29/0.57      ( power_power_int
% 0.29/0.57      = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_eq_if
% 0.29/0.57  thf(fact_4287_power__minus__mult,axiom,
% 0.29/0.57      ! [N2: nat,A: complex] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.29/0.57          = ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_minus_mult
% 0.29/0.57  thf(fact_4288_power__minus__mult,axiom,
% 0.29/0.57      ! [N2: nat,A: real] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.29/0.57          = ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_minus_mult
% 0.29/0.57  thf(fact_4289_power__minus__mult,axiom,
% 0.29/0.57      ! [N2: nat,A: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.29/0.57          = ( power_power_nat @ A @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_minus_mult
% 0.29/0.57  thf(fact_4290_power__minus__mult,axiom,
% 0.29/0.57      ! [N2: nat,A: int] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 0.29/0.57          = ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power_minus_mult
% 0.29/0.57  thf(fact_4291_diff__le__diff__pow,axiom,
% 0.29/0.57      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.57       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_le_diff_pow
% 0.29/0.57  thf(fact_4292_le__div__geq,axiom,
% 0.29/0.57      ! [N2: nat,M: nat] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.57       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.57         => ( ( divide_divide_nat @ M @ N2 )
% 0.29/0.57            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % le_div_geq
% 0.29/0.57  thf(fact_4293_even__diff__iff,axiom,
% 0.29/0.57      ! [K: int,L: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 0.29/0.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_diff_iff
% 0.29/0.57  thf(fact_4294_even__signed__take__bit__iff,axiom,
% 0.29/0.57      ! [M: nat,A: code_integer] :
% 0.29/0.57        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 0.29/0.57        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_signed_take_bit_iff
% 0.29/0.57  thf(fact_4295_even__signed__take__bit__iff,axiom,
% 0.29/0.57      ! [M: nat,A: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 0.29/0.57        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_signed_take_bit_iff
% 0.29/0.57  thf(fact_4296_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.29/0.57      ! [K: int,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 0.29/0.57        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_int_greater_eq_self_iff
% 0.29/0.57  thf(fact_4297_signed__take__bit__int__less__self__iff,axiom,
% 0.29/0.57      ! [N2: nat,K: int] :
% 0.29/0.57        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 0.29/0.57        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_int_less_self_iff
% 0.29/0.57  thf(fact_4298_div__pos__geq,axiom,
% 0.29/0.57      ! [L: int,K: int] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.29/0.57       => ( ( ord_less_eq_int @ L @ K )
% 0.29/0.57         => ( ( divide_divide_int @ K @ L )
% 0.29/0.57            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_pos_geq
% 0.29/0.57  thf(fact_4299_add__0__iff,axiom,
% 0.29/0.57      ! [B: complex,A: complex] :
% 0.29/0.57        ( ( B
% 0.29/0.57          = ( plus_plus_complex @ B @ A ) )
% 0.29/0.57        = ( A = zero_zero_complex ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_0_iff
% 0.29/0.57  thf(fact_4300_add__0__iff,axiom,
% 0.29/0.57      ! [B: real,A: real] :
% 0.29/0.57        ( ( B
% 0.29/0.57          = ( plus_plus_real @ B @ A ) )
% 0.29/0.57        = ( A = zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_0_iff
% 0.29/0.57  thf(fact_4301_add__0__iff,axiom,
% 0.29/0.57      ! [B: rat,A: rat] :
% 0.29/0.57        ( ( B
% 0.29/0.57          = ( plus_plus_rat @ B @ A ) )
% 0.29/0.57        = ( A = zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_0_iff
% 0.29/0.57  thf(fact_4302_add__0__iff,axiom,
% 0.29/0.57      ! [B: nat,A: nat] :
% 0.29/0.57        ( ( B
% 0.29/0.57          = ( plus_plus_nat @ B @ A ) )
% 0.29/0.57        = ( A = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_0_iff
% 0.29/0.57  thf(fact_4303_add__0__iff,axiom,
% 0.29/0.57      ! [B: int,A: int] :
% 0.29/0.57        ( ( B
% 0.29/0.57          = ( plus_plus_int @ B @ A ) )
% 0.29/0.57        = ( A = zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_0_iff
% 0.29/0.57  thf(fact_4304_crossproduct__eq,axiom,
% 0.29/0.57      ! [W: rat,Y: rat,X4: rat,Z: rat] :
% 0.29/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X4 @ Z ) )
% 0.29/0.57          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X4 @ Y ) ) )
% 0.29/0.57        = ( ( W = X4 )
% 0.29/0.57          | ( Y = Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_eq
% 0.29/0.57  thf(fact_4305_crossproduct__eq,axiom,
% 0.29/0.57      ! [W: complex,Y: complex,X4: complex,Z: complex] :
% 0.29/0.57        ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X4 @ Z ) )
% 0.29/0.57          = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X4 @ Y ) ) )
% 0.29/0.57        = ( ( W = X4 )
% 0.29/0.57          | ( Y = Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_eq
% 0.29/0.57  thf(fact_4306_crossproduct__eq,axiom,
% 0.29/0.57      ! [W: real,Y: real,X4: real,Z: real] :
% 0.29/0.57        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X4 @ Z ) )
% 0.29/0.57          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X4 @ Y ) ) )
% 0.29/0.57        = ( ( W = X4 )
% 0.29/0.57          | ( Y = Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_eq
% 0.29/0.57  thf(fact_4307_crossproduct__eq,axiom,
% 0.29/0.57      ! [W: nat,Y: nat,X4: nat,Z: nat] :
% 0.29/0.57        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X4 @ Z ) )
% 0.29/0.57          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X4 @ Y ) ) )
% 0.29/0.57        = ( ( W = X4 )
% 0.29/0.57          | ( Y = Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_eq
% 0.29/0.57  thf(fact_4308_crossproduct__eq,axiom,
% 0.29/0.57      ! [W: int,Y: int,X4: int,Z: int] :
% 0.29/0.57        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X4 @ Z ) )
% 0.29/0.57          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X4 @ Y ) ) )
% 0.29/0.57        = ( ( W = X4 )
% 0.29/0.57          | ( Y = Z ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_eq
% 0.29/0.57  thf(fact_4309_crossproduct__noteq,axiom,
% 0.29/0.57      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.57        ( ( ( A != B )
% 0.29/0.57          & ( C != D ) )
% 0.29/0.57        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 0.29/0.57         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_noteq
% 0.29/0.57  thf(fact_4310_crossproduct__noteq,axiom,
% 0.29/0.57      ! [A: complex,B: complex,C: complex,D: complex] :
% 0.29/0.57        ( ( ( A != B )
% 0.29/0.57          & ( C != D ) )
% 0.29/0.57        = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 0.29/0.57         != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_noteq
% 0.29/0.57  thf(fact_4311_crossproduct__noteq,axiom,
% 0.29/0.57      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.57        ( ( ( A != B )
% 0.29/0.57          & ( C != D ) )
% 0.29/0.57        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 0.29/0.57         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_noteq
% 0.29/0.57  thf(fact_4312_crossproduct__noteq,axiom,
% 0.29/0.57      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.57        ( ( ( A != B )
% 0.29/0.57          & ( C != D ) )
% 0.29/0.57        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.29/0.57         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_noteq
% 0.29/0.57  thf(fact_4313_crossproduct__noteq,axiom,
% 0.29/0.57      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.57        ( ( ( A != B )
% 0.29/0.57          & ( C != D ) )
% 0.29/0.57        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 0.29/0.57         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % crossproduct_noteq
% 0.29/0.57  thf(fact_4314_power2__diff,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat] :
% 0.29/0.57        ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_diff
% 0.29/0.57  thf(fact_4315_power2__diff,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex] :
% 0.29/0.57        ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_diff
% 0.29/0.57  thf(fact_4316_power2__diff,axiom,
% 0.29/0.57      ! [X4: real,Y: real] :
% 0.29/0.57        ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_diff
% 0.29/0.57  thf(fact_4317_power2__diff,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.57        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % power2_diff
% 0.29/0.57  thf(fact_4318_mult__exp__mod__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat,A: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.57       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_exp_mod_exp_eq
% 0.29/0.57  thf(fact_4319_mult__exp__mod__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat,A: int] :
% 0.29/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.57       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_exp_mod_exp_eq
% 0.29/0.57  thf(fact_4320_mult__exp__mod__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat,A: code_integer] :
% 0.29/0.57        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.57       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_exp_mod_exp_eq
% 0.29/0.57  thf(fact_4321_int__power__div__base,axiom,
% 0.29/0.57      ! [M: nat,K: int] :
% 0.29/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.57       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.57         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.29/0.57            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % int_power_div_base
% 0.29/0.57  thf(fact_4322_divmod__digit__1_I2_J,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.57           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.57              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_digit_1(2)
% 0.29/0.57  thf(fact_4323_divmod__digit__1_I2_J,axiom,
% 0.29/0.57      ! [A: nat,B: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.57           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.57              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_digit_1(2)
% 0.29/0.57  thf(fact_4324_divmod__digit__1_I2_J,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.29/0.57           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.29/0.57              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_digit_1(2)
% 0.29/0.57  thf(fact_4325_even__mask__div__iff_H,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff'
% 0.29/0.57  thf(fact_4326_even__mask__div__iff_H,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff'
% 0.29/0.57  thf(fact_4327_even__mask__div__iff_H,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff'
% 0.29/0.57  thf(fact_4328_even__mod__4__div__2,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.57          = ( suc @ zero_zero_nat ) )
% 0.29/0.57       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mod_4_div_2
% 0.29/0.57  thf(fact_4329_even__mask__div__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57            = zero_zero_nat )
% 0.29/0.57          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff
% 0.29/0.57  thf(fact_4330_even__mask__div__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57            = zero_zero_int )
% 0.29/0.57          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff
% 0.29/0.57  thf(fact_4331_even__mask__div__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( 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 ) ) @ N2 ) ) )
% 0.29/0.57        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57            = zero_z3403309356797280102nteger )
% 0.29/0.57          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % even_mask_div_iff
% 0.29/0.57  thf(fact_4332_exp__div__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57        = ( times_times_nat
% 0.29/0.57          @ ( zero_n2687167440665602831ol_nat
% 0.29/0.57            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.29/0.57               != zero_zero_nat )
% 0.29/0.57              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.29/0.57          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % exp_div_exp_eq
% 0.29/0.57  thf(fact_4333_exp__div__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57        = ( times_times_int
% 0.29/0.57          @ ( zero_n2684676970156552555ol_int
% 0.29/0.57            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.29/0.57               != zero_zero_int )
% 0.29/0.57              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.29/0.57          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % exp_div_exp_eq
% 0.29/0.57  thf(fact_4334_exp__div__exp__eq,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.57        = ( times_3573771949741848930nteger
% 0.29/0.57          @ ( zero_n356916108424825756nteger
% 0.29/0.57            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.29/0.57               != zero_z3403309356797280102nteger )
% 0.29/0.57              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 0.29/0.57          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % exp_div_exp_eq
% 0.29/0.57  thf(fact_4335_neg__zmod__mult__2,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.57       => ( ( 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 ) )
% 0.29/0.57          = ( 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 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_zmod_mult_2
% 0.29/0.57  thf(fact_4336_divmod__step__eq,axiom,
% 0.29/0.57      ! [L: num,R3: nat,Q3: nat] :
% 0.29/0.57        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.29/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 0.29/0.57            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.29/0.57        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.29/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 0.29/0.57            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_step_eq
% 0.29/0.57  thf(fact_4337_divmod__step__eq,axiom,
% 0.29/0.57      ! [L: num,R3: int,Q3: int] :
% 0.29/0.57        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.29/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.57            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.29/0.57        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.29/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.57            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_step_eq
% 0.29/0.57  thf(fact_4338_divmod__step__eq,axiom,
% 0.29/0.57      ! [L: num,R3: code_integer,Q3: code_integer] :
% 0.29/0.57        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.29/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 0.29/0.57            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.29/0.57        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.29/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 0.29/0.57            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divmod_step_eq
% 0.29/0.57  thf(fact_4339_signed__take__bit__rec,axiom,
% 0.29/0.57      ( bit_ri6519982836138164636nteger
% 0.29/0.57      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = 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 @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_rec
% 0.29/0.57  thf(fact_4340_signed__take__bit__rec,axiom,
% 0.29/0.57      ( bit_ri631733984087533419it_int
% 0.29/0.57      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = 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 @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % signed_take_bit_rec
% 0.29/0.57  thf(fact_4341_take__bit__rec,axiom,
% 0.29/0.57      ( bit_se1745604003318907178nteger
% 0.29/0.57      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_rec
% 0.29/0.57  thf(fact_4342_take__bit__rec,axiom,
% 0.29/0.57      ( bit_se2923211474154528505it_int
% 0.29/0.57      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ 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 ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_rec
% 0.29/0.57  thf(fact_4343_take__bit__rec,axiom,
% 0.29/0.57      ( bit_se2925701944663578781it_nat
% 0.29/0.57      = ( ^ [N: nat,A3: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ 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 ) ) ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_rec
% 0.29/0.57  thf(fact_4344_odd__mod__4__div__2,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.57          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.57       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % odd_mod_4_div_2
% 0.29/0.57  thf(fact_4345_Bernoulli__inequality__even,axiom,
% 0.29/0.57      ! [N2: nat,X4: real] :
% 0.29/0.57        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.57       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Bernoulli_inequality_even
% 0.29/0.57  thf(fact_4346_Suc__0__xor__eq,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.57        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.57          @ ( zero_n2687167440665602831ol_nat
% 0.29/0.57            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Suc_0_xor_eq
% 0.29/0.57  thf(fact_4347_add_Oinverse__inverse,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_inverse
% 0.29/0.57  thf(fact_4348_add_Oinverse__inverse,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_inverse
% 0.29/0.57  thf(fact_4349_add_Oinverse__inverse,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_inverse
% 0.29/0.57  thf(fact_4350_add_Oinverse__inverse,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_inverse
% 0.29/0.57  thf(fact_4351_add_Oinverse__inverse,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_inverse
% 0.29/0.57  thf(fact_4352_neg__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( ( uminus_uminus_real @ A )
% 0.29/0.57          = ( uminus_uminus_real @ B ) )
% 0.29/0.57        = ( A = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_iff_equal
% 0.29/0.57  thf(fact_4353_neg__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( ( uminus_uminus_int @ A )
% 0.29/0.57          = ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( A = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_iff_equal
% 0.29/0.57  thf(fact_4354_neg__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.57          = ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.57        = ( A = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_iff_equal
% 0.29/0.57  thf(fact_4355_neg__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.57          = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( A = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_iff_equal
% 0.29/0.57  thf(fact_4356_neg__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.57          = ( uminus_uminus_rat @ B ) )
% 0.29/0.57        = ( A = B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_iff_equal
% 0.29/0.57  thf(fact_4357_Compl__anti__mono,axiom,
% 0.29/0.57      ! [A2: set_int,B3: set_int] :
% 0.29/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.57       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Compl_anti_mono
% 0.29/0.57  thf(fact_4358_Compl__subset__Compl__iff,axiom,
% 0.29/0.57      ! [A2: set_int,B3: set_int] :
% 0.29/0.57        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 0.29/0.57        = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % Compl_subset_Compl_iff
% 0.29/0.57  thf(fact_4359_of__nat__eq__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ( semiri5074537144036343181t_real @ M )
% 0.29/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_iff
% 0.29/0.57  thf(fact_4360_of__nat__eq__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.29/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_iff
% 0.29/0.57  thf(fact_4361_of__nat__eq__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.29/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_iff
% 0.29/0.57  thf(fact_4362_semiring__norm_I90_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( bit1 @ M )
% 0.29/0.57          = ( bit1 @ N2 ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(90)
% 0.29/0.57  thf(fact_4363_bit_Oxor__left__self,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_se6526347334894502574or_int @ X4 @ Y ) )
% 0.29/0.57        = Y ) ).
% 0.29/0.57  
% 0.29/0.57  % bit.xor_left_self
% 0.29/0.57  thf(fact_4364_idiff__0,axiom,
% 0.29/0.57      ! [N2: extended_enat] :
% 0.29/0.57        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 0.29/0.57        = zero_z5237406670263579293d_enat ) ).
% 0.29/0.57  
% 0.29/0.57  % idiff_0
% 0.29/0.57  thf(fact_4365_idiff__0__right,axiom,
% 0.29/0.57      ! [N2: extended_enat] :
% 0.29/0.57        ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 0.29/0.57        = N2 ) ).
% 0.29/0.57  
% 0.29/0.57  % idiff_0_right
% 0.29/0.57  thf(fact_4366_neg__le__iff__le,axiom,
% 0.29/0.57      ! [B: real,A: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_iff_le
% 0.29/0.57  thf(fact_4367_neg__le__iff__le,axiom,
% 0.29/0.57      ! [B: code_integer,A: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_iff_le
% 0.29/0.57  thf(fact_4368_neg__le__iff__le,axiom,
% 0.29/0.57      ! [B: rat,A: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_iff_le
% 0.29/0.57  thf(fact_4369_neg__le__iff__le,axiom,
% 0.29/0.57      ! [B: int,A: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_iff_le
% 0.29/0.57  thf(fact_4370_add_Oinverse__neutral,axiom,
% 0.29/0.57      ( ( uminus_uminus_real @ zero_zero_real )
% 0.29/0.57      = zero_zero_real ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_neutral
% 0.29/0.57  thf(fact_4371_add_Oinverse__neutral,axiom,
% 0.29/0.57      ( ( uminus_uminus_int @ zero_zero_int )
% 0.29/0.57      = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_neutral
% 0.29/0.57  thf(fact_4372_add_Oinverse__neutral,axiom,
% 0.29/0.57      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 0.29/0.57      = zero_zero_complex ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_neutral
% 0.29/0.57  thf(fact_4373_add_Oinverse__neutral,axiom,
% 0.29/0.57      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.29/0.57      = zero_z3403309356797280102nteger ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_neutral
% 0.29/0.57  thf(fact_4374_add_Oinverse__neutral,axiom,
% 0.29/0.57      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.29/0.57      = zero_zero_rat ) ).
% 0.29/0.57  
% 0.29/0.57  % add.inverse_neutral
% 0.29/0.57  thf(fact_4375_neg__0__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( zero_zero_real
% 0.29/0.57          = ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( zero_zero_real = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_equal_iff_equal
% 0.29/0.57  thf(fact_4376_neg__0__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( zero_zero_int
% 0.29/0.57          = ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( zero_zero_int = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_equal_iff_equal
% 0.29/0.57  thf(fact_4377_neg__0__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( zero_zero_complex
% 0.29/0.57          = ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.57        = ( zero_zero_complex = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_equal_iff_equal
% 0.29/0.57  thf(fact_4378_neg__0__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( zero_z3403309356797280102nteger
% 0.29/0.57          = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_equal_iff_equal
% 0.29/0.57  thf(fact_4379_neg__0__equal__iff__equal,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( zero_zero_rat
% 0.29/0.57          = ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( zero_zero_rat = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_equal_iff_equal
% 0.29/0.57  thf(fact_4380_neg__equal__0__iff__equal,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ( uminus_uminus_real @ A )
% 0.29/0.57          = zero_zero_real )
% 0.29/0.57        = ( A = zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_0_iff_equal
% 0.29/0.57  thf(fact_4381_neg__equal__0__iff__equal,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ( uminus_uminus_int @ A )
% 0.29/0.57          = zero_zero_int )
% 0.29/0.57        = ( A = zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_0_iff_equal
% 0.29/0.57  thf(fact_4382_neg__equal__0__iff__equal,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.57          = zero_zero_complex )
% 0.29/0.57        = ( A = zero_zero_complex ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_0_iff_equal
% 0.29/0.57  thf(fact_4383_neg__equal__0__iff__equal,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.57          = zero_z3403309356797280102nteger )
% 0.29/0.57        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_0_iff_equal
% 0.29/0.57  thf(fact_4384_neg__equal__0__iff__equal,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.57          = zero_zero_rat )
% 0.29/0.57        = ( A = zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_0_iff_equal
% 0.29/0.57  thf(fact_4385_equal__neg__zero,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( A
% 0.29/0.57          = ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( A = zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % equal_neg_zero
% 0.29/0.57  thf(fact_4386_equal__neg__zero,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( A
% 0.29/0.57          = ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( A = zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % equal_neg_zero
% 0.29/0.57  thf(fact_4387_equal__neg__zero,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( A
% 0.29/0.57          = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % equal_neg_zero
% 0.29/0.57  thf(fact_4388_equal__neg__zero,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( A
% 0.29/0.57          = ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( A = zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % equal_neg_zero
% 0.29/0.57  thf(fact_4389_neg__equal__zero,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ( uminus_uminus_real @ A )
% 0.29/0.57          = A )
% 0.29/0.57        = ( A = zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_zero
% 0.29/0.57  thf(fact_4390_neg__equal__zero,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ( uminus_uminus_int @ A )
% 0.29/0.57          = A )
% 0.29/0.57        = ( A = zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_zero
% 0.29/0.57  thf(fact_4391_neg__equal__zero,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.57          = A )
% 0.29/0.57        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_zero
% 0.29/0.57  thf(fact_4392_neg__equal__zero,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.57          = A )
% 0.29/0.57        = ( A = zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_equal_zero
% 0.29/0.57  thf(fact_4393_neg__less__iff__less,axiom,
% 0.29/0.57      ! [B: real,A: real] :
% 0.29/0.57        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_real @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_iff_less
% 0.29/0.57  thf(fact_4394_neg__less__iff__less,axiom,
% 0.29/0.57      ! [B: int,A: int] :
% 0.29/0.57        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_iff_less
% 0.29/0.57  thf(fact_4395_neg__less__iff__less,axiom,
% 0.29/0.57      ! [B: code_integer,A: code_integer] :
% 0.29/0.57        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_iff_less
% 0.29/0.57  thf(fact_4396_neg__less__iff__less,axiom,
% 0.29/0.57      ! [B: rat,A: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_iff_less
% 0.29/0.57  thf(fact_4397_neg__numeral__eq__iff,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.29/0.57          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_numeral_eq_iff
% 0.29/0.57  thf(fact_4398_neg__numeral__eq__iff,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.29/0.57          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_numeral_eq_iff
% 0.29/0.57  thf(fact_4399_neg__numeral__eq__iff,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.29/0.57          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_numeral_eq_iff
% 0.29/0.57  thf(fact_4400_neg__numeral__eq__iff,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.29/0.57          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_numeral_eq_iff
% 0.29/0.57  thf(fact_4401_neg__numeral__eq__iff,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.29/0.57          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.57        = ( M = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_numeral_eq_iff
% 0.29/0.57  thf(fact_4402_mult__minus__left,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.57        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_left
% 0.29/0.57  thf(fact_4403_mult__minus__left,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.57        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_left
% 0.29/0.57  thf(fact_4404_mult__minus__left,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_left
% 0.29/0.57  thf(fact_4405_mult__minus__left,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_left
% 0.29/0.57  thf(fact_4406_mult__minus__left,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.57        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_left
% 0.29/0.57  thf(fact_4407_minus__mult__minus,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.29/0.57        = ( times_times_real @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_minus
% 0.29/0.57  thf(fact_4408_minus__mult__minus,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( times_times_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_minus
% 0.29/0.57  thf(fact_4409_minus__mult__minus,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.57        = ( times_times_complex @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_minus
% 0.29/0.57  thf(fact_4410_minus__mult__minus,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_minus
% 0.29/0.57  thf(fact_4411_minus__mult__minus,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.57        = ( times_times_rat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mult_minus
% 0.29/0.57  thf(fact_4412_mult__minus__right,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.57        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_right
% 0.29/0.57  thf(fact_4413_mult__minus__right,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_right
% 0.29/0.57  thf(fact_4414_mult__minus__right,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_right
% 0.29/0.57  thf(fact_4415_mult__minus__right,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_right
% 0.29/0.57  thf(fact_4416_mult__minus__right,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.57        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus_right
% 0.29/0.57  thf(fact_4417_minus__add__distrib,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.29/0.57        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_distrib
% 0.29/0.57  thf(fact_4418_minus__add__distrib,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.57        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_distrib
% 0.29/0.57  thf(fact_4419_minus__add__distrib,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.57        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_distrib
% 0.29/0.57  thf(fact_4420_minus__add__distrib,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.57        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_distrib
% 0.29/0.57  thf(fact_4421_minus__add__distrib,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.57        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_distrib
% 0.29/0.57  thf(fact_4422_minus__add__cancel,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_cancel
% 0.29/0.57  thf(fact_4423_minus__add__cancel,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_cancel
% 0.29/0.57  thf(fact_4424_minus__add__cancel,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_cancel
% 0.29/0.57  thf(fact_4425_minus__add__cancel,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_cancel
% 0.29/0.57  thf(fact_4426_minus__add__cancel,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_add_cancel
% 0.29/0.57  thf(fact_4427_add__minus__cancel,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % add_minus_cancel
% 0.29/0.57  thf(fact_4428_add__minus__cancel,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % add_minus_cancel
% 0.29/0.57  thf(fact_4429_add__minus__cancel,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % add_minus_cancel
% 0.29/0.57  thf(fact_4430_add__minus__cancel,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % add_minus_cancel
% 0.29/0.57  thf(fact_4431_add__minus__cancel,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.29/0.57        = B ) ).
% 0.29/0.57  
% 0.29/0.57  % add_minus_cancel
% 0.29/0.57  thf(fact_4432_minus__diff__eq,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.57        = ( minus_minus_real @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_diff_eq
% 0.29/0.57  thf(fact_4433_minus__diff__eq,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.57        = ( minus_minus_int @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_diff_eq
% 0.29/0.57  thf(fact_4434_minus__diff__eq,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 0.29/0.57        = ( minus_minus_complex @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_diff_eq
% 0.29/0.57  thf(fact_4435_minus__diff__eq,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.57        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_diff_eq
% 0.29/0.57  thf(fact_4436_minus__diff__eq,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.57        = ( minus_minus_rat @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_diff_eq
% 0.29/0.57  thf(fact_4437_div__minus__minus,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( divide_divide_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_minus_minus
% 0.29/0.57  thf(fact_4438_div__minus__minus,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_minus_minus
% 0.29/0.57  thf(fact_4439_dvd__minus__iff,axiom,
% 0.29/0.57      ! [X4: real,Y: real] :
% 0.29/0.57        ( ( dvd_dvd_real @ X4 @ ( uminus_uminus_real @ Y ) )
% 0.29/0.57        = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_iff
% 0.29/0.57  thf(fact_4440_dvd__minus__iff,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ X4 @ ( uminus_uminus_int @ Y ) )
% 0.29/0.57        = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_iff
% 0.29/0.57  thf(fact_4441_dvd__minus__iff,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex] :
% 0.29/0.57        ( ( dvd_dvd_complex @ X4 @ ( uminus1482373934393186551omplex @ Y ) )
% 0.29/0.57        = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_iff
% 0.29/0.57  thf(fact_4442_dvd__minus__iff,axiom,
% 0.29/0.57      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.57        ( ( dvd_dvd_Code_integer @ X4 @ ( uminus1351360451143612070nteger @ Y ) )
% 0.29/0.57        = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_iff
% 0.29/0.57  thf(fact_4443_dvd__minus__iff,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat] :
% 0.29/0.57        ( ( dvd_dvd_rat @ X4 @ ( uminus_uminus_rat @ Y ) )
% 0.29/0.57        = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % dvd_minus_iff
% 0.29/0.57  thf(fact_4444_minus__dvd__iff,axiom,
% 0.29/0.57      ! [X4: real,Y: real] :
% 0.29/0.57        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X4 ) @ Y )
% 0.29/0.57        = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_dvd_iff
% 0.29/0.57  thf(fact_4445_minus__dvd__iff,axiom,
% 0.29/0.57      ! [X4: int,Y: int] :
% 0.29/0.57        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X4 ) @ Y )
% 0.29/0.57        = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_dvd_iff
% 0.29/0.57  thf(fact_4446_minus__dvd__iff,axiom,
% 0.29/0.57      ! [X4: complex,Y: complex] :
% 0.29/0.57        ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y )
% 0.29/0.57        = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_dvd_iff
% 0.29/0.57  thf(fact_4447_minus__dvd__iff,axiom,
% 0.29/0.57      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.57        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X4 ) @ Y )
% 0.29/0.57        = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_dvd_iff
% 0.29/0.57  thf(fact_4448_minus__dvd__iff,axiom,
% 0.29/0.57      ! [X4: rat,Y: rat] :
% 0.29/0.57        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X4 ) @ Y )
% 0.29/0.57        = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_dvd_iff
% 0.29/0.57  thf(fact_4449_semiring__norm_I88_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( bit0 @ M )
% 0.29/0.57       != ( bit1 @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(88)
% 0.29/0.57  thf(fact_4450_semiring__norm_I89_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( bit1 @ M )
% 0.29/0.57       != ( bit0 @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(89)
% 0.29/0.57  thf(fact_4451_semiring__norm_I84_J,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( one
% 0.29/0.57       != ( bit1 @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(84)
% 0.29/0.57  thf(fact_4452_semiring__norm_I86_J,axiom,
% 0.29/0.57      ! [M: num] :
% 0.29/0.57        ( ( bit1 @ M )
% 0.29/0.57       != one ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(86)
% 0.29/0.57  thf(fact_4453_mod__minus__minus,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_minus_minus
% 0.29/0.57  thf(fact_4454_mod__minus__minus,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mod_minus_minus
% 0.29/0.57  thf(fact_4455_take__bit__of__0,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_of_0
% 0.29/0.57  thf(fact_4456_take__bit__of__0,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 0.29/0.57        = zero_zero_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_of_0
% 0.29/0.57  thf(fact_4457_real__add__minus__iff,axiom,
% 0.29/0.57      ! [X4: real,A: real] :
% 0.29/0.57        ( ( ( plus_plus_real @ X4 @ ( uminus_uminus_real @ A ) )
% 0.29/0.57          = zero_zero_real )
% 0.29/0.57        = ( X4 = A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % real_add_minus_iff
% 0.29/0.57  thf(fact_4458_bit_Oxor__self,axiom,
% 0.29/0.57      ! [X4: int] :
% 0.29/0.57        ( ( bit_se6526347334894502574or_int @ X4 @ X4 )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % bit.xor_self
% 0.29/0.57  thf(fact_4459_xor__self__eq,axiom,
% 0.29/0.57      ! [A: nat] :
% 0.29/0.57        ( ( bit_se6528837805403552850or_nat @ A @ A )
% 0.29/0.57        = zero_zero_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % xor_self_eq
% 0.29/0.57  thf(fact_4460_xor__self__eq,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( bit_se6526347334894502574or_int @ A @ A )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % xor_self_eq
% 0.29/0.57  thf(fact_4461_xor_Oleft__neutral,axiom,
% 0.29/0.57      ! [A: nat] :
% 0.29/0.57        ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % xor.left_neutral
% 0.29/0.57  thf(fact_4462_xor_Oleft__neutral,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % xor.left_neutral
% 0.29/0.57  thf(fact_4463_xor_Oright__neutral,axiom,
% 0.29/0.57      ! [A: nat] :
% 0.29/0.57        ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % xor.right_neutral
% 0.29/0.57  thf(fact_4464_xor_Oright__neutral,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 0.29/0.57        = A ) ).
% 0.29/0.57  
% 0.29/0.57  % xor.right_neutral
% 0.29/0.57  thf(fact_4465_take__bit__xor,axiom,
% 0.29/0.57      ! [N2: nat,A: int,B: int] :
% 0.29/0.57        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 0.29/0.57        = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_xor
% 0.29/0.57  thf(fact_4466_take__bit__xor,axiom,
% 0.29/0.57      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.57        ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 0.29/0.57        = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_xor
% 0.29/0.57  thf(fact_4467_concat__bit__of__zero__2,axiom,
% 0.29/0.57      ! [N2: nat,K: int] :
% 0.29/0.57        ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 0.29/0.57        = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 0.29/0.57  
% 0.29/0.57  % concat_bit_of_zero_2
% 0.29/0.57  thf(fact_4468_semiring__norm_I80_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.57        = ( ord_less_num @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(80)
% 0.29/0.57  thf(fact_4469_semiring__norm_I73_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.57        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % semiring_norm(73)
% 0.29/0.57  thf(fact_4470_neg__less__eq__nonneg,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.29/0.57        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_eq_nonneg
% 0.29/0.57  thf(fact_4471_neg__less__eq__nonneg,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.57        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_eq_nonneg
% 0.29/0.57  thf(fact_4472_neg__less__eq__nonneg,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.57        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_eq_nonneg
% 0.29/0.57  thf(fact_4473_neg__less__eq__nonneg,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.57        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_eq_nonneg
% 0.29/0.57  thf(fact_4474_less__eq__neg__nonpos,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_eq_neg_nonpos
% 0.29/0.57  thf(fact_4475_less__eq__neg__nonpos,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_eq_neg_nonpos
% 0.29/0.57  thf(fact_4476_less__eq__neg__nonpos,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_eq_neg_nonpos
% 0.29/0.57  thf(fact_4477_less__eq__neg__nonpos,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_eq_neg_nonpos
% 0.29/0.57  thf(fact_4478_neg__le__0__iff__le,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.29/0.57        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_0_iff_le
% 0.29/0.57  thf(fact_4479_neg__le__0__iff__le,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.57        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_0_iff_le
% 0.29/0.57  thf(fact_4480_neg__le__0__iff__le,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.57        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_0_iff_le
% 0.29/0.57  thf(fact_4481_neg__le__0__iff__le,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.57        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_le_0_iff_le
% 0.29/0.57  thf(fact_4482_neg__0__le__iff__le,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_le_iff_le
% 0.29/0.57  thf(fact_4483_neg__0__le__iff__le,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_le_iff_le
% 0.29/0.57  thf(fact_4484_neg__0__le__iff__le,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_le_iff_le
% 0.29/0.57  thf(fact_4485_neg__0__le__iff__le,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_le_iff_le
% 0.29/0.57  thf(fact_4486_less__neg__neg,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_neg_neg
% 0.29/0.57  thf(fact_4487_less__neg__neg,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_neg_neg
% 0.29/0.57  thf(fact_4488_less__neg__neg,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_neg_neg
% 0.29/0.57  thf(fact_4489_less__neg__neg,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % less_neg_neg
% 0.29/0.57  thf(fact_4490_neg__less__pos,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.29/0.57        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_pos
% 0.29/0.57  thf(fact_4491_neg__less__pos,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.57        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_pos
% 0.29/0.57  thf(fact_4492_neg__less__pos,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.57        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_pos
% 0.29/0.57  thf(fact_4493_neg__less__pos,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.57        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_pos
% 0.29/0.57  thf(fact_4494_neg__0__less__iff__less,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_less_iff_less
% 0.29/0.57  thf(fact_4495_neg__0__less__iff__less,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_less_iff_less
% 0.29/0.57  thf(fact_4496_neg__0__less__iff__less,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_less_iff_less
% 0.29/0.57  thf(fact_4497_neg__0__less__iff__less,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_0_less_iff_less
% 0.29/0.57  thf(fact_4498_neg__less__0__iff__less,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.29/0.57        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_0_iff_less
% 0.29/0.57  thf(fact_4499_neg__less__0__iff__less,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.57        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_0_iff_less
% 0.29/0.57  thf(fact_4500_neg__less__0__iff__less,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.57        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_0_iff_less
% 0.29/0.57  thf(fact_4501_neg__less__0__iff__less,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.57        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % neg_less_0_iff_less
% 0.29/0.57  thf(fact_4502_ab__left__minus,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.29/0.57        = zero_zero_real ) ).
% 0.29/0.57  
% 0.29/0.57  % ab_left_minus
% 0.29/0.57  thf(fact_4503_ab__left__minus,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % ab_left_minus
% 0.29/0.57  thf(fact_4504_ab__left__minus,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.29/0.57        = zero_zero_complex ) ).
% 0.29/0.57  
% 0.29/0.57  % ab_left_minus
% 0.29/0.57  thf(fact_4505_ab__left__minus,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.57        = zero_z3403309356797280102nteger ) ).
% 0.29/0.57  
% 0.29/0.57  % ab_left_minus
% 0.29/0.57  thf(fact_4506_ab__left__minus,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.57        = zero_zero_rat ) ).
% 0.29/0.57  
% 0.29/0.57  % ab_left_minus
% 0.29/0.57  thf(fact_4507_add_Oright__inverse,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.29/0.57        = zero_zero_real ) ).
% 0.29/0.57  
% 0.29/0.57  % add.right_inverse
% 0.29/0.57  thf(fact_4508_add_Oright__inverse,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % add.right_inverse
% 0.29/0.57  thf(fact_4509_add_Oright__inverse,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.57        = zero_zero_complex ) ).
% 0.29/0.57  
% 0.29/0.57  % add.right_inverse
% 0.29/0.57  thf(fact_4510_add_Oright__inverse,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.57        = zero_z3403309356797280102nteger ) ).
% 0.29/0.57  
% 0.29/0.57  % add.right_inverse
% 0.29/0.57  thf(fact_4511_add_Oright__inverse,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.57        = zero_zero_rat ) ).
% 0.29/0.57  
% 0.29/0.57  % add.right_inverse
% 0.29/0.57  thf(fact_4512_diff__0,axiom,
% 0.29/0.57      ! [A: real] :
% 0.29/0.57        ( ( minus_minus_real @ zero_zero_real @ A )
% 0.29/0.57        = ( uminus_uminus_real @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_0
% 0.29/0.57  thf(fact_4513_diff__0,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.29/0.57        = ( uminus_uminus_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_0
% 0.29/0.57  thf(fact_4514_diff__0,axiom,
% 0.29/0.57      ! [A: complex] :
% 0.29/0.57        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_0
% 0.29/0.57  thf(fact_4515_diff__0,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_0
% 0.29/0.57  thf(fact_4516_diff__0,axiom,
% 0.29/0.57      ! [A: rat] :
% 0.29/0.57        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.29/0.57        = ( uminus_uminus_rat @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_0
% 0.29/0.57  thf(fact_4517_add__neg__numeral__simps_I3_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.57        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_neg_numeral_simps(3)
% 0.29/0.57  thf(fact_4518_add__neg__numeral__simps_I3_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.57        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_neg_numeral_simps(3)
% 0.29/0.57  thf(fact_4519_add__neg__numeral__simps_I3_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_neg_numeral_simps(3)
% 0.29/0.57  thf(fact_4520_add__neg__numeral__simps_I3_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_neg_numeral_simps(3)
% 0.29/0.57  thf(fact_4521_add__neg__numeral__simps_I3_J,axiom,
% 0.29/0.57      ! [M: num,N2: num] :
% 0.29/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.57        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % add_neg_numeral_simps(3)
% 0.29/0.57  thf(fact_4522_mult__minus1,axiom,
% 0.29/0.57      ! [Z: real] :
% 0.29/0.57        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 0.29/0.57        = ( uminus_uminus_real @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1
% 0.29/0.57  thf(fact_4523_mult__minus1,axiom,
% 0.29/0.57      ! [Z: int] :
% 0.29/0.57        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.29/0.57        = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1
% 0.29/0.57  thf(fact_4524_mult__minus1,axiom,
% 0.29/0.57      ! [Z: complex] :
% 0.29/0.57        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1
% 0.29/0.57  thf(fact_4525_mult__minus1,axiom,
% 0.29/0.57      ! [Z: code_integer] :
% 0.29/0.57        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1
% 0.29/0.57  thf(fact_4526_mult__minus1,axiom,
% 0.29/0.57      ! [Z: rat] :
% 0.29/0.57        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.29/0.57        = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1
% 0.29/0.57  thf(fact_4527_mult__minus1__right,axiom,
% 0.29/0.57      ! [Z: real] :
% 0.29/0.57        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.57        = ( uminus_uminus_real @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1_right
% 0.29/0.57  thf(fact_4528_mult__minus1__right,axiom,
% 0.29/0.57      ! [Z: int] :
% 0.29/0.57        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.57        = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1_right
% 0.29/0.57  thf(fact_4529_mult__minus1__right,axiom,
% 0.29/0.57      ! [Z: complex] :
% 0.29/0.57        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1_right
% 0.29/0.57  thf(fact_4530_mult__minus1__right,axiom,
% 0.29/0.57      ! [Z: code_integer] :
% 0.29/0.57        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1_right
% 0.29/0.57  thf(fact_4531_mult__minus1__right,axiom,
% 0.29/0.57      ! [Z: rat] :
% 0.29/0.57        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.57        = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.57  
% 0.29/0.57  % mult_minus1_right
% 0.29/0.57  thf(fact_4532_uminus__add__conv__diff,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.57        = ( minus_minus_real @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % uminus_add_conv_diff
% 0.29/0.57  thf(fact_4533_uminus__add__conv__diff,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.57        = ( minus_minus_int @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % uminus_add_conv_diff
% 0.29/0.57  thf(fact_4534_uminus__add__conv__diff,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.29/0.57        = ( minus_minus_complex @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % uminus_add_conv_diff
% 0.29/0.57  thf(fact_4535_uminus__add__conv__diff,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.57        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % uminus_add_conv_diff
% 0.29/0.57  thf(fact_4536_uminus__add__conv__diff,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.57        = ( minus_minus_rat @ B @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % uminus_add_conv_diff
% 0.29/0.57  thf(fact_4537_diff__minus__eq__add,axiom,
% 0.29/0.57      ! [A: real,B: real] :
% 0.29/0.57        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.57        = ( plus_plus_real @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_minus_eq_add
% 0.29/0.57  thf(fact_4538_diff__minus__eq__add,axiom,
% 0.29/0.57      ! [A: int,B: int] :
% 0.29/0.57        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.57        = ( plus_plus_int @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_minus_eq_add
% 0.29/0.57  thf(fact_4539_diff__minus__eq__add,axiom,
% 0.29/0.57      ! [A: complex,B: complex] :
% 0.29/0.57        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.57        = ( plus_plus_complex @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_minus_eq_add
% 0.29/0.57  thf(fact_4540_diff__minus__eq__add,axiom,
% 0.29/0.57      ! [A: code_integer,B: code_integer] :
% 0.29/0.57        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.57        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_minus_eq_add
% 0.29/0.57  thf(fact_4541_diff__minus__eq__add,axiom,
% 0.29/0.57      ! [A: rat,B: rat] :
% 0.29/0.57        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.57        = ( plus_plus_rat @ A @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % diff_minus_eq_add
% 0.29/0.57  thf(fact_4542_divide__minus1,axiom,
% 0.29/0.57      ! [X4: real] :
% 0.29/0.57        ( ( divide_divide_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.57        = ( uminus_uminus_real @ X4 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_minus1
% 0.29/0.57  thf(fact_4543_divide__minus1,axiom,
% 0.29/0.57      ! [X4: complex] :
% 0.29/0.57        ( ( divide1717551699836669952omplex @ X4 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.57        = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_minus1
% 0.29/0.57  thf(fact_4544_divide__minus1,axiom,
% 0.29/0.57      ! [X4: rat] :
% 0.29/0.57        ( ( divide_divide_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.57        = ( uminus_uminus_rat @ X4 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % divide_minus1
% 0.29/0.57  thf(fact_4545_div__minus1__right,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.57        = ( uminus_uminus_int @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_minus1_right
% 0.29/0.57  thf(fact_4546_div__minus1__right,axiom,
% 0.29/0.57      ! [A: code_integer] :
% 0.29/0.57        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.57        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.29/0.57  
% 0.29/0.57  % div_minus1_right
% 0.29/0.57  thf(fact_4547_of__nat__0,axiom,
% 0.29/0.57      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.29/0.57      = zero_zero_complex ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0
% 0.29/0.57  thf(fact_4548_of__nat__0,axiom,
% 0.29/0.57      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.29/0.57      = zero_zero_rat ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0
% 0.29/0.57  thf(fact_4549_of__nat__0,axiom,
% 0.29/0.57      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.29/0.57      = zero_zero_real ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0
% 0.29/0.57  thf(fact_4550_of__nat__0,axiom,
% 0.29/0.57      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.29/0.57      = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0
% 0.29/0.57  thf(fact_4551_of__nat__0,axiom,
% 0.29/0.57      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.29/0.57      = zero_zero_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0
% 0.29/0.57  thf(fact_4552_of__nat__0__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( zero_zero_complex
% 0.29/0.57          = ( semiri8010041392384452111omplex @ N2 ) )
% 0.29/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0_eq_iff
% 0.29/0.57  thf(fact_4553_of__nat__0__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( zero_zero_rat
% 0.29/0.57          = ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0_eq_iff
% 0.29/0.57  thf(fact_4554_of__nat__0__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( zero_zero_real
% 0.29/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0_eq_iff
% 0.29/0.57  thf(fact_4555_of__nat__0__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( zero_zero_int
% 0.29/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0_eq_iff
% 0.29/0.57  thf(fact_4556_of__nat__0__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( zero_zero_nat
% 0.29/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.57        = ( zero_zero_nat = N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_0_eq_iff
% 0.29/0.57  thf(fact_4557_of__nat__eq__0__iff,axiom,
% 0.29/0.57      ! [M: nat] :
% 0.29/0.57        ( ( ( semiri8010041392384452111omplex @ M )
% 0.29/0.57          = zero_zero_complex )
% 0.29/0.57        = ( M = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_0_iff
% 0.29/0.57  thf(fact_4558_of__nat__eq__0__iff,axiom,
% 0.29/0.57      ! [M: nat] :
% 0.29/0.57        ( ( ( semiri681578069525770553at_rat @ M )
% 0.29/0.57          = zero_zero_rat )
% 0.29/0.57        = ( M = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_0_iff
% 0.29/0.57  thf(fact_4559_of__nat__eq__0__iff,axiom,
% 0.29/0.57      ! [M: nat] :
% 0.29/0.57        ( ( ( semiri5074537144036343181t_real @ M )
% 0.29/0.57          = zero_zero_real )
% 0.29/0.57        = ( M = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_0_iff
% 0.29/0.57  thf(fact_4560_of__nat__eq__0__iff,axiom,
% 0.29/0.57      ! [M: nat] :
% 0.29/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.29/0.57          = zero_zero_int )
% 0.29/0.57        = ( M = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_0_iff
% 0.29/0.57  thf(fact_4561_of__nat__eq__0__iff,axiom,
% 0.29/0.57      ! [M: nat] :
% 0.29/0.57        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.29/0.57          = zero_zero_nat )
% 0.29/0.57        = ( M = zero_zero_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_0_iff
% 0.29/0.57  thf(fact_4562_of__nat__less__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_less_iff
% 0.29/0.57  thf(fact_4563_of__nat__less__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_less_iff
% 0.29/0.57  thf(fact_4564_of__nat__less__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_less_iff
% 0.29/0.57  thf(fact_4565_of__nat__less__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.57        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_less_iff
% 0.29/0.57  thf(fact_4566_of__nat__le__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_le_iff
% 0.29/0.57  thf(fact_4567_of__nat__le__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_le_iff
% 0.29/0.57  thf(fact_4568_of__nat__le__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_le_iff
% 0.29/0.57  thf(fact_4569_of__nat__le__iff,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.57        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_le_iff
% 0.29/0.57  thf(fact_4570_of__nat__numeral,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.57        = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_numeral
% 0.29/0.57  thf(fact_4571_of__nat__numeral,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.57        = ( numera6690914467698888265omplex @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_numeral
% 0.29/0.57  thf(fact_4572_of__nat__numeral,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.57        = ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_numeral
% 0.29/0.57  thf(fact_4573_of__nat__numeral,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.57        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_numeral
% 0.29/0.57  thf(fact_4574_of__nat__numeral,axiom,
% 0.29/0.57      ! [N2: num] :
% 0.29/0.57        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.57        = ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_numeral
% 0.29/0.57  thf(fact_4575_minus__mod__self1,axiom,
% 0.29/0.57      ! [B: int,A: int] :
% 0.29/0.57        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 0.29/0.57        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_self1
% 0.29/0.57  thf(fact_4576_minus__mod__self1,axiom,
% 0.29/0.57      ! [B: code_integer,A: code_integer] :
% 0.29/0.57        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 0.29/0.57        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.57  
% 0.29/0.57  % minus_mod_self1
% 0.29/0.57  thf(fact_4577_of__nat__add,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.57        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_add
% 0.29/0.57  thf(fact_4578_of__nat__add,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.57        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_add
% 0.29/0.57  thf(fact_4579_of__nat__add,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.57        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_add
% 0.29/0.57  thf(fact_4580_of__nat__add,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.57        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_add
% 0.29/0.57  thf(fact_4581_of__nat__mult,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.57        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_mult
% 0.29/0.57  thf(fact_4582_of__nat__mult,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.57        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_mult
% 0.29/0.57  thf(fact_4583_of__nat__mult,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_mult
% 0.29/0.57  thf(fact_4584_of__nat__mult,axiom,
% 0.29/0.57      ! [M: nat,N2: nat] :
% 0.29/0.57        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 0.29/0.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_mult
% 0.29/0.57  thf(fact_4585_take__bit__0,axiom,
% 0.29/0.57      ! [A: int] :
% 0.29/0.57        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 0.29/0.57        = zero_zero_int ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_0
% 0.29/0.57  thf(fact_4586_take__bit__0,axiom,
% 0.29/0.57      ! [A: nat] :
% 0.29/0.57        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 0.29/0.57        = zero_zero_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_0
% 0.29/0.57  thf(fact_4587_of__nat__eq__1__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( semiri8010041392384452111omplex @ N2 )
% 0.29/0.57          = one_one_complex )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_1_iff
% 0.29/0.57  thf(fact_4588_of__nat__eq__1__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( semiri681578069525770553at_rat @ N2 )
% 0.29/0.57          = one_one_rat )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_1_iff
% 0.29/0.57  thf(fact_4589_of__nat__eq__1__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( semiri5074537144036343181t_real @ N2 )
% 0.29/0.57          = one_one_real )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_1_iff
% 0.29/0.57  thf(fact_4590_of__nat__eq__1__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( semiri1314217659103216013at_int @ N2 )
% 0.29/0.57          = one_one_int )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_1_iff
% 0.29/0.57  thf(fact_4591_of__nat__eq__1__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( ( semiri1316708129612266289at_nat @ N2 )
% 0.29/0.57          = one_one_nat )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_1_iff
% 0.29/0.57  thf(fact_4592_of__nat__1__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( one_one_complex
% 0.29/0.57          = ( semiri8010041392384452111omplex @ N2 ) )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1_eq_iff
% 0.29/0.57  thf(fact_4593_of__nat__1__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( one_one_rat
% 0.29/0.57          = ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1_eq_iff
% 0.29/0.57  thf(fact_4594_of__nat__1__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( one_one_real
% 0.29/0.57          = ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1_eq_iff
% 0.29/0.57  thf(fact_4595_of__nat__1__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( one_one_int
% 0.29/0.57          = ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1_eq_iff
% 0.29/0.57  thf(fact_4596_of__nat__1__eq__iff,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( one_one_nat
% 0.29/0.57          = ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.57        = ( N2 = one_one_nat ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1_eq_iff
% 0.29/0.57  thf(fact_4597_of__nat__1,axiom,
% 0.29/0.57      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.29/0.57      = one_one_complex ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1
% 0.29/0.57  thf(fact_4598_of__nat__1,axiom,
% 0.29/0.57      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.29/0.57      = one_one_rat ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1
% 0.29/0.57  thf(fact_4599_of__nat__1,axiom,
% 0.29/0.57      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.29/0.57      = one_one_real ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1
% 0.29/0.57  thf(fact_4600_of__nat__1,axiom,
% 0.29/0.57      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.29/0.57      = one_one_int ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1
% 0.29/0.57  thf(fact_4601_of__nat__1,axiom,
% 0.29/0.57      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.29/0.57      = one_one_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_1
% 0.29/0.57  thf(fact_4602_take__bit__Suc__1,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 0.29/0.57        = one_one_int ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_Suc_1
% 0.29/0.57  thf(fact_4603_take__bit__Suc__1,axiom,
% 0.29/0.57      ! [N2: nat] :
% 0.29/0.57        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.29/0.57        = one_one_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_Suc_1
% 0.29/0.57  thf(fact_4604_take__bit__numeral__1,axiom,
% 0.29/0.57      ! [L: num] :
% 0.29/0.57        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 0.29/0.57        = one_one_int ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_numeral_1
% 0.29/0.57  thf(fact_4605_take__bit__numeral__1,axiom,
% 0.29/0.57      ! [L: num] :
% 0.29/0.57        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 0.29/0.57        = one_one_nat ) ).
% 0.29/0.57  
% 0.29/0.57  % take_bit_numeral_1
% 0.29/0.57  thf(fact_4606_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.57      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.57        ( ( ( semiri8010041392384452111omplex @ X4 )
% 0.29/0.57          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 0.29/0.57        = ( X4
% 0.29/0.57          = ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.29/0.57  thf(fact_4607_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.57      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.57        ( ( ( semiri5074537144036343181t_real @ X4 )
% 0.29/0.57          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.29/0.57        = ( X4
% 0.29/0.57          = ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.29/0.57  thf(fact_4608_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.57      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.57        ( ( ( semiri1314217659103216013at_int @ X4 )
% 0.29/0.57          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.29/0.57        = ( X4
% 0.29/0.57          = ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.29/0.57  thf(fact_4609_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.57      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.57        ( ( ( semiri1316708129612266289at_nat @ X4 )
% 0.29/0.57          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.29/0.57        = ( X4
% 0.29/0.57          = ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.29/0.57  thf(fact_4610_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.29/0.57      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.57        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 0.29/0.57          = ( semiri8010041392384452111omplex @ X4 ) )
% 0.29/0.57        = ( ( power_power_nat @ B @ W )
% 0.29/0.57          = X4 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.29/0.57  thf(fact_4611_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.29/0.57      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.57        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 0.29/0.57          = ( semiri5074537144036343181t_real @ X4 ) )
% 0.29/0.57        = ( ( power_power_nat @ B @ W )
% 0.29/0.57          = X4 ) ) ).
% 0.29/0.57  
% 0.29/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.29/0.57  thf(fact_4612_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.29/0.57      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.57        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 0.29/0.58          = ( semiri1314217659103216013at_int @ X4 ) )
% 0.29/0.58        = ( ( power_power_nat @ B @ W )
% 0.29/0.58          = X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_eq_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4613_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 0.29/0.58          = ( semiri1316708129612266289at_nat @ X4 ) )
% 0.29/0.58        = ( ( power_power_nat @ B @ W )
% 0.29/0.58          = X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_eq_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4614_of__nat__power,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 0.29/0.58        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power
% 0.29/0.58  thf(fact_4615_of__nat__power,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 0.29/0.58        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power
% 0.29/0.58  thf(fact_4616_of__nat__power,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 0.29/0.58        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power
% 0.29/0.58  thf(fact_4617_of__nat__power,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 0.29/0.58        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power
% 0.29/0.58  thf(fact_4618_signed__take__bit__of__minus__1,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_of_minus_1
% 0.29/0.58  thf(fact_4619_signed__take__bit__of__minus__1,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_of_minus_1
% 0.29/0.58  thf(fact_4620_semiring__norm_I9_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.58        = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(9)
% 0.29/0.58  thf(fact_4621_semiring__norm_I7_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(7)
% 0.29/0.58  thf(fact_4622_semiring__norm_I15_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.58        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(15)
% 0.29/0.58  thf(fact_4623_semiring__norm_I14_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(14)
% 0.29/0.58  thf(fact_4624_semiring__norm_I81_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.58        = ( ord_less_num @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(81)
% 0.29/0.58  thf(fact_4625_semiring__norm_I72_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(72)
% 0.29/0.58  thf(fact_4626_semiring__norm_I77_J,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(77)
% 0.29/0.58  thf(fact_4627_semiring__norm_I70_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(70)
% 0.29/0.58  thf(fact_4628_dbl__simps_I1_J,axiom,
% 0.29/0.58      ! [K: num] :
% 0.29/0.58        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(1)
% 0.29/0.58  thf(fact_4629_dbl__simps_I1_J,axiom,
% 0.29/0.58      ! [K: num] :
% 0.29/0.58        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(1)
% 0.29/0.58  thf(fact_4630_dbl__simps_I1_J,axiom,
% 0.29/0.58      ! [K: num] :
% 0.29/0.58        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(1)
% 0.29/0.58  thf(fact_4631_dbl__simps_I1_J,axiom,
% 0.29/0.58      ! [K: num] :
% 0.29/0.58        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(1)
% 0.29/0.58  thf(fact_4632_dbl__simps_I1_J,axiom,
% 0.29/0.58      ! [K: num] :
% 0.29/0.58        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(1)
% 0.29/0.58  thf(fact_4633_of__nat__of__bool,axiom,
% 0.29/0.58      ! [P: $o] :
% 0.29/0.58        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.29/0.58        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_of_bool
% 0.29/0.58  thf(fact_4634_of__nat__of__bool,axiom,
% 0.29/0.58      ! [P: $o] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.29/0.58        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_of_bool
% 0.29/0.58  thf(fact_4635_of__nat__of__bool,axiom,
% 0.29/0.58      ! [P: $o] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.29/0.58        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_of_bool
% 0.29/0.58  thf(fact_4636_of__nat__of__bool,axiom,
% 0.29/0.58      ! [P: $o] :
% 0.29/0.58        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.29/0.58        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_of_bool
% 0.29/0.58  thf(fact_4637_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.58      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58      = zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(7)
% 0.29/0.58  thf(fact_4638_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.58      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58      = zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(7)
% 0.29/0.58  thf(fact_4639_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.58      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58      = zero_zero_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(7)
% 0.29/0.58  thf(fact_4640_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.58      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58      = zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(7)
% 0.29/0.58  thf(fact_4641_add__neg__numeral__special_I7_J,axiom,
% 0.29/0.58      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58      = zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(7)
% 0.29/0.58  thf(fact_4642_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.58      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.29/0.58      = zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(8)
% 0.29/0.58  thf(fact_4643_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.58      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.29/0.58      = zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(8)
% 0.29/0.58  thf(fact_4644_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.58      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.29/0.58      = zero_zero_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(8)
% 0.29/0.58  thf(fact_4645_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.58      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.29/0.58      = zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(8)
% 0.29/0.58  thf(fact_4646_add__neg__numeral__special_I8_J,axiom,
% 0.29/0.58      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.29/0.58      = zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(8)
% 0.29/0.58  thf(fact_4647_diff__numeral__special_I12_J,axiom,
% 0.29/0.58      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58      = zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(12)
% 0.29/0.58  thf(fact_4648_diff__numeral__special_I12_J,axiom,
% 0.29/0.58      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58      = zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(12)
% 0.29/0.58  thf(fact_4649_diff__numeral__special_I12_J,axiom,
% 0.29/0.58      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58      = zero_zero_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(12)
% 0.29/0.58  thf(fact_4650_diff__numeral__special_I12_J,axiom,
% 0.29/0.58      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58      = zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(12)
% 0.29/0.58  thf(fact_4651_diff__numeral__special_I12_J,axiom,
% 0.29/0.58      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58      = zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(12)
% 0.29/0.58  thf(fact_4652_numeral__eq__neg__one__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.58          = ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_eq_neg_one_iff
% 0.29/0.58  thf(fact_4653_numeral__eq__neg__one__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.58          = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_eq_neg_one_iff
% 0.29/0.58  thf(fact_4654_numeral__eq__neg__one__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_eq_neg_one_iff
% 0.29/0.58  thf(fact_4655_numeral__eq__neg__one__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_eq_neg_one_iff
% 0.29/0.58  thf(fact_4656_numeral__eq__neg__one__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.58          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_eq_neg_one_iff
% 0.29/0.58  thf(fact_4657_neg__one__eq__numeral__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_real @ one_one_real )
% 0.29/0.58          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_eq_numeral_iff
% 0.29/0.58  thf(fact_4658_neg__one__eq__numeral__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_int @ one_one_int )
% 0.29/0.58          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_eq_numeral_iff
% 0.29/0.58  thf(fact_4659_neg__one__eq__numeral__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_eq_numeral_iff
% 0.29/0.58  thf(fact_4660_neg__one__eq__numeral__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_eq_numeral_iff
% 0.29/0.58  thf(fact_4661_neg__one__eq__numeral__iff,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.29/0.58          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( N2 = one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_eq_numeral_iff
% 0.29/0.58  thf(fact_4662_of__nat__le__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.29/0.58        = ( M = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_0_iff
% 0.29/0.58  thf(fact_4663_of__nat__le__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.29/0.58        = ( M = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_0_iff
% 0.29/0.58  thf(fact_4664_of__nat__le__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.29/0.58        = ( M = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_0_iff
% 0.29/0.58  thf(fact_4665_of__nat__le__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.29/0.58        = ( M = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_0_iff
% 0.29/0.58  thf(fact_4666_left__minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat,A: real] :
% 0.29/0.58        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 0.29/0.58        = A ) ).
% 0.29/0.58  
% 0.29/0.58  % left_minus_one_mult_self
% 0.29/0.58  thf(fact_4667_left__minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat,A: int] :
% 0.29/0.58        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 0.29/0.58        = A ) ).
% 0.29/0.58  
% 0.29/0.58  % left_minus_one_mult_self
% 0.29/0.58  thf(fact_4668_left__minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat,A: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 0.29/0.58        = A ) ).
% 0.29/0.58  
% 0.29/0.58  % left_minus_one_mult_self
% 0.29/0.58  thf(fact_4669_left__minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat,A: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 0.29/0.58        = A ) ).
% 0.29/0.58  
% 0.29/0.58  % left_minus_one_mult_self
% 0.29/0.58  thf(fact_4670_left__minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat,A: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 0.29/0.58        = A ) ).
% 0.29/0.58  
% 0.29/0.58  % left_minus_one_mult_self
% 0.29/0.58  thf(fact_4671_minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 0.29/0.58        = one_one_real ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_one_mult_self
% 0.29/0.58  thf(fact_4672_minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 0.29/0.58        = one_one_int ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_one_mult_self
% 0.29/0.58  thf(fact_4673_minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 0.29/0.58        = one_one_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_one_mult_self
% 0.29/0.58  thf(fact_4674_minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 0.29/0.58        = one_one_Code_integer ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_one_mult_self
% 0.29/0.58  thf(fact_4675_minus__one__mult__self,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 0.29/0.58        = one_one_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_one_mult_self
% 0.29/0.58  thf(fact_4676_mod__minus1__right,axiom,
% 0.29/0.58      ! [A: int] :
% 0.29/0.58        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58        = zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus1_right
% 0.29/0.58  thf(fact_4677_mod__minus1__right,axiom,
% 0.29/0.58      ! [A: code_integer] :
% 0.29/0.58        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58        = zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus1_right
% 0.29/0.58  thf(fact_4678_of__nat__Suc,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 0.29/0.58        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_Suc
% 0.29/0.58  thf(fact_4679_of__nat__Suc,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.29/0.58        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_Suc
% 0.29/0.58  thf(fact_4680_of__nat__Suc,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.29/0.58        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_Suc
% 0.29/0.58  thf(fact_4681_of__nat__Suc,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.29/0.58        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_Suc
% 0.29/0.58  thf(fact_4682_of__nat__Suc,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.29/0.58        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_Suc
% 0.29/0.58  thf(fact_4683_take__bit__of__1__eq__0__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.29/0.58          = zero_zero_int )
% 0.29/0.58        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_1_eq_0_iff
% 0.29/0.58  thf(fact_4684_take__bit__of__1__eq__0__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.29/0.58          = zero_zero_nat )
% 0.29/0.58        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_1_eq_0_iff
% 0.29/0.58  thf(fact_4685_semiring__norm_I168_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: real] :
% 0.29/0.58        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.29/0.58        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(168)
% 0.29/0.58  thf(fact_4686_semiring__norm_I168_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: int] :
% 0.29/0.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.29/0.58        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(168)
% 0.29/0.58  thf(fact_4687_semiring__norm_I168_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: complex] :
% 0.29/0.58        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.29/0.58        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(168)
% 0.29/0.58  thf(fact_4688_semiring__norm_I168_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.29/0.58        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(168)
% 0.29/0.58  thf(fact_4689_semiring__norm_I168_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: rat] :
% 0.29/0.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.29/0.58        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(168)
% 0.29/0.58  thf(fact_4690_diff__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(3)
% 0.29/0.58  thf(fact_4691_diff__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(3)
% 0.29/0.58  thf(fact_4692_diff__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(3)
% 0.29/0.58  thf(fact_4693_diff__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(3)
% 0.29/0.58  thf(fact_4694_diff__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(3)
% 0.29/0.58  thf(fact_4695_diff__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(2)
% 0.29/0.58  thf(fact_4696_diff__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(2)
% 0.29/0.58  thf(fact_4697_diff__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.58        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(2)
% 0.29/0.58  thf(fact_4698_diff__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(2)
% 0.29/0.58  thf(fact_4699_diff__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_simps(2)
% 0.29/0.58  thf(fact_4700_zdiv__numeral__Bit1,axiom,
% 0.29/0.58      ! [V: num,W: num] :
% 0.29/0.58        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.29/0.58        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zdiv_numeral_Bit1
% 0.29/0.58  thf(fact_4701_semiring__norm_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 0.29/0.58        = ( bit1 @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(3)
% 0.29/0.58  thf(fact_4702_semiring__norm_I4_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(4)
% 0.29/0.58  thf(fact_4703_semiring__norm_I5_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 0.29/0.58        = ( bit1 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(5)
% 0.29/0.58  thf(fact_4704_semiring__norm_I8_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 0.29/0.58        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(8)
% 0.29/0.58  thf(fact_4705_semiring__norm_I10_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(10)
% 0.29/0.58  thf(fact_4706_semiring__norm_I172_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: real] :
% 0.29/0.58        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(172)
% 0.29/0.58  thf(fact_4707_semiring__norm_I172_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: int] :
% 0.29/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(172)
% 0.29/0.58  thf(fact_4708_semiring__norm_I172_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(172)
% 0.29/0.58  thf(fact_4709_semiring__norm_I172_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(172)
% 0.29/0.58  thf(fact_4710_semiring__norm_I172_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(172)
% 0.29/0.58  thf(fact_4711_semiring__norm_I171_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: real] :
% 0.29/0.58        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(171)
% 0.29/0.58  thf(fact_4712_semiring__norm_I171_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: int] :
% 0.29/0.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(171)
% 0.29/0.58  thf(fact_4713_semiring__norm_I171_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(171)
% 0.29/0.58  thf(fact_4714_semiring__norm_I171_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(171)
% 0.29/0.58  thf(fact_4715_semiring__norm_I171_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.29/0.58        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(171)
% 0.29/0.58  thf(fact_4716_semiring__norm_I170_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: real] :
% 0.29/0.58        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 0.29/0.58        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(170)
% 0.29/0.58  thf(fact_4717_semiring__norm_I170_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: int] :
% 0.29/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 0.29/0.58        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(170)
% 0.29/0.58  thf(fact_4718_semiring__norm_I170_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 0.29/0.58        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(170)
% 0.29/0.58  thf(fact_4719_semiring__norm_I170_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(170)
% 0.29/0.58  thf(fact_4720_semiring__norm_I170_J,axiom,
% 0.29/0.58      ! [V: num,W: num,Y: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 0.29/0.58        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(170)
% 0.29/0.58  thf(fact_4721_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(3)
% 0.29/0.58  thf(fact_4722_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(3)
% 0.29/0.58  thf(fact_4723_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(3)
% 0.29/0.58  thf(fact_4724_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(3)
% 0.29/0.58  thf(fact_4725_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(3)
% 0.29/0.58  thf(fact_4726_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(2)
% 0.29/0.58  thf(fact_4727_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(2)
% 0.29/0.58  thf(fact_4728_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(2)
% 0.29/0.58  thf(fact_4729_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(2)
% 0.29/0.58  thf(fact_4730_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(2)
% 0.29/0.58  thf(fact_4731_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(1)
% 0.29/0.58  thf(fact_4732_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(1)
% 0.29/0.58  thf(fact_4733_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.58        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(1)
% 0.29/0.58  thf(fact_4734_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(1)
% 0.29/0.58  thf(fact_4735_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_neg_numeral_simps(1)
% 0.29/0.58  thf(fact_4736_neg__numeral__le__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_iff
% 0.29/0.58  thf(fact_4737_neg__numeral__le__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_iff
% 0.29/0.58  thf(fact_4738_neg__numeral__le__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_iff
% 0.29/0.58  thf(fact_4739_neg__numeral__le__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_iff
% 0.29/0.58  thf(fact_4740_neg__numeral__less__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( ord_less_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_iff
% 0.29/0.58  thf(fact_4741_neg__numeral__less__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( ord_less_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_iff
% 0.29/0.58  thf(fact_4742_neg__numeral__less__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( ord_less_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_iff
% 0.29/0.58  thf(fact_4743_neg__numeral__less__iff,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( ord_less_num @ N2 @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_iff
% 0.29/0.58  thf(fact_4744_take__bit__of__Suc__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.58        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_Suc_0
% 0.29/0.58  thf(fact_4745_semiring__norm_I16_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(16)
% 0.29/0.58  thf(fact_4746_semiring__norm_I79_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(79)
% 0.29/0.58  thf(fact_4747_semiring__norm_I74_J,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.58        = ( ord_less_num @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % semiring_norm(74)
% 0.29/0.58  thf(fact_4748_not__neg__one__le__neg__numeral__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_le_neg_numeral_iff
% 0.29/0.58  thf(fact_4749_not__neg__one__le__neg__numeral__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_le_neg_numeral_iff
% 0.29/0.58  thf(fact_4750_not__neg__one__le__neg__numeral__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_le_neg_numeral_iff
% 0.29/0.58  thf(fact_4751_not__neg__one__le__neg__numeral__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_le_neg_numeral_iff
% 0.29/0.58  thf(fact_4752_le__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: real,B: real,W: num] :
% 0.29/0.58        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.29/0.58        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4753_le__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: rat,B: rat,W: num] :
% 0.29/0.58        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.58        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4754_divide__le__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: real,W: num,A: real] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.29/0.58        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_le_eq_numeral1(2)
% 0.29/0.58  thf(fact_4755_divide__le__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: rat,W: num,A: rat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.29/0.58        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_le_eq_numeral1(2)
% 0.29/0.58  thf(fact_4756_eq__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: real,B: real,W: num] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.29/0.58        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.58             != zero_zero_real )
% 0.29/0.58           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.58              = B ) )
% 0.29/0.58          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.58              = zero_zero_real )
% 0.29/0.58           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4757_eq__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: complex,B: complex,W: num] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.29/0.58        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.58             != zero_zero_complex )
% 0.29/0.58           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.58              = B ) )
% 0.29/0.58          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.58              = zero_zero_complex )
% 0.29/0.58           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4758_eq__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: rat,B: rat,W: num] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.58             != zero_zero_rat )
% 0.29/0.58           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.58              = B ) )
% 0.29/0.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.58              = zero_zero_rat )
% 0.29/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4759_divide__eq__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: real,W: num,A: real] :
% 0.29/0.58        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.58          = A )
% 0.29/0.58        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.58             != zero_zero_real )
% 0.29/0.58           => ( B
% 0.29/0.58              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 0.29/0.58          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.58              = zero_zero_real )
% 0.29/0.58           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_eq_eq_numeral1(2)
% 0.29/0.58  thf(fact_4760_divide__eq__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: complex,W: num,A: complex] :
% 0.29/0.58        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.58          = A )
% 0.29/0.58        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.58             != zero_zero_complex )
% 0.29/0.58           => ( B
% 0.29/0.58              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 0.29/0.58          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.58              = zero_zero_complex )
% 0.29/0.58           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_eq_eq_numeral1(2)
% 0.29/0.58  thf(fact_4761_divide__eq__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: rat,W: num,A: rat] :
% 0.29/0.58        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.58          = A )
% 0.29/0.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.58             != zero_zero_rat )
% 0.29/0.58           => ( B
% 0.29/0.58              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 0.29/0.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.58              = zero_zero_rat )
% 0.29/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_eq_eq_numeral1(2)
% 0.29/0.58  thf(fact_4762_neg__numeral__less__neg__one__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_neg_one_iff
% 0.29/0.58  thf(fact_4763_neg__numeral__less__neg__one__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_neg_one_iff
% 0.29/0.58  thf(fact_4764_neg__numeral__less__neg__one__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_neg_one_iff
% 0.29/0.58  thf(fact_4765_neg__numeral__less__neg__one__iff,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58        = ( M != one ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_neg_one_iff
% 0.29/0.58  thf(fact_4766_less__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: real,B: real,W: num] :
% 0.29/0.58        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.29/0.58        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4767_less__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [A: rat,B: rat,W: num] :
% 0.29/0.58        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.58        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_divide_eq_numeral1(2)
% 0.29/0.58  thf(fact_4768_divide__less__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: real,W: num,A: real] :
% 0.29/0.58        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.29/0.58        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_less_eq_numeral1(2)
% 0.29/0.58  thf(fact_4769_divide__less__eq__numeral1_I2_J,axiom,
% 0.29/0.58      ! [B: rat,W: num,A: rat] :
% 0.29/0.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.29/0.58        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % divide_less_eq_numeral1(2)
% 0.29/0.58  thf(fact_4770_of__nat__0__less__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_less_iff
% 0.29/0.58  thf(fact_4771_of__nat__0__less__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_less_iff
% 0.29/0.58  thf(fact_4772_of__nat__0__less__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_less_iff
% 0.29/0.58  thf(fact_4773_of__nat__0__less__iff,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_less_iff
% 0.29/0.58  thf(fact_4774_power2__minus,axiom,
% 0.29/0.58      ! [A: real] :
% 0.29/0.58        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power2_minus
% 0.29/0.58  thf(fact_4775_power2__minus,axiom,
% 0.29/0.58      ! [A: int] :
% 0.29/0.58        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power2_minus
% 0.29/0.58  thf(fact_4776_power2__minus,axiom,
% 0.29/0.58      ! [A: complex] :
% 0.29/0.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power2_minus
% 0.29/0.58  thf(fact_4777_power2__minus,axiom,
% 0.29/0.58      ! [A: code_integer] :
% 0.29/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power2_minus
% 0.29/0.58  thf(fact_4778_power2__minus,axiom,
% 0.29/0.58      ! [A: rat] :
% 0.29/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power2_minus
% 0.29/0.58  thf(fact_4779_xor__numerals_I3_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(3)
% 0.29/0.58  thf(fact_4780_xor__numerals_I3_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(3)
% 0.29/0.58  thf(fact_4781_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4782_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4783_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4784_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4785_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4786_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4787_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4788_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4789_xor__numerals_I1_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(1)
% 0.29/0.58  thf(fact_4790_xor__numerals_I1_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(1)
% 0.29/0.58  thf(fact_4791_xor__numerals_I2_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(2)
% 0.29/0.58  thf(fact_4792_xor__numerals_I2_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(2)
% 0.29/0.58  thf(fact_4793_xor__numerals_I5_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(5)
% 0.29/0.58  thf(fact_4794_xor__numerals_I5_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 0.29/0.58        = ( numeral_numeral_int @ ( bit1 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(5)
% 0.29/0.58  thf(fact_4795_xor__numerals_I8_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(8)
% 0.29/0.58  thf(fact_4796_xor__numerals_I8_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 0.29/0.58        = ( numeral_numeral_int @ ( bit0 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(8)
% 0.29/0.58  thf(fact_4797_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4798_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4799_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4800_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,B: nat,W: nat] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4801_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4802_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4803_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4804_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.29/0.58      ! [B: nat,W: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_of_nat_power_cancel_iff
% 0.29/0.58  thf(fact_4805_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [Y: nat,X4: num,N2: nat] :
% 0.29/0.58        ( ( ( semiri4216267220026989637d_enat @ Y )
% 0.29/0.58          = ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 ) )
% 0.29/0.58        = ( Y
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4806_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [Y: nat,X4: num,N2: nat] :
% 0.29/0.58        ( ( ( semiri8010041392384452111omplex @ Y )
% 0.29/0.58          = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 0.29/0.58        = ( Y
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4807_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [Y: nat,X4: num,N2: nat] :
% 0.29/0.58        ( ( ( semiri5074537144036343181t_real @ Y )
% 0.29/0.58          = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.58        = ( Y
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4808_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [Y: nat,X4: num,N2: nat] :
% 0.29/0.58        ( ( ( semiri1314217659103216013at_int @ Y )
% 0.29/0.58          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 0.29/0.58        = ( Y
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4809_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [Y: nat,X4: num,N2: nat] :
% 0.29/0.58        ( ( ( semiri1316708129612266289at_nat @ Y )
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 0.29/0.58        = ( Y
% 0.29/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4810_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: num,N2: nat,Y: nat] :
% 0.29/0.58        ( ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 )
% 0.29/0.58          = ( semiri4216267220026989637d_enat @ Y ) )
% 0.29/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4811_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: num,N2: nat,Y: nat] :
% 0.29/0.58        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 0.29/0.58          = ( semiri8010041392384452111omplex @ Y ) )
% 0.29/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4812_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: num,N2: nat,Y: nat] :
% 0.29/0.58        ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 0.29/0.58          = ( semiri5074537144036343181t_real @ Y ) )
% 0.29/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4813_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: num,N2: nat,Y: nat] :
% 0.29/0.58        ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.58          = ( semiri1314217659103216013at_int @ Y ) )
% 0.29/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4814_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [X4: num,N2: nat,Y: nat] :
% 0.29/0.58        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = ( semiri1316708129612266289at_nat @ Y ) )
% 0.29/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.58          = Y ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4815_real__of__nat__less__numeral__iff,axiom,
% 0.29/0.58      ! [N2: nat,W: num] :
% 0.29/0.58        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 0.29/0.58        = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_less_numeral_iff
% 0.29/0.58  thf(fact_4816_numeral__less__real__of__nat__iff,axiom,
% 0.29/0.58      ! [W: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_less_real_of_nat_iff
% 0.29/0.58  thf(fact_4817_numeral__le__real__of__nat__iff,axiom,
% 0.29/0.58      ! [N2: num,M: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_le_real_of_nat_iff
% 0.29/0.58  thf(fact_4818_take__bit__of__1,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 0.29/0.58        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_1
% 0.29/0.58  thf(fact_4819_take__bit__of__1,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 0.29/0.58        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_1
% 0.29/0.58  thf(fact_4820_take__bit__of__1,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 0.29/0.58        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_1
% 0.29/0.58  thf(fact_4821_add__neg__numeral__special_I9_J,axiom,
% 0.29/0.58      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(9)
% 0.29/0.58  thf(fact_4822_add__neg__numeral__special_I9_J,axiom,
% 0.29/0.58      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(9)
% 0.29/0.58  thf(fact_4823_add__neg__numeral__special_I9_J,axiom,
% 0.29/0.58      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(9)
% 0.29/0.58  thf(fact_4824_add__neg__numeral__special_I9_J,axiom,
% 0.29/0.58      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(9)
% 0.29/0.58  thf(fact_4825_add__neg__numeral__special_I9_J,axiom,
% 0.29/0.58      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_neg_numeral_special(9)
% 0.29/0.58  thf(fact_4826_diff__numeral__special_I10_J,axiom,
% 0.29/0.58      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.29/0.58      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(10)
% 0.29/0.58  thf(fact_4827_diff__numeral__special_I10_J,axiom,
% 0.29/0.58      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.29/0.58      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(10)
% 0.29/0.58  thf(fact_4828_diff__numeral__special_I10_J,axiom,
% 0.29/0.58      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.29/0.58      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(10)
% 0.29/0.58  thf(fact_4829_diff__numeral__special_I10_J,axiom,
% 0.29/0.58      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.29/0.58      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(10)
% 0.29/0.58  thf(fact_4830_diff__numeral__special_I10_J,axiom,
% 0.29/0.58      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.29/0.58      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(10)
% 0.29/0.58  thf(fact_4831_diff__numeral__special_I11_J,axiom,
% 0.29/0.58      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(11)
% 0.29/0.58  thf(fact_4832_diff__numeral__special_I11_J,axiom,
% 0.29/0.58      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(11)
% 0.29/0.58  thf(fact_4833_diff__numeral__special_I11_J,axiom,
% 0.29/0.58      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(11)
% 0.29/0.58  thf(fact_4834_diff__numeral__special_I11_J,axiom,
% 0.29/0.58      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(11)
% 0.29/0.58  thf(fact_4835_diff__numeral__special_I11_J,axiom,
% 0.29/0.58      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(11)
% 0.29/0.58  thf(fact_4836_minus__1__div__2__eq,axiom,
% 0.29/0.58      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.58      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_1_div_2_eq
% 0.29/0.58  thf(fact_4837_minus__1__div__2__eq,axiom,
% 0.29/0.58      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.58      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_1_div_2_eq
% 0.29/0.58  thf(fact_4838_bits__minus__1__mod__2__eq,axiom,
% 0.29/0.58      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.58      = one_one_int ) ).
% 0.29/0.58  
% 0.29/0.58  % bits_minus_1_mod_2_eq
% 0.29/0.58  thf(fact_4839_bits__minus__1__mod__2__eq,axiom,
% 0.29/0.58      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.58      = one_one_Code_integer ) ).
% 0.29/0.58  
% 0.29/0.58  % bits_minus_1_mod_2_eq
% 0.29/0.58  thf(fact_4840_minus__1__mod__2__eq,axiom,
% 0.29/0.58      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.58      = one_one_int ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_1_mod_2_eq
% 0.29/0.58  thf(fact_4841_minus__1__mod__2__eq,axiom,
% 0.29/0.58      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.58      = one_one_Code_integer ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_1_mod_2_eq
% 0.29/0.58  thf(fact_4842_of__nat__zero__less__power__iff,axiom,
% 0.29/0.58      ! [X4: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X4 ) @ N2 ) )
% 0.29/0.58        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_zero_less_power_iff
% 0.29/0.58  thf(fact_4843_of__nat__zero__less__power__iff,axiom,
% 0.29/0.58      ! [X4: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X4 ) @ N2 ) )
% 0.29/0.58        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_zero_less_power_iff
% 0.29/0.58  thf(fact_4844_of__nat__zero__less__power__iff,axiom,
% 0.29/0.58      ! [X4: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X4 ) @ N2 ) )
% 0.29/0.58        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_zero_less_power_iff
% 0.29/0.58  thf(fact_4845_of__nat__zero__less__power__iff,axiom,
% 0.29/0.58      ! [X4: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ N2 ) )
% 0.29/0.58        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.58          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_zero_less_power_iff
% 0.29/0.58  thf(fact_4846_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [A: real,N2: nat] :
% 0.29/0.58        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Power.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4847_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [A: int,N2: nat] :
% 0.29/0.58        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Power.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4848_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [A: complex,N2: nat] :
% 0.29/0.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Power.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4849_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [A: code_integer,N2: nat] :
% 0.29/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Power.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4850_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [A: rat,N2: nat] :
% 0.29/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Power.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4851_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [N2: nat,A: real] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 0.29/0.58          = ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Parity.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4852_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [N2: nat,A: int] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.29/0.58          = ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Parity.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4853_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [N2: nat,A: complex] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 0.29/0.58          = ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Parity.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4854_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [N2: nat,A: code_integer] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.29/0.58          = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Parity.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4855_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.29/0.58      ! [N2: nat,A: rat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.29/0.58          = ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Parity.ring_1_class.power_minus_even
% 0.29/0.58  thf(fact_4856_power__minus__odd,axiom,
% 0.29/0.58      ! [N2: nat,A: real] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_odd
% 0.29/0.58  thf(fact_4857_power__minus__odd,axiom,
% 0.29/0.58      ! [N2: nat,A: int] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_odd
% 0.29/0.58  thf(fact_4858_power__minus__odd,axiom,
% 0.29/0.58      ! [N2: nat,A: complex] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_odd
% 0.29/0.58  thf(fact_4859_power__minus__odd,axiom,
% 0.29/0.58      ! [N2: nat,A: code_integer] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_odd
% 0.29/0.58  thf(fact_4860_power__minus__odd,axiom,
% 0.29/0.58      ! [N2: nat,A: rat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_odd
% 0.29/0.58  thf(fact_4861_even__take__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,A: code_integer] :
% 0.29/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 0.29/0.58        = ( ( N2 = zero_zero_nat )
% 0.29/0.58          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_take_bit_eq
% 0.29/0.58  thf(fact_4862_even__take__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,A: int] :
% 0.29/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.29/0.58        = ( ( N2 = zero_zero_nat )
% 0.29/0.58          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_take_bit_eq
% 0.29/0.58  thf(fact_4863_even__take__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,A: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 0.29/0.58        = ( ( N2 = zero_zero_nat )
% 0.29/0.58          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_take_bit_eq
% 0.29/0.58  thf(fact_4864_xor__numerals_I7_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(7)
% 0.29/0.58  thf(fact_4865_xor__numerals_I7_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(7)
% 0.29/0.58  thf(fact_4866_diff__numeral__special_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(3)
% 0.29/0.58  thf(fact_4867_diff__numeral__special_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(3)
% 0.29/0.58  thf(fact_4868_diff__numeral__special_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.58        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(3)
% 0.29/0.58  thf(fact_4869_diff__numeral__special_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.58        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(3)
% 0.29/0.58  thf(fact_4870_diff__numeral__special_I3_J,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.58        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(3)
% 0.29/0.58  thf(fact_4871_diff__numeral__special_I4_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 0.29/0.58        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(4)
% 0.29/0.58  thf(fact_4872_diff__numeral__special_I4_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.29/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(4)
% 0.29/0.58  thf(fact_4873_diff__numeral__special_I4_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(4)
% 0.29/0.58  thf(fact_4874_diff__numeral__special_I4_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(4)
% 0.29/0.58  thf(fact_4875_diff__numeral__special_I4_J,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.29/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_numeral_special(4)
% 0.29/0.58  thf(fact_4876_Suc__div__eq__add3__div__numeral,axiom,
% 0.29/0.58      ! [M: nat,V: num] :
% 0.29/0.58        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.58        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Suc_div_eq_add3_div_numeral
% 0.29/0.58  thf(fact_4877_div__Suc__eq__div__add3,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.29/0.58        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_Suc_eq_div_add3
% 0.29/0.58  thf(fact_4878_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.29/0.58      ! [M: nat,V: num] :
% 0.29/0.58        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Suc_mod_eq_add3_mod_numeral
% 0.29/0.58  thf(fact_4879_mod__Suc__eq__mod__add3,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 0.29/0.58        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_Suc_eq_mod_add3
% 0.29/0.58  thf(fact_4880_signed__take__bit__Suc__minus__bit0,axiom,
% 0.29/0.58      ! [N2: nat,K: num] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.58        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_Suc_minus_bit0
% 0.29/0.58  thf(fact_4881_xor__nat__numerals_I4_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_nat_numerals(4)
% 0.29/0.58  thf(fact_4882_xor__nat__numerals_I3_J,axiom,
% 0.29/0.58      ! [X4: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_nat_numerals(3)
% 0.29/0.58  thf(fact_4883_xor__nat__numerals_I2_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_nat_numerals(2)
% 0.29/0.58  thf(fact_4884_xor__nat__numerals_I1_J,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_nat_numerals(1)
% 0.29/0.58  thf(fact_4885_dbl__simps_I4_J,axiom,
% 0.29/0.58      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.58      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(4)
% 0.29/0.58  thf(fact_4886_dbl__simps_I4_J,axiom,
% 0.29/0.58      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.58      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(4)
% 0.29/0.58  thf(fact_4887_dbl__simps_I4_J,axiom,
% 0.29/0.58      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.58      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(4)
% 0.29/0.58  thf(fact_4888_dbl__simps_I4_J,axiom,
% 0.29/0.58      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.58      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(4)
% 0.29/0.58  thf(fact_4889_dbl__simps_I4_J,axiom,
% 0.29/0.58      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.58      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dbl_simps(4)
% 0.29/0.58  thf(fact_4890_power__minus1__even,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = one_one_real ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus1_even
% 0.29/0.58  thf(fact_4891_power__minus1__even,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = one_one_int ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus1_even
% 0.29/0.58  thf(fact_4892_power__minus1__even,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = one_one_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus1_even
% 0.29/0.58  thf(fact_4893_power__minus1__even,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = one_one_Code_integer ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus1_even
% 0.29/0.58  thf(fact_4894_power__minus1__even,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = one_one_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus1_even
% 0.29/0.58  thf(fact_4895_neg__one__even__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 0.29/0.58          = one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_even_power
% 0.29/0.58  thf(fact_4896_neg__one__even__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.29/0.58          = one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_even_power
% 0.29/0.58  thf(fact_4897_neg__one__even__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 0.29/0.58          = one_one_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_even_power
% 0.29/0.58  thf(fact_4898_neg__one__even__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.29/0.58          = one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_even_power
% 0.29/0.58  thf(fact_4899_neg__one__even__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.29/0.58          = one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_even_power
% 0.29/0.58  thf(fact_4900_neg__one__odd__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_odd_power
% 0.29/0.58  thf(fact_4901_neg__one__odd__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_odd_power
% 0.29/0.58  thf(fact_4902_neg__one__odd__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_odd_power
% 0.29/0.58  thf(fact_4903_neg__one__odd__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_odd_power
% 0.29/0.58  thf(fact_4904_neg__one__odd__power,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.29/0.58          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_odd_power
% 0.29/0.58  thf(fact_4905_even__of__nat,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_of_nat
% 0.29/0.58  thf(fact_4906_even__of__nat,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_of_nat
% 0.29/0.58  thf(fact_4907_even__of__nat,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % even_of_nat
% 0.29/0.58  thf(fact_4908_take__bit__Suc__0,axiom,
% 0.29/0.58      ! [A: code_integer] :
% 0.29/0.58        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 0.29/0.58        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_Suc_0
% 0.29/0.58  thf(fact_4909_take__bit__Suc__0,axiom,
% 0.29/0.58      ! [A: int] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 0.29/0.58        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_Suc_0
% 0.29/0.58  thf(fact_4910_take__bit__Suc__0,axiom,
% 0.29/0.58      ! [A: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 0.29/0.58        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_Suc_0
% 0.29/0.58  thf(fact_4911_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4912_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4913_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4914_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4915_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4916_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4917_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4918_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 0.29/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4919_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4920_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4921_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4922_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.29/0.58      ! [X4: nat,I2: num,N2: nat] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.29/0.58  thf(fact_4923_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4924_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4925_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4926_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.29/0.58      ! [I2: num,N2: nat,X4: nat] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 0.29/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.29/0.58  thf(fact_4927_signed__take__bit__0,axiom,
% 0.29/0.58      ! [A: code_integer] :
% 0.29/0.58        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_0
% 0.29/0.58  thf(fact_4928_signed__take__bit__0,axiom,
% 0.29/0.58      ! [A: int] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.29/0.58        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_0
% 0.29/0.58  thf(fact_4929_xor__numerals_I4_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(4)
% 0.29/0.58  thf(fact_4930_xor__numerals_I4_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(4)
% 0.29/0.58  thf(fact_4931_xor__numerals_I6_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(6)
% 0.29/0.58  thf(fact_4932_xor__numerals_I6_J,axiom,
% 0.29/0.58      ! [X4: num,Y: num] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_numerals(6)
% 0.29/0.58  thf(fact_4933_take__bit__of__exp,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_exp
% 0.29/0.58  thf(fact_4934_take__bit__of__exp,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_exp
% 0.29/0.58  thf(fact_4935_take__bit__of__exp,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.58        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_exp
% 0.29/0.58  thf(fact_4936_take__bit__of__2,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_2
% 0.29/0.58  thf(fact_4937_take__bit__of__2,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_2
% 0.29/0.58  thf(fact_4938_take__bit__of__2,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.58        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_2
% 0.29/0.58  thf(fact_4939_zmod__numeral__Bit1,axiom,
% 0.29/0.58      ! [V: num,W: num] :
% 0.29/0.58        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.29/0.58        = ( 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 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zmod_numeral_Bit1
% 0.29/0.58  thf(fact_4940_signed__take__bit__Suc__bit1,axiom,
% 0.29/0.58      ! [N2: nat,K: num] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_Suc_bit1
% 0.29/0.58  thf(fact_4941_signed__take__bit__Suc__minus__bit1,axiom,
% 0.29/0.58      ! [N2: nat,K: num] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_Suc_minus_bit1
% 0.29/0.58  thf(fact_4942_signed__take__bit__minus,axiom,
% 0.29/0.58      ! [N2: nat,K: int] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 0.29/0.58        = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_minus
% 0.29/0.58  thf(fact_4943_minus__real__def,axiom,
% 0.29/0.58      ( minus_minus_real
% 0.29/0.58      = ( ^ [X: real,Y5: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y5 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_real_def
% 0.29/0.58  thf(fact_4944_xor_Oassoc,axiom,
% 0.29/0.58      ! [A: nat,B: nat,C: nat] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 0.29/0.58        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.assoc
% 0.29/0.58  thf(fact_4945_xor_Oassoc,axiom,
% 0.29/0.58      ! [A: int,B: int,C: int] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 0.29/0.58        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.assoc
% 0.29/0.58  thf(fact_4946_xor_Ocommute,axiom,
% 0.29/0.58      ( bit_se6528837805403552850or_nat
% 0.29/0.58      = ( ^ [A3: nat,B2: nat] : ( bit_se6528837805403552850or_nat @ B2 @ A3 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.commute
% 0.29/0.58  thf(fact_4947_xor_Ocommute,axiom,
% 0.29/0.58      ( bit_se6526347334894502574or_int
% 0.29/0.58      = ( ^ [A3: int,B2: int] : ( bit_se6526347334894502574or_int @ B2 @ A3 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.commute
% 0.29/0.58  thf(fact_4948_of__nat__xor__eq,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 0.29/0.58        = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_xor_eq
% 0.29/0.58  thf(fact_4949_of__nat__xor__eq,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 0.29/0.58        = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_xor_eq
% 0.29/0.58  thf(fact_4950_take__bit__of__nat,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 0.29/0.58        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_nat
% 0.29/0.58  thf(fact_4951_take__bit__of__nat,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 0.29/0.58        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_of_nat
% 0.29/0.58  thf(fact_4952_xor_Oleft__commute,axiom,
% 0.29/0.58      ! [B: nat,A: nat,C: nat] :
% 0.29/0.58        ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 0.29/0.58        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.left_commute
% 0.29/0.58  thf(fact_4953_xor_Oleft__commute,axiom,
% 0.29/0.58      ! [B: int,A: int,C: int] :
% 0.29/0.58        ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 0.29/0.58        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor.left_commute
% 0.29/0.58  thf(fact_4954_equation__minus__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % equation_minus_iff
% 0.29/0.58  thf(fact_4955_equation__minus__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % equation_minus_iff
% 0.29/0.58  thf(fact_4956_equation__minus__iff,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % equation_minus_iff
% 0.29/0.58  thf(fact_4957_equation__minus__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % equation_minus_iff
% 0.29/0.58  thf(fact_4958_equation__minus__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % equation_minus_iff
% 0.29/0.58  thf(fact_4959_minus__equation__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ( uminus_uminus_real @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( uminus_uminus_real @ B )
% 0.29/0.58          = A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_equation_iff
% 0.29/0.58  thf(fact_4960_minus__equation__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ( uminus_uminus_int @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( uminus_uminus_int @ B )
% 0.29/0.58          = A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_equation_iff
% 0.29/0.58  thf(fact_4961_minus__equation__iff,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( uminus1482373934393186551omplex @ B )
% 0.29/0.58          = A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_equation_iff
% 0.29/0.58  thf(fact_4962_minus__equation__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( uminus1351360451143612070nteger @ B )
% 0.29/0.58          = A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_equation_iff
% 0.29/0.58  thf(fact_4963_minus__equation__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( uminus_uminus_rat @ B )
% 0.29/0.58          = A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_equation_iff
% 0.29/0.58  thf(fact_4964_power__minus__Bit1,axiom,
% 0.29/0.58      ! [X4: real,K: num] :
% 0.29/0.58        ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_Bit1
% 0.29/0.58  thf(fact_4965_power__minus__Bit1,axiom,
% 0.29/0.58      ! [X4: int,K: num] :
% 0.29/0.58        ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_Bit1
% 0.29/0.58  thf(fact_4966_power__minus__Bit1,axiom,
% 0.29/0.58      ! [X4: complex,K: num] :
% 0.29/0.58        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_Bit1
% 0.29/0.58  thf(fact_4967_power__minus__Bit1,axiom,
% 0.29/0.58      ! [X4: code_integer,K: num] :
% 0.29/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_Bit1
% 0.29/0.58  thf(fact_4968_power__minus__Bit1,axiom,
% 0.29/0.58      ! [X4: rat,K: num] :
% 0.29/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % power_minus_Bit1
% 0.29/0.58  thf(fact_4969_take__bit__add,axiom,
% 0.29/0.58      ! [N2: nat,A: int,B: int] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 0.29/0.58        = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_add
% 0.29/0.58  thf(fact_4970_take__bit__add,axiom,
% 0.29/0.58      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.58        ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 0.29/0.58        = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_add
% 0.29/0.58  thf(fact_4971_take__bit__tightened,axiom,
% 0.29/0.58      ! [N2: nat,A: int,B: int,M: nat] :
% 0.29/0.58        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.29/0.58          = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 0.29/0.58       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 0.29/0.58            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_tightened
% 0.29/0.58  thf(fact_4972_take__bit__tightened,axiom,
% 0.29/0.58      ! [N2: nat,A: nat,B: nat,M: nat] :
% 0.29/0.58        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.29/0.58          = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 0.29/0.58       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 0.29/0.58            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_tightened
% 0.29/0.58  thf(fact_4973_take__bit__tightened__less__eq__nat,axiom,
% 0.29/0.58      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q3 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_tightened_less_eq_nat
% 0.29/0.58  thf(fact_4974_take__bit__nat__less__eq__self,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_nat_less_eq_self
% 0.29/0.58  thf(fact_4975_mult__of__nat__commute,axiom,
% 0.29/0.58      ! [X4: nat,Y: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X4 ) @ Y )
% 0.29/0.58        = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_of_nat_commute
% 0.29/0.58  thf(fact_4976_mult__of__nat__commute,axiom,
% 0.29/0.58      ! [X4: nat,Y: real] :
% 0.29/0.58        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ Y )
% 0.29/0.58        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_of_nat_commute
% 0.29/0.58  thf(fact_4977_mult__of__nat__commute,axiom,
% 0.29/0.58      ! [X4: nat,Y: int] :
% 0.29/0.58        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X4 ) @ Y )
% 0.29/0.58        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_of_nat_commute
% 0.29/0.58  thf(fact_4978_mult__of__nat__commute,axiom,
% 0.29/0.58      ! [X4: nat,Y: nat] :
% 0.29/0.58        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ Y )
% 0.29/0.58        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mult_of_nat_commute
% 0.29/0.58  thf(fact_4979_take__bit__mult,axiom,
% 0.29/0.58      ! [N2: nat,K: int,L: int] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 0.29/0.58        = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_mult
% 0.29/0.58  thf(fact_4980_le__imp__neg__le,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.58       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_imp_neg_le
% 0.29/0.58  thf(fact_4981_le__imp__neg__le,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.58       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_imp_neg_le
% 0.29/0.58  thf(fact_4982_le__imp__neg__le,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.58       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_imp_neg_le
% 0.29/0.58  thf(fact_4983_le__imp__neg__le,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.58       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_imp_neg_le
% 0.29/0.58  thf(fact_4984_minus__le__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.58        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_le_iff
% 0.29/0.58  thf(fact_4985_minus__le__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.58        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_le_iff
% 0.29/0.58  thf(fact_4986_minus__le__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.58        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_le_iff
% 0.29/0.58  thf(fact_4987_minus__le__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.58        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_le_iff
% 0.29/0.58  thf(fact_4988_le__minus__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_iff
% 0.29/0.58  thf(fact_4989_le__minus__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_iff
% 0.29/0.58  thf(fact_4990_le__minus__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_iff
% 0.29/0.58  thf(fact_4991_le__minus__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_iff
% 0.29/0.58  thf(fact_4992_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_real @ A @ B )
% 0.29/0.58       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_negate_coefficient(2)
% 0.29/0.58  thf(fact_4993_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_int @ A @ B )
% 0.29/0.58       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_negate_coefficient(2)
% 0.29/0.58  thf(fact_4994_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.58       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_negate_coefficient(2)
% 0.29/0.58  thf(fact_4995_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_rat @ A @ B )
% 0.29/0.58       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_negate_coefficient(2)
% 0.29/0.58  thf(fact_4996_minus__less__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.58        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_less_iff
% 0.29/0.58  thf(fact_4997_minus__less__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.58        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_less_iff
% 0.29/0.58  thf(fact_4998_minus__less__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.58        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_less_iff
% 0.29/0.58  thf(fact_4999_minus__less__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.58        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_less_iff
% 0.29/0.58  thf(fact_5000_less__minus__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_iff
% 0.29/0.58  thf(fact_5001_less__minus__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_iff
% 0.29/0.58  thf(fact_5002_less__minus__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_iff
% 0.29/0.58  thf(fact_5003_less__minus__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_iff
% 0.29/0.58  thf(fact_5004_verit__eq__simplify_I14_J,axiom,
% 0.29/0.58      ! [X22: num,X32: num] :
% 0.29/0.58        ( ( bit0 @ X22 )
% 0.29/0.58       != ( bit1 @ X32 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_eq_simplify(14)
% 0.29/0.58  thf(fact_5005_verit__eq__simplify_I12_J,axiom,
% 0.29/0.58      ! [X32: num] :
% 0.29/0.58        ( one
% 0.29/0.58       != ( bit1 @ X32 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % verit_eq_simplify(12)
% 0.29/0.58  thf(fact_5006_numeral__neq__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( numeral_numeral_real @ M )
% 0.29/0.58       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_numeral
% 0.29/0.58  thf(fact_5007_numeral__neq__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( numeral_numeral_int @ M )
% 0.29/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_numeral
% 0.29/0.58  thf(fact_5008_numeral__neq__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( numera6690914467698888265omplex @ M )
% 0.29/0.58       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_numeral
% 0.29/0.58  thf(fact_5009_numeral__neq__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( numera6620942414471956472nteger @ M )
% 0.29/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_numeral
% 0.29/0.58  thf(fact_5010_numeral__neq__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( numeral_numeral_rat @ M )
% 0.29/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_numeral
% 0.29/0.58  thf(fact_5011_neg__numeral__neq__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.29/0.58       != ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_neq_numeral
% 0.29/0.58  thf(fact_5012_neg__numeral__neq__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.29/0.58       != ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_neq_numeral
% 0.29/0.58  thf(fact_5013_neg__numeral__neq__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.29/0.58       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_neq_numeral
% 0.29/0.58  thf(fact_5014_neg__numeral__neq__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.29/0.58       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_neq_numeral
% 0.29/0.58  thf(fact_5015_neg__numeral__neq__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.29/0.58       != ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_neq_numeral
% 0.29/0.58  thf(fact_5016_square__eq__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ( times_times_real @ A @ A )
% 0.29/0.58          = ( times_times_real @ B @ B ) )
% 0.29/0.58        = ( ( A = B )
% 0.29/0.58          | ( A
% 0.29/0.58            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_iff
% 0.29/0.58  thf(fact_5017_square__eq__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ( times_times_int @ A @ A )
% 0.29/0.58          = ( times_times_int @ B @ B ) )
% 0.29/0.58        = ( ( A = B )
% 0.29/0.58          | ( A
% 0.29/0.58            = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_iff
% 0.29/0.58  thf(fact_5018_square__eq__iff,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( ( times_times_complex @ A @ A )
% 0.29/0.58          = ( times_times_complex @ B @ B ) )
% 0.29/0.58        = ( ( A = B )
% 0.29/0.58          | ( A
% 0.29/0.58            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_iff
% 0.29/0.58  thf(fact_5019_square__eq__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.29/0.58          = ( times_3573771949741848930nteger @ B @ B ) )
% 0.29/0.58        = ( ( A = B )
% 0.29/0.58          | ( A
% 0.29/0.58            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_iff
% 0.29/0.58  thf(fact_5020_square__eq__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ( times_times_rat @ A @ A )
% 0.29/0.58          = ( times_times_rat @ B @ B ) )
% 0.29/0.58        = ( ( A = B )
% 0.29/0.58          | ( A
% 0.29/0.58            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_iff
% 0.29/0.58  thf(fact_5021_minus__mult__commute,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.58        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_mult_commute
% 0.29/0.58  thf(fact_5022_minus__mult__commute,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.58        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_mult_commute
% 0.29/0.58  thf(fact_5023_minus__mult__commute,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.29/0.58        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_mult_commute
% 0.29/0.58  thf(fact_5024_minus__mult__commute,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.58        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_mult_commute
% 0.29/0.58  thf(fact_5025_minus__mult__commute,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.58        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_mult_commute
% 0.29/0.58  thf(fact_5026_one__neq__neg__one,axiom,
% 0.29/0.58      ( one_one_real
% 0.29/0.58     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_one
% 0.29/0.58  thf(fact_5027_one__neq__neg__one,axiom,
% 0.29/0.58      ( one_one_int
% 0.29/0.58     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_one
% 0.29/0.58  thf(fact_5028_one__neq__neg__one,axiom,
% 0.29/0.58      ( one_one_complex
% 0.29/0.58     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_one
% 0.29/0.58  thf(fact_5029_one__neq__neg__one,axiom,
% 0.29/0.58      ( one_one_Code_integer
% 0.29/0.58     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_one
% 0.29/0.58  thf(fact_5030_one__neq__neg__one,axiom,
% 0.29/0.58      ( one_one_rat
% 0.29/0.58     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_one
% 0.29/0.58  thf(fact_5031_add_Oinverse__distrib__swap,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.29/0.58        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_distrib_swap
% 0.29/0.58  thf(fact_5032_add_Oinverse__distrib__swap,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.58        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_distrib_swap
% 0.29/0.58  thf(fact_5033_add_Oinverse__distrib__swap,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.58        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_distrib_swap
% 0.29/0.58  thf(fact_5034_add_Oinverse__distrib__swap,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.58        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_distrib_swap
% 0.29/0.58  thf(fact_5035_add_Oinverse__distrib__swap,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.58        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_distrib_swap
% 0.29/0.58  thf(fact_5036_group__cancel_Oneg1,axiom,
% 0.29/0.58      ! [A2: real,K: real,A: real] :
% 0.29/0.58        ( ( A2
% 0.29/0.58          = ( plus_plus_real @ K @ A ) )
% 0.29/0.58       => ( ( uminus_uminus_real @ A2 )
% 0.29/0.58          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.neg1
% 0.29/0.58  thf(fact_5037_group__cancel_Oneg1,axiom,
% 0.29/0.58      ! [A2: int,K: int,A: int] :
% 0.29/0.58        ( ( A2
% 0.29/0.58          = ( plus_plus_int @ K @ A ) )
% 0.29/0.58       => ( ( uminus_uminus_int @ A2 )
% 0.29/0.58          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.neg1
% 0.29/0.58  thf(fact_5038_group__cancel_Oneg1,axiom,
% 0.29/0.58      ! [A2: complex,K: complex,A: complex] :
% 0.29/0.58        ( ( A2
% 0.29/0.58          = ( plus_plus_complex @ K @ A ) )
% 0.29/0.58       => ( ( uminus1482373934393186551omplex @ A2 )
% 0.29/0.58          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.neg1
% 0.29/0.58  thf(fact_5039_group__cancel_Oneg1,axiom,
% 0.29/0.58      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.29/0.58        ( ( A2
% 0.29/0.58          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.29/0.58       => ( ( uminus1351360451143612070nteger @ A2 )
% 0.29/0.58          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.neg1
% 0.29/0.58  thf(fact_5040_group__cancel_Oneg1,axiom,
% 0.29/0.58      ! [A2: rat,K: rat,A: rat] :
% 0.29/0.58        ( ( A2
% 0.29/0.58          = ( plus_plus_rat @ K @ A ) )
% 0.29/0.58       => ( ( uminus_uminus_rat @ A2 )
% 0.29/0.58          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.neg1
% 0.29/0.58  thf(fact_5041_is__num__normalize_I8_J,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.29/0.58        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % is_num_normalize(8)
% 0.29/0.58  thf(fact_5042_is__num__normalize_I8_J,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.58        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % is_num_normalize(8)
% 0.29/0.58  thf(fact_5043_is__num__normalize_I8_J,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.29/0.58        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % is_num_normalize(8)
% 0.29/0.58  thf(fact_5044_is__num__normalize_I8_J,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.58        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % is_num_normalize(8)
% 0.29/0.58  thf(fact_5045_is__num__normalize_I8_J,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.58        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % is_num_normalize(8)
% 0.29/0.58  thf(fact_5046_take__bit__diff,axiom,
% 0.29/0.58      ! [N2: nat,K: int,L: int] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 0.29/0.58        = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_diff
% 0.29/0.58  thf(fact_5047_minus__diff__minus,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_minus
% 0.29/0.58  thf(fact_5048_minus__diff__minus,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_minus
% 0.29/0.58  thf(fact_5049_minus__diff__minus,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_minus
% 0.29/0.58  thf(fact_5050_minus__diff__minus,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_minus
% 0.29/0.58  thf(fact_5051_minus__diff__minus,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_minus
% 0.29/0.58  thf(fact_5052_minus__diff__commute,axiom,
% 0.29/0.58      ! [B: real,A: real] :
% 0.29/0.58        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.29/0.58        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_commute
% 0.29/0.58  thf(fact_5053_minus__diff__commute,axiom,
% 0.29/0.58      ! [B: int,A: int] :
% 0.29/0.58        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.29/0.58        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_commute
% 0.29/0.58  thf(fact_5054_minus__diff__commute,axiom,
% 0.29/0.58      ! [B: complex,A: complex] :
% 0.29/0.58        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 0.29/0.58        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_commute
% 0.29/0.58  thf(fact_5055_minus__diff__commute,axiom,
% 0.29/0.58      ! [B: code_integer,A: code_integer] :
% 0.29/0.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.29/0.58        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_commute
% 0.29/0.58  thf(fact_5056_minus__diff__commute,axiom,
% 0.29/0.58      ! [B: rat,A: rat] :
% 0.29/0.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.29/0.58        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_diff_commute
% 0.29/0.58  thf(fact_5057_minus__divide__left,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.58        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_left
% 0.29/0.58  thf(fact_5058_minus__divide__left,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.58        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_left
% 0.29/0.58  thf(fact_5059_minus__divide__left,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.58        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_left
% 0.29/0.58  thf(fact_5060_minus__divide__divide,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( divide_divide_real @ A @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_divide
% 0.29/0.58  thf(fact_5061_minus__divide__divide,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_divide
% 0.29/0.58  thf(fact_5062_minus__divide__divide,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( divide_divide_rat @ A @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_divide
% 0.29/0.58  thf(fact_5063_minus__divide__right,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.58        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_right
% 0.29/0.58  thf(fact_5064_minus__divide__right,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.58        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_right
% 0.29/0.58  thf(fact_5065_minus__divide__right,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.58        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % minus_divide_right
% 0.29/0.58  thf(fact_5066_div__minus__right,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_minus_right
% 0.29/0.58  thf(fact_5067_div__minus__right,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_minus_right
% 0.29/0.58  thf(fact_5068_Diff__mono,axiom,
% 0.29/0.58      ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 0.29/0.58        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.29/0.58       => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 0.29/0.58         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Diff_mono
% 0.29/0.58  thf(fact_5069_Diff__mono,axiom,
% 0.29/0.58      ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 0.29/0.58        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.29/0.58       => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 0.29/0.58         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Diff_mono
% 0.29/0.58  thf(fact_5070_Diff__subset,axiom,
% 0.29/0.58      ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 0.29/0.58  
% 0.29/0.58  % Diff_subset
% 0.29/0.58  thf(fact_5071_Diff__subset,axiom,
% 0.29/0.58      ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 0.29/0.58  
% 0.29/0.58  % Diff_subset
% 0.29/0.58  thf(fact_5072_double__diff,axiom,
% 0.29/0.58      ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 0.29/0.58        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.29/0.58       => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 0.29/0.58         => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.29/0.58            = A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % double_diff
% 0.29/0.58  thf(fact_5073_double__diff,axiom,
% 0.29/0.58      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.29/0.58        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.29/0.58       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.29/0.58         => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.29/0.58            = A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % double_diff
% 0.29/0.58  thf(fact_5074_mod__minus__eq,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 0.29/0.58        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_eq
% 0.29/0.58  thf(fact_5075_mod__minus__eq,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 0.29/0.58        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_eq
% 0.29/0.58  thf(fact_5076_mod__minus__cong,axiom,
% 0.29/0.58      ! [A: int,B: int,A4: int] :
% 0.29/0.58        ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.58          = ( modulo_modulo_int @ A4 @ B ) )
% 0.29/0.58       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.58          = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_cong
% 0.29/0.58  thf(fact_5077_mod__minus__cong,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer,A4: code_integer] :
% 0.29/0.58        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.29/0.58          = ( modulo364778990260209775nteger @ A4 @ B ) )
% 0.29/0.58       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.58          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_cong
% 0.29/0.58  thf(fact_5078_mod__minus__right,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_right
% 0.29/0.58  thf(fact_5079_mod__minus__right,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % mod_minus_right
% 0.29/0.58  thf(fact_5080_psubset__imp__ex__mem,axiom,
% 0.29/0.58      ! [A2: set_real,B3: set_real] :
% 0.29/0.58        ( ( ord_less_set_real @ A2 @ B3 )
% 0.29/0.58       => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % psubset_imp_ex_mem
% 0.29/0.58  thf(fact_5081_psubset__imp__ex__mem,axiom,
% 0.29/0.58      ! [A2: set_complex,B3: set_complex] :
% 0.29/0.58        ( ( ord_less_set_complex @ A2 @ B3 )
% 0.29/0.58       => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % psubset_imp_ex_mem
% 0.29/0.58  thf(fact_5082_psubset__imp__ex__mem,axiom,
% 0.29/0.58      ! [A2: set_int,B3: set_int] :
% 0.29/0.58        ( ( ord_less_set_int @ A2 @ B3 )
% 0.29/0.58       => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % psubset_imp_ex_mem
% 0.29/0.58  thf(fact_5083_psubset__imp__ex__mem,axiom,
% 0.29/0.58      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.29/0.58        ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 0.29/0.58       => ? [B5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B5 @ ( minus_1356011639430497352at_nat @ B3 @ A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % psubset_imp_ex_mem
% 0.29/0.58  thf(fact_5084_psubset__imp__ex__mem,axiom,
% 0.29/0.58      ! [A2: set_nat,B3: set_nat] :
% 0.29/0.58        ( ( ord_less_set_nat @ A2 @ B3 )
% 0.29/0.58       => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % psubset_imp_ex_mem
% 0.29/0.58  thf(fact_5085_concat__bit__eq__iff,axiom,
% 0.29/0.58      ! [N2: nat,K: int,L: int,R3: int,S: int] :
% 0.29/0.58        ( ( ( bit_concat_bit @ N2 @ K @ L )
% 0.29/0.58          = ( bit_concat_bit @ N2 @ R3 @ S ) )
% 0.29/0.58        = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.58            = ( bit_se2923211474154528505it_int @ N2 @ R3 ) )
% 0.29/0.58          & ( L = S ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % concat_bit_eq_iff
% 0.29/0.58  thf(fact_5086_concat__bit__take__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,B: int] :
% 0.29/0.58        ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 0.29/0.58        = ( bit_concat_bit @ N2 @ B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % concat_bit_take_bit_eq
% 0.29/0.58  thf(fact_5087_real__of__nat__div2,axiom,
% 0.29/0.58      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_div2
% 0.29/0.58  thf(fact_5088_real__of__nat__div3,axiom,
% 0.29/0.58      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_div3
% 0.29/0.58  thf(fact_5089_of__nat__0__le__iff,axiom,
% 0.29/0.58      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_le_iff
% 0.29/0.58  thf(fact_5090_of__nat__0__le__iff,axiom,
% 0.29/0.58      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_le_iff
% 0.29/0.58  thf(fact_5091_of__nat__0__le__iff,axiom,
% 0.29/0.58      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_le_iff
% 0.29/0.58  thf(fact_5092_of__nat__0__le__iff,axiom,
% 0.29/0.58      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_0_le_iff
% 0.29/0.58  thf(fact_5093_of__nat__less__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_0_iff
% 0.29/0.58  thf(fact_5094_of__nat__less__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_0_iff
% 0.29/0.58  thf(fact_5095_of__nat__less__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_0_iff
% 0.29/0.58  thf(fact_5096_of__nat__less__0__iff,axiom,
% 0.29/0.58      ! [M: nat] :
% 0.29/0.58        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_0_iff
% 0.29/0.58  thf(fact_5097_of__nat__neq__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 0.29/0.58       != zero_zero_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_neq_0
% 0.29/0.58  thf(fact_5098_of__nat__neq__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 0.29/0.58       != zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_neq_0
% 0.29/0.58  thf(fact_5099_of__nat__neq__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 0.29/0.58       != zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_neq_0
% 0.29/0.58  thf(fact_5100_of__nat__neq__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 0.29/0.58       != zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_neq_0
% 0.29/0.58  thf(fact_5101_of__nat__neq__0,axiom,
% 0.29/0.58      ! [N2: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 0.29/0.58       != zero_zero_nat ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_neq_0
% 0.29/0.58  thf(fact_5102_div__mult2__eq_H,axiom,
% 0.29/0.58      ! [A: code_integer,M: nat,N2: nat] :
% 0.29/0.58        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 0.29/0.58        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_mult2_eq'
% 0.29/0.58  thf(fact_5103_div__mult2__eq_H,axiom,
% 0.29/0.58      ! [A: int,M: nat,N2: nat] :
% 0.29/0.58        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.58        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_mult2_eq'
% 0.29/0.58  thf(fact_5104_div__mult2__eq_H,axiom,
% 0.29/0.58      ! [A: nat,M: nat,N2: nat] :
% 0.29/0.58        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 0.29/0.58        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % div_mult2_eq'
% 0.29/0.58  thf(fact_5105_of__nat__less__imp__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.58       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_imp_less
% 0.29/0.58  thf(fact_5106_of__nat__less__imp__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.58       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_imp_less
% 0.29/0.58  thf(fact_5107_of__nat__less__imp__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.58       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_imp_less
% 0.29/0.58  thf(fact_5108_of__nat__less__imp__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.58       => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_less_imp_less
% 0.29/0.58  thf(fact_5109_less__imp__of__nat__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_imp_of_nat_less
% 0.29/0.58  thf(fact_5110_less__imp__of__nat__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_imp_of_nat_less
% 0.29/0.58  thf(fact_5111_less__imp__of__nat__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_imp_of_nat_less
% 0.29/0.58  thf(fact_5112_less__imp__of__nat__less,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( ord_less_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_imp_of_nat_less
% 0.29/0.58  thf(fact_5113_take__bit__tightened__less__eq__int,axiom,
% 0.29/0.58      ! [M: nat,N2: nat,K: int] :
% 0.29/0.58        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.58       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_tightened_less_eq_int
% 0.29/0.58  thf(fact_5114_of__nat__mono,axiom,
% 0.29/0.58      ! [I2: nat,J: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.58       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mono
% 0.29/0.58  thf(fact_5115_of__nat__mono,axiom,
% 0.29/0.58      ! [I2: nat,J: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.58       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mono
% 0.29/0.58  thf(fact_5116_of__nat__mono,axiom,
% 0.29/0.58      ! [I2: nat,J: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.58       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mono
% 0.29/0.58  thf(fact_5117_of__nat__mono,axiom,
% 0.29/0.58      ! [I2: nat,J: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.58       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mono
% 0.29/0.58  thf(fact_5118_take__bit__int__less__eq__self__iff,axiom,
% 0.29/0.58      ! [N2: nat,K: int] :
% 0.29/0.58        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 0.29/0.58        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_int_less_eq_self_iff
% 0.29/0.58  thf(fact_5119_take__bit__nonnegative,axiom,
% 0.29/0.58      ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_nonnegative
% 0.29/0.58  thf(fact_5120_take__bit__int__greater__self__iff,axiom,
% 0.29/0.58      ! [K: int,N2: nat] :
% 0.29/0.58        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 0.29/0.58        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_int_greater_self_iff
% 0.29/0.58  thf(fact_5121_not__take__bit__negative,axiom,
% 0.29/0.58      ! [N2: nat,K: int] :
% 0.29/0.58        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % not_take_bit_negative
% 0.29/0.58  thf(fact_5122_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,A: int,B: int] :
% 0.29/0.58        ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 0.29/0.58          = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 0.29/0.58        = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 0.29/0.58          = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_eq_iff_take_bit_eq
% 0.29/0.58  thf(fact_5123_signed__take__bit__take__bit,axiom,
% 0.29/0.58      ! [M: nat,N2: nat,A: int] :
% 0.29/0.58        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.29/0.58        = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 0.29/0.58  
% 0.29/0.58  % signed_take_bit_take_bit
% 0.29/0.58  thf(fact_5124_neg__numeral__le__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_numeral
% 0.29/0.58  thf(fact_5125_neg__numeral__le__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_numeral
% 0.29/0.58  thf(fact_5126_neg__numeral__le__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_numeral
% 0.29/0.58  thf(fact_5127_neg__numeral__le__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_numeral
% 0.29/0.58  thf(fact_5128_not__numeral__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_numeral
% 0.29/0.58  thf(fact_5129_not__numeral__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_numeral
% 0.29/0.58  thf(fact_5130_not__numeral__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_numeral
% 0.29/0.58  thf(fact_5131_not__numeral__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_numeral
% 0.29/0.58  thf(fact_5132_zero__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( zero_zero_real
% 0.29/0.58       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_numeral
% 0.29/0.58  thf(fact_5133_zero__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( zero_zero_int
% 0.29/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_numeral
% 0.29/0.58  thf(fact_5134_zero__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( zero_zero_complex
% 0.29/0.58       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_numeral
% 0.29/0.58  thf(fact_5135_zero__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( zero_z3403309356797280102nteger
% 0.29/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_numeral
% 0.29/0.58  thf(fact_5136_zero__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( zero_zero_rat
% 0.29/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_numeral
% 0.29/0.58  thf(fact_5137_not__numeral__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_numeral
% 0.29/0.58  thf(fact_5138_not__numeral__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_numeral
% 0.29/0.58  thf(fact_5139_not__numeral__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_numeral
% 0.29/0.58  thf(fact_5140_not__numeral__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] :
% 0.29/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_numeral
% 0.29/0.58  thf(fact_5141_neg__numeral__less__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_numeral
% 0.29/0.58  thf(fact_5142_neg__numeral__less__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_numeral
% 0.29/0.58  thf(fact_5143_neg__numeral__less__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_numeral
% 0.29/0.58  thf(fact_5144_neg__numeral__less__numeral,axiom,
% 0.29/0.58      ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_numeral
% 0.29/0.58  thf(fact_5145_le__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(4)
% 0.29/0.58  thf(fact_5146_le__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(4)
% 0.29/0.58  thf(fact_5147_le__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(4)
% 0.29/0.58  thf(fact_5148_le__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(4)
% 0.29/0.58  thf(fact_5149_le__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(2)
% 0.29/0.58  thf(fact_5150_le__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(2)
% 0.29/0.58  thf(fact_5151_le__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(2)
% 0.29/0.58  thf(fact_5152_le__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(2)
% 0.29/0.58  thf(fact_5153_zero__neq__neg__one,axiom,
% 0.29/0.58      ( zero_zero_real
% 0.29/0.58     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_one
% 0.29/0.58  thf(fact_5154_zero__neq__neg__one,axiom,
% 0.29/0.58      ( zero_zero_int
% 0.29/0.58     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_one
% 0.29/0.58  thf(fact_5155_zero__neq__neg__one,axiom,
% 0.29/0.58      ( zero_zero_complex
% 0.29/0.58     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_one
% 0.29/0.58  thf(fact_5156_zero__neq__neg__one,axiom,
% 0.29/0.58      ( zero_z3403309356797280102nteger
% 0.29/0.58     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_one
% 0.29/0.58  thf(fact_5157_zero__neq__neg__one,axiom,
% 0.29/0.58      ( zero_zero_rat
% 0.29/0.58     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zero_neq_neg_one
% 0.29/0.58  thf(fact_5158_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ( uminus_uminus_real @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( plus_plus_real @ A @ B )
% 0.29/0.58          = zero_zero_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_eq_iff_add_eq_0
% 0.29/0.58  thf(fact_5159_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ( uminus_uminus_int @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( plus_plus_int @ A @ B )
% 0.29/0.58          = zero_zero_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_eq_iff_add_eq_0
% 0.29/0.58  thf(fact_5160_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( plus_plus_complex @ A @ B )
% 0.29/0.58          = zero_zero_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_eq_iff_add_eq_0
% 0.29/0.58  thf(fact_5161_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_eq_iff_add_eq_0
% 0.29/0.58  thf(fact_5162_neg__eq__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.58          = B )
% 0.29/0.58        = ( ( plus_plus_rat @ A @ B )
% 0.29/0.58          = zero_zero_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_eq_iff_add_eq_0
% 0.29/0.58  thf(fact_5163_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_real @ B ) )
% 0.29/0.58        = ( ( plus_plus_real @ A @ B )
% 0.29/0.58          = zero_zero_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_neg_iff_add_eq_0
% 0.29/0.58  thf(fact_5164_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_int @ B ) )
% 0.29/0.58        = ( ( plus_plus_int @ A @ B )
% 0.29/0.58          = zero_zero_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_neg_iff_add_eq_0
% 0.29/0.58  thf(fact_5165_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58        = ( ( plus_plus_complex @ A @ B )
% 0.29/0.58          = zero_zero_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_neg_iff_add_eq_0
% 0.29/0.58  thf(fact_5166_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_neg_iff_add_eq_0
% 0.29/0.58  thf(fact_5167_eq__neg__iff__add__eq__0,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( A
% 0.29/0.58          = ( uminus_uminus_rat @ B ) )
% 0.29/0.58        = ( ( plus_plus_rat @ A @ B )
% 0.29/0.58          = zero_zero_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % eq_neg_iff_add_eq_0
% 0.29/0.58  thf(fact_5168_add_Oinverse__unique,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.58          = zero_zero_real )
% 0.29/0.58       => ( ( uminus_uminus_real @ A )
% 0.29/0.58          = B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_unique
% 0.29/0.58  thf(fact_5169_add_Oinverse__unique,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.58          = zero_zero_int )
% 0.29/0.58       => ( ( uminus_uminus_int @ A )
% 0.29/0.58          = B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_unique
% 0.29/0.58  thf(fact_5170_add_Oinverse__unique,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.58          = zero_zero_complex )
% 0.29/0.58       => ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.58          = B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_unique
% 0.29/0.58  thf(fact_5171_add_Oinverse__unique,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.58          = zero_z3403309356797280102nteger )
% 0.29/0.58       => ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.58          = B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_unique
% 0.29/0.58  thf(fact_5172_add_Oinverse__unique,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.58          = zero_zero_rat )
% 0.29/0.58       => ( ( uminus_uminus_rat @ A )
% 0.29/0.58          = B ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add.inverse_unique
% 0.29/0.58  thf(fact_5173_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.58      ! [A: real] :
% 0.29/0.58        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.29/0.58        = zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_left_minus
% 0.29/0.58  thf(fact_5174_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.58      ! [A: int] :
% 0.29/0.58        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.58        = zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_left_minus
% 0.29/0.58  thf(fact_5175_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.58      ! [A: complex] :
% 0.29/0.58        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.29/0.58        = zero_zero_complex ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_left_minus
% 0.29/0.58  thf(fact_5176_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.58      ! [A: code_integer] :
% 0.29/0.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.58        = zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_left_minus
% 0.29/0.58  thf(fact_5177_ab__group__add__class_Oab__left__minus,axiom,
% 0.29/0.58      ! [A: rat] :
% 0.29/0.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.58        = zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_left_minus
% 0.29/0.58  thf(fact_5178_add__eq__0__iff,axiom,
% 0.29/0.58      ! [A: real,B: real] :
% 0.29/0.58        ( ( ( plus_plus_real @ A @ B )
% 0.29/0.58          = zero_zero_real )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_eq_0_iff
% 0.29/0.58  thf(fact_5179_add__eq__0__iff,axiom,
% 0.29/0.58      ! [A: int,B: int] :
% 0.29/0.58        ( ( ( plus_plus_int @ A @ B )
% 0.29/0.58          = zero_zero_int )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_eq_0_iff
% 0.29/0.58  thf(fact_5180_add__eq__0__iff,axiom,
% 0.29/0.58      ! [A: complex,B: complex] :
% 0.29/0.58        ( ( ( plus_plus_complex @ A @ B )
% 0.29/0.58          = zero_zero_complex )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_eq_0_iff
% 0.29/0.58  thf(fact_5181_add__eq__0__iff,axiom,
% 0.29/0.58      ! [A: code_integer,B: code_integer] :
% 0.29/0.58        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.29/0.58          = zero_z3403309356797280102nteger )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_eq_0_iff
% 0.29/0.58  thf(fact_5182_add__eq__0__iff,axiom,
% 0.29/0.58      ! [A: rat,B: rat] :
% 0.29/0.58        ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.58          = zero_zero_rat )
% 0.29/0.58        = ( B
% 0.29/0.58          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_eq_0_iff
% 0.29/0.58  thf(fact_5183_xor__num_Ocases,axiom,
% 0.29/0.58      ! [X4: product_prod_num_num] :
% 0.29/0.58        ( ( X4
% 0.29/0.58         != ( product_Pair_num_num @ one @ one ) )
% 0.29/0.58       => ( ! [N3: num] :
% 0.29/0.58              ( X4
% 0.29/0.58             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 0.29/0.58         => ( ! [N3: num] :
% 0.29/0.58                ( X4
% 0.29/0.58               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 0.29/0.58           => ( ! [M5: num] :
% 0.29/0.58                  ( X4
% 0.29/0.58                 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 0.29/0.58             => ( ! [M5: num,N3: num] :
% 0.29/0.58                    ( X4
% 0.29/0.58                   != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 0.29/0.58               => ( ! [M5: num,N3: num] :
% 0.29/0.58                      ( X4
% 0.29/0.58                     != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 0.29/0.58                 => ( ! [M5: num] :
% 0.29/0.58                        ( X4
% 0.29/0.58                       != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 0.29/0.58                   => ( ! [M5: num,N3: num] :
% 0.29/0.58                          ( X4
% 0.29/0.58                         != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 0.29/0.58                     => ~ ! [M5: num,N3: num] :
% 0.29/0.58                            ( X4
% 0.29/0.58                           != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % xor_num.cases
% 0.29/0.58  thf(fact_5184_num_Oexhaust,axiom,
% 0.29/0.58      ! [Y: num] :
% 0.29/0.58        ( ( Y != one )
% 0.29/0.58       => ( ! [X23: num] :
% 0.29/0.58              ( Y
% 0.29/0.58             != ( bit0 @ X23 ) )
% 0.29/0.58         => ~ ! [X33: num] :
% 0.29/0.58                ( Y
% 0.29/0.58               != ( bit1 @ X33 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % num.exhaust
% 0.29/0.58  thf(fact_5185_less__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(2)
% 0.29/0.58  thf(fact_5186_less__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(2)
% 0.29/0.58  thf(fact_5187_less__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(2)
% 0.29/0.58  thf(fact_5188_less__minus__one__simps_I2_J,axiom,
% 0.29/0.58      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(2)
% 0.29/0.58  thf(fact_5189_less__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(4)
% 0.29/0.58  thf(fact_5190_less__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(4)
% 0.29/0.58  thf(fact_5191_less__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(4)
% 0.29/0.58  thf(fact_5192_less__minus__one__simps_I4_J,axiom,
% 0.29/0.58      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(4)
% 0.29/0.58  thf(fact_5193_numeral__times__minus__swap,axiom,
% 0.29/0.58      ! [W: num,X4: real] :
% 0.29/0.58        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.58        = ( times_times_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_times_minus_swap
% 0.29/0.58  thf(fact_5194_numeral__times__minus__swap,axiom,
% 0.29/0.58      ! [W: num,X4: int] :
% 0.29/0.58        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X4 ) )
% 0.29/0.58        = ( times_times_int @ X4 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_times_minus_swap
% 0.29/0.58  thf(fact_5195_numeral__times__minus__swap,axiom,
% 0.29/0.58      ! [W: num,X4: complex] :
% 0.29/0.58        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X4 ) )
% 0.29/0.58        = ( times_times_complex @ X4 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_times_minus_swap
% 0.29/0.58  thf(fact_5196_numeral__times__minus__swap,axiom,
% 0.29/0.58      ! [W: num,X4: code_integer] :
% 0.29/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X4 ) )
% 0.29/0.58        = ( times_3573771949741848930nteger @ X4 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_times_minus_swap
% 0.29/0.58  thf(fact_5197_numeral__times__minus__swap,axiom,
% 0.29/0.58      ! [W: num,X4: rat] :
% 0.29/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X4 ) )
% 0.29/0.58        = ( times_times_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_times_minus_swap
% 0.29/0.58  thf(fact_5198_nonzero__minus__divide__divide,axiom,
% 0.29/0.58      ! [B: real,A: real] :
% 0.29/0.58        ( ( B != zero_zero_real )
% 0.29/0.58       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.29/0.58          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_divide
% 0.29/0.58  thf(fact_5199_nonzero__minus__divide__divide,axiom,
% 0.29/0.58      ! [B: complex,A: complex] :
% 0.29/0.58        ( ( B != zero_zero_complex )
% 0.29/0.58       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_divide
% 0.29/0.58  thf(fact_5200_nonzero__minus__divide__divide,axiom,
% 0.29/0.58      ! [B: rat,A: rat] :
% 0.29/0.58        ( ( B != zero_zero_rat )
% 0.29/0.58       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_divide
% 0.29/0.58  thf(fact_5201_nonzero__minus__divide__right,axiom,
% 0.29/0.58      ! [B: real,A: real] :
% 0.29/0.58        ( ( B != zero_zero_real )
% 0.29/0.58       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.58          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_right
% 0.29/0.58  thf(fact_5202_nonzero__minus__divide__right,axiom,
% 0.29/0.58      ! [B: complex,A: complex] :
% 0.29/0.58        ( ( B != zero_zero_complex )
% 0.29/0.58       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.58          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_right
% 0.29/0.58  thf(fact_5203_nonzero__minus__divide__right,axiom,
% 0.29/0.58      ! [B: rat,A: rat] :
% 0.29/0.58        ( ( B != zero_zero_rat )
% 0.29/0.58       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.58          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % nonzero_minus_divide_right
% 0.29/0.58  thf(fact_5204_one__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( one_one_real
% 0.29/0.58       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_numeral
% 0.29/0.58  thf(fact_5205_one__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( one_one_int
% 0.29/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_numeral
% 0.29/0.58  thf(fact_5206_one__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( one_one_complex
% 0.29/0.58       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_numeral
% 0.29/0.58  thf(fact_5207_one__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( one_one_Code_integer
% 0.29/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_numeral
% 0.29/0.58  thf(fact_5208_one__neq__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( one_one_rat
% 0.29/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % one_neq_neg_numeral
% 0.29/0.58  thf(fact_5209_numeral__neq__neg__one,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_real @ N2 )
% 0.29/0.58       != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_one
% 0.29/0.58  thf(fact_5210_numeral__neq__neg__one,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_int @ N2 )
% 0.29/0.58       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_one
% 0.29/0.58  thf(fact_5211_numeral__neq__neg__one,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numera6690914467698888265omplex @ N2 )
% 0.29/0.58       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_one
% 0.29/0.58  thf(fact_5212_numeral__neq__neg__one,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numera6620942414471956472nteger @ N2 )
% 0.29/0.58       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_one
% 0.29/0.58  thf(fact_5213_numeral__neq__neg__one,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_rat @ N2 )
% 0.29/0.58       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_neq_neg_one
% 0.29/0.58  thf(fact_5214_square__eq__1__iff,axiom,
% 0.29/0.58      ! [X4: real] :
% 0.29/0.58        ( ( ( times_times_real @ X4 @ X4 )
% 0.29/0.58          = one_one_real )
% 0.29/0.58        = ( ( X4 = one_one_real )
% 0.29/0.58          | ( X4
% 0.29/0.58            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_1_iff
% 0.29/0.58  thf(fact_5215_square__eq__1__iff,axiom,
% 0.29/0.58      ! [X4: int] :
% 0.29/0.58        ( ( ( times_times_int @ X4 @ X4 )
% 0.29/0.58          = one_one_int )
% 0.29/0.58        = ( ( X4 = one_one_int )
% 0.29/0.58          | ( X4
% 0.29/0.58            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_1_iff
% 0.29/0.58  thf(fact_5216_square__eq__1__iff,axiom,
% 0.29/0.58      ! [X4: complex] :
% 0.29/0.58        ( ( ( times_times_complex @ X4 @ X4 )
% 0.29/0.58          = one_one_complex )
% 0.29/0.58        = ( ( X4 = one_one_complex )
% 0.29/0.58          | ( X4
% 0.29/0.58            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_1_iff
% 0.29/0.58  thf(fact_5217_square__eq__1__iff,axiom,
% 0.29/0.58      ! [X4: code_integer] :
% 0.29/0.58        ( ( ( times_3573771949741848930nteger @ X4 @ X4 )
% 0.29/0.58          = one_one_Code_integer )
% 0.29/0.58        = ( ( X4 = one_one_Code_integer )
% 0.29/0.58          | ( X4
% 0.29/0.58            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_1_iff
% 0.29/0.58  thf(fact_5218_square__eq__1__iff,axiom,
% 0.29/0.58      ! [X4: rat] :
% 0.29/0.58        ( ( ( times_times_rat @ X4 @ X4 )
% 0.29/0.58          = one_one_rat )
% 0.29/0.58        = ( ( X4 = one_one_rat )
% 0.29/0.58          | ( X4
% 0.29/0.58            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % square_eq_1_iff
% 0.29/0.58  thf(fact_5219_group__cancel_Osub2,axiom,
% 0.29/0.58      ! [B3: real,K: real,B: real,A: real] :
% 0.29/0.58        ( ( B3
% 0.29/0.58          = ( plus_plus_real @ K @ B ) )
% 0.29/0.58       => ( ( minus_minus_real @ A @ B3 )
% 0.29/0.58          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.sub2
% 0.29/0.58  thf(fact_5220_group__cancel_Osub2,axiom,
% 0.29/0.58      ! [B3: int,K: int,B: int,A: int] :
% 0.29/0.58        ( ( B3
% 0.29/0.58          = ( plus_plus_int @ K @ B ) )
% 0.29/0.58       => ( ( minus_minus_int @ A @ B3 )
% 0.29/0.58          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.sub2
% 0.29/0.58  thf(fact_5221_group__cancel_Osub2,axiom,
% 0.29/0.58      ! [B3: complex,K: complex,B: complex,A: complex] :
% 0.29/0.58        ( ( B3
% 0.29/0.58          = ( plus_plus_complex @ K @ B ) )
% 0.29/0.58       => ( ( minus_minus_complex @ A @ B3 )
% 0.29/0.58          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.sub2
% 0.29/0.58  thf(fact_5222_group__cancel_Osub2,axiom,
% 0.29/0.58      ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.29/0.58        ( ( B3
% 0.29/0.58          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.29/0.58       => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 0.29/0.58          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.sub2
% 0.29/0.58  thf(fact_5223_group__cancel_Osub2,axiom,
% 0.29/0.58      ! [B3: rat,K: rat,B: rat,A: rat] :
% 0.29/0.58        ( ( B3
% 0.29/0.58          = ( plus_plus_rat @ K @ B ) )
% 0.29/0.58       => ( ( minus_minus_rat @ A @ B3 )
% 0.29/0.58          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % group_cancel.sub2
% 0.29/0.58  thf(fact_5224_diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_real
% 0.29/0.58      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_conv_add_uminus
% 0.29/0.58  thf(fact_5225_diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_int
% 0.29/0.58      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_conv_add_uminus
% 0.29/0.58  thf(fact_5226_diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_complex
% 0.29/0.58      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_conv_add_uminus
% 0.29/0.58  thf(fact_5227_diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_8373710615458151222nteger
% 0.29/0.58      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_conv_add_uminus
% 0.29/0.58  thf(fact_5228_diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_rat
% 0.29/0.58      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % diff_conv_add_uminus
% 0.29/0.58  thf(fact_5229_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_real
% 0.29/0.58      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.29/0.58  thf(fact_5230_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_int
% 0.29/0.58      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.29/0.58  thf(fact_5231_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_complex
% 0.29/0.58      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.29/0.58  thf(fact_5232_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_8373710615458151222nteger
% 0.29/0.58      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.29/0.58  thf(fact_5233_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.29/0.58      ( minus_minus_rat
% 0.29/0.58      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.29/0.58  thf(fact_5234_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.58        = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.29/0.58  thf(fact_5235_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.58        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.29/0.58  thf(fact_5236_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.58        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.29/0.58  thf(fact_5237_of__nat__dvd__iff,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_dvd_iff
% 0.29/0.58  thf(fact_5238_of__nat__dvd__iff,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_dvd_iff
% 0.29/0.58  thf(fact_5239_of__nat__dvd__iff,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 0.29/0.58        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_dvd_iff
% 0.29/0.58  thf(fact_5240_take__bit__unset__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: int] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_unset_bit_eq
% 0.29/0.58  thf(fact_5241_take__bit__unset__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: nat] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_unset_bit_eq
% 0.29/0.58  thf(fact_5242_take__bit__set__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: int] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_set_bit_eq
% 0.29/0.58  thf(fact_5243_take__bit__set__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: nat] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_set_bit_eq
% 0.29/0.58  thf(fact_5244_take__bit__flip__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: int] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.29/0.58            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_flip_bit_eq
% 0.29/0.58  thf(fact_5245_take__bit__flip__bit__eq,axiom,
% 0.29/0.58      ! [N2: nat,M: nat,A: nat] :
% 0.29/0.58        ( ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 0.29/0.58        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.29/0.58            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_flip_bit_eq
% 0.29/0.58  thf(fact_5246_dvd__div__neg,axiom,
% 0.29/0.58      ! [B: real,A: real] :
% 0.29/0.58        ( ( dvd_dvd_real @ B @ A )
% 0.29/0.58       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 0.29/0.58          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_div_neg
% 0.29/0.58  thf(fact_5247_dvd__div__neg,axiom,
% 0.29/0.58      ! [B: int,A: int] :
% 0.29/0.58        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.58       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.58          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_div_neg
% 0.29/0.58  thf(fact_5248_dvd__div__neg,axiom,
% 0.29/0.58      ! [B: complex,A: complex] :
% 0.29/0.58        ( ( dvd_dvd_complex @ B @ A )
% 0.29/0.58       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_div_neg
% 0.29/0.58  thf(fact_5249_dvd__div__neg,axiom,
% 0.29/0.58      ! [B: code_integer,A: code_integer] :
% 0.29/0.58        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.58       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_div_neg
% 0.29/0.58  thf(fact_5250_dvd__div__neg,axiom,
% 0.29/0.58      ! [B: rat,A: rat] :
% 0.29/0.58        ( ( dvd_dvd_rat @ B @ A )
% 0.29/0.58       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.58          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_div_neg
% 0.29/0.58  thf(fact_5251_dvd__neg__div,axiom,
% 0.29/0.58      ! [B: real,A: real] :
% 0.29/0.58        ( ( dvd_dvd_real @ B @ A )
% 0.29/0.58       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.58          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_neg_div
% 0.29/0.58  thf(fact_5252_dvd__neg__div,axiom,
% 0.29/0.58      ! [B: int,A: int] :
% 0.29/0.58        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.58       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.58          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_neg_div
% 0.29/0.58  thf(fact_5253_dvd__neg__div,axiom,
% 0.29/0.58      ! [B: complex,A: complex] :
% 0.29/0.58        ( ( dvd_dvd_complex @ B @ A )
% 0.29/0.58       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.29/0.58          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_neg_div
% 0.29/0.58  thf(fact_5254_dvd__neg__div,axiom,
% 0.29/0.58      ! [B: code_integer,A: code_integer] :
% 0.29/0.58        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.29/0.58       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.58          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_neg_div
% 0.29/0.58  thf(fact_5255_dvd__neg__div,axiom,
% 0.29/0.58      ! [B: rat,A: rat] :
% 0.29/0.58        ( ( dvd_dvd_rat @ B @ A )
% 0.29/0.58       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.58          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % dvd_neg_div
% 0.29/0.58  thf(fact_5256_real__of__nat__div4,axiom,
% 0.29/0.58      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_div4
% 0.29/0.58  thf(fact_5257_of__nat__mod,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.58        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mod
% 0.29/0.58  thf(fact_5258_of__nat__mod,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.58        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mod
% 0.29/0.58  thf(fact_5259_of__nat__mod,axiom,
% 0.29/0.58      ! [M: nat,N2: nat] :
% 0.29/0.58        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 0.29/0.58        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_mod
% 0.29/0.58  thf(fact_5260_real__minus__mult__self__le,axiom,
% 0.29/0.58      ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X4 @ X4 ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_minus_mult_self_le
% 0.29/0.58  thf(fact_5261_real__of__nat__div,axiom,
% 0.29/0.58      ! [D: nat,N2: nat] :
% 0.29/0.58        ( ( dvd_dvd_nat @ D @ N2 )
% 0.29/0.58       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 0.29/0.58          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % real_of_nat_div
% 0.29/0.58  thf(fact_5262_zmod__zminus1__not__zero,axiom,
% 0.29/0.58      ! [K: int,L: int] :
% 0.29/0.58        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.29/0.58         != zero_zero_int )
% 0.29/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.58         != zero_zero_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zmod_zminus1_not_zero
% 0.29/0.58  thf(fact_5263_zmod__zminus2__not__zero,axiom,
% 0.29/0.58      ! [K: int,L: int] :
% 0.29/0.58        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 0.29/0.58         != zero_zero_int )
% 0.29/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.29/0.58         != zero_zero_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % zmod_zminus2_not_zero
% 0.29/0.58  thf(fact_5264_take__bit__Suc__minus__bit0,axiom,
% 0.29/0.58      ! [N2: nat,K: num] :
% 0.29/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.58        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_Suc_minus_bit0
% 0.29/0.58  thf(fact_5265_Bernoulli__inequality,axiom,
% 0.29/0.58      ! [X4: real,N2: nat] :
% 0.29/0.58        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.58       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % Bernoulli_inequality
% 0.29/0.58  thf(fact_5266_add__diff__assoc__enat,axiom,
% 0.29/0.58      ! [Z: extended_enat,Y: extended_enat,X4: extended_enat] :
% 0.29/0.58        ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 0.29/0.58       => ( ( plus_p3455044024723400733d_enat @ X4 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 0.29/0.58          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % add_diff_assoc_enat
% 0.29/0.58  thf(fact_5267_take__bit__signed__take__bit,axiom,
% 0.29/0.58      ! [M: nat,N2: nat,A: int] :
% 0.29/0.58        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.58       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 0.29/0.58          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_signed_take_bit
% 0.29/0.58  thf(fact_5268_neg__numeral__le__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_zero
% 0.29/0.58  thf(fact_5269_neg__numeral__le__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_zero
% 0.29/0.58  thf(fact_5270_neg__numeral__le__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_zero
% 0.29/0.58  thf(fact_5271_neg__numeral__le__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_zero
% 0.29/0.58  thf(fact_5272_not__zero__le__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_le_neg_numeral
% 0.29/0.58  thf(fact_5273_not__zero__le__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_le_neg_numeral
% 0.29/0.58  thf(fact_5274_not__zero__le__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_le_neg_numeral
% 0.29/0.58  thf(fact_5275_not__zero__le__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_le_neg_numeral
% 0.29/0.58  thf(fact_5276_not__zero__less__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_less_neg_numeral
% 0.29/0.58  thf(fact_5277_not__zero__less__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_less_neg_numeral
% 0.29/0.58  thf(fact_5278_not__zero__less__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_less_neg_numeral
% 0.29/0.58  thf(fact_5279_not__zero__less__neg__numeral,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_zero_less_neg_numeral
% 0.29/0.58  thf(fact_5280_neg__numeral__less__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_zero
% 0.29/0.58  thf(fact_5281_neg__numeral__less__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_zero
% 0.29/0.58  thf(fact_5282_neg__numeral__less__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_zero
% 0.29/0.58  thf(fact_5283_neg__numeral__less__zero,axiom,
% 0.29/0.58      ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_less_zero
% 0.29/0.58  thf(fact_5284_le__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(3)
% 0.29/0.58  thf(fact_5285_le__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(3)
% 0.29/0.58  thf(fact_5286_le__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(3)
% 0.29/0.58  thf(fact_5287_le__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(3)
% 0.29/0.58  thf(fact_5288_le__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(1)
% 0.29/0.58  thf(fact_5289_le__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(1)
% 0.29/0.58  thf(fact_5290_le__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(1)
% 0.29/0.58  thf(fact_5291_le__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.29/0.58  
% 0.29/0.58  % le_minus_one_simps(1)
% 0.29/0.58  thf(fact_5292_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5293_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5294_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5295_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5296_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5297_numeral__Bit1,axiom,
% 0.29/0.58      ! [N2: num] :
% 0.29/0.58        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.29/0.58        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % numeral_Bit1
% 0.29/0.58  thf(fact_5298_take__bit__decr__eq,axiom,
% 0.29/0.58      ! [N2: nat,K: int] :
% 0.29/0.58        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.58         != zero_zero_int )
% 0.29/0.58       => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 0.29/0.58          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % take_bit_decr_eq
% 0.29/0.58  thf(fact_5299_less__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(1)
% 0.29/0.58  thf(fact_5300_less__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(1)
% 0.29/0.58  thf(fact_5301_less__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(1)
% 0.29/0.58  thf(fact_5302_less__minus__one__simps_I1_J,axiom,
% 0.29/0.58      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(1)
% 0.29/0.58  thf(fact_5303_less__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(3)
% 0.29/0.58  thf(fact_5304_less__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(3)
% 0.29/0.58  thf(fact_5305_less__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(3)
% 0.29/0.58  thf(fact_5306_less__minus__one__simps_I3_J,axiom,
% 0.29/0.58      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % less_minus_one_simps(3)
% 0.29/0.58  thf(fact_5307_of__nat__diff,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.58          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_diff
% 0.29/0.58  thf(fact_5308_of__nat__diff,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.58          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_diff
% 0.29/0.58  thf(fact_5309_of__nat__diff,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.58          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_diff
% 0.29/0.58  thf(fact_5310_of__nat__diff,axiom,
% 0.29/0.58      ! [N2: nat,M: nat] :
% 0.29/0.58        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.58       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 0.29/0.58          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % of_nat_diff
% 0.29/0.58  thf(fact_5311_not__one__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_le_neg_numeral
% 0.29/0.58  thf(fact_5312_not__one__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_le_neg_numeral
% 0.29/0.58  thf(fact_5313_not__one__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_le_neg_numeral
% 0.29/0.58  thf(fact_5314_not__one__le__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_le_neg_numeral
% 0.29/0.58  thf(fact_5315_not__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_one
% 0.29/0.58  thf(fact_5316_not__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_one
% 0.29/0.58  thf(fact_5317_not__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_one
% 0.29/0.58  thf(fact_5318_not__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_le_neg_one
% 0.29/0.58  thf(fact_5319_neg__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_neg_one
% 0.29/0.58  thf(fact_5320_neg__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_neg_one
% 0.29/0.58  thf(fact_5321_neg__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_neg_one
% 0.29/0.58  thf(fact_5322_neg__numeral__le__neg__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_neg_one
% 0.29/0.58  thf(fact_5323_neg__one__le__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_le_numeral
% 0.29/0.58  thf(fact_5324_neg__one__le__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_le_numeral
% 0.29/0.58  thf(fact_5325_neg__one__le__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_le_numeral
% 0.29/0.58  thf(fact_5326_neg__one__le__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_le_numeral
% 0.29/0.58  thf(fact_5327_neg__numeral__le__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_one
% 0.29/0.58  thf(fact_5328_neg__numeral__le__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_one
% 0.29/0.58  thf(fact_5329_neg__numeral__le__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_one
% 0.29/0.58  thf(fact_5330_neg__numeral__le__one,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_numeral_le_one
% 0.29/0.58  thf(fact_5331_not__neg__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_less_neg_numeral
% 0.29/0.58  thf(fact_5332_not__neg__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_less_neg_numeral
% 0.29/0.58  thf(fact_5333_not__neg__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_less_neg_numeral
% 0.29/0.58  thf(fact_5334_not__neg__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_neg_one_less_neg_numeral
% 0.29/0.58  thf(fact_5335_not__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_less_neg_numeral
% 0.29/0.58  thf(fact_5336_not__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_less_neg_numeral
% 0.29/0.58  thf(fact_5337_not__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_less_neg_numeral
% 0.29/0.58  thf(fact_5338_not__one__less__neg__numeral,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_one_less_neg_numeral
% 0.29/0.58  thf(fact_5339_not__numeral__less__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_one
% 0.29/0.58  thf(fact_5340_not__numeral__less__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_one
% 0.29/0.58  thf(fact_5341_not__numeral__less__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_one
% 0.29/0.58  thf(fact_5342_not__numeral__less__neg__one,axiom,
% 0.29/0.58      ! [M: num] :
% 0.29/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.58  
% 0.29/0.58  % not_numeral_less_neg_one
% 0.29/0.58  thf(fact_5343_neg__one__less__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_less_numeral
% 0.29/0.58  thf(fact_5344_neg__one__less__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.29/0.58  
% 0.29/0.58  % neg_one_less_numeral
% 0.29/0.58  thf(fact_5345_neg__one__less__numeral,axiom,
% 0.29/0.58      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_less_numeral
% 0.29/0.59  thf(fact_5346_neg__one__less__numeral,axiom,
% 0.29/0.59      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_less_numeral
% 0.29/0.59  thf(fact_5347_neg__numeral__less__one,axiom,
% 0.29/0.59      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_numeral_less_one
% 0.29/0.59  thf(fact_5348_neg__numeral__less__one,axiom,
% 0.29/0.59      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_numeral_less_one
% 0.29/0.59  thf(fact_5349_neg__numeral__less__one,axiom,
% 0.29/0.59      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_numeral_less_one
% 0.29/0.59  thf(fact_5350_neg__numeral__less__one,axiom,
% 0.29/0.59      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_numeral_less_one
% 0.29/0.59  thf(fact_5351_eq__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: real,B: real,C: real] :
% 0.29/0.59        ( ( A
% 0.29/0.59          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_real )
% 0.29/0.59           => ( ( times_times_real @ A @ C )
% 0.29/0.59              = ( uminus_uminus_real @ B ) ) )
% 0.29/0.59          & ( ( C = zero_zero_real )
% 0.29/0.59           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_minus_divide_eq
% 0.29/0.59  thf(fact_5352_eq__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: complex,B: complex,C: complex] :
% 0.29/0.59        ( ( A
% 0.29/0.59          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_complex )
% 0.29/0.59           => ( ( times_times_complex @ A @ C )
% 0.29/0.59              = ( uminus1482373934393186551omplex @ B ) ) )
% 0.29/0.59          & ( ( C = zero_zero_complex )
% 0.29/0.59           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_minus_divide_eq
% 0.29/0.59  thf(fact_5353_eq__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: rat,B: rat,C: rat] :
% 0.29/0.59        ( ( A
% 0.29/0.59          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_rat )
% 0.29/0.59           => ( ( times_times_rat @ A @ C )
% 0.29/0.59              = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59          & ( ( C = zero_zero_rat )
% 0.29/0.59           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_minus_divide_eq
% 0.29/0.59  thf(fact_5354_minus__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: real,C: real,A: real] :
% 0.29/0.59        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 0.29/0.59          = A )
% 0.29/0.59        = ( ( ( C != zero_zero_real )
% 0.29/0.59           => ( ( uminus_uminus_real @ B )
% 0.29/0.59              = ( times_times_real @ A @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_real )
% 0.29/0.59           => ( A = zero_zero_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_eq_eq
% 0.29/0.59  thf(fact_5355_minus__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: complex,C: complex,A: complex] :
% 0.29/0.59        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.59          = A )
% 0.29/0.59        = ( ( ( C != zero_zero_complex )
% 0.29/0.59           => ( ( uminus1482373934393186551omplex @ B )
% 0.29/0.59              = ( times_times_complex @ A @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_complex )
% 0.29/0.59           => ( A = zero_zero_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_eq_eq
% 0.29/0.59  thf(fact_5356_minus__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: rat,C: rat,A: rat] :
% 0.29/0.59        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.59          = A )
% 0.29/0.59        = ( ( ( C != zero_zero_rat )
% 0.29/0.59           => ( ( uminus_uminus_rat @ B )
% 0.29/0.59              = ( times_times_rat @ A @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_rat )
% 0.29/0.59           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_eq_eq
% 0.29/0.59  thf(fact_5357_nonzero__neg__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: real,A: real,C: real] :
% 0.29/0.59        ( ( B != zero_zero_real )
% 0.29/0.59       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.59            = C )
% 0.29/0.59          = ( ( uminus_uminus_real @ A )
% 0.29/0.59            = ( times_times_real @ C @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq
% 0.29/0.59  thf(fact_5358_nonzero__neg__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: complex,A: complex,C: complex] :
% 0.29/0.59        ( ( B != zero_zero_complex )
% 0.29/0.59       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.59            = C )
% 0.29/0.59          = ( ( uminus1482373934393186551omplex @ A )
% 0.29/0.59            = ( times_times_complex @ C @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq
% 0.29/0.59  thf(fact_5359_nonzero__neg__divide__eq__eq,axiom,
% 0.29/0.59      ! [B: rat,A: rat,C: rat] :
% 0.29/0.59        ( ( B != zero_zero_rat )
% 0.29/0.59       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.59            = C )
% 0.29/0.59          = ( ( uminus_uminus_rat @ A )
% 0.29/0.59            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq
% 0.29/0.59  thf(fact_5360_nonzero__neg__divide__eq__eq2,axiom,
% 0.29/0.59      ! [B: real,C: real,A: real] :
% 0.29/0.59        ( ( B != zero_zero_real )
% 0.29/0.59       => ( ( C
% 0.29/0.59            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.29/0.59          = ( ( times_times_real @ C @ B )
% 0.29/0.59            = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq2
% 0.29/0.59  thf(fact_5361_nonzero__neg__divide__eq__eq2,axiom,
% 0.29/0.59      ! [B: complex,C: complex,A: complex] :
% 0.29/0.59        ( ( B != zero_zero_complex )
% 0.29/0.59       => ( ( C
% 0.29/0.59            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.59          = ( ( times_times_complex @ C @ B )
% 0.29/0.59            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq2
% 0.29/0.59  thf(fact_5362_nonzero__neg__divide__eq__eq2,axiom,
% 0.29/0.59      ! [B: rat,C: rat,A: rat] :
% 0.29/0.59        ( ( B != zero_zero_rat )
% 0.29/0.59       => ( ( C
% 0.29/0.59            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.29/0.59          = ( ( times_times_rat @ C @ B )
% 0.29/0.59            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_neg_divide_eq_eq2
% 0.29/0.59  thf(fact_5363_divide__eq__minus__1__iff,axiom,
% 0.29/0.59      ! [A: real,B: real] :
% 0.29/0.59        ( ( ( divide_divide_real @ A @ B )
% 0.29/0.59          = ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.59        = ( ( B != zero_zero_real )
% 0.29/0.59          & ( A
% 0.29/0.59            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_minus_1_iff
% 0.29/0.59  thf(fact_5364_divide__eq__minus__1__iff,axiom,
% 0.29/0.59      ! [A: complex,B: complex] :
% 0.29/0.59        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.29/0.59          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.59        = ( ( B != zero_zero_complex )
% 0.29/0.59          & ( A
% 0.29/0.59            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_minus_1_iff
% 0.29/0.59  thf(fact_5365_divide__eq__minus__1__iff,axiom,
% 0.29/0.59      ! [A: rat,B: rat] :
% 0.29/0.59        ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.59          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.59        = ( ( B != zero_zero_rat )
% 0.29/0.59          & ( A
% 0.29/0.59            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_minus_1_iff
% 0.29/0.59  thf(fact_5366_mult__1s__ring__1_I1_J,axiom,
% 0.29/0.59      ! [B: real] :
% 0.29/0.59        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.29/0.59        = ( uminus_uminus_real @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(1)
% 0.29/0.59  thf(fact_5367_mult__1s__ring__1_I1_J,axiom,
% 0.29/0.59      ! [B: int] :
% 0.29/0.59        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.29/0.59        = ( uminus_uminus_int @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(1)
% 0.29/0.59  thf(fact_5368_mult__1s__ring__1_I1_J,axiom,
% 0.29/0.59      ! [B: complex] :
% 0.29/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(1)
% 0.29/0.59  thf(fact_5369_mult__1s__ring__1_I1_J,axiom,
% 0.29/0.59      ! [B: code_integer] :
% 0.29/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(1)
% 0.29/0.59  thf(fact_5370_mult__1s__ring__1_I1_J,axiom,
% 0.29/0.59      ! [B: rat] :
% 0.29/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.29/0.59        = ( uminus_uminus_rat @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(1)
% 0.29/0.59  thf(fact_5371_mult__1s__ring__1_I2_J,axiom,
% 0.29/0.59      ! [B: real] :
% 0.29/0.59        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.29/0.59        = ( uminus_uminus_real @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(2)
% 0.29/0.59  thf(fact_5372_mult__1s__ring__1_I2_J,axiom,
% 0.29/0.59      ! [B: int] :
% 0.29/0.59        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(2)
% 0.29/0.59  thf(fact_5373_mult__1s__ring__1_I2_J,axiom,
% 0.29/0.59      ! [B: complex] :
% 0.29/0.59        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(2)
% 0.29/0.59  thf(fact_5374_mult__1s__ring__1_I2_J,axiom,
% 0.29/0.59      ! [B: code_integer] :
% 0.29/0.59        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(2)
% 0.29/0.59  thf(fact_5375_mult__1s__ring__1_I2_J,axiom,
% 0.29/0.59      ! [B: rat] :
% 0.29/0.59        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.29/0.59        = ( uminus_uminus_rat @ B ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_1s_ring_1(2)
% 0.29/0.59  thf(fact_5376_uminus__numeral__One,axiom,
% 0.29/0.59      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.29/0.59      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_numeral_One
% 0.29/0.59  thf(fact_5377_uminus__numeral__One,axiom,
% 0.29/0.59      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.29/0.59      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_numeral_One
% 0.29/0.59  thf(fact_5378_uminus__numeral__One,axiom,
% 0.29/0.59      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.29/0.59      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_numeral_One
% 0.29/0.59  thf(fact_5379_uminus__numeral__One,axiom,
% 0.29/0.59      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.29/0.59      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_numeral_One
% 0.29/0.59  thf(fact_5380_uminus__numeral__One,axiom,
% 0.29/0.59      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.29/0.59      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_numeral_One
% 0.29/0.59  thf(fact_5381_power__minus,axiom,
% 0.29/0.59      ! [A: real,N2: nat] :
% 0.29/0.59        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 0.29/0.59        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus
% 0.29/0.59  thf(fact_5382_power__minus,axiom,
% 0.29/0.59      ! [A: int,N2: nat] :
% 0.29/0.59        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.29/0.59        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus
% 0.29/0.59  thf(fact_5383_power__minus,axiom,
% 0.29/0.59      ! [A: complex,N2: nat] :
% 0.29/0.59        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 0.29/0.59        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus
% 0.29/0.59  thf(fact_5384_power__minus,axiom,
% 0.29/0.59      ! [A: code_integer,N2: nat] :
% 0.29/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.29/0.59        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus
% 0.29/0.59  thf(fact_5385_power__minus,axiom,
% 0.29/0.59      ! [A: rat,N2: nat] :
% 0.29/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.29/0.59        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus
% 0.29/0.59  thf(fact_5386_eval__nat__numeral_I3_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.29/0.59        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eval_nat_numeral(3)
% 0.29/0.59  thf(fact_5387_cong__exp__iff__simps_I10_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(10)
% 0.29/0.59  thf(fact_5388_cong__exp__iff__simps_I10_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(10)
% 0.29/0.59  thf(fact_5389_cong__exp__iff__simps_I10_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(10)
% 0.29/0.59  thf(fact_5390_cong__exp__iff__simps_I12_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(12)
% 0.29/0.59  thf(fact_5391_cong__exp__iff__simps_I12_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(12)
% 0.29/0.59  thf(fact_5392_cong__exp__iff__simps_I12_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(12)
% 0.29/0.59  thf(fact_5393_cong__exp__iff__simps_I13_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.29/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(13)
% 0.29/0.59  thf(fact_5394_cong__exp__iff__simps_I13_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.29/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(13)
% 0.29/0.59  thf(fact_5395_cong__exp__iff__simps_I13_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.29/0.59          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(13)
% 0.29/0.59  thf(fact_5396_power__minus__Bit0,axiom,
% 0.29/0.59      ! [X4: real,K: num] :
% 0.29/0.59        ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus_Bit0
% 0.29/0.59  thf(fact_5397_power__minus__Bit0,axiom,
% 0.29/0.59      ! [X4: int,K: num] :
% 0.29/0.59        ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus_Bit0
% 0.29/0.59  thf(fact_5398_power__minus__Bit0,axiom,
% 0.29/0.59      ! [X4: complex,K: num] :
% 0.29/0.59        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus_Bit0
% 0.29/0.59  thf(fact_5399_power__minus__Bit0,axiom,
% 0.29/0.59      ! [X4: code_integer,K: num] :
% 0.29/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus_Bit0
% 0.29/0.59  thf(fact_5400_power__minus__Bit0,axiom,
% 0.29/0.59      ! [X4: rat,K: num] :
% 0.29/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus_Bit0
% 0.29/0.59  thf(fact_5401_reals__Archimedean3,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ! [Y4: real] :
% 0.29/0.59          ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % reals_Archimedean3
% 0.29/0.59  thf(fact_5402_take__bit__Suc__bit1,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_bit1
% 0.29/0.59  thf(fact_5403_take__bit__Suc__bit1,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_bit1
% 0.29/0.59  thf(fact_5404_take__bit__Suc__minus__1__eq,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_minus_1_eq
% 0.29/0.59  thf(fact_5405_take__bit__Suc__minus__1__eq,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_minus_1_eq
% 0.29/0.59  thf(fact_5406_take__bit__numeral__minus__1__eq,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_minus_1_eq
% 0.29/0.59  thf(fact_5407_take__bit__numeral__minus__1__eq,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_minus_1_eq
% 0.29/0.59  thf(fact_5408_real__0__less__add__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.59        = ( ord_less_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_0_less_add_iff
% 0.29/0.59  thf(fact_5409_real__add__less__0__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 0.29/0.59        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_add_less_0_iff
% 0.29/0.59  thf(fact_5410_real__0__le__add__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.59        = ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_0_le_add_iff
% 0.29/0.59  thf(fact_5411_real__add__le__0__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 0.29/0.59        = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_add_le_0_iff
% 0.29/0.59  thf(fact_5412_real__of__nat__div__aux,axiom,
% 0.29/0.59      ! [X4: nat,D: nat] :
% 0.29/0.59        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( semiri5074537144036343181t_real @ D ) )
% 0.29/0.59        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X4 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X4 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_of_nat_div_aux
% 0.29/0.59  thf(fact_5413_zmod__zminus1__eq__if,axiom,
% 0.29/0.59      ! [A: int,B: int] :
% 0.29/0.59        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59            = zero_zero_int )
% 0.29/0.59         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.59            = zero_zero_int ) )
% 0.29/0.59        & ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59           != zero_zero_int )
% 0.29/0.59         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.59            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zmod_zminus1_eq_if
% 0.29/0.59  thf(fact_5414_zmod__zminus2__eq__if,axiom,
% 0.29/0.59      ! [A: int,B: int] :
% 0.29/0.59        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59            = zero_zero_int )
% 0.29/0.59         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.59            = zero_zero_int ) )
% 0.29/0.59        & ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59           != zero_zero_int )
% 0.29/0.59         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.59            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zmod_zminus2_eq_if
% 0.29/0.59  thf(fact_5415_mod__mult2__eq_H,axiom,
% 0.29/0.59      ! [A: code_integer,M: nat,N2: nat] :
% 0.29/0.59        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 0.29/0.59        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mod_mult2_eq'
% 0.29/0.59  thf(fact_5416_mod__mult2__eq_H,axiom,
% 0.29/0.59      ! [A: int,M: nat,N2: nat] :
% 0.29/0.59        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mod_mult2_eq'
% 0.29/0.59  thf(fact_5417_mod__mult2__eq_H,axiom,
% 0.29/0.59      ! [A: nat,M: nat,N2: nat] :
% 0.29/0.59        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 0.29/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mod_mult2_eq'
% 0.29/0.59  thf(fact_5418_take__bit__minus__small__eq,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.59       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59         => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 0.29/0.59            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_minus_small_eq
% 0.29/0.59  thf(fact_5419_numeral__Bit1__div__2,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59        = ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_Bit1_div_2
% 0.29/0.59  thf(fact_5420_numeral__Bit1__div__2,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.59        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_Bit1_div_2
% 0.29/0.59  thf(fact_5421_numeral__Bit1__div__2,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.59        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_Bit1_div_2
% 0.29/0.59  thf(fact_5422_pos__minus__divide__less__eq,axiom,
% 0.29/0.59      ! [C: real,B: real,A: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_minus_divide_less_eq
% 0.29/0.59  thf(fact_5423_pos__minus__divide__less__eq,axiom,
% 0.29/0.59      ! [C: rat,B: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_minus_divide_less_eq
% 0.29/0.59  thf(fact_5424_pos__less__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: real,A: real,B: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_less_minus_divide_eq
% 0.29/0.59  thf(fact_5425_pos__less__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_less_minus_divide_eq
% 0.29/0.59  thf(fact_5426_neg__minus__divide__less__eq,axiom,
% 0.29/0.59      ! [C: real,B: real,A: real] :
% 0.29/0.59        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_minus_divide_less_eq
% 0.29/0.59  thf(fact_5427_neg__minus__divide__less__eq,axiom,
% 0.29/0.59      ! [C: rat,B: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_minus_divide_less_eq
% 0.29/0.59  thf(fact_5428_neg__less__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: real,A: real,B: real] :
% 0.29/0.59        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_less_minus_divide_eq
% 0.29/0.59  thf(fact_5429_neg__less__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_less_minus_divide_eq
% 0.29/0.59  thf(fact_5430_minus__divide__less__eq,axiom,
% 0.29/0.59      ! [B: real,C: real,A: real] :
% 0.29/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_less_eq
% 0.29/0.59  thf(fact_5431_minus__divide__less__eq,axiom,
% 0.29/0.59      ! [B: rat,C: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_less_eq
% 0.29/0.59  thf(fact_5432_less__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: real,B: real,C: real] :
% 0.29/0.59        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_minus_divide_eq
% 0.29/0.59  thf(fact_5433_less__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: rat,B: rat,C: rat] :
% 0.29/0.59        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_minus_divide_eq
% 0.29/0.59  thf(fact_5434_eq__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: real,C: real] :
% 0.29/0.59        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.59          = ( divide_divide_real @ B @ C ) )
% 0.29/0.59        = ( ( ( C != zero_zero_real )
% 0.29/0.59           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 0.29/0.59              = B ) )
% 0.29/0.59          & ( ( C = zero_zero_real )
% 0.29/0.59           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.59              = zero_zero_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5435_eq__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: complex,C: complex] :
% 0.29/0.59        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.59          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.29/0.59        = ( ( ( C != zero_zero_complex )
% 0.29/0.59           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 0.29/0.59              = B ) )
% 0.29/0.59          & ( ( C = zero_zero_complex )
% 0.29/0.59           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.59              = zero_zero_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5436_eq__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: rat,C: rat] :
% 0.29/0.59        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.59          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.59        = ( ( ( C != zero_zero_rat )
% 0.29/0.59           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 0.29/0.59              = B ) )
% 0.29/0.59          & ( ( C = zero_zero_rat )
% 0.29/0.59           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.59              = zero_zero_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5437_divide__eq__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: real,C: real,W: num] :
% 0.29/0.59        ( ( ( divide_divide_real @ B @ C )
% 0.29/0.59          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_real )
% 0.29/0.59           => ( B
% 0.29/0.59              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_real )
% 0.29/0.59           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.59              = zero_zero_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_eq_numeral(2)
% 0.29/0.59  thf(fact_5438_divide__eq__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: complex,C: complex,W: num] :
% 0.29/0.59        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.29/0.59          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_complex )
% 0.29/0.59           => ( B
% 0.29/0.59              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_complex )
% 0.29/0.59           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.59              = zero_zero_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_eq_numeral(2)
% 0.29/0.59  thf(fact_5439_divide__eq__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: rat,C: rat,W: num] :
% 0.29/0.59        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.59          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.59        = ( ( ( C != zero_zero_rat )
% 0.29/0.59           => ( B
% 0.29/0.59              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ( C = zero_zero_rat )
% 0.29/0.59           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.59              = zero_zero_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_eq_eq_numeral(2)
% 0.29/0.59  thf(fact_5440_odd__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral
% 0.29/0.59  thf(fact_5441_odd__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral
% 0.29/0.59  thf(fact_5442_odd__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral
% 0.29/0.59  thf(fact_5443_minus__divide__add__eq__iff,axiom,
% 0.29/0.59      ! [Z: real,X4: real,Y: real] :
% 0.29/0.59        ( ( Z != zero_zero_real )
% 0.29/0.59       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_add_eq_iff
% 0.29/0.59  thf(fact_5444_minus__divide__add__eq__iff,axiom,
% 0.29/0.59      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.59        ( ( Z != zero_zero_complex )
% 0.29/0.59       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_add_eq_iff
% 0.29/0.59  thf(fact_5445_minus__divide__add__eq__iff,axiom,
% 0.29/0.59      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.59        ( ( Z != zero_zero_rat )
% 0.29/0.59       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_add_eq_iff
% 0.29/0.59  thf(fact_5446_add__divide__eq__if__simps_I3_J,axiom,
% 0.29/0.59      ! [Z: real,A: real,B: real] :
% 0.29/0.59        ( ( ( Z = zero_zero_real )
% 0.29/0.59         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.29/0.59            = B ) )
% 0.29/0.59        & ( ( Z != zero_zero_real )
% 0.29/0.59         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(3)
% 0.29/0.59  thf(fact_5447_add__divide__eq__if__simps_I3_J,axiom,
% 0.29/0.59      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.59        ( ( ( Z = zero_zero_complex )
% 0.29/0.59         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.29/0.59            = B ) )
% 0.29/0.59        & ( ( Z != zero_zero_complex )
% 0.29/0.59         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(3)
% 0.29/0.59  thf(fact_5448_add__divide__eq__if__simps_I3_J,axiom,
% 0.29/0.59      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ( Z = zero_zero_rat )
% 0.29/0.59         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.59            = B ) )
% 0.29/0.59        & ( ( Z != zero_zero_rat )
% 0.29/0.59         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(3)
% 0.29/0.59  thf(fact_5449_cong__exp__iff__simps_I3_J,axiom,
% 0.29/0.59      ! [N2: num,Q3: num] :
% 0.29/0.59        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != zero_zero_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(3)
% 0.29/0.59  thf(fact_5450_cong__exp__iff__simps_I3_J,axiom,
% 0.29/0.59      ! [N2: num,Q3: num] :
% 0.29/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != zero_zero_int ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(3)
% 0.29/0.59  thf(fact_5451_cong__exp__iff__simps_I3_J,axiom,
% 0.29/0.59      ! [N2: num,Q3: num] :
% 0.29/0.59        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59       != zero_z3403309356797280102nteger ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(3)
% 0.29/0.59  thf(fact_5452_add__divide__eq__if__simps_I6_J,axiom,
% 0.29/0.59      ! [Z: real,A: real,B: real] :
% 0.29/0.59        ( ( ( Z = zero_zero_real )
% 0.29/0.59         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.29/0.59            = ( uminus_uminus_real @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_real )
% 0.29/0.59         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(6)
% 0.29/0.59  thf(fact_5453_add__divide__eq__if__simps_I6_J,axiom,
% 0.29/0.59      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.59        ( ( ( Z = zero_zero_complex )
% 0.29/0.59         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.29/0.59            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_complex )
% 0.29/0.59         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(6)
% 0.29/0.59  thf(fact_5454_add__divide__eq__if__simps_I6_J,axiom,
% 0.29/0.59      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ( Z = zero_zero_rat )
% 0.29/0.59         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.59            = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_rat )
% 0.29/0.59         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.59            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(6)
% 0.29/0.59  thf(fact_5455_add__divide__eq__if__simps_I5_J,axiom,
% 0.29/0.59      ! [Z: real,A: real,B: real] :
% 0.29/0.59        ( ( ( Z = zero_zero_real )
% 0.29/0.59         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.59            = ( uminus_uminus_real @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_real )
% 0.29/0.59         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.29/0.59            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(5)
% 0.29/0.59  thf(fact_5456_add__divide__eq__if__simps_I5_J,axiom,
% 0.29/0.59      ! [Z: complex,A: complex,B: complex] :
% 0.29/0.59        ( ( ( Z = zero_zero_complex )
% 0.29/0.59         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.59            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_complex )
% 0.29/0.59         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.29/0.59            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(5)
% 0.29/0.59  thf(fact_5457_add__divide__eq__if__simps_I5_J,axiom,
% 0.29/0.59      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ( Z = zero_zero_rat )
% 0.29/0.59         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.59            = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59        & ( ( Z != zero_zero_rat )
% 0.29/0.59         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.59            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_divide_eq_if_simps(5)
% 0.29/0.59  thf(fact_5458_minus__divide__diff__eq__iff,axiom,
% 0.29/0.59      ! [Z: real,X4: real,Y: real] :
% 0.29/0.59        ( ( Z != zero_zero_real )
% 0.29/0.59       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_diff_eq_iff
% 0.29/0.59  thf(fact_5459_minus__divide__diff__eq__iff,axiom,
% 0.29/0.59      ! [Z: complex,X4: complex,Y: complex] :
% 0.29/0.59        ( ( Z != zero_zero_complex )
% 0.29/0.59       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_diff_eq_iff
% 0.29/0.59  thf(fact_5460_minus__divide__diff__eq__iff,axiom,
% 0.29/0.59      ! [Z: rat,X4: rat,Y: rat] :
% 0.29/0.59        ( ( Z != zero_zero_rat )
% 0.29/0.59       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 0.29/0.59          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_diff_eq_iff
% 0.29/0.59  thf(fact_5461_power3__eq__cube,axiom,
% 0.29/0.59      ! [A: complex] :
% 0.29/0.59        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.59        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power3_eq_cube
% 0.29/0.59  thf(fact_5462_power3__eq__cube,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.59        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power3_eq_cube
% 0.29/0.59  thf(fact_5463_power3__eq__cube,axiom,
% 0.29/0.59      ! [A: nat] :
% 0.29/0.59        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.59        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power3_eq_cube
% 0.29/0.59  thf(fact_5464_power3__eq__cube,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.29/0.59        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power3_eq_cube
% 0.29/0.59  thf(fact_5465_even__minus,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % even_minus
% 0.29/0.59  thf(fact_5466_even__minus,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.59        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % even_minus
% 0.29/0.59  thf(fact_5467_numeral__3__eq__3,axiom,
% 0.29/0.59      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.29/0.59      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_3_eq_3
% 0.29/0.59  thf(fact_5468_even__xor__iff,axiom,
% 0.29/0.59      ! [A: code_integer,B: code_integer] :
% 0.29/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 0.29/0.59        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.59          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % even_xor_iff
% 0.29/0.59  thf(fact_5469_even__xor__iff,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 0.29/0.59        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.59          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % even_xor_iff
% 0.29/0.59  thf(fact_5470_even__xor__iff,axiom,
% 0.29/0.59      ! [A: int,B: int] :
% 0.29/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 0.29/0.59        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.59          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % even_xor_iff
% 0.29/0.59  thf(fact_5471_power2__eq__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59        = ( ( X4 = Y )
% 0.29/0.59          | ( X4
% 0.29/0.59            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_iff
% 0.29/0.59  thf(fact_5472_power2__eq__iff,axiom,
% 0.29/0.59      ! [X4: int,Y: int] :
% 0.29/0.59        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59        = ( ( X4 = Y )
% 0.29/0.59          | ( X4
% 0.29/0.59            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_iff
% 0.29/0.59  thf(fact_5473_power2__eq__iff,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex] :
% 0.29/0.59        ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59        = ( ( X4 = Y )
% 0.29/0.59          | ( X4
% 0.29/0.59            = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_iff
% 0.29/0.59  thf(fact_5474_power2__eq__iff,axiom,
% 0.29/0.59      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.59        ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59        = ( ( X4 = Y )
% 0.29/0.59          | ( X4
% 0.29/0.59            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_iff
% 0.29/0.59  thf(fact_5475_power2__eq__iff,axiom,
% 0.29/0.59      ! [X4: rat,Y: rat] :
% 0.29/0.59        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59        = ( ( X4 = Y )
% 0.29/0.59          | ( X4
% 0.29/0.59            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_iff
% 0.29/0.59  thf(fact_5476_Suc3__eq__add__3,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 0.29/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc3_eq_add_3
% 0.29/0.59  thf(fact_5477_field__char__0__class_Oof__nat__div,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.59        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % field_char_0_class.of_nat_div
% 0.29/0.59  thf(fact_5478_field__char__0__class_Oof__nat__div,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.59        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % field_char_0_class.of_nat_div
% 0.29/0.59  thf(fact_5479_field__char__0__class_Oof__nat__div,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 0.29/0.59        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % field_char_0_class.of_nat_div
% 0.29/0.59  thf(fact_5480_nat__less__real__le,axiom,
% 0.29/0.59      ( ord_less_nat
% 0.29/0.59      = ( ^ [N: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_less_real_le
% 0.29/0.59  thf(fact_5481_nat__le__real__less,axiom,
% 0.29/0.59      ( ord_less_eq_nat
% 0.29/0.59      = ( ^ [N: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_le_real_less
% 0.29/0.59  thf(fact_5482_verit__less__mono__div__int2,axiom,
% 0.29/0.59      ! [A2: int,B3: int,N2: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ A2 @ B3 )
% 0.29/0.59       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 0.29/0.59         => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % verit_less_mono_div_int2
% 0.29/0.59  thf(fact_5483_div__eq__minus1,axiom,
% 0.29/0.59      ! [B: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.59       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.29/0.59          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % div_eq_minus1
% 0.29/0.59  thf(fact_5484_take__bit__Suc__bit0,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_bit0
% 0.29/0.59  thf(fact_5485_take__bit__Suc__bit0,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_bit0
% 0.29/0.59  thf(fact_5486_take__bit__eq__mod,axiom,
% 0.29/0.59      ( bit_se1745604003318907178nteger
% 0.29/0.59      = ( ^ [N: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_mod
% 0.29/0.59  thf(fact_5487_take__bit__eq__mod,axiom,
% 0.29/0.59      ( bit_se2923211474154528505it_int
% 0.29/0.59      = ( ^ [N: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_mod
% 0.29/0.59  thf(fact_5488_take__bit__eq__mod,axiom,
% 0.29/0.59      ( bit_se2925701944663578781it_nat
% 0.29/0.59      = ( ^ [N: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_mod
% 0.29/0.59  thf(fact_5489_take__bit__nat__eq__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 0.29/0.59          = M )
% 0.29/0.59        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_nat_eq_self_iff
% 0.29/0.59  thf(fact_5490_take__bit__nat__less__exp,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_nat_less_exp
% 0.29/0.59  thf(fact_5491_take__bit__nat__eq__self,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59       => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 0.29/0.59          = M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_nat_eq_self
% 0.29/0.59  thf(fact_5492_num_Osize__gen_I3_J,axiom,
% 0.29/0.59      ! [X32: num] :
% 0.29/0.59        ( ( size_num @ ( bit1 @ X32 ) )
% 0.29/0.59        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % num.size_gen(3)
% 0.29/0.59  thf(fact_5493_num_Osize_I6_J,axiom,
% 0.29/0.59      ! [X32: num] :
% 0.29/0.59        ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.29/0.59        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % num.size(6)
% 0.29/0.59  thf(fact_5494_take__bit__nat__def,axiom,
% 0.29/0.59      ( bit_se2925701944663578781it_nat
% 0.29/0.59      = ( ^ [N: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_nat_def
% 0.29/0.59  thf(fact_5495_of__nat__less__two__power,axiom,
% 0.29/0.59      ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % of_nat_less_two_power
% 0.29/0.59  thf(fact_5496_of__nat__less__two__power,axiom,
% 0.29/0.59      ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % of_nat_less_two_power
% 0.29/0.59  thf(fact_5497_of__nat__less__two__power,axiom,
% 0.29/0.59      ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % of_nat_less_two_power
% 0.29/0.59  thf(fact_5498_inverse__of__nat__le,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59       => ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inverse_of_nat_le
% 0.29/0.59  thf(fact_5499_inverse__of__nat__le,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59       => ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inverse_of_nat_le
% 0.29/0.59  thf(fact_5500_take__bit__int__less__exp,axiom,
% 0.29/0.59      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_less_exp
% 0.29/0.59  thf(fact_5501_le__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: real,B: real,C: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_minus_divide_eq
% 0.29/0.59  thf(fact_5502_le__minus__divide__eq,axiom,
% 0.29/0.59      ! [A: rat,B: rat,C: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_minus_divide_eq
% 0.29/0.59  thf(fact_5503_minus__divide__le__eq,axiom,
% 0.29/0.59      ! [B: real,C: real,A: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_le_eq
% 0.29/0.59  thf(fact_5504_minus__divide__le__eq,axiom,
% 0.29/0.59      ! [B: rat,C: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_divide_le_eq
% 0.29/0.59  thf(fact_5505_neg__le__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: real,A: real,B: real] :
% 0.29/0.59        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_le_minus_divide_eq
% 0.29/0.59  thf(fact_5506_neg__le__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_le_minus_divide_eq
% 0.29/0.59  thf(fact_5507_neg__minus__divide__le__eq,axiom,
% 0.29/0.59      ! [C: real,B: real,A: real] :
% 0.29/0.59        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_minus_divide_le_eq
% 0.29/0.59  thf(fact_5508_neg__minus__divide__le__eq,axiom,
% 0.29/0.59      ! [C: rat,B: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_minus_divide_le_eq
% 0.29/0.59  thf(fact_5509_pos__le__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: real,A: real,B: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_le_minus_divide_eq
% 0.29/0.59  thf(fact_5510_pos__le__minus__divide__eq,axiom,
% 0.29/0.59      ! [C: rat,A: rat,B: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.59          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_le_minus_divide_eq
% 0.29/0.59  thf(fact_5511_pos__minus__divide__le__eq,axiom,
% 0.29/0.59      ! [C: real,B: real,A: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_minus_divide_le_eq
% 0.29/0.59  thf(fact_5512_pos__minus__divide__le__eq,axiom,
% 0.29/0.59      ! [C: rat,B: rat,A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.29/0.59          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_minus_divide_le_eq
% 0.29/0.59  thf(fact_5513_less__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: real,C: real] :
% 0.29/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5514_less__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: rat,C: rat] :
% 0.29/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5515_divide__less__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: real,C: real,W: num] :
% 0.29/0.59        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_less_eq_numeral(2)
% 0.29/0.59  thf(fact_5516_divide__less__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: rat,C: rat,W: num] :
% 0.29/0.59        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_less_eq_numeral(2)
% 0.29/0.59  thf(fact_5517_take__bit__int__def,axiom,
% 0.29/0.59      ( bit_se2923211474154528505it_int
% 0.29/0.59      = ( ^ [N: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_def
% 0.29/0.59  thf(fact_5518_cong__exp__iff__simps_I7_J,axiom,
% 0.29/0.59      ! [Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.29/0.59          = zero_zero_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(7)
% 0.29/0.59  thf(fact_5519_cong__exp__iff__simps_I7_J,axiom,
% 0.29/0.59      ! [Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 0.29/0.59          = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(7)
% 0.29/0.59  thf(fact_5520_cong__exp__iff__simps_I7_J,axiom,
% 0.29/0.59      ! [Q3: num,N2: num] :
% 0.29/0.59        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.29/0.59          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(7)
% 0.29/0.59  thf(fact_5521_cong__exp__iff__simps_I11_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num] :
% 0.29/0.59        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 0.29/0.59          = zero_zero_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(11)
% 0.29/0.59  thf(fact_5522_cong__exp__iff__simps_I11_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num] :
% 0.29/0.59        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 0.29/0.59          = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(11)
% 0.29/0.59  thf(fact_5523_cong__exp__iff__simps_I11_J,axiom,
% 0.29/0.59      ! [M: num,Q3: num] :
% 0.29/0.59        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 0.29/0.59          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 0.29/0.59        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 0.29/0.59          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % cong_exp_iff_simps(11)
% 0.29/0.59  thf(fact_5524_power2__eq__1__iff,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_real )
% 0.29/0.59        = ( ( A = one_one_real )
% 0.29/0.59          | ( A
% 0.29/0.59            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_1_iff
% 0.29/0.59  thf(fact_5525_power2__eq__1__iff,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_int )
% 0.29/0.59        = ( ( A = one_one_int )
% 0.29/0.59          | ( A
% 0.29/0.59            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_1_iff
% 0.29/0.59  thf(fact_5526_power2__eq__1__iff,axiom,
% 0.29/0.59      ! [A: complex] :
% 0.29/0.59        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_complex )
% 0.29/0.59        = ( ( A = one_one_complex )
% 0.29/0.59          | ( A
% 0.29/0.59            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_1_iff
% 0.29/0.59  thf(fact_5527_power2__eq__1__iff,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_Code_integer )
% 0.29/0.59        = ( ( A = one_one_Code_integer )
% 0.29/0.59          | ( A
% 0.29/0.59            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_1_iff
% 0.29/0.59  thf(fact_5528_power2__eq__1__iff,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_rat )
% 0.29/0.59        = ( ( A = one_one_rat )
% 0.29/0.59          | ( A
% 0.29/0.59            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power2_eq_1_iff
% 0.29/0.59  thf(fact_5529_real__archimedian__rdiv__eq__0,axiom,
% 0.29/0.59      ! [X4: real,C: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.59         => ( ! [M5: nat] :
% 0.29/0.59                ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 0.29/0.59               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X4 ) @ C ) )
% 0.29/0.59           => ( X4 = zero_zero_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_archimedian_rdiv_eq_0
% 0.29/0.59  thf(fact_5530_uminus__power__if,axiom,
% 0.29/0.59      ! [N2: nat,A: real] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 0.29/0.59            = ( power_power_real @ A @ N2 ) ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_power_if
% 0.29/0.59  thf(fact_5531_uminus__power__if,axiom,
% 0.29/0.59      ! [N2: nat,A: int] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.29/0.59            = ( power_power_int @ A @ N2 ) ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_power_if
% 0.29/0.59  thf(fact_5532_uminus__power__if,axiom,
% 0.29/0.59      ! [N2: nat,A: complex] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 0.29/0.59            = ( power_power_complex @ A @ N2 ) ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 0.29/0.59            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_power_if
% 0.29/0.59  thf(fact_5533_uminus__power__if,axiom,
% 0.29/0.59      ! [N2: nat,A: code_integer] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.29/0.59            = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 0.29/0.59            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_power_if
% 0.29/0.59  thf(fact_5534_uminus__power__if,axiom,
% 0.29/0.59      ! [N2: nat,A: rat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.29/0.59            = ( power_power_rat @ A @ N2 ) ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % uminus_power_if
% 0.29/0.59  thf(fact_5535_Suc__div__eq__add3__div,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 0.29/0.59        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_div_eq_add3_div
% 0.29/0.59  thf(fact_5536_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.59          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.29/0.59  thf(fact_5537_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.59          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.29/0.59  thf(fact_5538_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.59          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.29/0.59  thf(fact_5539_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.59          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.29/0.59  thf(fact_5540_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 0.29/0.59          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.29/0.59  thf(fact_5541_Suc__mod__eq__add3__mod,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 0.29/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_mod_eq_add3_mod
% 0.29/0.59  thf(fact_5542_realpow__square__minus__le,axiom,
% 0.29/0.59      ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % realpow_square_minus_le
% 0.29/0.59  thf(fact_5543_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 0.29/0.59        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_less_eq_self_iff
% 0.29/0.59  thf(fact_5544_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.29/0.59      ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_greater_eq_minus_exp
% 0.29/0.59  thf(fact_5545_signed__take__bit__int__greater__self__iff,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 0.29/0.59        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_greater_self_iff
% 0.29/0.59  thf(fact_5546_take__bit__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,A: code_integer] :
% 0.29/0.59        ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.29/0.59          = zero_z3403309356797280102nteger )
% 0.29/0.59        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_0_iff
% 0.29/0.59  thf(fact_5547_take__bit__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,A: int] :
% 0.29/0.59        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.29/0.59          = zero_zero_int )
% 0.29/0.59        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_0_iff
% 0.29/0.59  thf(fact_5548_take__bit__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,A: nat] :
% 0.29/0.59        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.29/0.59          = zero_zero_nat )
% 0.29/0.59        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_eq_0_iff
% 0.29/0.59  thf(fact_5549_minus__mod__int__eq,axiom,
% 0.29/0.59      ! [L: int,K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.29/0.59       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.29/0.59          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_mod_int_eq
% 0.29/0.59  thf(fact_5550_zmod__minus1,axiom,
% 0.29/0.59      ! [B: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.59       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.29/0.59          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zmod_minus1
% 0.29/0.59  thf(fact_5551_zdiv__zminus1__eq__if,axiom,
% 0.29/0.59      ! [B: int,A: int] :
% 0.29/0.59        ( ( B != zero_zero_int )
% 0.29/0.59       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59              = zero_zero_int )
% 0.29/0.59           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.59              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.29/0.59          & ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59             != zero_zero_int )
% 0.29/0.59           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.59              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zdiv_zminus1_eq_if
% 0.29/0.59  thf(fact_5552_zdiv__zminus2__eq__if,axiom,
% 0.29/0.59      ! [B: int,A: int] :
% 0.29/0.59        ( ( B != zero_zero_int )
% 0.29/0.59       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59              = zero_zero_int )
% 0.29/0.59           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.59              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.29/0.59          & ( ( ( modulo_modulo_int @ A @ B )
% 0.29/0.59             != zero_zero_int )
% 0.29/0.59           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.59              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zdiv_zminus2_eq_if
% 0.29/0.59  thf(fact_5553_take__bit__nat__less__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 0.29/0.59        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_nat_less_self_iff
% 0.29/0.59  thf(fact_5554_zminus1__lemma,axiom,
% 0.29/0.59      ! [A: int,B: int,Q3: int,R3: int] :
% 0.29/0.59        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 0.29/0.59       => ( ( B != zero_zero_int )
% 0.29/0.59         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zminus1_lemma
% 0.29/0.59  thf(fact_5555_take__bit__int__less__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 0.29/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_less_self_iff
% 0.29/0.59  thf(fact_5556_take__bit__int__greater__eq__self__iff,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 0.29/0.59        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_greater_eq_self_iff
% 0.29/0.59  thf(fact_5557_le__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: real,C: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5558_le__divide__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [W: num,B: rat,C: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_divide_eq_numeral(2)
% 0.29/0.59  thf(fact_5559_divide__le__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: real,C: real,W: num] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.59           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.29/0.59              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.59               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_le_eq_numeral(2)
% 0.29/0.59  thf(fact_5560_divide__le__eq__numeral_I2_J,axiom,
% 0.29/0.59      ! [B: rat,C: rat,W: num] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.59               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divide_le_eq_numeral(2)
% 0.29/0.59  thf(fact_5561_square__le__1,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.59         => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_le_1
% 0.29/0.59  thf(fact_5562_square__le__1,axiom,
% 0.29/0.59      ! [X4: code_integer] :
% 0.29/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 0.29/0.59       => ( ( ord_le3102999989581377725nteger @ X4 @ one_one_Code_integer )
% 0.29/0.59         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_le_1
% 0.29/0.59  thf(fact_5563_square__le__1,axiom,
% 0.29/0.59      ! [X4: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_rat @ X4 @ one_one_rat )
% 0.29/0.59         => ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_le_1
% 0.29/0.59  thf(fact_5564_square__le__1,axiom,
% 0.29/0.59      ! [X4: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_int @ X4 @ one_one_int )
% 0.29/0.59         => ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_le_1
% 0.29/0.59  thf(fact_5565_minus__power__mult__self,axiom,
% 0.29/0.59      ! [A: real,N2: nat] :
% 0.29/0.59        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 0.29/0.59        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_power_mult_self
% 0.29/0.59  thf(fact_5566_minus__power__mult__self,axiom,
% 0.29/0.59      ! [A: int,N2: nat] :
% 0.29/0.59        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 0.29/0.59        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_power_mult_self
% 0.29/0.59  thf(fact_5567_minus__power__mult__self,axiom,
% 0.29/0.59      ! [A: complex,N2: nat] :
% 0.29/0.59        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 0.29/0.59        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_power_mult_self
% 0.29/0.59  thf(fact_5568_minus__power__mult__self,axiom,
% 0.29/0.59      ! [A: code_integer,N2: nat] :
% 0.29/0.59        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 0.29/0.59        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_power_mult_self
% 0.29/0.59  thf(fact_5569_minus__power__mult__self,axiom,
% 0.29/0.59      ! [A: rat,N2: nat] :
% 0.29/0.59        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 0.29/0.59        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_power_mult_self
% 0.29/0.59  thf(fact_5570_minus__one__power__iff,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 0.29/0.59            = one_one_real ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_power_iff
% 0.29/0.59  thf(fact_5571_minus__one__power__iff,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.29/0.59            = one_one_int ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_power_iff
% 0.29/0.59  thf(fact_5572_minus__one__power__iff,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 0.29/0.59            = one_one_complex ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 0.29/0.59            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_power_iff
% 0.29/0.59  thf(fact_5573_minus__one__power__iff,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.29/0.59            = one_one_Code_integer ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 0.29/0.59            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_power_iff
% 0.29/0.59  thf(fact_5574_minus__one__power__iff,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.29/0.59            = one_one_rat ) )
% 0.29/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 0.29/0.59            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_power_iff
% 0.29/0.59  thf(fact_5575_signed__take__bit__int__eq__self,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 0.29/0.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59         => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 0.29/0.59            = K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_eq_self
% 0.29/0.59  thf(fact_5576_signed__take__bit__int__eq__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 0.29/0.59          = K )
% 0.29/0.59        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 0.29/0.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_eq_self_iff
% 0.29/0.59  thf(fact_5577_minus__1__div__exp__eq__int,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_1_div_exp_eq_int
% 0.29/0.59  thf(fact_5578_div__pos__neg__trivial,axiom,
% 0.29/0.59      ! [K: int,L: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.59       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.29/0.59         => ( ( divide_divide_int @ K @ L )
% 0.29/0.59            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % div_pos_neg_trivial
% 0.29/0.59  thf(fact_5579_take__bit__int__eq__self,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59         => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.59            = K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_eq_self
% 0.29/0.59  thf(fact_5580_take__bit__int__eq__self__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.59          = K )
% 0.29/0.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_eq_self_iff
% 0.29/0.59  thf(fact_5581_signed__take__bit__eq__take__bit__shift,axiom,
% 0.29/0.59      ( bit_ri631733984087533419it_int
% 0.29/0.59      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_eq_take_bit_shift
% 0.29/0.59  thf(fact_5582_take__bit__incr__eq,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.59         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 0.29/0.59       => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.29/0.59          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_incr_eq
% 0.29/0.59  thf(fact_5583_power__minus1__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus1_odd
% 0.29/0.59  thf(fact_5584_power__minus1__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus1_odd
% 0.29/0.59  thf(fact_5585_power__minus1__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus1_odd
% 0.29/0.59  thf(fact_5586_power__minus1__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus1_odd
% 0.29/0.59  thf(fact_5587_power__minus1__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_minus1_odd
% 0.29/0.59  thf(fact_5588_take__bit__Suc,axiom,
% 0.29/0.59      ! [N2: nat,A: code_integer] :
% 0.29/0.59        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 0.29/0.59        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc
% 0.29/0.59  thf(fact_5589_take__bit__Suc,axiom,
% 0.29/0.59      ! [N2: nat,A: int] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc
% 0.29/0.59  thf(fact_5590_take__bit__Suc,axiom,
% 0.29/0.59      ! [N2: nat,A: nat] :
% 0.29/0.59        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 0.29/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc
% 0.29/0.59  thf(fact_5591_int__bit__induct,axiom,
% 0.29/0.59      ! [P: int > $o,K: int] :
% 0.29/0.59        ( ( P @ zero_zero_int )
% 0.29/0.59       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59         => ( ! [K2: int] :
% 0.29/0.59                ( ( P @ K2 )
% 0.29/0.59               => ( ( K2 != zero_zero_int )
% 0.29/0.59                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.59           => ( ! [K2: int] :
% 0.29/0.59                  ( ( P @ K2 )
% 0.29/0.59                 => ( ( K2
% 0.29/0.59                     != ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.29/0.59             => ( P @ K ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_bit_induct
% 0.29/0.59  thf(fact_5592_take__bit__int__less__eq,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 0.29/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_less_eq
% 0.29/0.59  thf(fact_5593_xor__nat__unfold,axiom,
% 0.29/0.59      ( bit_se6528837805403552850or_nat
% 0.29/0.59      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = 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 @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_nat_unfold
% 0.29/0.59  thf(fact_5594_take__bit__int__greater__eq,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_int_greater_eq
% 0.29/0.59  thf(fact_5595_xor__nat__rec,axiom,
% 0.29/0.59      ( bit_se6528837805403552850or_nat
% 0.29/0.59      = ( ^ [M6: nat,N: nat] :
% 0.29/0.59            ( plus_plus_nat
% 0.29/0.59            @ ( zero_n2687167440665602831ol_nat
% 0.29/0.59              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 0.29/0.59               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.29/0.59            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_nat_rec
% 0.29/0.59  thf(fact_5596_stable__imp__take__bit__eq,axiom,
% 0.29/0.59      ! [A: code_integer,N2: nat] :
% 0.29/0.59        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.59          = A )
% 0.29/0.59       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.29/0.59              = zero_z3403309356797280102nteger ) )
% 0.29/0.59          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 0.29/0.59              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % stable_imp_take_bit_eq
% 0.29/0.59  thf(fact_5597_stable__imp__take__bit__eq,axiom,
% 0.29/0.59      ! [A: int,N2: nat] :
% 0.29/0.59        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.59          = A )
% 0.29/0.59       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.29/0.59              = zero_zero_int ) )
% 0.29/0.59          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.29/0.59              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % stable_imp_take_bit_eq
% 0.29/0.59  thf(fact_5598_stable__imp__take__bit__eq,axiom,
% 0.29/0.59      ! [A: nat,N2: nat] :
% 0.29/0.59        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = A )
% 0.29/0.59       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.29/0.59              = zero_zero_nat ) )
% 0.29/0.59          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.59           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 0.29/0.59              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % stable_imp_take_bit_eq
% 0.29/0.59  thf(fact_5599_xor__one__eq,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 0.29/0.59        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n356916108424825756nteger
% 0.29/0.59            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_one_eq
% 0.29/0.59  thf(fact_5600_xor__one__eq,axiom,
% 0.29/0.59      ! [A: nat] :
% 0.29/0.59        ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 0.29/0.59        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.29/0.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_one_eq
% 0.29/0.59  thf(fact_5601_xor__one__eq,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 0.29/0.59        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n2684676970156552555ol_int
% 0.29/0.59            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_one_eq
% 0.29/0.59  thf(fact_5602_one__xor__eq,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 0.29/0.59        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n356916108424825756nteger
% 0.29/0.59            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % one_xor_eq
% 0.29/0.59  thf(fact_5603_one__xor__eq,axiom,
% 0.29/0.59      ! [A: nat] :
% 0.29/0.59        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 0.29/0.59        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.29/0.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % one_xor_eq
% 0.29/0.59  thf(fact_5604_one__xor__eq,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 0.29/0.59        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.59          @ ( zero_n2684676970156552555ol_int
% 0.29/0.59            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % one_xor_eq
% 0.29/0.59  thf(fact_5605_signed__take__bit__int__greater__eq,axiom,
% 0.29/0.59      ! [K: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_int_greater_eq
% 0.29/0.59  thf(fact_5606_xor__Suc__0__eq,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.59        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.29/0.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_Suc_0_eq
% 0.29/0.59  thf(fact_5607_real__average__minus__first,axiom,
% 0.29/0.59      ! [A: real,B: real] :
% 0.29/0.59        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.29/0.59        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_average_minus_first
% 0.29/0.59  thf(fact_5608_real__average__minus__second,axiom,
% 0.29/0.59      ! [B: real,A: real] :
% 0.29/0.59        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.29/0.59        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_average_minus_second
% 0.29/0.59  thf(fact_5609_linear__plus__1__le__power,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X4 @ one_one_real ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % linear_plus_1_le_power
% 0.29/0.59  thf(fact_5610_mod__exhaust__less__4,axiom,
% 0.29/0.59      ! [M: nat] :
% 0.29/0.59        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.59          = zero_zero_nat )
% 0.29/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.59          = one_one_nat )
% 0.29/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.59          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.59          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mod_exhaust_less_4
% 0.29/0.59  thf(fact_5611_nat__approx__posE,axiom,
% 0.29/0.59      ! [E2: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_approx_posE
% 0.29/0.59  thf(fact_5612_nat__approx__posE,axiom,
% 0.29/0.59      ! [E2: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_approx_posE
% 0.29/0.59  thf(fact_5613_compl__le__compl__iff,axiom,
% 0.29/0.59      ! [X4: set_int,Y: set_int] :
% 0.29/0.59        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 0.29/0.59        = ( ord_less_eq_set_int @ Y @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % compl_le_compl_iff
% 0.29/0.59  thf(fact_5614_dbl__dec__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.59      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(4)
% 0.29/0.59  thf(fact_5615_dbl__dec__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(4)
% 0.29/0.59  thf(fact_5616_dbl__dec__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.59      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(4)
% 0.29/0.59  thf(fact_5617_dbl__dec__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(4)
% 0.29/0.59  thf(fact_5618_dbl__dec__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.59      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(4)
% 0.29/0.59  thf(fact_5619_int__eq__iff__numeral,axiom,
% 0.29/0.59      ! [M: nat,V: num] :
% 0.29/0.59        ( ( ( semiri1314217659103216013at_int @ M )
% 0.29/0.59          = ( numeral_numeral_int @ V ) )
% 0.29/0.59        = ( M
% 0.29/0.59          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_eq_iff_numeral
% 0.29/0.59  thf(fact_5620_xor__nonnegative__int__iff,axiom,
% 0.29/0.59      ! [K: int,L: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.29/0.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.59          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_nonnegative_int_iff
% 0.29/0.59  thf(fact_5621_xor__negative__int__iff,axiom,
% 0.29/0.59      ! [K: int,L: int] :
% 0.29/0.59        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 0.29/0.59        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.59         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_negative_int_iff
% 0.29/0.59  thf(fact_5622_negative__zle,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % negative_zle
% 0.29/0.59  thf(fact_5623_dbl__dec__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.29/0.59      = one_one_complex ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(3)
% 0.29/0.59  thf(fact_5624_dbl__dec__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.29/0.59      = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(3)
% 0.29/0.59  thf(fact_5625_dbl__dec__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.29/0.59      = one_one_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(3)
% 0.29/0.59  thf(fact_5626_dbl__dec__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.29/0.59      = one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(3)
% 0.29/0.59  thf(fact_5627_negative__zless,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.29/0.59  
% 0.29/0.59  % negative_zless
% 0.29/0.59  thf(fact_5628_dbl__dec__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.29/0.59      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(2)
% 0.29/0.59  thf(fact_5629_dbl__dec__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.29/0.59      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(2)
% 0.29/0.59  thf(fact_5630_dbl__dec__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.29/0.59      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(2)
% 0.29/0.59  thf(fact_5631_dbl__dec__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.29/0.59      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(2)
% 0.29/0.59  thf(fact_5632_dbl__dec__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.29/0.59      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(2)
% 0.29/0.59  thf(fact_5633_take__bit__minus,axiom,
% 0.29/0.59      ! [N2: nat,K: int] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 0.29/0.59        = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_minus
% 0.29/0.59  thf(fact_5634_int__cases,axiom,
% 0.29/0.59      ! [Z: int] :
% 0.29/0.59        ( ! [N3: nat] :
% 0.29/0.59            ( Z
% 0.29/0.59           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( Z
% 0.29/0.59             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_cases
% 0.29/0.59  thf(fact_5635_int__of__nat__induct,axiom,
% 0.29/0.59      ! [P: int > $o,Z: int] :
% 0.29/0.59        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 0.29/0.59       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 0.29/0.59         => ( P @ Z ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_of_nat_induct
% 0.29/0.59  thf(fact_5636_not__int__zless__negative,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % not_int_zless_negative
% 0.29/0.59  thf(fact_5637_XOR__lower,axiom,
% 0.29/0.59      ! [X4: int,Y: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.59         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % XOR_lower
% 0.29/0.59  thf(fact_5638_int__cases4,axiom,
% 0.29/0.59      ! [M: int] :
% 0.29/0.59        ( ! [N3: nat] :
% 0.29/0.59            ( M
% 0.29/0.59           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.59             => ( M
% 0.29/0.59               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_cases4
% 0.29/0.59  thf(fact_5639_int__ops_I3_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.59        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_ops(3)
% 0.29/0.59  thf(fact_5640_int__zle__neg,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.29/0.59        = ( ( N2 = zero_zero_nat )
% 0.29/0.59          & ( M = zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_zle_neg
% 0.29/0.59  thf(fact_5641_nat__int__comparison_I2_J,axiom,
% 0.29/0.59      ( ord_less_nat
% 0.29/0.59      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_int_comparison(2)
% 0.29/0.59  thf(fact_5642_zle__int,axiom,
% 0.29/0.59      ! [M: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.59        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zle_int
% 0.29/0.59  thf(fact_5643_nat__int__comparison_I3_J,axiom,
% 0.29/0.59      ( ord_less_eq_nat
% 0.29/0.59      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nat_int_comparison(3)
% 0.29/0.59  thf(fact_5644_nonneg__int__cases,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( K
% 0.29/0.59             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonneg_int_cases
% 0.29/0.59  thf(fact_5645_zero__le__imp__eq__int,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.59       => ? [N3: nat] :
% 0.29/0.59            ( K
% 0.29/0.59            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_le_imp_eq_int
% 0.29/0.59  thf(fact_5646_negative__zle__0,axiom,
% 0.29/0.59      ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 0.29/0.59  
% 0.29/0.59  % negative_zle_0
% 0.29/0.59  thf(fact_5647_nonpos__int__cases,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( K
% 0.29/0.59             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonpos_int_cases
% 0.29/0.59  thf(fact_5648_zadd__int__left,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: int] :
% 0.29/0.59        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 0.29/0.59        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zadd_int_left
% 0.29/0.59  thf(fact_5649_int__plus,axiom,
% 0.29/0.59      ! [N2: nat,M: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_plus
% 0.29/0.59  thf(fact_5650_int__ops_I5_J,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.59        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_ops(5)
% 0.29/0.59  thf(fact_5651_int__ops_I2_J,axiom,
% 0.29/0.59      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.29/0.59      = one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % int_ops(2)
% 0.29/0.59  thf(fact_5652_zle__iff__zadd,axiom,
% 0.29/0.59      ( ord_less_eq_int
% 0.29/0.59      = ( ^ [W3: int,Z5: int] :
% 0.29/0.59          ? [N: nat] :
% 0.29/0.59            ( Z5
% 0.29/0.59            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zle_iff_zadd
% 0.29/0.59  thf(fact_5653_zdiv__int,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.29/0.59        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zdiv_int
% 0.29/0.59  thf(fact_5654_zmod__int,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.29/0.59        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zmod_int
% 0.29/0.59  thf(fact_5655_int__cases3,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( K != zero_zero_int )
% 0.29/0.59       => ( ! [N3: nat] :
% 0.29/0.59              ( ( K
% 0.29/0.59                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.29/0.59             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.29/0.59         => ~ ! [N3: nat] :
% 0.29/0.59                ( ( K
% 0.29/0.59                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.29/0.59               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_cases3
% 0.29/0.59  thf(fact_5656_not__zle__0__negative,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % not_zle_0_negative
% 0.29/0.59  thf(fact_5657_negD,axiom,
% 0.29/0.59      ! [X4: int] :
% 0.29/0.59        ( ( ord_less_int @ X4 @ zero_zero_int )
% 0.29/0.59       => ? [N3: nat] :
% 0.29/0.59            ( X4
% 0.29/0.59            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % negD
% 0.29/0.59  thf(fact_5658_negative__zless__0,axiom,
% 0.29/0.59      ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 0.29/0.59  
% 0.29/0.59  % negative_zless_0
% 0.29/0.59  thf(fact_5659_int__Suc,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 0.29/0.59        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_Suc
% 0.29/0.59  thf(fact_5660_int__ops_I4_J,axiom,
% 0.29/0.59      ! [A: nat] :
% 0.29/0.59        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.29/0.59        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_ops(4)
% 0.29/0.59  thf(fact_5661_zless__iff__Suc__zadd,axiom,
% 0.29/0.59      ( ord_less_int
% 0.29/0.59      = ( ^ [W3: int,Z5: int] :
% 0.29/0.59          ? [N: nat] :
% 0.29/0.59            ( Z5
% 0.29/0.59            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zless_iff_Suc_zadd
% 0.29/0.59  thf(fact_5662_pos__int__cases,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( ( K
% 0.29/0.59                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.29/0.59             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pos_int_cases
% 0.29/0.59  thf(fact_5663_zero__less__imp__eq__int,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.29/0.59       => ? [N3: nat] :
% 0.29/0.59            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.59            & ( K
% 0.29/0.59              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_imp_eq_int
% 0.29/0.59  thf(fact_5664_neg__int__cases,axiom,
% 0.29/0.59      ! [K: int] :
% 0.29/0.59        ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.59       => ~ ! [N3: nat] :
% 0.29/0.59              ( ( K
% 0.29/0.59                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.29/0.59             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % neg_int_cases
% 0.29/0.59  thf(fact_5665_zmult__zless__mono2__lemma,axiom,
% 0.29/0.59      ! [I2: int,J: int,K: nat] :
% 0.29/0.59        ( ( ord_less_int @ I2 @ J )
% 0.29/0.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.59         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zmult_zless_mono2_lemma
% 0.29/0.59  thf(fact_5666_int__ops_I6_J,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.29/0.59         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.59            = zero_zero_int ) )
% 0.29/0.59        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.29/0.59         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.59            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % int_ops(6)
% 0.29/0.59  thf(fact_5667_zdiff__int__split,axiom,
% 0.29/0.59      ! [P: int > $o,X4: nat,Y: nat] :
% 0.29/0.59        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X4 @ Y ) ) )
% 0.29/0.59        = ( ( ( ord_less_eq_nat @ Y @ X4 )
% 0.29/0.59           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.29/0.59          & ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.59           => ( P @ zero_zero_int ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zdiff_int_split
% 0.29/0.59  thf(fact_5668_dbl__dec__def,axiom,
% 0.29/0.59      ( neg_nu6511756317524482435omplex
% 0.29/0.59      = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_def
% 0.29/0.59  thf(fact_5669_dbl__dec__def,axiom,
% 0.29/0.59      ( neg_nu6075765906172075777c_real
% 0.29/0.59      = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_def
% 0.29/0.59  thf(fact_5670_dbl__dec__def,axiom,
% 0.29/0.59      ( neg_nu3179335615603231917ec_rat
% 0.29/0.59      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_def
% 0.29/0.59  thf(fact_5671_dbl__dec__def,axiom,
% 0.29/0.59      ( neg_nu3811975205180677377ec_int
% 0.29/0.59      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_def
% 0.29/0.59  thf(fact_5672_compl__le__swap2,axiom,
% 0.29/0.59      ! [Y: set_int,X4: set_int] :
% 0.29/0.59        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X4 )
% 0.29/0.59       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ Y ) ) ).
% 0.29/0.59  
% 0.29/0.59  % compl_le_swap2
% 0.29/0.59  thf(fact_5673_compl__le__swap1,axiom,
% 0.29/0.59      ! [Y: set_int,X4: set_int] :
% 0.29/0.59        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X4 ) )
% 0.29/0.59       => ( ord_less_eq_set_int @ X4 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % compl_le_swap1
% 0.29/0.59  thf(fact_5674_compl__mono,axiom,
% 0.29/0.59      ! [X4: set_int,Y: set_int] :
% 0.29/0.59        ( ( ord_less_eq_set_int @ X4 @ Y )
% 0.29/0.59       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % compl_mono
% 0.29/0.59  thf(fact_5675_XOR__upper,axiom,
% 0.29/0.59      ! [X4: int,N2: nat,Y: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.59       => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % XOR_upper
% 0.29/0.59  thf(fact_5676_real__arch__simple,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59      ? [N3: nat] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_arch_simple
% 0.29/0.59  thf(fact_5677_real__arch__simple,axiom,
% 0.29/0.59      ! [X4: rat] :
% 0.29/0.59      ? [N3: nat] : ( ord_less_eq_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % real_arch_simple
% 0.29/0.59  thf(fact_5678_reals__Archimedean2,axiom,
% 0.29/0.59      ! [X4: rat] :
% 0.29/0.59      ? [N3: nat] : ( ord_less_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % reals_Archimedean2
% 0.29/0.59  thf(fact_5679_reals__Archimedean2,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59      ? [N3: nat] : ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % reals_Archimedean2
% 0.29/0.59  thf(fact_5680_exists__least__lemma,axiom,
% 0.29/0.59      ! [P: nat > $o] :
% 0.29/0.59        ( ~ ( P @ zero_zero_nat )
% 0.29/0.59       => ( ? [X_1: nat] : ( P @ X_1 )
% 0.29/0.59         => ? [N3: nat] :
% 0.29/0.59              ( ~ ( P @ N3 )
% 0.29/0.59              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % exists_least_lemma
% 0.29/0.59  thf(fact_5681_xor__int__rec,axiom,
% 0.29/0.59      ( bit_se6526347334894502574or_int
% 0.29/0.59      = ( ^ [K3: int,L2: int] :
% 0.29/0.59            ( plus_plus_int
% 0.29/0.59            @ ( zero_n2684676970156552555ol_int
% 0.29/0.59              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 0.29/0.59               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.29/0.59            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % xor_int_rec
% 0.29/0.59  thf(fact_5682_Bolzano,axiom,
% 0.29/0.59      ! [A: real,B: real,P: real > real > $o] :
% 0.29/0.59        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.59       => ( ! [A5: real,B5: real,C3: real] :
% 0.29/0.59              ( ( P @ A5 @ B5 )
% 0.29/0.59             => ( ( P @ B5 @ C3 )
% 0.29/0.59               => ( ( ord_less_eq_real @ A5 @ B5 )
% 0.29/0.59                 => ( ( ord_less_eq_real @ B5 @ C3 )
% 0.29/0.59                   => ( P @ A5 @ C3 ) ) ) ) )
% 0.29/0.59         => ( ! [X5: real] :
% 0.29/0.59                ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.59               => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.59                 => ? [D6: real] :
% 0.29/0.59                      ( ( ord_less_real @ zero_zero_real @ D6 )
% 0.29/0.59                      & ! [A5: real,B5: real] :
% 0.29/0.59                          ( ( ( ord_less_eq_real @ A5 @ X5 )
% 0.29/0.59                            & ( ord_less_eq_real @ X5 @ B5 )
% 0.29/0.59                            & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D6 ) )
% 0.29/0.59                         => ( P @ A5 @ B5 ) ) ) ) )
% 0.29/0.59           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Bolzano
% 0.29/0.59  thf(fact_5683_ex__less__of__nat__mult,axiom,
% 0.29/0.59      ! [X4: rat,Y: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.59       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ex_less_of_nat_mult
% 0.29/0.59  thf(fact_5684_ex__less__of__nat__mult,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ex_less_of_nat_mult
% 0.29/0.59  thf(fact_5685_signed__take__bit__numeral__minus__bit1,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_numeral_minus_bit1
% 0.29/0.59  thf(fact_5686_divmod__algorithm__code_I7_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(7)
% 0.29/0.59  thf(fact_5687_divmod__algorithm__code_I7_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(7)
% 0.29/0.59  thf(fact_5688_divmod__algorithm__code_I7_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 0.29/0.59         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(7)
% 0.29/0.59  thf(fact_5689_divmod__algorithm__code_I8_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(8)
% 0.29/0.59  thf(fact_5690_divmod__algorithm__code_I8_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(8)
% 0.29/0.59  thf(fact_5691_divmod__algorithm__code_I8_J,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.29/0.59        & ( ~ ( ord_less_num @ M @ N2 )
% 0.29/0.59         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.59            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(8)
% 0.29/0.59  thf(fact_5692_take__bit__Suc__minus__bit1,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_Suc_minus_bit1
% 0.29/0.59  thf(fact_5693_lemma__termdiff3,axiom,
% 0.29/0.59      ! [H: real,Z: real,K5: real,N2: nat] :
% 0.29/0.59        ( ( H != zero_zero_real )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 0.29/0.59         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K5 )
% 0.29/0.59           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % lemma_termdiff3
% 0.29/0.59  thf(fact_5694_lemma__termdiff3,axiom,
% 0.29/0.59      ! [H: complex,Z: complex,K5: real,N2: nat] :
% 0.29/0.59        ( ( H != zero_zero_complex )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 0.29/0.59         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K5 )
% 0.29/0.59           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % lemma_termdiff3
% 0.29/0.59  thf(fact_5695_signed__take__bit__numeral__bit1,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_numeral_bit1
% 0.29/0.59  thf(fact_5696_dbl__inc__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.29/0.59      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(3)
% 0.29/0.59  thf(fact_5697_dbl__inc__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.29/0.59      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(3)
% 0.29/0.59  thf(fact_5698_dbl__inc__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.29/0.59      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(3)
% 0.29/0.59  thf(fact_5699_dbl__inc__simps_I3_J,axiom,
% 0.29/0.59      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.29/0.59      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(3)
% 0.29/0.59  thf(fact_5700_pred__numeral__simps_I1_J,axiom,
% 0.29/0.59      ( ( pred_numeral @ one )
% 0.29/0.59      = zero_zero_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % pred_numeral_simps(1)
% 0.29/0.59  thf(fact_5701_Suc__eq__numeral,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( ( suc @ N2 )
% 0.29/0.59          = ( numeral_numeral_nat @ K ) )
% 0.29/0.59        = ( N2
% 0.29/0.59          = ( pred_numeral @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_eq_numeral
% 0.29/0.59  thf(fact_5702_eq__numeral__Suc,axiom,
% 0.29/0.59      ! [K: num,N2: nat] :
% 0.29/0.59        ( ( ( numeral_numeral_nat @ K )
% 0.29/0.59          = ( suc @ N2 ) )
% 0.29/0.59        = ( ( pred_numeral @ K )
% 0.29/0.59          = N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eq_numeral_Suc
% 0.29/0.59  thf(fact_5703_dbl__inc__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.29/0.59      = one_one_complex ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(2)
% 0.29/0.59  thf(fact_5704_dbl__inc__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.29/0.59      = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(2)
% 0.29/0.59  thf(fact_5705_dbl__inc__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.29/0.59      = one_one_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(2)
% 0.29/0.59  thf(fact_5706_dbl__inc__simps_I2_J,axiom,
% 0.29/0.59      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.29/0.59      = one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(2)
% 0.29/0.59  thf(fact_5707_pred__numeral__inc,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( pred_numeral @ ( inc @ K ) )
% 0.29/0.59        = ( numeral_numeral_nat @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pred_numeral_inc
% 0.29/0.59  thf(fact_5708_dbl__inc__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.59      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(4)
% 0.29/0.59  thf(fact_5709_dbl__inc__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(4)
% 0.29/0.59  thf(fact_5710_dbl__inc__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.59      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(4)
% 0.29/0.59  thf(fact_5711_dbl__inc__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(4)
% 0.29/0.59  thf(fact_5712_dbl__inc__simps_I4_J,axiom,
% 0.29/0.59      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.59      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(4)
% 0.29/0.59  thf(fact_5713_dbl__inc__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.29/0.59        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(5)
% 0.29/0.59  thf(fact_5714_dbl__inc__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 0.29/0.59        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(5)
% 0.29/0.59  thf(fact_5715_dbl__inc__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 0.29/0.59        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(5)
% 0.29/0.59  thf(fact_5716_pred__numeral__simps_I3_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.29/0.59        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pred_numeral_simps(3)
% 0.29/0.59  thf(fact_5717_less__numeral__Suc,axiom,
% 0.29/0.59      ! [K: num,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.29/0.59        = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_numeral_Suc
% 0.29/0.59  thf(fact_5718_less__Suc__numeral,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.59        = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % less_Suc_numeral
% 0.29/0.59  thf(fact_5719_le__Suc__numeral,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.59        = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_Suc_numeral
% 0.29/0.59  thf(fact_5720_le__numeral__Suc,axiom,
% 0.29/0.59      ! [K: num,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.29/0.59        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % le_numeral_Suc
% 0.29/0.59  thf(fact_5721_diff__Suc__numeral,axiom,
% 0.29/0.59      ! [N2: nat,K: num] :
% 0.29/0.59        ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.59        = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_Suc_numeral
% 0.29/0.59  thf(fact_5722_diff__numeral__Suc,axiom,
% 0.29/0.59      ! [K: num,N2: nat] :
% 0.29/0.59        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.29/0.59        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_Suc
% 0.29/0.59  thf(fact_5723_minus__numeral__div__numeral,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_numeral_div_numeral
% 0.29/0.59  thf(fact_5724_numeral__div__minus__numeral,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_div_minus_numeral
% 0.29/0.59  thf(fact_5725_dbl__inc__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(1)
% 0.29/0.59  thf(fact_5726_dbl__inc__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(1)
% 0.29/0.59  thf(fact_5727_dbl__inc__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(1)
% 0.29/0.59  thf(fact_5728_dbl__inc__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(1)
% 0.29/0.59  thf(fact_5729_dbl__inc__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_simps(1)
% 0.29/0.59  thf(fact_5730_dbl__dec__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(1)
% 0.29/0.59  thf(fact_5731_dbl__dec__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(1)
% 0.29/0.59  thf(fact_5732_dbl__dec__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(1)
% 0.29/0.59  thf(fact_5733_dbl__dec__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(1)
% 0.29/0.59  thf(fact_5734_dbl__dec__simps_I1_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.59        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(1)
% 0.29/0.59  thf(fact_5735_dvd__numeral__simp,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.59        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_numeral_simp
% 0.29/0.59  thf(fact_5736_dvd__numeral__simp,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.59        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_numeral_simp
% 0.29/0.59  thf(fact_5737_dvd__numeral__simp,axiom,
% 0.29/0.59      ! [M: num,N2: num] :
% 0.29/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.59        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_numeral_simp
% 0.29/0.59  thf(fact_5738_divmod__algorithm__code_I2_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( unique5052692396658037445od_int @ M @ one )
% 0.29/0.59        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(2)
% 0.29/0.59  thf(fact_5739_divmod__algorithm__code_I2_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.29/0.59        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(2)
% 0.29/0.59  thf(fact_5740_divmod__algorithm__code_I2_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( unique3479559517661332726nteger @ M @ one )
% 0.29/0.59        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(2)
% 0.29/0.59  thf(fact_5741_add__neg__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(5)
% 0.29/0.59  thf(fact_5742_add__neg__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(5)
% 0.29/0.59  thf(fact_5743_add__neg__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(5)
% 0.29/0.59  thf(fact_5744_add__neg__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(5)
% 0.29/0.59  thf(fact_5745_add__neg__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(5)
% 0.29/0.59  thf(fact_5746_add__neg__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(6)
% 0.29/0.59  thf(fact_5747_add__neg__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(6)
% 0.29/0.59  thf(fact_5748_add__neg__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(6)
% 0.29/0.59  thf(fact_5749_add__neg__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(6)
% 0.29/0.59  thf(fact_5750_add__neg__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_neg_numeral_special(6)
% 0.29/0.59  thf(fact_5751_diff__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.59        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(6)
% 0.29/0.59  thf(fact_5752_diff__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.59        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(6)
% 0.29/0.59  thf(fact_5753_diff__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.59        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(6)
% 0.29/0.59  thf(fact_5754_diff__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.59        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(6)
% 0.29/0.59  thf(fact_5755_diff__numeral__special_I6_J,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.59        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(6)
% 0.29/0.59  thf(fact_5756_diff__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(5)
% 0.29/0.59  thf(fact_5757_diff__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(5)
% 0.29/0.59  thf(fact_5758_diff__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(5)
% 0.29/0.59  thf(fact_5759_diff__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(5)
% 0.29/0.59  thf(fact_5760_diff__numeral__special_I5_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % diff_numeral_special(5)
% 0.29/0.59  thf(fact_5761_divmod__algorithm__code_I3_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 0.29/0.59        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(3)
% 0.29/0.59  thf(fact_5762_divmod__algorithm__code_I3_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 0.29/0.59        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(3)
% 0.29/0.59  thf(fact_5763_divmod__algorithm__code_I3_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 0.29/0.59        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(3)
% 0.29/0.59  thf(fact_5764_divmod__algorithm__code_I4_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 0.29/0.59        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(4)
% 0.29/0.59  thf(fact_5765_divmod__algorithm__code_I4_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 0.29/0.59        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(4)
% 0.29/0.59  thf(fact_5766_divmod__algorithm__code_I4_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 0.29/0.59        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_algorithm_code(4)
% 0.29/0.59  thf(fact_5767_one__div__minus__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % one_div_minus_numeral
% 0.29/0.59  thf(fact_5768_minus__one__div__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.59        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % minus_one_div_numeral
% 0.29/0.59  thf(fact_5769_signed__take__bit__numeral__bit0,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_numeral_bit0
% 0.29/0.59  thf(fact_5770_signed__take__bit__numeral__minus__bit0,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.59        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_numeral_minus_bit0
% 0.29/0.59  thf(fact_5771_num__induct,axiom,
% 0.29/0.59      ! [P: num > $o,X4: num] :
% 0.29/0.59        ( ( P @ one )
% 0.29/0.59       => ( ! [X5: num] :
% 0.29/0.59              ( ( P @ X5 )
% 0.29/0.59             => ( P @ ( inc @ X5 ) ) )
% 0.29/0.59         => ( P @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % num_induct
% 0.29/0.59  thf(fact_5772_add__inc,axiom,
% 0.29/0.59      ! [X4: num,Y: num] :
% 0.29/0.59        ( ( plus_plus_num @ X4 @ ( inc @ Y ) )
% 0.29/0.59        = ( inc @ ( plus_plus_num @ X4 @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_inc
% 0.29/0.59  thf(fact_5773_numeral__eq__Suc,axiom,
% 0.29/0.59      ( numeral_numeral_nat
% 0.29/0.59      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_eq_Suc
% 0.29/0.59  thf(fact_5774_inc_Osimps_I1_J,axiom,
% 0.29/0.59      ( ( inc @ one )
% 0.29/0.59      = ( bit0 @ one ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inc.simps(1)
% 0.29/0.59  thf(fact_5775_inc_Osimps_I2_J,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( inc @ ( bit0 @ X4 ) )
% 0.29/0.59        = ( bit1 @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inc.simps(2)
% 0.29/0.59  thf(fact_5776_inc_Osimps_I3_J,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( inc @ ( bit1 @ X4 ) )
% 0.29/0.59        = ( bit0 @ ( inc @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inc.simps(3)
% 0.29/0.59  thf(fact_5777_add__One,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( plus_plus_num @ X4 @ one )
% 0.29/0.59        = ( inc @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % add_One
% 0.29/0.59  thf(fact_5778_mult__inc,axiom,
% 0.29/0.59      ! [X4: num,Y: num] :
% 0.29/0.59        ( ( times_times_num @ X4 @ ( inc @ Y ) )
% 0.29/0.59        = ( plus_plus_num @ ( times_times_num @ X4 @ Y ) @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % mult_inc
% 0.29/0.59  thf(fact_5779_pred__numeral__def,axiom,
% 0.29/0.59      ( pred_numeral
% 0.29/0.59      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pred_numeral_def
% 0.29/0.59  thf(fact_5780_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numeral_numeral_rat @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5781_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numera1916890842035813515d_enat @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5782_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numera6690914467698888265omplex @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5783_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numeral_numeral_real @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5784_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numeral_numeral_nat @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5785_numeral__inc,axiom,
% 0.29/0.59      ! [X4: num] :
% 0.29/0.59        ( ( numeral_numeral_int @ ( inc @ X4 ) )
% 0.29/0.59        = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_inc
% 0.29/0.59  thf(fact_5786_dbl__inc__def,axiom,
% 0.29/0.59      ( neg_nu8557863876264182079omplex
% 0.29/0.59      = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_def
% 0.29/0.59  thf(fact_5787_dbl__inc__def,axiom,
% 0.29/0.59      ( neg_nu8295874005876285629c_real
% 0.29/0.59      = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_def
% 0.29/0.59  thf(fact_5788_dbl__inc__def,axiom,
% 0.29/0.59      ( neg_nu5219082963157363817nc_rat
% 0.29/0.59      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_def
% 0.29/0.59  thf(fact_5789_dbl__inc__def,axiom,
% 0.29/0.59      ( neg_nu5851722552734809277nc_int
% 0.29/0.59      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_inc_def
% 0.29/0.59  thf(fact_5790_divmod__int__def,axiom,
% 0.29/0.59      ( unique5052692396658037445od_int
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_int_def
% 0.29/0.59  thf(fact_5791_divmod__def,axiom,
% 0.29/0.59      ( unique5052692396658037445od_int
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_def
% 0.29/0.59  thf(fact_5792_divmod__def,axiom,
% 0.29/0.59      ( unique5055182867167087721od_nat
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_def
% 0.29/0.59  thf(fact_5793_divmod__def,axiom,
% 0.29/0.59      ( unique3479559517661332726nteger
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_def
% 0.29/0.59  thf(fact_5794_divmod_H__nat__def,axiom,
% 0.29/0.59      ( unique5055182867167087721od_nat
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod'_nat_def
% 0.29/0.59  thf(fact_5795_take__bit__numeral__minus__bit1,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_minus_bit1
% 0.29/0.59  thf(fact_5796_take__bit__numeral__bit0,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_bit0
% 0.29/0.59  thf(fact_5797_take__bit__numeral__bit0,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.29/0.59        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_bit0
% 0.29/0.59  thf(fact_5798_take__bit__numeral__minus__bit0,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.59        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_minus_bit0
% 0.29/0.59  thf(fact_5799_divmod__divmod__step,axiom,
% 0.29/0.59      ( unique5055182867167087721od_nat
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_divmod_step
% 0.29/0.59  thf(fact_5800_divmod__divmod__step,axiom,
% 0.29/0.59      ( unique5052692396658037445od_int
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_divmod_step
% 0.29/0.59  thf(fact_5801_divmod__divmod__step,axiom,
% 0.29/0.59      ( unique3479559517661332726nteger
% 0.29/0.59      = ( ^ [M6: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_divmod_step
% 0.29/0.59  thf(fact_5802_take__bit__numeral__bit1,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_bit1
% 0.29/0.59  thf(fact_5803_take__bit__numeral__bit1,axiom,
% 0.29/0.59      ! [L: num,K: num] :
% 0.29/0.59        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.29/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % take_bit_numeral_bit1
% 0.29/0.59  thf(fact_5804_norm__divide__numeral,axiom,
% 0.29/0.59      ! [A: real,W: num] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_divide_numeral
% 0.29/0.59  thf(fact_5805_norm__divide__numeral,axiom,
% 0.29/0.59      ! [A: complex,W: num] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.59        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_divide_numeral
% 0.29/0.59  thf(fact_5806_norm__mult__numeral2,axiom,
% 0.29/0.59      ! [A: real,W: num] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_numeral2
% 0.29/0.59  thf(fact_5807_norm__mult__numeral2,axiom,
% 0.29/0.59      ! [A: complex,W: num] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.59        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_numeral2
% 0.29/0.59  thf(fact_5808_norm__mult__numeral1,axiom,
% 0.29/0.59      ! [W: num,A: real] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.29/0.59        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_numeral1
% 0.29/0.59  thf(fact_5809_norm__mult__numeral1,axiom,
% 0.29/0.59      ! [W: num,A: complex] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.29/0.59        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_numeral1
% 0.29/0.59  thf(fact_5810_norm__neg__numeral,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.59        = ( numeral_numeral_real @ W ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_neg_numeral
% 0.29/0.59  thf(fact_5811_norm__neg__numeral,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.59        = ( numeral_numeral_real @ W ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_neg_numeral
% 0.29/0.59  thf(fact_5812_norm__le__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ zero_zero_real )
% 0.29/0.59        = ( X4 = zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_le_zero_iff
% 0.29/0.59  thf(fact_5813_norm__le__zero__iff,axiom,
% 0.29/0.59      ! [X4: complex] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real )
% 0.29/0.59        = ( X4 = zero_zero_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_le_zero_iff
% 0.29/0.59  thf(fact_5814_zero__less__norm__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X4 ) )
% 0.29/0.59        = ( X4 != zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_norm_iff
% 0.29/0.59  thf(fact_5815_zero__less__norm__iff,axiom,
% 0.29/0.59      ! [X4: complex] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) )
% 0.29/0.59        = ( X4 != zero_zero_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_norm_iff
% 0.29/0.59  thf(fact_5816_norm__numeral,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.59        = ( numeral_numeral_real @ W ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_numeral
% 0.29/0.59  thf(fact_5817_norm__numeral,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.59        = ( numeral_numeral_real @ W ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_numeral
% 0.29/0.59  thf(fact_5818_norm__one,axiom,
% 0.29/0.59      ( ( real_V7735802525324610683m_real @ one_one_real )
% 0.29/0.59      = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_one
% 0.29/0.59  thf(fact_5819_norm__one,axiom,
% 0.29/0.59      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 0.29/0.59      = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_one
% 0.29/0.59  thf(fact_5820_norm__not__less__zero,axiom,
% 0.29/0.59      ! [X4: complex] :
% 0.29/0.59        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_not_less_zero
% 0.29/0.59  thf(fact_5821_norm__ge__zero,axiom,
% 0.29/0.59      ! [X4: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_ge_zero
% 0.29/0.59  thf(fact_5822_norm__divide,axiom,
% 0.29/0.59      ! [A: real,B: real] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.59        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_divide
% 0.29/0.59  thf(fact_5823_norm__divide,axiom,
% 0.29/0.59      ! [A: complex,B: complex] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.59        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_divide
% 0.29/0.59  thf(fact_5824_norm__power,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.59        = ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power
% 0.29/0.59  thf(fact_5825_norm__power,axiom,
% 0.29/0.59      ! [X4: complex,N2: nat] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) )
% 0.29/0.59        = ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power
% 0.29/0.59  thf(fact_5826_norm__uminus__minus,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ Y ) )
% 0.29/0.59        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_uminus_minus
% 0.29/0.59  thf(fact_5827_norm__uminus__minus,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex] :
% 0.29/0.59        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y ) )
% 0.29/0.59        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_uminus_minus
% 0.29/0.59  thf(fact_5828_nonzero__norm__divide,axiom,
% 0.29/0.59      ! [B: real,A: real] :
% 0.29/0.59        ( ( B != zero_zero_real )
% 0.29/0.59       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.59          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_norm_divide
% 0.29/0.59  thf(fact_5829_nonzero__norm__divide,axiom,
% 0.29/0.59      ! [B: complex,A: complex] :
% 0.29/0.59        ( ( B != zero_zero_complex )
% 0.29/0.59       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.59          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % nonzero_norm_divide
% 0.29/0.59  thf(fact_5830_power__eq__imp__eq__norm,axiom,
% 0.29/0.59      ! [W: real,N2: nat,Z: real] :
% 0.29/0.59        ( ( ( power_power_real @ W @ N2 )
% 0.29/0.59          = ( power_power_real @ Z @ N2 ) )
% 0.29/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59         => ( ( real_V7735802525324610683m_real @ W )
% 0.29/0.59            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_eq_imp_eq_norm
% 0.29/0.59  thf(fact_5831_power__eq__imp__eq__norm,axiom,
% 0.29/0.59      ! [W: complex,N2: nat,Z: complex] :
% 0.29/0.59        ( ( ( power_power_complex @ W @ N2 )
% 0.29/0.59          = ( power_power_complex @ Z @ N2 ) )
% 0.29/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59         => ( ( real_V1022390504157884413omplex @ W )
% 0.29/0.59            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_eq_imp_eq_norm
% 0.29/0.59  thf(fact_5832_norm__mult__less,axiom,
% 0.29/0.59      ! [X4: real,R3: real,Y: real,S: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.29/0.59         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_less
% 0.29/0.59  thf(fact_5833_norm__mult__less,axiom,
% 0.29/0.59      ! [X4: complex,R3: real,Y: complex,S: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.29/0.59         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_less
% 0.29/0.59  thf(fact_5834_norm__mult__ineq,axiom,
% 0.29/0.59      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_ineq
% 0.29/0.59  thf(fact_5835_norm__mult__ineq,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_mult_ineq
% 0.29/0.59  thf(fact_5836_norm__triangle__lt,axiom,
% 0.29/0.59      ! [X4: real,Y: real,E2: real] :
% 0.29/0.59        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_lt
% 0.29/0.59  thf(fact_5837_norm__triangle__lt,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex,E2: real] :
% 0.29/0.59        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_lt
% 0.29/0.59  thf(fact_5838_norm__add__less,axiom,
% 0.29/0.59      ! [X4: real,R3: real,Y: real,S: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.29/0.59         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_add_less
% 0.29/0.59  thf(fact_5839_norm__add__less,axiom,
% 0.29/0.59      ! [X4: complex,R3: real,Y: complex,S: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.29/0.59         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_add_less
% 0.29/0.59  thf(fact_5840_norm__add__leD,axiom,
% 0.29/0.59      ! [A: real,B: real,C: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_add_leD
% 0.29/0.59  thf(fact_5841_norm__add__leD,axiom,
% 0.29/0.59      ! [A: complex,B: complex,C: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_add_leD
% 0.29/0.59  thf(fact_5842_norm__triangle__le,axiom,
% 0.29/0.59      ! [X4: real,Y: real,E2: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_le
% 0.29/0.59  thf(fact_5843_norm__triangle__le,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex,E2: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_le
% 0.29/0.59  thf(fact_5844_norm__triangle__ineq,axiom,
% 0.29/0.59      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq
% 0.29/0.59  thf(fact_5845_norm__triangle__ineq,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq
% 0.29/0.59  thf(fact_5846_norm__triangle__mono,axiom,
% 0.29/0.59      ! [A: real,R3: real,B: real,S: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R3 )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 0.29/0.59         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_mono
% 0.29/0.59  thf(fact_5847_norm__triangle__mono,axiom,
% 0.29/0.59      ! [A: complex,R3: real,B: complex,S: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R3 )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 0.29/0.59         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_mono
% 0.29/0.59  thf(fact_5848_norm__diff__triangle__less,axiom,
% 0.29/0.59      ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 0.29/0.59         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_less
% 0.29/0.59  thf(fact_5849_norm__diff__triangle__less,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 0.29/0.59        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 0.29/0.59       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 0.29/0.59         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_less
% 0.29/0.59  thf(fact_5850_norm__power__ineq,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power_ineq
% 0.29/0.59  thf(fact_5851_norm__power__ineq,axiom,
% 0.29/0.59      ! [X4: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power_ineq
% 0.29/0.59  thf(fact_5852_norm__triangle__sub,axiom,
% 0.29/0.59      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_sub
% 0.29/0.59  thf(fact_5853_norm__triangle__sub,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_sub
% 0.29/0.59  thf(fact_5854_norm__triangle__ineq4,axiom,
% 0.29/0.59      ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq4
% 0.29/0.59  thf(fact_5855_norm__triangle__ineq4,axiom,
% 0.29/0.59      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq4
% 0.29/0.59  thf(fact_5856_norm__diff__triangle__le,axiom,
% 0.29/0.59      ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 0.29/0.59         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_le
% 0.29/0.59  thf(fact_5857_norm__diff__triangle__le,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 0.29/0.59         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_le
% 0.29/0.59  thf(fact_5858_norm__triangle__le__diff,axiom,
% 0.29/0.59      ! [X4: real,Y: real,E2: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_le_diff
% 0.29/0.59  thf(fact_5859_norm__triangle__le__diff,axiom,
% 0.29/0.59      ! [X4: complex,Y: complex,E2: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_le_diff
% 0.29/0.59  thf(fact_5860_norm__diff__ineq,axiom,
% 0.29/0.59      ! [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 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_ineq
% 0.29/0.59  thf(fact_5861_norm__diff__ineq,axiom,
% 0.29/0.59      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_ineq
% 0.29/0.59  thf(fact_5862_norm__triangle__ineq2,axiom,
% 0.29/0.59      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq2
% 0.29/0.59  thf(fact_5863_norm__triangle__ineq2,axiom,
% 0.29/0.59      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_triangle_ineq2
% 0.29/0.59  thf(fact_5864_power__eq__1__iff,axiom,
% 0.29/0.59      ! [W: real,N2: nat] :
% 0.29/0.59        ( ( ( power_power_real @ W @ N2 )
% 0.29/0.59          = one_one_real )
% 0.29/0.59       => ( ( ( real_V7735802525324610683m_real @ W )
% 0.29/0.59            = one_one_real )
% 0.29/0.59          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_eq_1_iff
% 0.29/0.59  thf(fact_5865_power__eq__1__iff,axiom,
% 0.29/0.59      ! [W: complex,N2: nat] :
% 0.29/0.59        ( ( ( power_power_complex @ W @ N2 )
% 0.29/0.59          = one_one_complex )
% 0.29/0.59       => ( ( ( real_V1022390504157884413omplex @ W )
% 0.29/0.59            = one_one_real )
% 0.29/0.59          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % power_eq_1_iff
% 0.29/0.59  thf(fact_5866_norm__diff__triangle__ineq,axiom,
% 0.29/0.59      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_ineq
% 0.29/0.59  thf(fact_5867_norm__diff__triangle__ineq,axiom,
% 0.29/0.59      ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_diff_triangle_ineq
% 0.29/0.59  thf(fact_5868_square__norm__one,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_real )
% 0.29/0.59       => ( ( real_V7735802525324610683m_real @ X4 )
% 0.29/0.59          = one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_norm_one
% 0.29/0.59  thf(fact_5869_square__norm__one,axiom,
% 0.29/0.59      ! [X4: complex] :
% 0.29/0.59        ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59          = one_one_complex )
% 0.29/0.59       => ( ( real_V1022390504157884413omplex @ X4 )
% 0.29/0.59          = one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % square_norm_one
% 0.29/0.59  thf(fact_5870_norm__power__diff,axiom,
% 0.29/0.59      ! [Z: real,W: real,M: nat] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 0.29/0.59         => ( 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 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power_diff
% 0.29/0.59  thf(fact_5871_norm__power__diff,axiom,
% 0.29/0.59      ! [Z: complex,W: complex,M: nat] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 0.29/0.59         => ( 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 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % norm_power_diff
% 0.29/0.59  thf(fact_5872_arcosh__1,axiom,
% 0.29/0.59      ( ( arcosh_real @ one_one_real )
% 0.29/0.59      = zero_zero_real ) ).
% 0.29/0.59  
% 0.29/0.59  % arcosh_1
% 0.29/0.59  thf(fact_5873_pochhammer__double,axiom,
% 0.29/0.59      ! [Z: rat,N2: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_double
% 0.29/0.59  thf(fact_5874_pochhammer__double,axiom,
% 0.29/0.59      ! [Z: complex,N2: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_double
% 0.29/0.59  thf(fact_5875_pochhammer__double,axiom,
% 0.29/0.59      ! [Z: real,N2: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_double
% 0.29/0.59  thf(fact_5876_ln__one__minus__pos__lower__bound,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.59         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_one_minus_pos_lower_bound
% 0.29/0.59  thf(fact_5877_central__binomial__lower__bound,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % central_binomial_lower_bound
% 0.29/0.59  thf(fact_5878_divmod__BitM__2__eq,axiom,
% 0.29/0.59      ! [M: num] :
% 0.29/0.59        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.29/0.59        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % divmod_BitM_2_eq
% 0.29/0.59  thf(fact_5879_ln__one,axiom,
% 0.29/0.59      ( ( ln_ln_real @ one_one_real )
% 0.29/0.59      = zero_zero_real ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_one
% 0.29/0.59  thf(fact_5880_ln__inj__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ( ( ln_ln_real @ X4 )
% 0.29/0.59              = ( ln_ln_real @ Y ) )
% 0.29/0.59            = ( X4 = Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_inj_iff
% 0.29/0.59  thf(fact_5881_ln__less__cancel__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 0.29/0.59            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_less_cancel_iff
% 0.29/0.59  thf(fact_5882_pochhammer__0,axiom,
% 0.29/0.59      ! [A: complex] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 0.29/0.59        = one_one_complex ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0
% 0.29/0.59  thf(fact_5883_pochhammer__0,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 0.29/0.59        = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0
% 0.29/0.59  thf(fact_5884_pochhammer__0,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.29/0.59        = one_one_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0
% 0.29/0.59  thf(fact_5885_pochhammer__0,axiom,
% 0.29/0.59      ! [A: nat] :
% 0.29/0.59        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.29/0.59        = one_one_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0
% 0.29/0.59  thf(fact_5886_pochhammer__0,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.29/0.59        = one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0
% 0.29/0.59  thf(fact_5887_dbl__dec__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.29/0.59        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(5)
% 0.29/0.59  thf(fact_5888_dbl__dec__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 0.29/0.59        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(5)
% 0.29/0.59  thf(fact_5889_dbl__dec__simps_I5_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 0.29/0.59        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dbl_dec_simps(5)
% 0.29/0.59  thf(fact_5890_ln__le__cancel__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 0.29/0.59            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_le_cancel_iff
% 0.29/0.59  thf(fact_5891_ln__less__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 0.29/0.59          = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_less_zero_iff
% 0.29/0.59  thf(fact_5892_ln__gt__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.59          = ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_gt_zero_iff
% 0.29/0.59  thf(fact_5893_ln__eq__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ( ln_ln_real @ X4 )
% 0.29/0.59            = zero_zero_real )
% 0.29/0.59          = ( X4 = one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_eq_zero_iff
% 0.29/0.59  thf(fact_5894_pred__numeral__simps_I2_J,axiom,
% 0.29/0.59      ! [K: num] :
% 0.29/0.59        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.29/0.59        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pred_numeral_simps(2)
% 0.29/0.59  thf(fact_5895_ln__ge__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.59          = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_ge_zero_iff
% 0.29/0.59  thf(fact_5896_ln__le__zero__iff,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 0.29/0.59          = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_le_zero_iff
% 0.29/0.59  thf(fact_5897_semiring__norm_I26_J,axiom,
% 0.29/0.59      ( ( bitM @ one )
% 0.29/0.59      = one ) ).
% 0.29/0.59  
% 0.29/0.59  % semiring_norm(26)
% 0.29/0.59  thf(fact_5898_ln__less__self,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_less_self
% 0.29/0.59  thf(fact_5899_pochhammer__pos,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_pos
% 0.29/0.59  thf(fact_5900_pochhammer__pos,axiom,
% 0.29/0.59      ! [X4: rat,N2: nat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.59       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_pos
% 0.29/0.59  thf(fact_5901_pochhammer__pos,axiom,
% 0.29/0.59      ! [X4: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.59       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_pos
% 0.29/0.59  thf(fact_5902_pochhammer__pos,axiom,
% 0.29/0.59      ! [X4: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ X4 )
% 0.29/0.59       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_pos
% 0.29/0.59  thf(fact_5903_pochhammer__neq__0__mono,axiom,
% 0.29/0.59      ! [A: complex,M: nat,N2: nat] :
% 0.29/0.59        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.29/0.59         != zero_zero_complex )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.29/0.59           != zero_zero_complex ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_neq_0_mono
% 0.29/0.59  thf(fact_5904_pochhammer__neq__0__mono,axiom,
% 0.29/0.59      ! [A: real,M: nat,N2: nat] :
% 0.29/0.59        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.29/0.59         != zero_zero_real )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.29/0.59           != zero_zero_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_neq_0_mono
% 0.29/0.59  thf(fact_5905_pochhammer__neq__0__mono,axiom,
% 0.29/0.59      ! [A: rat,M: nat,N2: nat] :
% 0.29/0.59        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.29/0.59         != zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.29/0.59           != zero_zero_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_neq_0_mono
% 0.29/0.59  thf(fact_5906_pochhammer__eq__0__mono,axiom,
% 0.29/0.59      ! [A: complex,N2: nat,M: nat] :
% 0.29/0.59        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.29/0.59          = zero_zero_complex )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 0.29/0.59            = zero_zero_complex ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_mono
% 0.29/0.59  thf(fact_5907_pochhammer__eq__0__mono,axiom,
% 0.29/0.59      ! [A: real,N2: nat,M: nat] :
% 0.29/0.59        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.29/0.59          = zero_zero_real )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 0.29/0.59            = zero_zero_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_mono
% 0.29/0.59  thf(fact_5908_pochhammer__eq__0__mono,axiom,
% 0.29/0.59      ! [A: rat,N2: nat,M: nat] :
% 0.29/0.59        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.29/0.59          = zero_zero_rat )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.59         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.29/0.59            = zero_zero_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_mono
% 0.29/0.59  thf(fact_5909_semiring__norm_I27_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( bitM @ ( bit0 @ N2 ) )
% 0.29/0.59        = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % semiring_norm(27)
% 0.29/0.59  thf(fact_5910_semiring__norm_I28_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( bitM @ ( bit1 @ N2 ) )
% 0.29/0.59        = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % semiring_norm(28)
% 0.29/0.59  thf(fact_5911_inc__BitM__eq,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( inc @ ( bitM @ N2 ) )
% 0.29/0.59        = ( bit0 @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % inc_BitM_eq
% 0.29/0.59  thf(fact_5912_BitM__inc__eq,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( bitM @ ( inc @ N2 ) )
% 0.29/0.59        = ( bit1 @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % BitM_inc_eq
% 0.29/0.59  thf(fact_5913_ln__bound,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_bound
% 0.29/0.59  thf(fact_5914_ln__gt__zero__imp__gt__one,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59         => ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_gt_zero_imp_gt_one
% 0.29/0.59  thf(fact_5915_ln__less__zero,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.59         => ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_less_zero
% 0.29/0.59  thf(fact_5916_ln__gt__zero,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.59       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_gt_zero
% 0.29/0.59  thf(fact_5917_ln__ge__zero,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_ge_zero
% 0.29/0.59  thf(fact_5918_pochhammer__nonneg,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_nonneg
% 0.29/0.59  thf(fact_5919_pochhammer__nonneg,axiom,
% 0.29/0.59      ! [X4: rat,N2: nat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.59       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_nonneg
% 0.29/0.59  thf(fact_5920_pochhammer__nonneg,axiom,
% 0.29/0.59      ! [X4: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 0.29/0.59       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_nonneg
% 0.29/0.59  thf(fact_5921_pochhammer__nonneg,axiom,
% 0.29/0.59      ! [X4: int,N2: nat] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ X4 )
% 0.29/0.59       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_nonneg
% 0.29/0.59  thf(fact_5922_pochhammer__0__left,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( N2 = zero_zero_nat )
% 0.29/0.59         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 0.29/0.59            = one_one_complex ) )
% 0.29/0.59        & ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 0.29/0.59            = zero_zero_complex ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0_left
% 0.29/0.59  thf(fact_5923_pochhammer__0__left,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( N2 = zero_zero_nat )
% 0.29/0.59         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 0.29/0.59            = one_one_real ) )
% 0.29/0.59        & ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 0.29/0.59            = zero_zero_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0_left
% 0.29/0.59  thf(fact_5924_pochhammer__0__left,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( N2 = zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.29/0.59            = one_one_rat ) )
% 0.29/0.59        & ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 0.29/0.59            = zero_zero_rat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0_left
% 0.29/0.59  thf(fact_5925_pochhammer__0__left,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( N2 = zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.29/0.59            = one_one_nat ) )
% 0.29/0.59        & ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 0.29/0.59            = zero_zero_nat ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0_left
% 0.29/0.59  thf(fact_5926_pochhammer__0__left,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( ( N2 = zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.29/0.59            = one_one_int ) )
% 0.29/0.59        & ( ( N2 != zero_zero_nat )
% 0.29/0.59         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 0.29/0.59            = zero_zero_int ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_0_left
% 0.29/0.59  thf(fact_5927_eval__nat__numeral_I2_J,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.29/0.59        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % eval_nat_numeral(2)
% 0.29/0.59  thf(fact_5928_ln__ge__zero__imp__ge__one,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59         => ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_ge_zero_imp_ge_one
% 0.29/0.59  thf(fact_5929_one__plus__BitM,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 0.29/0.59        = ( bit0 @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % one_plus_BitM
% 0.29/0.59  thf(fact_5930_BitM__plus__one,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 0.29/0.59        = ( bit0 @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % BitM_plus_one
% 0.29/0.59  thf(fact_5931_ln__add__one__self__le__self,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_add_one_self_le_self
% 0.29/0.59  thf(fact_5932_ln__mult,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ( ln_ln_real @ ( times_times_real @ X4 @ Y ) )
% 0.29/0.59            = ( plus_plus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_mult
% 0.29/0.59  thf(fact_5933_ln__eq__minus__one,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ( ln_ln_real @ X4 )
% 0.29/0.59            = ( minus_minus_real @ X4 @ one_one_real ) )
% 0.29/0.59         => ( X4 = one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_eq_minus_one
% 0.29/0.59  thf(fact_5934_ln__div,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ( ln_ln_real @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.59            = ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_div
% 0.29/0.59  thf(fact_5935_pochhammer__rec,axiom,
% 0.29/0.59      ! [A: rat,N2: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec
% 0.29/0.59  thf(fact_5936_pochhammer__rec,axiom,
% 0.29/0.59      ! [A: complex,N2: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec
% 0.29/0.59  thf(fact_5937_pochhammer__rec,axiom,
% 0.29/0.59      ! [A: real,N2: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec
% 0.29/0.59  thf(fact_5938_pochhammer__rec,axiom,
% 0.29/0.59      ! [A: nat,N2: nat] :
% 0.29/0.59        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec
% 0.29/0.59  thf(fact_5939_pochhammer__rec,axiom,
% 0.29/0.59      ! [A: int,N2: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec
% 0.29/0.59  thf(fact_5940_pochhammer__rec_H,axiom,
% 0.29/0.59      ! [Z: rat,N2: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec'
% 0.29/0.59  thf(fact_5941_pochhammer__rec_H,axiom,
% 0.29/0.59      ! [Z: complex,N2: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec'
% 0.29/0.59  thf(fact_5942_pochhammer__rec_H,axiom,
% 0.29/0.59      ! [Z: real,N2: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec'
% 0.29/0.59  thf(fact_5943_pochhammer__rec_H,axiom,
% 0.29/0.59      ! [Z: int,N2: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec'
% 0.29/0.59  thf(fact_5944_pochhammer__rec_H,axiom,
% 0.29/0.59      ! [Z: nat,N2: nat] :
% 0.29/0.59        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_rec'
% 0.29/0.59  thf(fact_5945_pochhammer__Suc,axiom,
% 0.29/0.59      ! [A: rat,N2: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_Suc
% 0.29/0.59  thf(fact_5946_pochhammer__Suc,axiom,
% 0.29/0.59      ! [A: complex,N2: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_Suc
% 0.29/0.59  thf(fact_5947_pochhammer__Suc,axiom,
% 0.29/0.59      ! [A: real,N2: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_Suc
% 0.29/0.59  thf(fact_5948_pochhammer__Suc,axiom,
% 0.29/0.59      ! [A: int,N2: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_Suc
% 0.29/0.59  thf(fact_5949_pochhammer__Suc,axiom,
% 0.29/0.59      ! [A: nat,N2: nat] :
% 0.29/0.59        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 0.29/0.59        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_Suc
% 0.29/0.59  thf(fact_5950_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma
% 0.29/0.59  thf(fact_5951_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.29/0.59          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma
% 0.29/0.59  thf(fact_5952_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma
% 0.29/0.59  thf(fact_5953_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma
% 0.29/0.59  thf(fact_5954_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma
% 0.29/0.59  thf(fact_5955_pochhammer__of__nat__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_complex )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_iff
% 0.29/0.59  thf(fact_5956_pochhammer__of__nat__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.29/0.59          = zero_z3403309356797280102nteger )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_iff
% 0.29/0.59  thf(fact_5957_pochhammer__of__nat__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_rat )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_iff
% 0.29/0.59  thf(fact_5958_pochhammer__of__nat__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_real )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_iff
% 0.29/0.59  thf(fact_5959_pochhammer__of__nat__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.29/0.59          = zero_zero_int )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_iff
% 0.29/0.59  thf(fact_5960_pochhammer__eq__0__iff,axiom,
% 0.29/0.59      ! [A: complex,N2: nat] :
% 0.29/0.59        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 0.29/0.59          = zero_zero_complex )
% 0.29/0.59        = ( ? [K3: nat] :
% 0.29/0.59              ( ( ord_less_nat @ K3 @ N2 )
% 0.29/0.59              & ( A
% 0.29/0.59                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_iff
% 0.29/0.59  thf(fact_5961_pochhammer__eq__0__iff,axiom,
% 0.29/0.59      ! [A: rat,N2: nat] :
% 0.29/0.59        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 0.29/0.59          = zero_zero_rat )
% 0.29/0.59        = ( ? [K3: nat] :
% 0.29/0.59              ( ( ord_less_nat @ K3 @ N2 )
% 0.29/0.59              & ( A
% 0.29/0.59                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_iff
% 0.29/0.59  thf(fact_5962_pochhammer__eq__0__iff,axiom,
% 0.29/0.59      ! [A: real,N2: nat] :
% 0.29/0.59        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 0.29/0.59          = zero_zero_real )
% 0.29/0.59        = ( ? [K3: nat] :
% 0.29/0.59              ( ( ord_less_nat @ K3 @ N2 )
% 0.29/0.59              & ( A
% 0.29/0.59                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_eq_0_iff
% 0.29/0.59  thf(fact_5963_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 0.29/0.59         != zero_zero_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma'
% 0.29/0.59  thf(fact_5964_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 0.29/0.59         != zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma'
% 0.29/0.59  thf(fact_5965_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 0.29/0.59         != zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma'
% 0.29/0.59  thf(fact_5966_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 0.29/0.59         != zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma'
% 0.29/0.59  thf(fact_5967_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 0.29/0.59         != zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_of_nat_eq_0_lemma'
% 0.29/0.59  thf(fact_5968_pochhammer__product_H,axiom,
% 0.29/0.59      ! [Z: rat,N2: nat,M: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product'
% 0.29/0.59  thf(fact_5969_pochhammer__product_H,axiom,
% 0.29/0.59      ! [Z: complex,N2: nat,M: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product'
% 0.29/0.59  thf(fact_5970_pochhammer__product_H,axiom,
% 0.29/0.59      ! [Z: real,N2: nat,M: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product'
% 0.29/0.59  thf(fact_5971_pochhammer__product_H,axiom,
% 0.29/0.59      ! [Z: int,N2: nat,M: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product'
% 0.29/0.59  thf(fact_5972_pochhammer__product_H,axiom,
% 0.29/0.59      ! [Z: nat,N2: nat,M: nat] :
% 0.29/0.59        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 0.29/0.59        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product'
% 0.29/0.59  thf(fact_5973_binomial__maximum_H,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_maximum'
% 0.29/0.59  thf(fact_5974_binomial__mono,axiom,
% 0.29/0.59      ! [K: nat,K6: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ K6 )
% 0.29/0.59       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 0.29/0.59         => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_mono
% 0.29/0.59  thf(fact_5975_ln__2__less__1,axiom,
% 0.29/0.59      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.29/0.59  
% 0.29/0.59  % ln_2_less_1
% 0.29/0.59  thf(fact_5976_numeral__BitM,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 0.29/0.59        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_BitM
% 0.29/0.59  thf(fact_5977_numeral__BitM,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 0.29/0.59        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_BitM
% 0.29/0.59  thf(fact_5978_numeral__BitM,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 0.29/0.59        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_BitM
% 0.29/0.59  thf(fact_5979_numeral__BitM,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 0.29/0.59        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % numeral_BitM
% 0.29/0.59  thf(fact_5980_binomial__antimono,axiom,
% 0.29/0.59      ! [K: nat,K6: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ K6 )
% 0.29/0.59       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.29/0.59         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 0.29/0.59           => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_antimono
% 0.29/0.59  thf(fact_5981_binomial__maximum,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_maximum
% 0.29/0.59  thf(fact_5982_odd__numeral__BitM,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral_BitM
% 0.29/0.59  thf(fact_5983_odd__numeral__BitM,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral_BitM
% 0.29/0.59  thf(fact_5984_odd__numeral__BitM,axiom,
% 0.29/0.59      ! [W: num] :
% 0.29/0.59        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % odd_numeral_BitM
% 0.29/0.59  thf(fact_5985_ln__le__minus__one,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_le_minus_one
% 0.29/0.59  thf(fact_5986_ln__diff__le,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.59         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X4 @ Y ) @ Y ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_diff_le
% 0.29/0.59  thf(fact_5987_ln__add__one__self__le__self2,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.59       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_add_one_self_le_self2
% 0.29/0.59  thf(fact_5988_ln__realpow,axiom,
% 0.29/0.59      ! [X4: real,N2: nat] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ln_ln_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.59          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_realpow
% 0.29/0.59  thf(fact_5989_pochhammer__product,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: rat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59       => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 0.29/0.59          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product
% 0.29/0.59  thf(fact_5990_pochhammer__product,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: complex] :
% 0.29/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59       => ( ( comm_s2602460028002588243omplex @ Z @ N2 )
% 0.29/0.59          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product
% 0.29/0.59  thf(fact_5991_pochhammer__product,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: real] :
% 0.29/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59       => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 0.29/0.59          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product
% 0.29/0.59  thf(fact_5992_pochhammer__product,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: int] :
% 0.29/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59       => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 0.29/0.59          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product
% 0.29/0.59  thf(fact_5993_pochhammer__product,axiom,
% 0.29/0.59      ! [M: nat,N2: nat,Z: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59       => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 0.29/0.59          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_product
% 0.29/0.59  thf(fact_5994_binomial__strict__antimono,axiom,
% 0.29/0.59      ! [K: nat,K6: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ K @ K6 )
% 0.29/0.59       => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.29/0.59         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 0.29/0.59           => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_strict_antimono
% 0.29/0.59  thf(fact_5995_binomial__strict__mono,axiom,
% 0.29/0.59      ! [K: nat,K6: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ K @ K6 )
% 0.29/0.59       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 0.29/0.59         => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_strict_mono
% 0.29/0.59  thf(fact_5996_binomial__less__binomial__Suc,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.59       => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_less_binomial_Suc
% 0.29/0.59  thf(fact_5997_central__binomial__odd,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.59       => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.59          = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % central_binomial_odd
% 0.29/0.59  thf(fact_5998_ln__one__minus__pos__upper__bound,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.59         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_one_minus_pos_upper_bound
% 0.29/0.59  thf(fact_5999_pochhammer__absorb__comp,axiom,
% 0.29/0.59      ! [R3: complex,K: nat] :
% 0.29/0.59        ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K ) )
% 0.29/0.59        = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_absorb_comp
% 0.29/0.59  thf(fact_6000_pochhammer__absorb__comp,axiom,
% 0.29/0.59      ! [R3: code_integer,K: nat] :
% 0.29/0.59        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 0.29/0.59        = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_absorb_comp
% 0.29/0.59  thf(fact_6001_pochhammer__absorb__comp,axiom,
% 0.29/0.59      ! [R3: rat,K: nat] :
% 0.29/0.59        ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 0.29/0.59        = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_absorb_comp
% 0.29/0.59  thf(fact_6002_pochhammer__absorb__comp,axiom,
% 0.29/0.59      ! [R3: real,K: nat] :
% 0.29/0.59        ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K ) )
% 0.29/0.59        = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_absorb_comp
% 0.29/0.59  thf(fact_6003_pochhammer__absorb__comp,axiom,
% 0.29/0.59      ! [R3: int,K: nat] :
% 0.29/0.59        ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 0.29/0.59        = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_absorb_comp
% 0.29/0.59  thf(fact_6004_pochhammer__minus,axiom,
% 0.29/0.59      ! [B: complex,K: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 0.29/0.59        = ( 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 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus
% 0.29/0.59  thf(fact_6005_pochhammer__minus,axiom,
% 0.29/0.59      ! [B: code_integer,K: nat] :
% 0.29/0.59        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.29/0.59        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus
% 0.29/0.59  thf(fact_6006_pochhammer__minus,axiom,
% 0.29/0.59      ! [B: rat,K: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.29/0.59        = ( 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 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus
% 0.29/0.59  thf(fact_6007_pochhammer__minus,axiom,
% 0.29/0.59      ! [B: real,K: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 0.29/0.59        = ( 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 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus
% 0.29/0.59  thf(fact_6008_pochhammer__minus,axiom,
% 0.29/0.59      ! [B: int,K: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.29/0.59        = ( 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 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus
% 0.29/0.59  thf(fact_6009_pochhammer__minus_H,axiom,
% 0.29/0.59      ! [B: complex,K: nat] :
% 0.29/0.59        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 0.29/0.59        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus'
% 0.29/0.59  thf(fact_6010_pochhammer__minus_H,axiom,
% 0.29/0.59      ! [B: code_integer,K: nat] :
% 0.29/0.59        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.29/0.59        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus'
% 0.29/0.59  thf(fact_6011_pochhammer__minus_H,axiom,
% 0.29/0.59      ! [B: rat,K: nat] :
% 0.29/0.59        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.29/0.59        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus'
% 0.29/0.59  thf(fact_6012_pochhammer__minus_H,axiom,
% 0.29/0.59      ! [B: real,K: nat] :
% 0.29/0.59        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 0.29/0.59        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus'
% 0.29/0.59  thf(fact_6013_pochhammer__minus_H,axiom,
% 0.29/0.59      ! [B: int,K: nat] :
% 0.29/0.59        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.29/0.59        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % pochhammer_minus'
% 0.29/0.59  thf(fact_6014_ln__one__plus__pos__lower__bound,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.59         => ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % ln_one_plus_pos_lower_bound
% 0.29/0.59  thf(fact_6015_zero__less__binomial__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 0.29/0.59        = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_binomial_iff
% 0.29/0.59  thf(fact_6016_artanh__def,axiom,
% 0.29/0.59      ( artanh_real
% 0.29/0.59      = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % artanh_def
% 0.29/0.59  thf(fact_6017_choose__two,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.59        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % choose_two
% 0.29/0.59  thf(fact_6018_binomial__n__0,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ N2 @ zero_zero_nat )
% 0.29/0.59        = one_one_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_n_0
% 0.29/0.59  thf(fact_6019_binomial__Suc__Suc,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 0.29/0.59        = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_Suc_Suc
% 0.29/0.59  thf(fact_6020_binomial__eq__0__iff,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ( binomial @ N2 @ K )
% 0.29/0.59          = zero_zero_nat )
% 0.29/0.59        = ( ord_less_nat @ N2 @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_eq_0_iff
% 0.29/0.59  thf(fact_6021_binomial__Suc__n,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ ( suc @ N2 ) @ N2 )
% 0.29/0.59        = ( suc @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_Suc_n
% 0.29/0.59  thf(fact_6022_binomial__n__n,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ N2 @ N2 )
% 0.29/0.59        = one_one_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_n_n
% 0.29/0.59  thf(fact_6023_binomial__0__Suc,axiom,
% 0.29/0.59      ! [K: nat] :
% 0.29/0.59        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.29/0.59        = zero_zero_nat ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_0_Suc
% 0.29/0.59  thf(fact_6024_binomial__1,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.59        = N2 ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_1
% 0.29/0.59  thf(fact_6025_choose__one,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( binomial @ N2 @ one_one_nat )
% 0.29/0.59        = N2 ) ).
% 0.29/0.59  
% 0.29/0.59  % choose_one
% 0.29/0.59  thf(fact_6026_binomial__eq__0,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ N2 @ K )
% 0.29/0.59       => ( ( binomial @ N2 @ K )
% 0.29/0.59          = zero_zero_nat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_eq_0
% 0.29/0.59  thf(fact_6027_Suc__times__binomial,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 0.29/0.59        = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_times_binomial
% 0.29/0.59  thf(fact_6028_Suc__times__binomial__eq,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 0.29/0.59        = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_times_binomial_eq
% 0.29/0.59  thf(fact_6029_binomial__symmetric,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ( binomial @ N2 @ K )
% 0.29/0.59          = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_symmetric
% 0.29/0.59  thf(fact_6030_choose__mult__lemma,axiom,
% 0.29/0.59      ! [M: nat,R3: nat,K: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 0.29/0.59        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R3 ) @ M ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % choose_mult_lemma
% 0.29/0.59  thf(fact_6031_binomial__le__pow,axiom,
% 0.29/0.59      ! [R3: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ R3 @ N2 )
% 0.29/0.59       => ( ord_less_eq_nat @ ( binomial @ N2 @ R3 ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_le_pow
% 0.29/0.59  thf(fact_6032_zero__less__binomial,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_binomial
% 0.29/0.59  thf(fact_6033_Suc__times__binomial__add,axiom,
% 0.29/0.59      ! [A: nat,B: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.29/0.59        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % Suc_times_binomial_add
% 0.29/0.59  thf(fact_6034_choose__mult,axiom,
% 0.29/0.59      ! [K: nat,M: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.59       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.59         => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 0.29/0.59            = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % choose_mult
% 0.29/0.59  thf(fact_6035_binomial__Suc__Suc__eq__times,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 0.29/0.59        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_Suc_Suc_eq_times
% 0.29/0.59  thf(fact_6036_binomial__absorb__comp,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 0.29/0.59        = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_absorb_comp
% 0.29/0.59  thf(fact_6037_binomial__absorption,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 0.29/0.59        = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_absorption
% 0.29/0.59  thf(fact_6038_binomial__ge__n__over__k__pow__k,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_ge_n_over_k_pow_k
% 0.29/0.59  thf(fact_6039_binomial__ge__n__over__k__pow__k,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.59       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_ge_n_over_k_pow_k
% 0.29/0.59  thf(fact_6040_binomial__le__pow2,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_le_pow2
% 0.29/0.59  thf(fact_6041_choose__reduce__nat,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.59         => ( ( binomial @ N2 @ K )
% 0.29/0.59            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % choose_reduce_nat
% 0.29/0.59  thf(fact_6042_times__binomial__minus1__eq,axiom,
% 0.29/0.59      ! [K: nat,N2: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.59       => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 0.29/0.59          = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % times_binomial_minus1_eq
% 0.29/0.59  thf(fact_6043_binomial__addition__formula,axiom,
% 0.29/0.59      ! [N2: nat,K: nat] :
% 0.29/0.59        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.59       => ( ( binomial @ N2 @ ( suc @ K ) )
% 0.29/0.59          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % binomial_addition_formula
% 0.29/0.59  thf(fact_6044_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.59         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.29/0.59  thf(fact_6045_tanh__ln__real,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( tanh_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.59          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % tanh_ln_real
% 0.29/0.59  thf(fact_6046_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.59       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_ln_one_plus_x_minus_x_bound
% 0.29/0.59  thf(fact_6047_signed__take__bit__eq__take__bit__minus,axiom,
% 0.29/0.59      ( bit_ri631733984087533419it_int
% 0.29/0.59      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % signed_take_bit_eq_take_bit_minus
% 0.29/0.59  thf(fact_6048_fact__double,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % fact_double
% 0.29/0.59  thf(fact_6049_fact__double,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % fact_double
% 0.29/0.59  thf(fact_6050_fact__double,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.59        = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % fact_double
% 0.29/0.59  thf(fact_6051_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 0.29/0.59      ! [X4: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.59       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.59         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_ln_one_plus_x_minus_x_bound_nonneg
% 0.29/0.59  thf(fact_6052_abs__abs,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.29/0.59        = ( abs_abs_real @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_abs
% 0.29/0.59  thf(fact_6053_abs__abs,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.29/0.59        = ( abs_abs_int @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_abs
% 0.29/0.59  thf(fact_6054_abs__abs,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_abs
% 0.29/0.59  thf(fact_6055_abs__abs,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_abs
% 0.29/0.59  thf(fact_6056_abs__idempotent,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.29/0.59        = ( abs_abs_real @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_idempotent
% 0.29/0.59  thf(fact_6057_abs__idempotent,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.29/0.59        = ( abs_abs_int @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_idempotent
% 0.29/0.59  thf(fact_6058_abs__idempotent,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_idempotent
% 0.29/0.59  thf(fact_6059_abs__idempotent,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_idempotent
% 0.29/0.59  thf(fact_6060_abs__0,axiom,
% 0.29/0.59      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.29/0.59      = zero_z3403309356797280102nteger ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0
% 0.29/0.59  thf(fact_6061_abs__0,axiom,
% 0.29/0.59      ( ( abs_abs_complex @ zero_zero_complex )
% 0.29/0.59      = zero_zero_complex ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0
% 0.29/0.59  thf(fact_6062_abs__0,axiom,
% 0.29/0.59      ( ( abs_abs_real @ zero_zero_real )
% 0.29/0.59      = zero_zero_real ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0
% 0.29/0.59  thf(fact_6063_abs__0,axiom,
% 0.29/0.59      ( ( abs_abs_rat @ zero_zero_rat )
% 0.29/0.59      = zero_zero_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0
% 0.29/0.59  thf(fact_6064_abs__0,axiom,
% 0.29/0.59      ( ( abs_abs_int @ zero_zero_int )
% 0.29/0.59      = zero_zero_int ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0
% 0.29/0.59  thf(fact_6065_abs__0__eq,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( zero_z3403309356797280102nteger
% 0.29/0.59          = ( abs_abs_Code_integer @ A ) )
% 0.29/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0_eq
% 0.29/0.59  thf(fact_6066_abs__0__eq,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( zero_zero_real
% 0.29/0.59          = ( abs_abs_real @ A ) )
% 0.29/0.59        = ( A = zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0_eq
% 0.29/0.59  thf(fact_6067_abs__0__eq,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( zero_zero_rat
% 0.29/0.59          = ( abs_abs_rat @ A ) )
% 0.29/0.59        = ( A = zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0_eq
% 0.29/0.59  thf(fact_6068_abs__0__eq,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( zero_zero_int
% 0.29/0.59          = ( abs_abs_int @ A ) )
% 0.29/0.59        = ( A = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_0_eq
% 0.29/0.59  thf(fact_6069_abs__eq__0,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ( abs_abs_Code_integer @ A )
% 0.29/0.59          = zero_z3403309356797280102nteger )
% 0.29/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_eq_0
% 0.29/0.59  thf(fact_6070_abs__eq__0,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ( abs_abs_real @ A )
% 0.29/0.59          = zero_zero_real )
% 0.29/0.59        = ( A = zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_eq_0
% 0.29/0.59  thf(fact_6071_abs__eq__0,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ( abs_abs_rat @ A )
% 0.29/0.59          = zero_zero_rat )
% 0.29/0.59        = ( A = zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_eq_0
% 0.29/0.59  thf(fact_6072_abs__eq__0,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ( abs_abs_int @ A )
% 0.29/0.59          = zero_zero_int )
% 0.29/0.59        = ( A = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_eq_0
% 0.29/0.59  thf(fact_6073_abs__zero,axiom,
% 0.29/0.59      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.29/0.59      = zero_z3403309356797280102nteger ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_zero
% 0.29/0.59  thf(fact_6074_abs__zero,axiom,
% 0.29/0.59      ( ( abs_abs_real @ zero_zero_real )
% 0.29/0.59      = zero_zero_real ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_zero
% 0.29/0.59  thf(fact_6075_abs__zero,axiom,
% 0.29/0.59      ( ( abs_abs_rat @ zero_zero_rat )
% 0.29/0.59      = zero_zero_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_zero
% 0.29/0.59  thf(fact_6076_abs__zero,axiom,
% 0.29/0.59      ( ( abs_abs_int @ zero_zero_int )
% 0.29/0.59      = zero_zero_int ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_zero
% 0.29/0.59  thf(fact_6077_abs__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 0.29/0.59        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_numeral
% 0.29/0.59  thf(fact_6078_abs__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.59        = ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_numeral
% 0.29/0.59  thf(fact_6079_abs__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.59        = ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_numeral
% 0.29/0.59  thf(fact_6080_abs__numeral,axiom,
% 0.29/0.59      ! [N2: num] :
% 0.29/0.59        ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.59        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_numeral
% 0.29/0.59  thf(fact_6081_abs__mult__self__eq,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.59        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_mult_self_eq
% 0.29/0.59  thf(fact_6082_abs__mult__self__eq,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.29/0.59        = ( times_times_rat @ A @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_mult_self_eq
% 0.29/0.59  thf(fact_6083_abs__mult__self__eq,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.29/0.59        = ( times_times_real @ A @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_mult_self_eq
% 0.29/0.59  thf(fact_6084_abs__mult__self__eq,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.29/0.59        = ( times_times_int @ A @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_mult_self_eq
% 0.29/0.59  thf(fact_6085_abs__1,axiom,
% 0.29/0.59      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.29/0.59      = one_one_Code_integer ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_1
% 0.29/0.59  thf(fact_6086_abs__1,axiom,
% 0.29/0.59      ( ( abs_abs_complex @ one_one_complex )
% 0.29/0.59      = one_one_complex ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_1
% 0.29/0.59  thf(fact_6087_abs__1,axiom,
% 0.29/0.59      ( ( abs_abs_real @ one_one_real )
% 0.29/0.59      = one_one_real ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_1
% 0.29/0.59  thf(fact_6088_abs__1,axiom,
% 0.29/0.59      ( ( abs_abs_rat @ one_one_rat )
% 0.29/0.59      = one_one_rat ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_1
% 0.29/0.59  thf(fact_6089_abs__1,axiom,
% 0.29/0.59      ( ( abs_abs_int @ one_one_int )
% 0.29/0.59      = one_one_int ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_1
% 0.29/0.59  thf(fact_6090_abs__add__abs,axiom,
% 0.29/0.59      ! [A: code_integer,B: code_integer] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.29/0.59        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_add_abs
% 0.29/0.59  thf(fact_6091_abs__add__abs,axiom,
% 0.29/0.59      ! [A: real,B: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.29/0.59        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_add_abs
% 0.29/0.59  thf(fact_6092_abs__add__abs,axiom,
% 0.29/0.59      ! [A: rat,B: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.29/0.59        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_add_abs
% 0.29/0.59  thf(fact_6093_abs__add__abs,axiom,
% 0.29/0.59      ! [A: int,B: int] :
% 0.29/0.59        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.29/0.59        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_add_abs
% 0.29/0.59  thf(fact_6094_abs__divide,axiom,
% 0.29/0.59      ! [A: rat,B: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.59        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_divide
% 0.29/0.59  thf(fact_6095_abs__divide,axiom,
% 0.29/0.59      ! [A: real,B: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.59        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_divide
% 0.29/0.59  thf(fact_6096_abs__divide,axiom,
% 0.29/0.59      ! [A: complex,B: complex] :
% 0.29/0.59        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.59        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_divide
% 0.29/0.59  thf(fact_6097_abs__minus,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.59        = ( abs_abs_real @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus
% 0.29/0.59  thf(fact_6098_abs__minus,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.59        = ( abs_abs_int @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus
% 0.29/0.59  thf(fact_6099_abs__minus,axiom,
% 0.29/0.59      ! [A: complex] :
% 0.29/0.59        ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.59        = ( abs_abs_complex @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus
% 0.29/0.59  thf(fact_6100_abs__minus,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus
% 0.29/0.59  thf(fact_6101_abs__minus,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus
% 0.29/0.59  thf(fact_6102_abs__minus__cancel,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.59        = ( abs_abs_real @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus_cancel
% 0.29/0.59  thf(fact_6103_abs__minus__cancel,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.59        = ( abs_abs_int @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus_cancel
% 0.29/0.59  thf(fact_6104_abs__minus__cancel,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus_cancel
% 0.29/0.59  thf(fact_6105_abs__minus__cancel,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_minus_cancel
% 0.29/0.59  thf(fact_6106_abs__dvd__iff,axiom,
% 0.29/0.59      ! [M: real,K: real] :
% 0.29/0.59        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 0.29/0.59        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_dvd_iff
% 0.29/0.59  thf(fact_6107_abs__dvd__iff,axiom,
% 0.29/0.59      ! [M: int,K: int] :
% 0.29/0.59        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 0.29/0.59        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_dvd_iff
% 0.29/0.59  thf(fact_6108_abs__dvd__iff,axiom,
% 0.29/0.59      ! [M: code_integer,K: code_integer] :
% 0.29/0.59        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 0.29/0.59        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_dvd_iff
% 0.29/0.59  thf(fact_6109_abs__dvd__iff,axiom,
% 0.29/0.59      ! [M: rat,K: rat] :
% 0.29/0.59        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 0.29/0.59        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_dvd_iff
% 0.29/0.59  thf(fact_6110_dvd__abs__iff,axiom,
% 0.29/0.59      ! [M: real,K: real] :
% 0.29/0.59        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 0.29/0.59        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_abs_iff
% 0.29/0.59  thf(fact_6111_dvd__abs__iff,axiom,
% 0.29/0.59      ! [M: int,K: int] :
% 0.29/0.59        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 0.29/0.59        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_abs_iff
% 0.29/0.59  thf(fact_6112_dvd__abs__iff,axiom,
% 0.29/0.59      ! [M: code_integer,K: code_integer] :
% 0.29/0.59        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 0.29/0.59        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_abs_iff
% 0.29/0.59  thf(fact_6113_dvd__abs__iff,axiom,
% 0.29/0.59      ! [M: rat,K: rat] :
% 0.29/0.59        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 0.29/0.59        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.29/0.59  
% 0.29/0.59  % dvd_abs_iff
% 0.29/0.59  thf(fact_6114_abs__of__nat,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.29/0.59        = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nat
% 0.29/0.59  thf(fact_6115_abs__of__nat,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.59        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nat
% 0.29/0.59  thf(fact_6116_abs__of__nat,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.59        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nat
% 0.29/0.59  thf(fact_6117_abs__of__nat,axiom,
% 0.29/0.59      ! [N2: nat] :
% 0.29/0.59        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.59        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nat
% 0.29/0.59  thf(fact_6118_abs__bool__eq,axiom,
% 0.29/0.59      ! [P: $o] :
% 0.29/0.59        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.29/0.59        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_bool_eq
% 0.29/0.59  thf(fact_6119_abs__bool__eq,axiom,
% 0.29/0.59      ! [P: $o] :
% 0.29/0.59        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.29/0.59        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_bool_eq
% 0.29/0.59  thf(fact_6120_abs__bool__eq,axiom,
% 0.29/0.59      ! [P: $o] :
% 0.29/0.59        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.29/0.59        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_bool_eq
% 0.29/0.59  thf(fact_6121_abs__bool__eq,axiom,
% 0.29/0.59      ! [P: $o] :
% 0.29/0.59        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 0.29/0.59        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_bool_eq
% 0.29/0.59  thf(fact_6122_tanh__real__less__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 0.29/0.59        = ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.59  
% 0.29/0.59  % tanh_real_less_iff
% 0.29/0.59  thf(fact_6123_tanh__real__le__iff,axiom,
% 0.29/0.59      ! [X4: real,Y: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 0.29/0.59        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.59  
% 0.29/0.59  % tanh_real_le_iff
% 0.29/0.59  thf(fact_6124_abs__le__zero__iff,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_zero_iff
% 0.29/0.59  thf(fact_6125_abs__le__zero__iff,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.29/0.59        = ( A = zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_zero_iff
% 0.29/0.59  thf(fact_6126_abs__le__zero__iff,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.29/0.59        = ( A = zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_zero_iff
% 0.29/0.59  thf(fact_6127_abs__le__zero__iff,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.29/0.59        = ( A = zero_zero_int ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_zero_iff
% 0.29/0.59  thf(fact_6128_abs__le__self__iff,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.29/0.59        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_self_iff
% 0.29/0.59  thf(fact_6129_abs__le__self__iff,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.29/0.59        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_self_iff
% 0.29/0.59  thf(fact_6130_abs__le__self__iff,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.29/0.59        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_self_iff
% 0.29/0.59  thf(fact_6131_abs__le__self__iff,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.29/0.59        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_le_self_iff
% 0.29/0.59  thf(fact_6132_abs__of__nonneg,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.59       => ( ( abs_abs_Code_integer @ A )
% 0.29/0.59          = A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nonneg
% 0.29/0.59  thf(fact_6133_abs__of__nonneg,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.59       => ( ( abs_abs_real @ A )
% 0.29/0.59          = A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nonneg
% 0.29/0.59  thf(fact_6134_abs__of__nonneg,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.59       => ( ( abs_abs_rat @ A )
% 0.29/0.59          = A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nonneg
% 0.29/0.59  thf(fact_6135_abs__of__nonneg,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.59       => ( ( abs_abs_int @ A )
% 0.29/0.59          = A ) ) ).
% 0.29/0.59  
% 0.29/0.59  % abs_of_nonneg
% 0.29/0.59  thf(fact_6136_zero__less__abs__iff,axiom,
% 0.29/0.59      ! [A: code_integer] :
% 0.29/0.59        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.59        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_abs_iff
% 0.29/0.59  thf(fact_6137_zero__less__abs__iff,axiom,
% 0.29/0.59      ! [A: real] :
% 0.29/0.59        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.29/0.59        = ( A != zero_zero_real ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_abs_iff
% 0.29/0.59  thf(fact_6138_zero__less__abs__iff,axiom,
% 0.29/0.59      ! [A: rat] :
% 0.29/0.59        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.59        = ( A != zero_zero_rat ) ) ).
% 0.29/0.59  
% 0.29/0.59  % zero_less_abs_iff
% 0.29/0.59  thf(fact_6139_zero__less__abs__iff,axiom,
% 0.29/0.59      ! [A: int] :
% 0.29/0.59        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.29/0.60        = ( A != zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_abs_iff
% 0.29/0.60  thf(fact_6140_abs__neg__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.60        = ( numeral_numeral_real @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_numeral
% 0.29/0.60  thf(fact_6141_abs__neg__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.60        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_numeral
% 0.29/0.60  thf(fact_6142_abs__neg__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.60        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_numeral
% 0.29/0.60  thf(fact_6143_abs__neg__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.60        = ( numeral_numeral_rat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_numeral
% 0.29/0.60  thf(fact_6144_abs__neg__one,axiom,
% 0.29/0.60      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_one
% 0.29/0.60  thf(fact_6145_abs__neg__one,axiom,
% 0.29/0.60      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_one
% 0.29/0.60  thf(fact_6146_abs__neg__one,axiom,
% 0.29/0.60      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60      = one_one_Code_integer ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_one
% 0.29/0.60  thf(fact_6147_abs__neg__one,axiom,
% 0.29/0.60      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_neg_one
% 0.29/0.60  thf(fact_6148_abs__power__minus,axiom,
% 0.29/0.60      ! [A: real,N2: nat] :
% 0.29/0.60        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 0.29/0.60        = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power_minus
% 0.29/0.60  thf(fact_6149_abs__power__minus,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 0.29/0.60        = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power_minus
% 0.29/0.60  thf(fact_6150_abs__power__minus,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 0.29/0.60        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power_minus
% 0.29/0.60  thf(fact_6151_abs__power__minus,axiom,
% 0.29/0.60      ! [A: rat,N2: nat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 0.29/0.60        = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power_minus
% 0.29/0.60  thf(fact_6152_fact__0,axiom,
% 0.29/0.60      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_0
% 0.29/0.60  thf(fact_6153_fact__0,axiom,
% 0.29/0.60      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_0
% 0.29/0.60  thf(fact_6154_fact__0,axiom,
% 0.29/0.60      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_0
% 0.29/0.60  thf(fact_6155_fact__0,axiom,
% 0.29/0.60      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.29/0.60      = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_0
% 0.29/0.60  thf(fact_6156_fact__0,axiom,
% 0.29/0.60      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_0
% 0.29/0.60  thf(fact_6157_fact__1,axiom,
% 0.29/0.60      ( ( semiri5044797733671781792omplex @ one_one_nat )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_1
% 0.29/0.60  thf(fact_6158_fact__1,axiom,
% 0.29/0.60      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_1
% 0.29/0.60  thf(fact_6159_fact__1,axiom,
% 0.29/0.60      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_1
% 0.29/0.60  thf(fact_6160_fact__1,axiom,
% 0.29/0.60      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 0.29/0.60      = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_1
% 0.29/0.60  thf(fact_6161_fact__1,axiom,
% 0.29/0.60      ( ( semiri2265585572941072030t_real @ one_one_nat )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_1
% 0.29/0.60  thf(fact_6162_tanh__real__neg__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_neg_iff
% 0.29/0.60  thf(fact_6163_tanh__real__pos__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_pos_iff
% 0.29/0.60  thf(fact_6164_tanh__real__nonneg__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 0.29/0.60        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_nonneg_iff
% 0.29/0.60  thf(fact_6165_tanh__real__nonpos__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_nonpos_iff
% 0.29/0.60  thf(fact_6166_divide__le__0__abs__iff,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.29/0.60        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.60          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_le_0_abs_iff
% 0.29/0.60  thf(fact_6167_divide__le__0__abs__iff,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.29/0.60        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.60          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_le_0_abs_iff
% 0.29/0.60  thf(fact_6168_zero__le__divide__abs__iff,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.29/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.60          | ( B = zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_divide_abs_iff
% 0.29/0.60  thf(fact_6169_zero__le__divide__abs__iff,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.29/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.60          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_divide_abs_iff
% 0.29/0.60  thf(fact_6170_abs__of__nonpos,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.60       => ( ( abs_abs_real @ A )
% 0.29/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_nonpos
% 0.29/0.60  thf(fact_6171_abs__of__nonpos,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.29/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_nonpos
% 0.29/0.60  thf(fact_6172_abs__of__nonpos,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.29/0.60       => ( ( abs_abs_rat @ A )
% 0.29/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_nonpos
% 0.29/0.60  thf(fact_6173_abs__of__nonpos,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.29/0.60       => ( ( abs_abs_int @ A )
% 0.29/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_nonpos
% 0.29/0.60  thf(fact_6174_bit__numeral__Bit0__Suc__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_Bit0_Suc_iff
% 0.29/0.60  thf(fact_6175_bit__numeral__Bit0__Suc__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_Bit0_Suc_iff
% 0.29/0.60  thf(fact_6176_fact__Suc__0,axiom,
% 0.29/0.60      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc_0
% 0.29/0.60  thf(fact_6177_fact__Suc__0,axiom,
% 0.29/0.60      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc_0
% 0.29/0.60  thf(fact_6178_fact__Suc__0,axiom,
% 0.29/0.60      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc_0
% 0.29/0.60  thf(fact_6179_fact__Suc__0,axiom,
% 0.29/0.60      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc_0
% 0.29/0.60  thf(fact_6180_fact__Suc__0,axiom,
% 0.29/0.60      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc_0
% 0.29/0.60  thf(fact_6181_bit__numeral__Bit1__Suc__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_Bit1_Suc_iff
% 0.29/0.60  thf(fact_6182_bit__numeral__Bit1__Suc__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_Bit1_Suc_iff
% 0.29/0.60  thf(fact_6183_fact__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 0.29/0.60        = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc
% 0.29/0.60  thf(fact_6184_fact__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 0.29/0.60        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc
% 0.29/0.60  thf(fact_6185_fact__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 0.29/0.60        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc
% 0.29/0.60  thf(fact_6186_fact__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 0.29/0.60        = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_Suc
% 0.29/0.60  thf(fact_6187_artanh__minus__real,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.60       => ( ( artanh_real @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.60          = ( uminus_uminus_real @ ( artanh_real @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % artanh_minus_real
% 0.29/0.60  thf(fact_6188_signed__take__bit__nonnegative__iff,axiom,
% 0.29/0.60      ! [N2: nat,K: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % signed_take_bit_nonnegative_iff
% 0.29/0.60  thf(fact_6189_signed__take__bit__negative__iff,axiom,
% 0.29/0.60      ! [N2: nat,K: int] :
% 0.29/0.60        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % signed_take_bit_negative_iff
% 0.29/0.60  thf(fact_6190_zero__less__power__abs__iff,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 0.29/0.60        = ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_power_abs_iff
% 0.29/0.60  thf(fact_6191_zero__less__power__abs__iff,axiom,
% 0.29/0.60      ! [A: real,N2: nat] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 0.29/0.60        = ( ( A != zero_zero_real )
% 0.29/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_power_abs_iff
% 0.29/0.60  thf(fact_6192_zero__less__power__abs__iff,axiom,
% 0.29/0.60      ! [A: rat,N2: nat] :
% 0.29/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 0.29/0.60        = ( ( A != zero_zero_rat )
% 0.29/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_power_abs_iff
% 0.29/0.60  thf(fact_6193_zero__less__power__abs__iff,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 0.29/0.60        = ( ( A != zero_zero_int )
% 0.29/0.60          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_power_abs_iff
% 0.29/0.60  thf(fact_6194_power2__abs,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_abs
% 0.29/0.60  thf(fact_6195_power2__abs,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_abs
% 0.29/0.60  thf(fact_6196_power2__abs,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_abs
% 0.29/0.60  thf(fact_6197_power2__abs,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_abs
% 0.29/0.60  thf(fact_6198_abs__power2,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power2
% 0.29/0.60  thf(fact_6199_abs__power2,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power2
% 0.29/0.60  thf(fact_6200_abs__power2,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power2
% 0.29/0.60  thf(fact_6201_abs__power2,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_power2
% 0.29/0.60  thf(fact_6202_fact__2,axiom,
% 0.29/0.60      ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_2
% 0.29/0.60  thf(fact_6203_fact__2,axiom,
% 0.29/0.60      ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_2
% 0.29/0.60  thf(fact_6204_fact__2,axiom,
% 0.29/0.60      ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_2
% 0.29/0.60  thf(fact_6205_fact__2,axiom,
% 0.29/0.60      ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_2
% 0.29/0.60  thf(fact_6206_fact__2,axiom,
% 0.29/0.60      ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_2
% 0.29/0.60  thf(fact_6207_bit__numeral__simps_I2_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(2)
% 0.29/0.60  thf(fact_6208_bit__numeral__simps_I2_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(2)
% 0.29/0.60  thf(fact_6209_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.29/0.60      ! [W: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_minus_numeral_Bit0_Suc_iff
% 0.29/0.60  thf(fact_6210_bit__numeral__simps_I3_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(3)
% 0.29/0.60  thf(fact_6211_bit__numeral__simps_I3_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(3)
% 0.29/0.60  thf(fact_6212_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.29/0.60      ! [W: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_minus_numeral_Bit1_Suc_iff
% 0.29/0.60  thf(fact_6213_bit__0,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 0.29/0.60        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_0
% 0.29/0.60  thf(fact_6214_bit__0,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 0.29/0.60        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_0
% 0.29/0.60  thf(fact_6215_bit__0,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 0.29/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_0
% 0.29/0.60  thf(fact_6216_power__even__abs__numeral,axiom,
% 0.29/0.60      ! [W: num,A: code_integer] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs_numeral
% 0.29/0.60  thf(fact_6217_power__even__abs__numeral,axiom,
% 0.29/0.60      ! [W: num,A: rat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs_numeral
% 0.29/0.60  thf(fact_6218_power__even__abs__numeral,axiom,
% 0.29/0.60      ! [W: num,A: real] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs_numeral
% 0.29/0.60  thf(fact_6219_power__even__abs__numeral,axiom,
% 0.29/0.60      ! [W: num,A: int] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.29/0.60          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs_numeral
% 0.29/0.60  thf(fact_6220_bit__minus__numeral__int_I1_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_minus_numeral_int(1)
% 0.29/0.60  thf(fact_6221_bit__minus__numeral__int_I2_J,axiom,
% 0.29/0.60      ! [W: num,N2: num] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_minus_numeral_int(2)
% 0.29/0.60  thf(fact_6222_bit__mod__2__iff,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 )
% 0.29/0.60        = ( ( N2 = zero_zero_nat )
% 0.29/0.60          & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_mod_2_iff
% 0.29/0.60  thf(fact_6223_bit__mod__2__iff,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 0.29/0.60        = ( ( N2 = zero_zero_nat )
% 0.29/0.60          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_mod_2_iff
% 0.29/0.60  thf(fact_6224_bit__mod__2__iff,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 0.29/0.60        = ( ( N2 = zero_zero_nat )
% 0.29/0.60          & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_mod_2_iff
% 0.29/0.60  thf(fact_6225_bit__numeral__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_iff
% 0.29/0.60  thf(fact_6226_bit__numeral__iff,axiom,
% 0.29/0.60      ! [M: num,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_iff
% 0.29/0.60  thf(fact_6227_bit__of__nat__iff__bit,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N2 )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_of_nat_iff_bit
% 0.29/0.60  thf(fact_6228_bit__of__nat__iff__bit,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_of_nat_iff_bit
% 0.29/0.60  thf(fact_6229_bit__disjunctive__add__iff,axiom,
% 0.29/0.60      ! [A: int,B: int,N2: nat] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 0.29/0.60            | ~ ( bit_se1146084159140164899it_int @ B @ N3 ) )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.29/0.60          = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60            | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_disjunctive_add_iff
% 0.29/0.60  thf(fact_6230_bit__disjunctive__add__iff,axiom,
% 0.29/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 0.29/0.60            | ~ ( bit_se1148574629649215175it_nat @ B @ N3 ) )
% 0.29/0.60       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.29/0.60          = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60            | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_disjunctive_add_iff
% 0.29/0.60  thf(fact_6231_abs__ge__self,axiom,
% 0.29/0.60      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_self
% 0.29/0.60  thf(fact_6232_abs__ge__self,axiom,
% 0.29/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_self
% 0.29/0.60  thf(fact_6233_abs__ge__self,axiom,
% 0.29/0.60      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_self
% 0.29/0.60  thf(fact_6234_abs__ge__self,axiom,
% 0.29/0.60      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_self
% 0.29/0.60  thf(fact_6235_abs__le__D1,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D1
% 0.29/0.60  thf(fact_6236_abs__le__D1,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.60       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D1
% 0.29/0.60  thf(fact_6237_abs__le__D1,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D1
% 0.29/0.60  thf(fact_6238_abs__le__D1,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D1
% 0.29/0.60  thf(fact_6239_abs__eq__0__iff,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.29/0.60          = zero_z3403309356797280102nteger )
% 0.29/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_0_iff
% 0.29/0.60  thf(fact_6240_abs__eq__0__iff,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( ( abs_abs_complex @ A )
% 0.29/0.60          = zero_zero_complex )
% 0.29/0.60        = ( A = zero_zero_complex ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_0_iff
% 0.29/0.60  thf(fact_6241_abs__eq__0__iff,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( abs_abs_real @ A )
% 0.29/0.60          = zero_zero_real )
% 0.29/0.60        = ( A = zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_0_iff
% 0.29/0.60  thf(fact_6242_abs__eq__0__iff,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( abs_abs_rat @ A )
% 0.29/0.60          = zero_zero_rat )
% 0.29/0.60        = ( A = zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_0_iff
% 0.29/0.60  thf(fact_6243_abs__eq__0__iff,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( abs_abs_int @ A )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60        = ( A = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_0_iff
% 0.29/0.60  thf(fact_6244_abs__mult,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.29/0.60        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult
% 0.29/0.60  thf(fact_6245_abs__mult,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.60        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult
% 0.29/0.60  thf(fact_6246_abs__mult,axiom,
% 0.29/0.60      ! [A: complex,B: complex] :
% 0.29/0.60        ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 0.29/0.60        = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult
% 0.29/0.60  thf(fact_6247_abs__mult,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.29/0.60        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult
% 0.29/0.60  thf(fact_6248_abs__mult,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.29/0.60        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult
% 0.29/0.60  thf(fact_6249_abs__one,axiom,
% 0.29/0.60      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.29/0.60      = one_one_Code_integer ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_one
% 0.29/0.60  thf(fact_6250_abs__one,axiom,
% 0.29/0.60      ( ( abs_abs_real @ one_one_real )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_one
% 0.29/0.60  thf(fact_6251_abs__one,axiom,
% 0.29/0.60      ( ( abs_abs_rat @ one_one_rat )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_one
% 0.29/0.60  thf(fact_6252_abs__one,axiom,
% 0.29/0.60      ( ( abs_abs_int @ one_one_int )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_one
% 0.29/0.60  thf(fact_6253_abs__minus__commute,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.60        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_commute
% 0.29/0.60  thf(fact_6254_abs__minus__commute,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.60        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_commute
% 0.29/0.60  thf(fact_6255_abs__minus__commute,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.60        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_commute
% 0.29/0.60  thf(fact_6256_abs__minus__commute,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.60        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_commute
% 0.29/0.60  thf(fact_6257_abs__eq__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ( abs_abs_real @ X4 )
% 0.29/0.60          = ( abs_abs_real @ Y ) )
% 0.29/0.60        = ( ( X4 = Y )
% 0.29/0.60          | ( X4
% 0.29/0.60            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff
% 0.29/0.60  thf(fact_6258_abs__eq__iff,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ( abs_abs_int @ X4 )
% 0.29/0.60          = ( abs_abs_int @ Y ) )
% 0.29/0.60        = ( ( X4 = Y )
% 0.29/0.60          | ( X4
% 0.29/0.60            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff
% 0.29/0.60  thf(fact_6259_abs__eq__iff,axiom,
% 0.29/0.60      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.60        ( ( ( abs_abs_Code_integer @ X4 )
% 0.29/0.60          = ( abs_abs_Code_integer @ Y ) )
% 0.29/0.60        = ( ( X4 = Y )
% 0.29/0.60          | ( X4
% 0.29/0.60            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff
% 0.29/0.60  thf(fact_6260_abs__eq__iff,axiom,
% 0.29/0.60      ! [X4: rat,Y: rat] :
% 0.29/0.60        ( ( ( abs_abs_rat @ X4 )
% 0.29/0.60          = ( abs_abs_rat @ Y ) )
% 0.29/0.60        = ( ( X4 = Y )
% 0.29/0.60          | ( X4
% 0.29/0.60            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff
% 0.29/0.60  thf(fact_6261_fact__ge__self,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_self
% 0.29/0.60  thf(fact_6262_fact__mono__nat,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mono_nat
% 0.29/0.60  thf(fact_6263_power__abs,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.29/0.60        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_abs
% 0.29/0.60  thf(fact_6264_power__abs,axiom,
% 0.29/0.60      ! [A: rat,N2: nat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) )
% 0.29/0.60        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_abs
% 0.29/0.60  thf(fact_6265_power__abs,axiom,
% 0.29/0.60      ! [A: real,N2: nat] :
% 0.29/0.60        ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 0.29/0.60        = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_abs
% 0.29/0.60  thf(fact_6266_power__abs,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 0.29/0.60        = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_abs
% 0.29/0.60  thf(fact_6267_dvd__if__abs__eq,axiom,
% 0.29/0.60      ! [L: real,K: real] :
% 0.29/0.60        ( ( ( abs_abs_real @ L )
% 0.29/0.60          = ( abs_abs_real @ K ) )
% 0.29/0.60       => ( dvd_dvd_real @ L @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_if_abs_eq
% 0.29/0.60  thf(fact_6268_dvd__if__abs__eq,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( ( abs_abs_int @ L )
% 0.29/0.60          = ( abs_abs_int @ K ) )
% 0.29/0.60       => ( dvd_dvd_int @ L @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_if_abs_eq
% 0.29/0.60  thf(fact_6269_dvd__if__abs__eq,axiom,
% 0.29/0.60      ! [L: code_integer,K: code_integer] :
% 0.29/0.60        ( ( ( abs_abs_Code_integer @ L )
% 0.29/0.60          = ( abs_abs_Code_integer @ K ) )
% 0.29/0.60       => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_if_abs_eq
% 0.29/0.60  thf(fact_6270_dvd__if__abs__eq,axiom,
% 0.29/0.60      ! [L: rat,K: rat] :
% 0.29/0.60        ( ( ( abs_abs_rat @ L )
% 0.29/0.60          = ( abs_abs_rat @ K ) )
% 0.29/0.60       => ( dvd_dvd_rat @ L @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_if_abs_eq
% 0.29/0.60  thf(fact_6271_bit__xor__iff,axiom,
% 0.29/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ N2 )
% 0.29/0.60        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60         != ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_xor_iff
% 0.29/0.60  thf(fact_6272_bit__xor__iff,axiom,
% 0.29/0.60      ! [A: int,B: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ N2 )
% 0.29/0.60        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60         != ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_xor_iff
% 0.29/0.60  thf(fact_6273_bit__unset__bit__iff,axiom,
% 0.29/0.60      ! [M: nat,A: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N2 )
% 0.29/0.60        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60          & ( M != N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_unset_bit_iff
% 0.29/0.60  thf(fact_6274_bit__unset__bit__iff,axiom,
% 0.29/0.60      ! [M: nat,A: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N2 )
% 0.29/0.60        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60          & ( M != N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_unset_bit_iff
% 0.29/0.60  thf(fact_6275_bit__xor__int__iff,axiom,
% 0.29/0.60      ! [K: int,L: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N2 )
% 0.29/0.60        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 0.29/0.60         != ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_xor_int_iff
% 0.29/0.60  thf(fact_6276_not__bit__1__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_bit_1_Suc
% 0.29/0.60  thf(fact_6277_not__bit__1__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_bit_1_Suc
% 0.29/0.60  thf(fact_6278_bit__1__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_1_iff
% 0.29/0.60  thf(fact_6279_bit__1__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_1_iff
% 0.29/0.60  thf(fact_6280_abs__ge__zero,axiom,
% 0.29/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_zero
% 0.29/0.60  thf(fact_6281_abs__ge__zero,axiom,
% 0.29/0.60      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_zero
% 0.29/0.60  thf(fact_6282_abs__ge__zero,axiom,
% 0.29/0.60      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_zero
% 0.29/0.60  thf(fact_6283_abs__ge__zero,axiom,
% 0.29/0.60      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_zero
% 0.29/0.60  thf(fact_6284_bit__numeral__simps_I1_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(1)
% 0.29/0.60  thf(fact_6285_bit__numeral__simps_I1_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_numeral_simps(1)
% 0.29/0.60  thf(fact_6286_abs__of__pos,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_pos
% 0.29/0.60  thf(fact_6287_abs__of__pos,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.60       => ( ( abs_abs_real @ A )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_pos
% 0.29/0.60  thf(fact_6288_abs__of__pos,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.60       => ( ( abs_abs_rat @ A )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_pos
% 0.29/0.60  thf(fact_6289_abs__of__pos,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.60       => ( ( abs_abs_int @ A )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_pos
% 0.29/0.60  thf(fact_6290_abs__not__less__zero,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_not_less_zero
% 0.29/0.60  thf(fact_6291_abs__not__less__zero,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_not_less_zero
% 0.29/0.60  thf(fact_6292_abs__not__less__zero,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_not_less_zero
% 0.29/0.60  thf(fact_6293_abs__not__less__zero,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_not_less_zero
% 0.29/0.60  thf(fact_6294_abs__triangle__ineq,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq
% 0.29/0.60  thf(fact_6295_abs__triangle__ineq,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq
% 0.29/0.60  thf(fact_6296_abs__triangle__ineq,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq
% 0.29/0.60  thf(fact_6297_abs__triangle__ineq,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq
% 0.29/0.60  thf(fact_6298_abs__mult__less,axiom,
% 0.29/0.60      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.29/0.60       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 0.29/0.60         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_less
% 0.29/0.60  thf(fact_6299_abs__mult__less,axiom,
% 0.29/0.60      ! [A: real,C: real,B: real,D: real] :
% 0.29/0.60        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 0.29/0.60       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 0.29/0.60         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_less
% 0.29/0.60  thf(fact_6300_abs__mult__less,axiom,
% 0.29/0.60      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.29/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.29/0.60       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 0.29/0.60         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_less
% 0.29/0.60  thf(fact_6301_abs__mult__less,axiom,
% 0.29/0.60      ! [A: int,C: int,B: int,D: int] :
% 0.29/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.29/0.60       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 0.29/0.60         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_less
% 0.29/0.60  thf(fact_6302_abs__triangle__ineq2__sym,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2_sym
% 0.29/0.60  thf(fact_6303_abs__triangle__ineq2__sym,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2_sym
% 0.29/0.60  thf(fact_6304_abs__triangle__ineq2__sym,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2_sym
% 0.29/0.60  thf(fact_6305_abs__triangle__ineq2__sym,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2_sym
% 0.29/0.60  thf(fact_6306_abs__triangle__ineq3,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq3
% 0.29/0.60  thf(fact_6307_abs__triangle__ineq3,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq3
% 0.29/0.60  thf(fact_6308_abs__triangle__ineq3,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq3
% 0.29/0.60  thf(fact_6309_abs__triangle__ineq3,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq3
% 0.29/0.60  thf(fact_6310_abs__triangle__ineq2,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2
% 0.29/0.60  thf(fact_6311_abs__triangle__ineq2,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2
% 0.29/0.60  thf(fact_6312_abs__triangle__ineq2,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2
% 0.29/0.60  thf(fact_6313_abs__triangle__ineq2,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq2
% 0.29/0.60  thf(fact_6314_abs__ge__minus__self,axiom,
% 0.29/0.60      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_minus_self
% 0.29/0.60  thf(fact_6315_abs__ge__minus__self,axiom,
% 0.29/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_minus_self
% 0.29/0.60  thf(fact_6316_abs__ge__minus__self,axiom,
% 0.29/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_minus_self
% 0.29/0.60  thf(fact_6317_abs__ge__minus__self,axiom,
% 0.29/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_ge_minus_self
% 0.29/0.60  thf(fact_6318_abs__le__iff,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_eq_real @ A @ B )
% 0.29/0.60          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_iff
% 0.29/0.60  thf(fact_6319_abs__le__iff,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.60        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.60          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_iff
% 0.29/0.60  thf(fact_6320_abs__le__iff,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.60          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_iff
% 0.29/0.60  thf(fact_6321_abs__le__iff,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_eq_int @ A @ B )
% 0.29/0.60          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_iff
% 0.29/0.60  thf(fact_6322_abs__le__D2,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D2
% 0.29/0.60  thf(fact_6323_abs__le__D2,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.60       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D2
% 0.29/0.60  thf(fact_6324_abs__le__D2,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D2
% 0.29/0.60  thf(fact_6325_abs__le__D2,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.60       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_D2
% 0.29/0.60  thf(fact_6326_abs__leI,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.60       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.29/0.60         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_leI
% 0.29/0.60  thf(fact_6327_abs__leI,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.60       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.60         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_leI
% 0.29/0.60  thf(fact_6328_abs__leI,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.60       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.60         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_leI
% 0.29/0.60  thf(fact_6329_abs__leI,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.60       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.60         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_leI
% 0.29/0.60  thf(fact_6330_nonzero__abs__divide,axiom,
% 0.29/0.60      ! [B: rat,A: rat] :
% 0.29/0.60        ( ( B != zero_zero_rat )
% 0.29/0.60       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.60          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % nonzero_abs_divide
% 0.29/0.60  thf(fact_6331_nonzero__abs__divide,axiom,
% 0.29/0.60      ! [B: real,A: real] :
% 0.29/0.60        ( ( B != zero_zero_real )
% 0.29/0.60       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.60          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % nonzero_abs_divide
% 0.29/0.60  thf(fact_6332_abs__less__iff,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_real @ A @ B )
% 0.29/0.60          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_less_iff
% 0.29/0.60  thf(fact_6333_abs__less__iff,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_int @ A @ B )
% 0.29/0.60          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_less_iff
% 0.29/0.60  thf(fact_6334_abs__less__iff,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.29/0.60        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.60          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_less_iff
% 0.29/0.60  thf(fact_6335_abs__less__iff,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.29/0.60        = ( ( ord_less_rat @ A @ B )
% 0.29/0.60          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_less_iff
% 0.29/0.60  thf(fact_6336_fact__less__mono__nat,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.60       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.60         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_less_mono_nat
% 0.29/0.60  thf(fact_6337_bit__take__bit__iff,axiom,
% 0.29/0.60      ! [M: nat,A: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 0.29/0.60        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.60          & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_take_bit_iff
% 0.29/0.60  thf(fact_6338_bit__take__bit__iff,axiom,
% 0.29/0.60      ! [M: nat,A: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 0.29/0.60        = ( ( ord_less_nat @ N2 @ M )
% 0.29/0.60          & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_take_bit_iff
% 0.29/0.60  thf(fact_6339_bit__of__bool__iff,axiom,
% 0.29/0.60      ! [B: $o,N2: nat] :
% 0.29/0.60        ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N2 )
% 0.29/0.60        = ( B
% 0.29/0.60          & ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_of_bool_iff
% 0.29/0.60  thf(fact_6340_bit__of__bool__iff,axiom,
% 0.29/0.60      ! [B: $o,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N2 )
% 0.29/0.60        = ( B
% 0.29/0.60          & ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_of_bool_iff
% 0.29/0.60  thf(fact_6341_bit__of__bool__iff,axiom,
% 0.29/0.60      ! [B: $o,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N2 )
% 0.29/0.60        = ( B
% 0.29/0.60          & ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_of_bool_iff
% 0.29/0.60  thf(fact_6342_fact__ge__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_zero
% 0.29/0.60  thf(fact_6343_fact__ge__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_zero
% 0.29/0.60  thf(fact_6344_fact__ge__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_zero
% 0.29/0.60  thf(fact_6345_fact__ge__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_zero
% 0.29/0.60  thf(fact_6346_fact__not__neg,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_not_neg
% 0.29/0.60  thf(fact_6347_fact__not__neg,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_not_neg
% 0.29/0.60  thf(fact_6348_fact__not__neg,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_not_neg
% 0.29/0.60  thf(fact_6349_fact__not__neg,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_not_neg
% 0.29/0.60  thf(fact_6350_fact__gt__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_gt_zero
% 0.29/0.60  thf(fact_6351_fact__gt__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_gt_zero
% 0.29/0.60  thf(fact_6352_fact__gt__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_gt_zero
% 0.29/0.60  thf(fact_6353_fact__gt__zero,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_gt_zero
% 0.29/0.60  thf(fact_6354_fact__ge__1,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_1
% 0.29/0.60  thf(fact_6355_fact__ge__1,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_1
% 0.29/0.60  thf(fact_6356_fact__ge__1,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_1
% 0.29/0.60  thf(fact_6357_fact__ge__1,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_1
% 0.29/0.60  thf(fact_6358_fact__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mono
% 0.29/0.60  thf(fact_6359_fact__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mono
% 0.29/0.60  thf(fact_6360_fact__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mono
% 0.29/0.60  thf(fact_6361_fact__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mono
% 0.29/0.60  thf(fact_6362_signed__take__bit__eq__if__positive,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60       => ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 0.29/0.60          = ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % signed_take_bit_eq_if_positive
% 0.29/0.60  thf(fact_6363_fact__dvd,axiom,
% 0.29/0.60      ! [N2: nat,M: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.60       => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_dvd
% 0.29/0.60  thf(fact_6364_fact__dvd,axiom,
% 0.29/0.60      ! [N2: nat,M: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.60       => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_dvd
% 0.29/0.60  thf(fact_6365_fact__dvd,axiom,
% 0.29/0.60      ! [N2: nat,M: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.60       => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_dvd
% 0.29/0.60  thf(fact_6366_fact__dvd,axiom,
% 0.29/0.60      ! [N2: nat,M: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.60       => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_dvd
% 0.29/0.60  thf(fact_6367_pochhammer__fact,axiom,
% 0.29/0.60      ( semiri5044797733671781792omplex
% 0.29/0.60      = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_fact
% 0.29/0.60  thf(fact_6368_pochhammer__fact,axiom,
% 0.29/0.60      ( semiri773545260158071498ct_rat
% 0.29/0.60      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_fact
% 0.29/0.60  thf(fact_6369_pochhammer__fact,axiom,
% 0.29/0.60      ( semiri1406184849735516958ct_int
% 0.29/0.60      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_fact
% 0.29/0.60  thf(fact_6370_pochhammer__fact,axiom,
% 0.29/0.60      ( semiri1408675320244567234ct_nat
% 0.29/0.60      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_fact
% 0.29/0.60  thf(fact_6371_pochhammer__fact,axiom,
% 0.29/0.60      ( semiri2265585572941072030t_real
% 0.29/0.60      = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_fact
% 0.29/0.60  thf(fact_6372_tanh__real__lt__1,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_real @ ( tanh_real @ X4 ) @ one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_lt_1
% 0.29/0.60  thf(fact_6373_dense__eq0__I,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ! [E: real] :
% 0.29/0.60            ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.60           => ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ E ) )
% 0.29/0.60       => ( X4 = zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dense_eq0_I
% 0.29/0.60  thf(fact_6374_dense__eq0__I,axiom,
% 0.29/0.60      ! [X4: rat] :
% 0.29/0.60        ( ! [E: rat] :
% 0.29/0.60            ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.29/0.60           => ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ E ) )
% 0.29/0.60       => ( X4 = zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dense_eq0_I
% 0.29/0.60  thf(fact_6375_abs__eq__mult,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.60            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.29/0.60          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.60            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.29/0.60          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_mult
% 0.29/0.60  thf(fact_6376_abs__eq__mult,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.60            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.29/0.60          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.60            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.29/0.60       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.29/0.60          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_mult
% 0.29/0.60  thf(fact_6377_abs__eq__mult,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.60            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.29/0.60          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.60            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.29/0.60       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.60          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_mult
% 0.29/0.60  thf(fact_6378_abs__eq__mult,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.60            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.29/0.60          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.60            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.29/0.60       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.29/0.60          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_mult
% 0.29/0.60  thf(fact_6379_abs__mult__pos,axiom,
% 0.29/0.60      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 0.29/0.60       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X4 )
% 0.29/0.60          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_pos
% 0.29/0.60  thf(fact_6380_abs__mult__pos,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X4 )
% 0.29/0.60          = ( abs_abs_real @ ( times_times_real @ Y @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_pos
% 0.29/0.60  thf(fact_6381_abs__mult__pos,axiom,
% 0.29/0.60      ! [X4: rat,Y: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.60       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X4 )
% 0.29/0.60          = ( abs_abs_rat @ ( times_times_rat @ Y @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_pos
% 0.29/0.60  thf(fact_6382_abs__mult__pos,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.60       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X4 )
% 0.29/0.60          = ( abs_abs_int @ ( times_times_int @ Y @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_pos
% 0.29/0.60  thf(fact_6383_abs__minus__le__zero,axiom,
% 0.29/0.60      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_le_zero
% 0.29/0.60  thf(fact_6384_abs__minus__le__zero,axiom,
% 0.29/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_le_zero
% 0.29/0.60  thf(fact_6385_abs__minus__le__zero,axiom,
% 0.29/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_le_zero
% 0.29/0.60  thf(fact_6386_abs__minus__le__zero,axiom,
% 0.29/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_minus_le_zero
% 0.29/0.60  thf(fact_6387_eq__abs__iff_H,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( A
% 0.29/0.60          = ( abs_abs_real @ B ) )
% 0.29/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.60          & ( ( B = A )
% 0.29/0.60            | ( B
% 0.29/0.60              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eq_abs_iff'
% 0.29/0.60  thf(fact_6388_eq__abs__iff_H,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( A
% 0.29/0.60          = ( abs_abs_Code_integer @ B ) )
% 0.29/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.60          & ( ( B = A )
% 0.29/0.60            | ( B
% 0.29/0.60              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eq_abs_iff'
% 0.29/0.60  thf(fact_6389_eq__abs__iff_H,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( A
% 0.29/0.60          = ( abs_abs_rat @ B ) )
% 0.29/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.60          & ( ( B = A )
% 0.29/0.60            | ( B
% 0.29/0.60              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eq_abs_iff'
% 0.29/0.60  thf(fact_6390_eq__abs__iff_H,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( A
% 0.29/0.60          = ( abs_abs_int @ B ) )
% 0.29/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.60          & ( ( B = A )
% 0.29/0.60            | ( B
% 0.29/0.60              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eq_abs_iff'
% 0.29/0.60  thf(fact_6391_abs__eq__iff_H,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( ( abs_abs_real @ A )
% 0.29/0.60          = B )
% 0.29/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.60          & ( ( A = B )
% 0.29/0.60            | ( A
% 0.29/0.60              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff'
% 0.29/0.60  thf(fact_6392_abs__eq__iff_H,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.29/0.60          = B )
% 0.29/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.60          & ( ( A = B )
% 0.29/0.60            | ( A
% 0.29/0.60              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff'
% 0.29/0.60  thf(fact_6393_abs__eq__iff_H,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( ( abs_abs_rat @ A )
% 0.29/0.60          = B )
% 0.29/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.60          & ( ( A = B )
% 0.29/0.60            | ( A
% 0.29/0.60              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff'
% 0.29/0.60  thf(fact_6394_abs__eq__iff_H,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ( abs_abs_int @ A )
% 0.29/0.60          = B )
% 0.29/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.60          & ( ( A = B )
% 0.29/0.60            | ( A
% 0.29/0.60              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_eq_iff'
% 0.29/0.60  thf(fact_6395_zero__le__power__abs,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_power_abs
% 0.29/0.60  thf(fact_6396_zero__le__power__abs,axiom,
% 0.29/0.60      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_power_abs
% 0.29/0.60  thf(fact_6397_zero__le__power__abs,axiom,
% 0.29/0.60      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_power_abs
% 0.29/0.60  thf(fact_6398_zero__le__power__abs,axiom,
% 0.29/0.60      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_power_abs
% 0.29/0.60  thf(fact_6399_abs__div__pos,axiom,
% 0.29/0.60      ! [Y: rat,X4: rat] :
% 0.29/0.60        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.29/0.60       => ( ( divide_divide_rat @ ( abs_abs_rat @ X4 ) @ Y )
% 0.29/0.60          = ( abs_abs_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_div_pos
% 0.29/0.60  thf(fact_6400_abs__div__pos,axiom,
% 0.29/0.60      ! [Y: real,X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.60       => ( ( divide_divide_real @ ( abs_abs_real @ X4 ) @ Y )
% 0.29/0.60          = ( abs_abs_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_div_pos
% 0.29/0.60  thf(fact_6401_abs__if,axiom,
% 0.29/0.60      ( abs_abs_real
% 0.29/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if
% 0.29/0.60  thf(fact_6402_abs__if,axiom,
% 0.29/0.60      ( abs_abs_int
% 0.29/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if
% 0.29/0.60  thf(fact_6403_abs__if,axiom,
% 0.29/0.60      ( abs_abs_Code_integer
% 0.29/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if
% 0.29/0.60  thf(fact_6404_abs__if,axiom,
% 0.29/0.60      ( abs_abs_rat
% 0.29/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if
% 0.29/0.60  thf(fact_6405_abs__of__neg,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.60       => ( ( abs_abs_real @ A )
% 0.29/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_neg
% 0.29/0.60  thf(fact_6406_abs__of__neg,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.60       => ( ( abs_abs_int @ A )
% 0.29/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_neg
% 0.29/0.60  thf(fact_6407_abs__of__neg,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.29/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_neg
% 0.29/0.60  thf(fact_6408_abs__of__neg,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.60       => ( ( abs_abs_rat @ A )
% 0.29/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_of_neg
% 0.29/0.60  thf(fact_6409_abs__if__raw,axiom,
% 0.29/0.60      ( abs_abs_real
% 0.29/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if_raw
% 0.29/0.60  thf(fact_6410_abs__if__raw,axiom,
% 0.29/0.60      ( abs_abs_int
% 0.29/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if_raw
% 0.29/0.60  thf(fact_6411_abs__if__raw,axiom,
% 0.29/0.60      ( abs_abs_Code_integer
% 0.29/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if_raw
% 0.29/0.60  thf(fact_6412_abs__if__raw,axiom,
% 0.29/0.60      ( abs_abs_rat
% 0.29/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_if_raw
% 0.29/0.60  thf(fact_6413_abs__diff__le__iff,axiom,
% 0.29/0.60      ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_le3102999989581377725nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_le_iff
% 0.29/0.60  thf(fact_6414_abs__diff__le__iff,axiom,
% 0.29/0.60      ! [X4: real,A: real,R3: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_eq_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_le_iff
% 0.29/0.60  thf(fact_6415_abs__diff__le__iff,axiom,
% 0.29/0.60      ! [X4: rat,A: rat,R3: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_le_iff
% 0.29/0.60  thf(fact_6416_abs__diff__le__iff,axiom,
% 0.29/0.60      ! [X4: int,A: int,R3: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_eq_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_le_iff
% 0.29/0.60  thf(fact_6417_abs__triangle__ineq4,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq4
% 0.29/0.60  thf(fact_6418_abs__triangle__ineq4,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq4
% 0.29/0.60  thf(fact_6419_abs__triangle__ineq4,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq4
% 0.29/0.60  thf(fact_6420_abs__triangle__ineq4,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_triangle_ineq4
% 0.29/0.60  thf(fact_6421_abs__diff__triangle__ineq,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_triangle_ineq
% 0.29/0.60  thf(fact_6422_abs__diff__triangle__ineq,axiom,
% 0.29/0.60      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_triangle_ineq
% 0.29/0.60  thf(fact_6423_abs__diff__triangle__ineq,axiom,
% 0.29/0.60      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_triangle_ineq
% 0.29/0.60  thf(fact_6424_abs__diff__triangle__ineq,axiom,
% 0.29/0.60      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_triangle_ineq
% 0.29/0.60  thf(fact_6425_abs__diff__less__iff,axiom,
% 0.29/0.60      ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_le6747313008572928689nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_less_iff
% 0.29/0.60  thf(fact_6426_abs__diff__less__iff,axiom,
% 0.29/0.60      ! [X4: real,A: real,R3: real] :
% 0.29/0.60        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_less_iff
% 0.29/0.60  thf(fact_6427_abs__diff__less__iff,axiom,
% 0.29/0.60      ! [X4: rat,A: rat,R3: rat] :
% 0.29/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_less_iff
% 0.29/0.60  thf(fact_6428_abs__diff__less__iff,axiom,
% 0.29/0.60      ! [X4: int,A: int,R3: int] :
% 0.29/0.60        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 0.29/0.60        = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 0.29/0.60          & ( ord_less_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_diff_less_iff
% 0.29/0.60  thf(fact_6429_fact__ge__Suc__0__nat,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_ge_Suc_0_nat
% 0.29/0.60  thf(fact_6430_dvd__fact,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.29/0.60       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_fact
% 0.29/0.60  thf(fact_6431_bit__not__int__iff_H,axiom,
% 0.29/0.60      ! [K: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_not_int_iff'
% 0.29/0.60  thf(fact_6432_abs__real__def,axiom,
% 0.29/0.60      ( abs_abs_real
% 0.29/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_real_def
% 0.29/0.60  thf(fact_6433_fact__less__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.60       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.60         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_less_mono
% 0.29/0.60  thf(fact_6434_fact__less__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.60       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.60         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_less_mono
% 0.29/0.60  thf(fact_6435_fact__less__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.60       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.60         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_less_mono
% 0.29/0.60  thf(fact_6436_fact__less__mono,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.60       => ( ( ord_less_nat @ M @ N2 )
% 0.29/0.60         => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_less_mono
% 0.29/0.60  thf(fact_6437_lemma__interval__lt,axiom,
% 0.29/0.60      ! [A: real,X4: real,B: real] :
% 0.29/0.60        ( ( ord_less_real @ A @ X4 )
% 0.29/0.60       => ( ( ord_less_real @ X4 @ B )
% 0.29/0.60         => ? [D3: real] :
% 0.29/0.60              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.60              & ! [Y4: real] :
% 0.29/0.60                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 0.29/0.60                 => ( ( ord_less_real @ A @ Y4 )
% 0.29/0.60                    & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % lemma_interval_lt
% 0.29/0.60  thf(fact_6438_fact__fact__dvd__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_fact_dvd_fact
% 0.29/0.60  thf(fact_6439_fact__fact__dvd__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_fact_dvd_fact
% 0.29/0.60  thf(fact_6440_fact__fact__dvd__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_fact_dvd_fact
% 0.29/0.60  thf(fact_6441_fact__fact__dvd__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_fact_dvd_fact
% 0.29/0.60  thf(fact_6442_fact__mod,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 0.29/0.60          = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mod
% 0.29/0.60  thf(fact_6443_fact__mod,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 0.29/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mod
% 0.29/0.60  thf(fact_6444_fact__mod,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 0.29/0.60          = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_mod
% 0.29/0.60  thf(fact_6445_fact__le__power,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_le_power
% 0.29/0.60  thf(fact_6446_fact__le__power,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_le_power
% 0.29/0.60  thf(fact_6447_fact__le__power,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_le_power
% 0.29/0.60  thf(fact_6448_fact__le__power,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_le_power
% 0.29/0.60  thf(fact_6449_sin__bound__lemma,axiom,
% 0.29/0.60      ! [X4: real,Y: real,U: real,V: real] :
% 0.29/0.60        ( ( X4 = Y )
% 0.29/0.60       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 0.29/0.60         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X4 @ U ) @ Y ) ) @ V ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sin_bound_lemma
% 0.29/0.60  thf(fact_6450_flip__bit__eq__if,axiom,
% 0.29/0.60      ( bit_se2159334234014336723it_int
% 0.29/0.60      = ( ^ [N: nat,A3: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A3 @ N ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % flip_bit_eq_if
% 0.29/0.60  thf(fact_6451_flip__bit__eq__if,axiom,
% 0.29/0.60      ( bit_se2161824704523386999it_nat
% 0.29/0.60      = ( ^ [N: nat,A3: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A3 @ N ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % flip_bit_eq_if
% 0.29/0.60  thf(fact_6452_tanh__real__gt__neg1,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_gt_neg1
% 0.29/0.60  thf(fact_6453_abs__add__one__gt__zero,axiom,
% 0.29/0.60      ! [X4: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_add_one_gt_zero
% 0.29/0.60  thf(fact_6454_abs__add__one__gt__zero,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_add_one_gt_zero
% 0.29/0.60  thf(fact_6455_abs__add__one__gt__zero,axiom,
% 0.29/0.60      ! [X4: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_add_one_gt_zero
% 0.29/0.60  thf(fact_6456_abs__add__one__gt__zero,axiom,
% 0.29/0.60      ! [X4: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_add_one_gt_zero
% 0.29/0.60  thf(fact_6457_fact__diff__Suc,axiom,
% 0.29/0.60      ! [N2: nat,M: nat] :
% 0.29/0.60        ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.29/0.60       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 0.29/0.60          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_diff_Suc
% 0.29/0.60  thf(fact_6458_fact__div__fact__le__pow,axiom,
% 0.29/0.60      ! [R3: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ R3 @ N2 )
% 0.29/0.60       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R3 ) ) ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_div_fact_le_pow
% 0.29/0.60  thf(fact_6459_binomial__fact__lemma,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 0.29/0.60          = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % binomial_fact_lemma
% 0.29/0.60  thf(fact_6460_bit__imp__take__bit__positive,axiom,
% 0.29/0.60      ! [N2: nat,M: nat,K: int] :
% 0.29/0.60        ( ( ord_less_nat @ N2 @ M )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 0.29/0.60         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_imp_take_bit_positive
% 0.29/0.60  thf(fact_6461_lemma__interval,axiom,
% 0.29/0.60      ! [A: real,X4: real,B: real] :
% 0.29/0.60        ( ( ord_less_real @ A @ X4 )
% 0.29/0.60       => ( ( ord_less_real @ X4 @ B )
% 0.29/0.60         => ? [D3: real] :
% 0.29/0.60              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.60              & ! [Y4: real] :
% 0.29/0.60                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 0.29/0.60                 => ( ( ord_less_eq_real @ A @ Y4 )
% 0.29/0.60                    & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % lemma_interval
% 0.29/0.60  thf(fact_6462_norm__triangle__ineq3,axiom,
% 0.29/0.60      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_triangle_ineq3
% 0.29/0.60  thf(fact_6463_norm__triangle__ineq3,axiom,
% 0.29/0.60      ! [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 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_triangle_ineq3
% 0.29/0.60  thf(fact_6464_bit__concat__bit__iff,axiom,
% 0.29/0.60      ! [M: nat,K: int,L: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 0.29/0.60        = ( ( ( ord_less_nat @ N2 @ M )
% 0.29/0.60            & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 0.29/0.60          | ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_concat_bit_iff
% 0.29/0.60  thf(fact_6465_choose__dvd,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % choose_dvd
% 0.29/0.60  thf(fact_6466_choose__dvd,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % choose_dvd
% 0.29/0.60  thf(fact_6467_choose__dvd,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % choose_dvd
% 0.29/0.60  thf(fact_6468_choose__dvd,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % choose_dvd
% 0.29/0.60  thf(fact_6469_fact__numeral,axiom,
% 0.29/0.60      ! [K: num] :
% 0.29/0.60        ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.60        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_numeral
% 0.29/0.60  thf(fact_6470_fact__numeral,axiom,
% 0.29/0.60      ! [K: num] :
% 0.29/0.60        ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 0.29/0.60        = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_numeral
% 0.29/0.60  thf(fact_6471_fact__numeral,axiom,
% 0.29/0.60      ! [K: num] :
% 0.29/0.60        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_numeral
% 0.29/0.60  thf(fact_6472_fact__numeral,axiom,
% 0.29/0.60      ! [K: num] :
% 0.29/0.60        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.60        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_numeral
% 0.29/0.60  thf(fact_6473_fact__numeral,axiom,
% 0.29/0.60      ! [K: num] :
% 0.29/0.60        ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 0.29/0.60        = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_numeral
% 0.29/0.60  thf(fact_6474_signed__take__bit__eq__concat__bit,axiom,
% 0.29/0.60      ( bit_ri631733984087533419it_int
% 0.29/0.60      = ( ^ [N: nat,K3: int] : ( bit_concat_bit @ N @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % signed_take_bit_eq_concat_bit
% 0.29/0.60  thf(fact_6475_exp__eq__0__imp__not__bit,axiom,
% 0.29/0.60      ! [N2: nat,A: int] :
% 0.29/0.60        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60       => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_eq_0_imp_not_bit
% 0.29/0.60  thf(fact_6476_exp__eq__0__imp__not__bit,axiom,
% 0.29/0.60      ! [N2: nat,A: nat] :
% 0.29/0.60        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60          = zero_zero_nat )
% 0.29/0.60       => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_eq_0_imp_not_bit
% 0.29/0.60  thf(fact_6477_bit__Suc,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( bit_se9216721137139052372nteger @ A @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_Suc
% 0.29/0.60  thf(fact_6478_bit__Suc,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_Suc
% 0.29/0.60  thf(fact_6479_bit__Suc,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 0.29/0.60        = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_Suc
% 0.29/0.60  thf(fact_6480_stable__imp__bit__iff__odd,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.60          = A )
% 0.29/0.60       => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.29/0.60          = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % stable_imp_bit_iff_odd
% 0.29/0.60  thf(fact_6481_stable__imp__bit__iff__odd,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.60          = A )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60          = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % stable_imp_bit_iff_odd
% 0.29/0.60  thf(fact_6482_stable__imp__bit__iff__odd,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = A )
% 0.29/0.60       => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % stable_imp_bit_iff_odd
% 0.29/0.60  thf(fact_6483_bit__iff__idd__imp__stable,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ( bit_se9216721137139052372nteger @ A @ N3 )
% 0.29/0.60            = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.60       => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_idd_imp_stable
% 0.29/0.60  thf(fact_6484_bit__iff__idd__imp__stable,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ( bit_se1146084159140164899it_int @ A @ N3 )
% 0.29/0.60            = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.60       => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_idd_imp_stable
% 0.29/0.60  thf(fact_6485_bit__iff__idd__imp__stable,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ( bit_se1148574629649215175it_nat @ A @ N3 )
% 0.29/0.60            = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.29/0.60       => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_idd_imp_stable
% 0.29/0.60  thf(fact_6486_abs__le__square__iff,axiom,
% 0.29/0.60      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ Y ) )
% 0.29/0.60        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_square_iff
% 0.29/0.60  thf(fact_6487_abs__le__square__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) )
% 0.29/0.60        = ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_square_iff
% 0.29/0.60  thf(fact_6488_abs__le__square__iff,axiom,
% 0.29/0.60      ! [X4: rat,Y: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ ( abs_abs_rat @ Y ) )
% 0.29/0.60        = ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_square_iff
% 0.29/0.60  thf(fact_6489_abs__le__square__iff,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) )
% 0.29/0.60        = ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_le_square_iff
% 0.29/0.60  thf(fact_6490_abs__square__eq__1,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = one_one_Code_integer )
% 0.29/0.60        = ( ( abs_abs_Code_integer @ X4 )
% 0.29/0.60          = one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_eq_1
% 0.29/0.60  thf(fact_6491_abs__square__eq__1,axiom,
% 0.29/0.60      ! [X4: rat] :
% 0.29/0.60        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = one_one_rat )
% 0.29/0.60        = ( ( abs_abs_rat @ X4 )
% 0.29/0.60          = one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_eq_1
% 0.29/0.60  thf(fact_6492_abs__square__eq__1,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = one_one_real )
% 0.29/0.60        = ( ( abs_abs_real @ X4 )
% 0.29/0.60          = one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_eq_1
% 0.29/0.60  thf(fact_6493_abs__square__eq__1,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.60          = one_one_int )
% 0.29/0.60        = ( ( abs_abs_int @ X4 )
% 0.29/0.60          = one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_eq_1
% 0.29/0.60  thf(fact_6494_power__even__abs,axiom,
% 0.29/0.60      ! [N2: nat,A: code_integer] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 0.29/0.60          = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs
% 0.29/0.60  thf(fact_6495_power__even__abs,axiom,
% 0.29/0.60      ! [N2: nat,A: rat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 )
% 0.29/0.60          = ( power_power_rat @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs
% 0.29/0.60  thf(fact_6496_power__even__abs,axiom,
% 0.29/0.60      ! [N2: nat,A: real] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 0.29/0.60          = ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs
% 0.29/0.60  thf(fact_6497_power__even__abs,axiom,
% 0.29/0.60      ! [N2: nat,A: int] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 0.29/0.60          = ( power_power_int @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_even_abs
% 0.29/0.60  thf(fact_6498_int__bit__bound,axiom,
% 0.29/0.60      ! [K: int] :
% 0.29/0.60        ~ ! [N3: nat] :
% 0.29/0.60            ( ! [M2: nat] :
% 0.29/0.60                ( ( ord_less_eq_nat @ N3 @ M2 )
% 0.29/0.60               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 0.29/0.60                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 0.29/0.60           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.60               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.29/0.60                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % int_bit_bound
% 0.29/0.60  thf(fact_6499_binomial__altdef__nat,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( binomial @ N2 @ K )
% 0.29/0.60          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % binomial_altdef_nat
% 0.29/0.60  thf(fact_6500_bit__iff__odd,axiom,
% 0.29/0.60      ( bit_se9216721137139052372nteger
% 0.29/0.60      = ( ^ [A3: code_integer,N: nat] :
% 0.29/0.60            ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_odd
% 0.29/0.60  thf(fact_6501_bit__iff__odd,axiom,
% 0.29/0.60      ( bit_se1146084159140164899it_int
% 0.29/0.60      = ( ^ [A3: int,N: nat] :
% 0.29/0.60            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_odd
% 0.29/0.60  thf(fact_6502_bit__iff__odd,axiom,
% 0.29/0.60      ( bit_se1148574629649215175it_nat
% 0.29/0.60      = ( ^ [A3: nat,N: nat] :
% 0.29/0.60            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_iff_odd
% 0.29/0.60  thf(fact_6503_power2__le__iff__abs__le,axiom,
% 0.29/0.60      ! [Y: code_integer,X4: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.29/0.60       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_le_iff_abs_le
% 0.29/0.60  thf(fact_6504_power2__le__iff__abs__le,axiom,
% 0.29/0.60      ! [Y: real,X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.60       => ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60          = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_le_iff_abs_le
% 0.29/0.60  thf(fact_6505_power2__le__iff__abs__le,axiom,
% 0.29/0.60      ! [Y: rat,X4: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.29/0.60       => ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60          = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_le_iff_abs_le
% 0.29/0.60  thf(fact_6506_power2__le__iff__abs__le,axiom,
% 0.29/0.60      ! [Y: int,X4: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.60          = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power2_le_iff_abs_le
% 0.29/0.60  thf(fact_6507_abs__square__le__1,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.29/0.60        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_le_1
% 0.29/0.60  thf(fact_6508_abs__square__le__1,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.29/0.60        = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_le_1
% 0.29/0.60  thf(fact_6509_abs__square__le__1,axiom,
% 0.29/0.60      ! [X4: rat] :
% 0.29/0.60        ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.29/0.60        = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_le_1
% 0.29/0.60  thf(fact_6510_abs__square__le__1,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.29/0.60        = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_le_1
% 0.29/0.60  thf(fact_6511_abs__square__less__1,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.29/0.60        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_less_1
% 0.29/0.60  thf(fact_6512_abs__square__less__1,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.29/0.60        = ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_less_1
% 0.29/0.60  thf(fact_6513_abs__square__less__1,axiom,
% 0.29/0.60      ! [X4: rat] :
% 0.29/0.60        ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.29/0.60        = ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_less_1
% 0.29/0.60  thf(fact_6514_abs__square__less__1,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.29/0.60        = ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_square_less_1
% 0.29/0.60  thf(fact_6515_square__fact__le__2__fact,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % square_fact_le_2_fact
% 0.29/0.60  thf(fact_6516_power__mono__even,axiom,
% 0.29/0.60      ! [N2: nat,A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.29/0.60         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_mono_even
% 0.29/0.60  thf(fact_6517_power__mono__even,axiom,
% 0.29/0.60      ! [N2: nat,A: real,B: real] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.29/0.60         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_mono_even
% 0.29/0.60  thf(fact_6518_power__mono__even,axiom,
% 0.29/0.60      ! [N2: nat,A: rat,B: rat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 0.29/0.60         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_mono_even
% 0.29/0.60  thf(fact_6519_power__mono__even,axiom,
% 0.29/0.60      ! [N2: nat,A: int,B: int] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.29/0.60         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_mono_even
% 0.29/0.60  thf(fact_6520_bit__int__def,axiom,
% 0.29/0.60      ( bit_se1146084159140164899it_int
% 0.29/0.60      = ( ^ [K3: int,N: nat] :
% 0.29/0.60            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_int_def
% 0.29/0.60  thf(fact_6521_fact__num__eq__if,axiom,
% 0.29/0.60      ( semiri773545260158071498ct_rat
% 0.29/0.60      = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_num_eq_if
% 0.29/0.60  thf(fact_6522_fact__num__eq__if,axiom,
% 0.29/0.60      ( semiri5044797733671781792omplex
% 0.29/0.60      = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_num_eq_if
% 0.29/0.60  thf(fact_6523_fact__num__eq__if,axiom,
% 0.29/0.60      ( semiri1406184849735516958ct_int
% 0.29/0.60      = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_num_eq_if
% 0.29/0.60  thf(fact_6524_fact__num__eq__if,axiom,
% 0.29/0.60      ( semiri1408675320244567234ct_nat
% 0.29/0.60      = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_num_eq_if
% 0.29/0.60  thf(fact_6525_fact__num__eq__if,axiom,
% 0.29/0.60      ( semiri2265585572941072030t_real
% 0.29/0.60      = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_num_eq_if
% 0.29/0.60  thf(fact_6526_fact__reduce,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( semiri5044797733671781792omplex @ N2 )
% 0.29/0.60          = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_reduce
% 0.29/0.60  thf(fact_6527_fact__reduce,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( semiri1406184849735516958ct_int @ N2 )
% 0.29/0.60          = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_reduce
% 0.29/0.60  thf(fact_6528_fact__reduce,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( semiri1408675320244567234ct_nat @ N2 )
% 0.29/0.60          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_reduce
% 0.29/0.60  thf(fact_6529_fact__reduce,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( semiri2265585572941072030t_real @ N2 )
% 0.29/0.60          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_reduce
% 0.29/0.60  thf(fact_6530_pochhammer__same,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 0.29/0.60        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_same
% 0.29/0.60  thf(fact_6531_pochhammer__same,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 0.29/0.60        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_same
% 0.29/0.60  thf(fact_6532_pochhammer__same,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 0.29/0.60        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_same
% 0.29/0.60  thf(fact_6533_pochhammer__same,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 0.29/0.60        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_same
% 0.29/0.60  thf(fact_6534_pochhammer__same,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 0.29/0.60        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % pochhammer_same
% 0.29/0.60  thf(fact_6535_binomial__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 0.29/0.60          = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % binomial_fact
% 0.29/0.60  thf(fact_6536_binomial__fact,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 0.29/0.60          = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % binomial_fact
% 0.29/0.60  thf(fact_6537_fact__binomial,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 0.29/0.60          = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_binomial
% 0.29/0.60  thf(fact_6538_fact__binomial,axiom,
% 0.29/0.60      ! [K: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.60       => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 0.29/0.60          = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_binomial
% 0.29/0.60  thf(fact_6539_even__bit__succ__iff,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 0.29/0.60          = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_bit_succ_iff
% 0.29/0.60  thf(fact_6540_even__bit__succ__iff,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 0.29/0.60          = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_bit_succ_iff
% 0.29/0.60  thf(fact_6541_even__bit__succ__iff,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 0.29/0.60          = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_bit_succ_iff
% 0.29/0.60  thf(fact_6542_odd__bit__iff__bit__pred,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 0.29/0.60          = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % odd_bit_iff_bit_pred
% 0.29/0.60  thf(fact_6543_odd__bit__iff__bit__pred,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60          = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % odd_bit_iff_bit_pred
% 0.29/0.60  thf(fact_6544_odd__bit__iff__bit__pred,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.60       => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60          = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 0.29/0.60            | ( N2 = zero_zero_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % odd_bit_iff_bit_pred
% 0.29/0.60  thf(fact_6545_bit__sum__mult__2__cases,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer,N2: nat] :
% 0.29/0.60        ( ! [J2: nat] :
% 0.29/0.60            ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 0.29/0.60       => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.29/0.60          = ( ( ( N2 = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.60            & ( ( N2 != zero_zero_nat )
% 0.29/0.60             => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_sum_mult_2_cases
% 0.29/0.60  thf(fact_6546_bit__sum__mult__2__cases,axiom,
% 0.29/0.60      ! [A: int,B: int,N2: nat] :
% 0.29/0.60        ( ! [J2: nat] :
% 0.29/0.60            ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 0.29/0.60       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.29/0.60          = ( ( ( N2 = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.60            & ( ( N2 != zero_zero_nat )
% 0.29/0.60             => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_sum_mult_2_cases
% 0.29/0.60  thf(fact_6547_bit__sum__mult__2__cases,axiom,
% 0.29/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.60        ( ! [J2: nat] :
% 0.29/0.60            ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 0.29/0.60       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 0.29/0.60          = ( ( ( N2 = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.29/0.60            & ( ( N2 != zero_zero_nat )
% 0.29/0.60             => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_sum_mult_2_cases
% 0.29/0.60  thf(fact_6548_bit__rec,axiom,
% 0.29/0.60      ( bit_se9216721137139052372nteger
% 0.29/0.60      = ( ^ [A3: code_integer,N: nat] :
% 0.29/0.60            ( ( ( N = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 0.29/0.60            & ( ( N != zero_zero_nat )
% 0.29/0.60             => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_rec
% 0.29/0.60  thf(fact_6549_bit__rec,axiom,
% 0.29/0.60      ( bit_se1146084159140164899it_int
% 0.29/0.60      = ( ^ [A3: int,N: nat] :
% 0.29/0.60            ( ( ( N = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 0.29/0.60            & ( ( N != zero_zero_nat )
% 0.29/0.60             => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_rec
% 0.29/0.60  thf(fact_6550_bit__rec,axiom,
% 0.29/0.60      ( bit_se1148574629649215175it_nat
% 0.29/0.60      = ( ^ [A3: nat,N: nat] :
% 0.29/0.60            ( ( ( N = zero_zero_nat )
% 0.29/0.60             => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 0.29/0.60            & ( ( N != zero_zero_nat )
% 0.29/0.60             => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_rec
% 0.29/0.60  thf(fact_6551_set__bit__eq,axiom,
% 0.29/0.60      ( bit_se7879613467334960850it_int
% 0.29/0.60      = ( ^ [N: nat,K3: int] :
% 0.29/0.60            ( plus_plus_int @ K3
% 0.29/0.60            @ ( times_times_int
% 0.29/0.60              @ ( zero_n2684676970156552555ol_int
% 0.29/0.60                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 0.29/0.60              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % set_bit_eq
% 0.29/0.60  thf(fact_6552_unset__bit__eq,axiom,
% 0.29/0.60      ( bit_se4203085406695923979it_int
% 0.29/0.60      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % unset_bit_eq
% 0.29/0.60  thf(fact_6553_take__bit__Suc__from__most,axiom,
% 0.29/0.60      ! [N2: nat,K: int] :
% 0.29/0.60        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 0.29/0.60        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_Suc_from_most
% 0.29/0.60  thf(fact_6554_abs__sqrt__wlog,axiom,
% 0.29/0.60      ! [P: code_integer > code_integer > $o,X4: code_integer] :
% 0.29/0.60        ( ! [X5: code_integer] :
% 0.29/0.60            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 0.29/0.60           => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.60       => ( P @ ( abs_abs_Code_integer @ X4 ) @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sqrt_wlog
% 0.29/0.60  thf(fact_6555_abs__sqrt__wlog,axiom,
% 0.29/0.60      ! [P: real > real > $o,X4: real] :
% 0.29/0.60        ( ! [X5: real] :
% 0.29/0.60            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 0.29/0.60           => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.60       => ( P @ ( abs_abs_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sqrt_wlog
% 0.29/0.60  thf(fact_6556_abs__sqrt__wlog,axiom,
% 0.29/0.60      ! [P: rat > rat > $o,X4: rat] :
% 0.29/0.60        ( ! [X5: rat] :
% 0.29/0.60            ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 0.29/0.60           => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.60       => ( P @ ( abs_abs_rat @ X4 ) @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sqrt_wlog
% 0.29/0.60  thf(fact_6557_abs__sqrt__wlog,axiom,
% 0.29/0.60      ! [P: int > int > $o,X4: int] :
% 0.29/0.60        ( ! [X5: int] :
% 0.29/0.60            ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.29/0.60           => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.60       => ( P @ ( abs_abs_int @ X4 ) @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sqrt_wlog
% 0.29/0.60  thf(fact_6558_sin__coeff__def,axiom,
% 0.29/0.60      ( sin_coeff
% 0.29/0.60      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sin_coeff_def
% 0.29/0.60  thf(fact_6559_binomial__code,axiom,
% 0.29/0.60      ( binomial
% 0.29/0.60      = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % binomial_code
% 0.29/0.60  thf(fact_6560_cos__coeff__def,axiom,
% 0.29/0.60      ( cos_coeff
% 0.29/0.60      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % cos_coeff_def
% 0.29/0.60  thf(fact_6561_arctan__double,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.60       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X4 ) )
% 0.29/0.60          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_double
% 0.29/0.60  thf(fact_6562_fact__code,axiom,
% 0.29/0.60      ( semiri1406184849735516958ct_int
% 0.29/0.60      = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_code
% 0.29/0.60  thf(fact_6563_fact__code,axiom,
% 0.29/0.60      ( semiri1408675320244567234ct_nat
% 0.29/0.60      = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_code
% 0.29/0.60  thf(fact_6564_fact__code,axiom,
% 0.29/0.60      ( semiri2265585572941072030t_real
% 0.29/0.60      = ( ^ [N: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fact_code
% 0.29/0.60  thf(fact_6565_zabs__less__one__iff,axiom,
% 0.29/0.60      ! [Z: int] :
% 0.29/0.60        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.29/0.60        = ( Z = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zabs_less_one_iff
% 0.29/0.60  thf(fact_6566_zero__less__arctan__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X4 ) )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_less_arctan_iff
% 0.29/0.60  thf(fact_6567_arctan__less__zero__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( arctan @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_less_zero_iff
% 0.29/0.60  thf(fact_6568_zero__le__arctan__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X4 ) )
% 0.29/0.60        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_arctan_iff
% 0.29/0.60  thf(fact_6569_arctan__le__zero__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( arctan @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_le_zero_iff
% 0.29/0.60  thf(fact_6570_cos__coeff__0,axiom,
% 0.29/0.60      ( ( cos_coeff @ zero_zero_nat )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % cos_coeff_0
% 0.29/0.60  thf(fact_6571_arctan__less__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 0.29/0.60        = ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_less_iff
% 0.29/0.60  thf(fact_6572_arctan__monotone,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.60       => ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_monotone
% 0.29/0.60  thf(fact_6573_arctan__le__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_le_iff
% 0.29/0.60  thf(fact_6574_arctan__monotone_H,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.60       => ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_monotone'
% 0.29/0.60  thf(fact_6575_bit__Suc__0__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_Suc_0_iff
% 0.29/0.60  thf(fact_6576_not__bit__Suc__0__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_bit_Suc_0_Suc
% 0.29/0.60  thf(fact_6577_abs__div,axiom,
% 0.29/0.60      ! [Y: int,X4: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ Y @ X4 )
% 0.29/0.60       => ( ( abs_abs_int @ ( divide_divide_int @ X4 @ Y ) )
% 0.29/0.60          = ( divide_divide_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_div
% 0.29/0.60  thf(fact_6578_sin__coeff__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( sin_coeff @ ( suc @ N2 ) )
% 0.29/0.60        = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sin_coeff_Suc
% 0.29/0.60  thf(fact_6579_not__bit__Suc__0__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_bit_Suc_0_numeral
% 0.29/0.60  thf(fact_6580_zabs__def,axiom,
% 0.29/0.60      ( abs_abs_int
% 0.29/0.60      = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zabs_def
% 0.29/0.60  thf(fact_6581_dvd__imp__le__int,axiom,
% 0.29/0.60      ! [I2: int,D: int] :
% 0.29/0.60        ( ( I2 != zero_zero_int )
% 0.29/0.60       => ( ( dvd_dvd_int @ D @ I2 )
% 0.29/0.60         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % dvd_imp_le_int
% 0.29/0.60  thf(fact_6582_abs__mod__less,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( L != zero_zero_int )
% 0.29/0.60       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mod_less
% 0.29/0.60  thf(fact_6583_cos__coeff__Suc,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( cos_coeff @ ( suc @ N2 ) )
% 0.29/0.60        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % cos_coeff_Suc
% 0.29/0.60  thf(fact_6584_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.29/0.60      ! [X4: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.29/0.60        ( ( ( set_fo2584398358068434914at_nat @ X4 @ Xa @ Xb @ Xc )
% 0.29/0.60          = Y )
% 0.29/0.60       => ( ( ( ord_less_nat @ Xb @ Xa )
% 0.29/0.60           => ( Y = Xc ) )
% 0.29/0.60          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.29/0.60           => ( Y
% 0.29/0.60              = ( set_fo2584398358068434914at_nat @ X4 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X4 @ Xa @ Xc ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fold_atLeastAtMost_nat.elims
% 0.29/0.60  thf(fact_6585_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.29/0.60      ( set_fo2584398358068434914at_nat
% 0.29/0.60      = ( ^ [F3: nat > nat > nat,A3: nat,B2: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % fold_atLeastAtMost_nat.simps
% 0.29/0.60  thf(fact_6586_even__add__abs__iff,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 0.29/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_add_abs_iff
% 0.29/0.60  thf(fact_6587_even__abs__add__iff,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 0.29/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_abs_add_iff
% 0.29/0.60  thf(fact_6588_bit__nat__def,axiom,
% 0.29/0.60      ( bit_se1148574629649215175it_nat
% 0.29/0.60      = ( ^ [M6: nat,N: nat] :
% 0.29/0.60            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_nat_def
% 0.29/0.60  thf(fact_6589_nat__intermed__int__val,axiom,
% 0.29/0.60      ! [M: nat,N2: nat,F: nat > int,K: int] :
% 0.29/0.60        ( ! [I4: nat] :
% 0.29/0.60            ( ( ( ord_less_eq_nat @ M @ I4 )
% 0.29/0.60              & ( ord_less_nat @ I4 @ N2 ) )
% 0.29/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.29/0.60       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.29/0.60           => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.29/0.60             => ? [I4: nat] :
% 0.29/0.60                  ( ( ord_less_eq_nat @ M @ I4 )
% 0.29/0.60                  & ( ord_less_eq_nat @ I4 @ N2 )
% 0.29/0.60                  & ( ( F @ I4 )
% 0.29/0.60                    = K ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % nat_intermed_int_val
% 0.29/0.60  thf(fact_6590_incr__lemma,axiom,
% 0.29/0.60      ! [D: int,Z: int,X4: int] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.60       => ( ord_less_int @ Z @ ( plus_plus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % incr_lemma
% 0.29/0.60  thf(fact_6591_decr__lemma,axiom,
% 0.29/0.60      ! [D: int,X4: int,Z: int] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.60       => ( ord_less_int @ ( minus_minus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 0.29/0.60  
% 0.29/0.60  % decr_lemma
% 0.29/0.60  thf(fact_6592_nat__ivt__aux,axiom,
% 0.29/0.60      ! [N2: nat,F: nat > int,K: int] :
% 0.29/0.60        ( ! [I4: nat] :
% 0.29/0.60            ( ( ord_less_nat @ I4 @ N2 )
% 0.29/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.29/0.60       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.29/0.60         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.29/0.60           => ? [I4: nat] :
% 0.29/0.60                ( ( ord_less_eq_nat @ I4 @ N2 )
% 0.29/0.60                & ( ( F @ I4 )
% 0.29/0.60                  = K ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % nat_ivt_aux
% 0.29/0.60  thf(fact_6593_complex__mod__minus__le__complex__mod,axiom,
% 0.29/0.60      ! [X4: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % complex_mod_minus_le_complex_mod
% 0.29/0.60  thf(fact_6594_complex__mod__triangle__ineq2,axiom,
% 0.29/0.60      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % complex_mod_triangle_ineq2
% 0.29/0.60  thf(fact_6595_nat0__intermed__int__val,axiom,
% 0.29/0.60      ! [N2: nat,F: nat > int,K: int] :
% 0.29/0.60        ( ! [I4: nat] :
% 0.29/0.60            ( ( ord_less_nat @ I4 @ N2 )
% 0.29/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.29/0.60       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.29/0.60         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 0.29/0.60           => ? [I4: nat] :
% 0.29/0.60                ( ( ord_less_eq_nat @ I4 @ N2 )
% 0.29/0.60                & ( ( F @ I4 )
% 0.29/0.60                  = K ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % nat0_intermed_int_val
% 0.29/0.60  thf(fact_6596_arctan__add,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.60       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.60         => ( ( plus_plus_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 0.29/0.60            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_add
% 0.29/0.60  thf(fact_6597_xor__int__unfold,axiom,
% 0.29/0.60      ( bit_se6526347334894502574or_int
% 0.29/0.60      = ( ^ [K3: int,L2: int] :
% 0.29/0.60            ( if_int
% 0.29/0.60            @ ( K3
% 0.29/0.60              = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 0.29/0.60            @ ( if_int
% 0.29/0.60              @ ( L2
% 0.29/0.60                = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 0.29/0.60              @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = 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 @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % xor_int_unfold
% 0.29/0.60  thf(fact_6598_mask__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_numeral
% 0.29/0.60  thf(fact_6599_mask__numeral,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_numeral
% 0.29/0.60  thf(fact_6600_modulo__int__unfold,axiom,
% 0.29/0.60      ! [L: int,K: int,N2: nat,M: nat] :
% 0.29/0.60        ( ( ( ( ( sgn_sgn_int @ L )
% 0.29/0.60              = zero_zero_int )
% 0.29/0.60            | ( ( sgn_sgn_int @ K )
% 0.29/0.60              = zero_zero_int )
% 0.29/0.60            | ( N2 = zero_zero_nat ) )
% 0.29/0.60         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.29/0.60        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.29/0.60                = zero_zero_int )
% 0.29/0.60              | ( ( sgn_sgn_int @ K )
% 0.29/0.60                = zero_zero_int )
% 0.29/0.60              | ( N2 = zero_zero_nat ) )
% 0.29/0.60         => ( ( ( ( sgn_sgn_int @ K )
% 0.29/0.60                = ( sgn_sgn_int @ L ) )
% 0.29/0.60             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 0.29/0.60            & ( ( ( sgn_sgn_int @ K )
% 0.29/0.60               != ( sgn_sgn_int @ L ) )
% 0.29/0.60             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60                = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.29/0.60                  @ ( minus_minus_int
% 0.29/0.60                    @ ( semiri1314217659103216013at_int
% 0.29/0.60                      @ ( times_times_nat @ N2
% 0.29/0.60                        @ ( zero_n2687167440665602831ol_nat
% 0.29/0.60                          @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 0.29/0.60                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % modulo_int_unfold
% 0.29/0.60  thf(fact_6601_divide__int__unfold,axiom,
% 0.29/0.60      ! [L: int,K: int,N2: nat,M: nat] :
% 0.29/0.60        ( ( ( ( ( sgn_sgn_int @ L )
% 0.29/0.60              = zero_zero_int )
% 0.29/0.60            | ( ( sgn_sgn_int @ K )
% 0.29/0.60              = zero_zero_int )
% 0.29/0.60            | ( N2 = zero_zero_nat ) )
% 0.29/0.60         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60            = zero_zero_int ) )
% 0.29/0.60        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.29/0.60                = zero_zero_int )
% 0.29/0.60              | ( ( sgn_sgn_int @ K )
% 0.29/0.60                = zero_zero_int )
% 0.29/0.60              | ( N2 = zero_zero_nat ) )
% 0.29/0.60         => ( ( ( ( sgn_sgn_int @ K )
% 0.29/0.60                = ( sgn_sgn_int @ L ) )
% 0.29/0.60             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 0.29/0.60            & ( ( ( sgn_sgn_int @ K )
% 0.29/0.60               != ( sgn_sgn_int @ L ) )
% 0.29/0.60             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.29/0.60                = ( uminus_uminus_int
% 0.29/0.60                  @ ( semiri1314217659103216013at_int
% 0.29/0.60                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 0.29/0.60                      @ ( zero_n2687167440665602831ol_nat
% 0.29/0.60                        @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_int_unfold
% 0.29/0.60  thf(fact_6602_tanh__real__altdef,axiom,
% 0.29/0.60      ( tanh_real
% 0.29/0.60      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_real_altdef
% 0.29/0.60  thf(fact_6603_and__int__unfold,axiom,
% 0.29/0.60      ( bit_se725231765392027082nd_int
% 0.29/0.60      = ( ^ [K3: int,L2: int] :
% 0.29/0.60            ( if_int
% 0.29/0.60            @ ( ( K3 = zero_zero_int )
% 0.29/0.60              | ( L2 = zero_zero_int ) )
% 0.29/0.60            @ zero_zero_int
% 0.29/0.60            @ ( if_int
% 0.29/0.60              @ ( K3
% 0.29/0.60                = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60              @ L2
% 0.29/0.60              @ ( if_int
% 0.29/0.60                @ ( L2
% 0.29/0.60                  = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60                @ K3
% 0.29/0.60                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_int_unfold
% 0.29/0.60  thf(fact_6604_and_Oidem,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ A @ A )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.idem
% 0.29/0.60  thf(fact_6605_and_Oidem,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.idem
% 0.29/0.60  thf(fact_6606_and_Oleft__idem,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_idem
% 0.29/0.60  thf(fact_6607_and_Oleft__idem,axiom,
% 0.29/0.60      ! [A: nat,B: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_idem
% 0.29/0.60  thf(fact_6608_and_Oright__idem,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.right_idem
% 0.29/0.60  thf(fact_6609_and_Oright__idem,axiom,
% 0.29/0.60      ! [A: nat,B: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.right_idem
% 0.29/0.60  thf(fact_6610_sgn__sgn,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60        = ( sgn_sgn_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_sgn
% 0.29/0.60  thf(fact_6611_sgn__sgn,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60        = ( sgn_sgn_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_sgn
% 0.29/0.60  thf(fact_6612_sgn__sgn,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 0.29/0.60        = ( sgn_sgn_complex @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_sgn
% 0.29/0.60  thf(fact_6613_sgn__sgn,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60        = ( sgn_sgn_Code_integer @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_sgn
% 0.29/0.60  thf(fact_6614_sgn__sgn,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60        = ( sgn_sgn_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_sgn
% 0.29/0.60  thf(fact_6615_bit_Odouble__compl,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.double_compl
% 0.29/0.60  thf(fact_6616_bit_Ocompl__eq__compl__iff,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ( bit_ri7919022796975470100ot_int @ X4 )
% 0.29/0.60          = ( bit_ri7919022796975470100ot_int @ Y ) )
% 0.29/0.60        = ( X4 = Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.compl_eq_compl_iff
% 0.29/0.60  thf(fact_6617_mask__nat__positive__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.29/0.60        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_nat_positive_iff
% 0.29/0.60  thf(fact_6618_and__zero__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_zero_eq
% 0.29/0.60  thf(fact_6619_and__zero__eq,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 0.29/0.60        = zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % and_zero_eq
% 0.29/0.60  thf(fact_6620_zero__and__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_and_eq
% 0.29/0.60  thf(fact_6621_zero__and__eq,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 0.29/0.60        = zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_and_eq
% 0.29/0.60  thf(fact_6622_bit_Oconj__zero__left,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X4 )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_zero_left
% 0.29/0.60  thf(fact_6623_bit_Oconj__zero__right,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ X4 @ zero_zero_int )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_zero_right
% 0.29/0.60  thf(fact_6624_sgn__0,axiom,
% 0.29/0.60      ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 0.29/0.60      = zero_z3403309356797280102nteger ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0
% 0.29/0.60  thf(fact_6625_sgn__0,axiom,
% 0.29/0.60      ( ( sgn_sgn_complex @ zero_zero_complex )
% 0.29/0.60      = zero_zero_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0
% 0.29/0.60  thf(fact_6626_sgn__0,axiom,
% 0.29/0.60      ( ( sgn_sgn_real @ zero_zero_real )
% 0.29/0.60      = zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0
% 0.29/0.60  thf(fact_6627_sgn__0,axiom,
% 0.29/0.60      ( ( sgn_sgn_rat @ zero_zero_rat )
% 0.29/0.60      = zero_zero_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0
% 0.29/0.60  thf(fact_6628_sgn__0,axiom,
% 0.29/0.60      ( ( sgn_sgn_int @ zero_zero_int )
% 0.29/0.60      = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0
% 0.29/0.60  thf(fact_6629_sgn__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_int @ one_one_int )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1
% 0.29/0.60  thf(fact_6630_sgn__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_real @ one_one_real )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1
% 0.29/0.60  thf(fact_6631_sgn__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_complex @ one_one_complex )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1
% 0.29/0.60  thf(fact_6632_sgn__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 0.29/0.60      = one_one_Code_integer ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1
% 0.29/0.60  thf(fact_6633_sgn__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_rat @ one_one_rat )
% 0.29/0.60      = one_one_rat ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1
% 0.29/0.60  thf(fact_6634_sgn__one,axiom,
% 0.29/0.60      ( ( sgn_sgn_real @ one_one_real )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_one
% 0.29/0.60  thf(fact_6635_sgn__one,axiom,
% 0.29/0.60      ( ( sgn_sgn_complex @ one_one_complex )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_one
% 0.29/0.60  thf(fact_6636_sgn__divide,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.60        = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_divide
% 0.29/0.60  thf(fact_6637_sgn__divide,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.60        = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_divide
% 0.29/0.60  thf(fact_6638_sgn__divide,axiom,
% 0.29/0.60      ! [A: complex,B: complex] :
% 0.29/0.60        ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.60        = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_divide
% 0.29/0.60  thf(fact_6639_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.60        = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.sgn_minus
% 0.29/0.60  thf(fact_6640_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.60        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.sgn_minus
% 0.29/0.60  thf(fact_6641_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.60        = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.sgn_minus
% 0.29/0.60  thf(fact_6642_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.60        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.sgn_minus
% 0.29/0.60  thf(fact_6643_idom__abs__sgn__class_Osgn__minus,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.60        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.sgn_minus
% 0.29/0.60  thf(fact_6644_power__sgn,axiom,
% 0.29/0.60      ! [A: code_integer,N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 0.29/0.60        = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_sgn
% 0.29/0.60  thf(fact_6645_power__sgn,axiom,
% 0.29/0.60      ! [A: rat,N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N2 ) )
% 0.29/0.60        = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_sgn
% 0.29/0.60  thf(fact_6646_power__sgn,axiom,
% 0.29/0.60      ! [A: real,N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( power_power_real @ A @ N2 ) )
% 0.29/0.60        = ( power_power_real @ ( sgn_sgn_real @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_sgn
% 0.29/0.60  thf(fact_6647_power__sgn,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( power_power_int @ A @ N2 ) )
% 0.29/0.60        = ( power_power_int @ ( sgn_sgn_int @ A ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % power_sgn
% 0.29/0.60  thf(fact_6648_exp__less__cancel__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 0.29/0.60        = ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_less_cancel_iff
% 0.29/0.60  thf(fact_6649_exp__less__mono,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.60       => ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_less_mono
% 0.29/0.60  thf(fact_6650_take__bit__and,axiom,
% 0.29/0.60      ! [N2: nat,A: int,B: int] :
% 0.29/0.60        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_and
% 0.29/0.60  thf(fact_6651_take__bit__and,axiom,
% 0.29/0.60      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.60        ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_and
% 0.29/0.60  thf(fact_6652_exp__le__cancel__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_le_cancel_iff
% 0.29/0.60  thf(fact_6653_bit_Oxor__compl__left,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ Y )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_compl_left
% 0.29/0.60  thf(fact_6654_bit_Oxor__compl__right,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ Y ) )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_compl_right
% 0.29/0.60  thf(fact_6655_sgn__less,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.60        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_less
% 0.29/0.60  thf(fact_6656_sgn__less,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_less
% 0.29/0.60  thf(fact_6657_sgn__less,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 0.29/0.60        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_less
% 0.29/0.60  thf(fact_6658_sgn__less,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 0.29/0.60        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_less
% 0.29/0.60  thf(fact_6659_sgn__greater,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_greater
% 0.29/0.60  thf(fact_6660_sgn__greater,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_greater
% 0.29/0.60  thf(fact_6661_sgn__greater,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_greater
% 0.29/0.60  thf(fact_6662_sgn__greater,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_greater
% 0.29/0.60  thf(fact_6663_exp__zero,axiom,
% 0.29/0.60      ( ( exp_complex @ zero_zero_complex )
% 0.29/0.60      = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_zero
% 0.29/0.60  thf(fact_6664_exp__zero,axiom,
% 0.29/0.60      ( ( exp_real @ zero_zero_real )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_zero
% 0.29/0.60  thf(fact_6665_bit_Oconj__one__right,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( bit_se3949692690581998587nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_one_right
% 0.29/0.60  thf(fact_6666_bit_Oconj__one__right,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_one_right
% 0.29/0.60  thf(fact_6667_and_Oright__neutral,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.right_neutral
% 0.29/0.60  thf(fact_6668_and_Oright__neutral,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.right_neutral
% 0.29/0.60  thf(fact_6669_and_Oleft__neutral,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_neutral
% 0.29/0.60  thf(fact_6670_and_Oleft__neutral,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_neutral
% 0.29/0.60  thf(fact_6671_divide__sgn,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 0.29/0.60        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_sgn
% 0.29/0.60  thf(fact_6672_divide__sgn,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 0.29/0.60        = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_sgn
% 0.29/0.60  thf(fact_6673_mask__0,axiom,
% 0.29/0.60      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 0.29/0.60      = zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_0
% 0.29/0.60  thf(fact_6674_mask__0,axiom,
% 0.29/0.60      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 0.29/0.60      = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_0
% 0.29/0.60  thf(fact_6675_mask__eq__0__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 0.29/0.60          = zero_zero_nat )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_eq_0_iff
% 0.29/0.60  thf(fact_6676_mask__eq__0__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_eq_0_iff
% 0.29/0.60  thf(fact_6677_bit_Oconj__cancel__left,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_cancel_left
% 0.29/0.60  thf(fact_6678_bit_Oconj__cancel__right,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_cancel_right
% 0.29/0.60  thf(fact_6679_exp__eq__one__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ( exp_real @ X4 )
% 0.29/0.60          = one_one_real )
% 0.29/0.60        = ( X4 = zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_eq_one_iff
% 0.29/0.60  thf(fact_6680_and__nonnegative__int__iff,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.29/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.60          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_nonnegative_int_iff
% 0.29/0.60  thf(fact_6681_and__negative__int__iff,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 0.29/0.60        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.60          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_negative_int_iff
% 0.29/0.60  thf(fact_6682_sgn__pos,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.60       => ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_pos
% 0.29/0.60  thf(fact_6683_sgn__pos,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.60       => ( ( sgn_sgn_real @ A )
% 0.29/0.60          = one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_pos
% 0.29/0.60  thf(fact_6684_sgn__pos,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.60       => ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_pos
% 0.29/0.60  thf(fact_6685_sgn__pos,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.60       => ( ( sgn_sgn_int @ A )
% 0.29/0.60          = one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_pos
% 0.29/0.60  thf(fact_6686_bit_Ocompl__one,axiom,
% 0.29/0.60      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60      = zero_z3403309356797280102nteger ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.compl_one
% 0.29/0.60  thf(fact_6687_bit_Ocompl__one,axiom,
% 0.29/0.60      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60      = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.compl_one
% 0.29/0.60  thf(fact_6688_bit_Ocompl__zero,axiom,
% 0.29/0.60      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 0.29/0.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.compl_zero
% 0.29/0.60  thf(fact_6689_bit_Ocompl__zero,axiom,
% 0.29/0.60      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 0.29/0.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.compl_zero
% 0.29/0.60  thf(fact_6690_and__numerals_I2_J,axiom,
% 0.29/0.60      ! [Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.60        = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(2)
% 0.29/0.60  thf(fact_6691_and__numerals_I2_J,axiom,
% 0.29/0.60      ! [Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.60        = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(2)
% 0.29/0.60  thf(fact_6692_and__numerals_I8_J,axiom,
% 0.29/0.60      ! [X4: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 0.29/0.60        = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(8)
% 0.29/0.60  thf(fact_6693_and__numerals_I8_J,axiom,
% 0.29/0.60      ! [X4: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 0.29/0.60        = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(8)
% 0.29/0.60  thf(fact_6694_abs__sgn__eq__1,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60          = one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq_1
% 0.29/0.60  thf(fact_6695_abs__sgn__eq__1,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( A != zero_zero_real )
% 0.29/0.60       => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60          = one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq_1
% 0.29/0.60  thf(fact_6696_abs__sgn__eq__1,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( A != zero_zero_rat )
% 0.29/0.60       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60          = one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq_1
% 0.29/0.60  thf(fact_6697_abs__sgn__eq__1,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( A != zero_zero_int )
% 0.29/0.60       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60          = one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq_1
% 0.29/0.60  thf(fact_6698_sgn__mult__self__eq,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_self_eq
% 0.29/0.60  thf(fact_6699_sgn__mult__self__eq,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 0.29/0.60        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_self_eq
% 0.29/0.60  thf(fact_6700_sgn__mult__self__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.29/0.60        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_self_eq
% 0.29/0.60  thf(fact_6701_sgn__mult__self__eq,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_self_eq
% 0.29/0.60  thf(fact_6702_mask__Suc__0,axiom,
% 0.29/0.60      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_Suc_0
% 0.29/0.60  thf(fact_6703_mask__Suc__0,axiom,
% 0.29/0.60      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 0.29/0.60      = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_Suc_0
% 0.29/0.60  thf(fact_6704_bit_Oxor__one__left,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 0.29/0.60        = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_one_left
% 0.29/0.60  thf(fact_6705_bit_Oxor__one__left,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_one_left
% 0.29/0.60  thf(fact_6706_bit_Oxor__one__right,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( bit_se3222712562003087583nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_one_right
% 0.29/0.60  thf(fact_6707_bit_Oxor__one__right,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_one_right
% 0.29/0.60  thf(fact_6708_bit_Oxor__cancel__left,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X4 ) @ X4 )
% 0.29/0.60        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_cancel_left
% 0.29/0.60  thf(fact_6709_bit_Oxor__cancel__left,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 0.29/0.60        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_cancel_left
% 0.29/0.60  thf(fact_6710_bit_Oxor__cancel__right,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( bit_se3222712562003087583nteger @ X4 @ ( bit_ri7632146776885996613nteger @ X4 ) )
% 0.29/0.60        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_cancel_right
% 0.29/0.60  thf(fact_6711_bit_Oxor__cancel__right,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 0.29/0.60        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.xor_cancel_right
% 0.29/0.60  thf(fact_6712_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 0.29/0.60        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.abs_sgn
% 0.29/0.60  thf(fact_6713_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 0.29/0.60        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.abs_sgn
% 0.29/0.60  thf(fact_6714_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 0.29/0.60        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.abs_sgn
% 0.29/0.60  thf(fact_6715_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 0.29/0.60        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.abs_sgn
% 0.29/0.60  thf(fact_6716_idom__abs__sgn__class_Oabs__sgn,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.60        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % idom_abs_sgn_class.abs_sgn
% 0.29/0.60  thf(fact_6717_sgn__abs,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 0.29/0.60        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_abs
% 0.29/0.60  thf(fact_6718_sgn__abs,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_abs
% 0.29/0.60  thf(fact_6719_sgn__abs,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_abs
% 0.29/0.60  thf(fact_6720_sgn__abs,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_abs
% 0.29/0.60  thf(fact_6721_sgn__abs,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_abs
% 0.29/0.60  thf(fact_6722_one__less__exp__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % one_less_exp_iff
% 0.29/0.60  thf(fact_6723_exp__less__one__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( exp_real @ X4 ) @ one_one_real )
% 0.29/0.60        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_less_one_iff
% 0.29/0.60  thf(fact_6724_exp__le__one__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ one_one_real )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_le_one_iff
% 0.29/0.60  thf(fact_6725_one__le__exp__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X4 ) )
% 0.29/0.60        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % one_le_exp_iff
% 0.29/0.60  thf(fact_6726_take__bit__minus__one__eq__mask,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_minus_one_eq_mask
% 0.29/0.60  thf(fact_6727_take__bit__minus__one__eq__mask,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_minus_one_eq_mask
% 0.29/0.60  thf(fact_6728_not__negative__int__iff,axiom,
% 0.29/0.60      ! [K: int] :
% 0.29/0.60        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.29/0.60        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_negative_int_iff
% 0.29/0.60  thf(fact_6729_not__nonnegative__int__iff,axiom,
% 0.29/0.60      ! [K: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.29/0.60        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_nonnegative_int_iff
% 0.29/0.60  thf(fact_6730_exp__ln,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.60          = X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ln
% 0.29/0.60  thf(fact_6731_exp__ln__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.60          = X4 )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ln_iff
% 0.29/0.60  thf(fact_6732_minus__not__numeral__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 0.29/0.60        = ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_not_numeral_eq
% 0.29/0.60  thf(fact_6733_minus__not__numeral__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.60        = ( numeral_numeral_int @ ( inc @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_not_numeral_eq
% 0.29/0.60  thf(fact_6734_and__numerals_I1_J,axiom,
% 0.29/0.60      ! [Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(1)
% 0.29/0.60  thf(fact_6735_and__numerals_I1_J,axiom,
% 0.29/0.60      ! [Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.60        = zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(1)
% 0.29/0.60  thf(fact_6736_and__numerals_I5_J,axiom,
% 0.29/0.60      ! [X4: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(5)
% 0.29/0.60  thf(fact_6737_and__numerals_I5_J,axiom,
% 0.29/0.60      ! [X4: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 0.29/0.60        = zero_zero_nat ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(5)
% 0.29/0.60  thf(fact_6738_sgn__neg,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.60       => ( ( sgn_sgn_real @ A )
% 0.29/0.60          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_neg
% 0.29/0.60  thf(fact_6739_sgn__neg,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ord_less_int @ A @ zero_zero_int )
% 0.29/0.60       => ( ( sgn_sgn_int @ A )
% 0.29/0.60          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_neg
% 0.29/0.60  thf(fact_6740_sgn__neg,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.60       => ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_neg
% 0.29/0.60  thf(fact_6741_sgn__neg,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.60       => ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_neg
% 0.29/0.60  thf(fact_6742_and__numerals_I3_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(3)
% 0.29/0.60  thf(fact_6743_and__numerals_I3_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.60        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(3)
% 0.29/0.60  thf(fact_6744_even__not__iff,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 0.29/0.60        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_not_iff
% 0.29/0.60  thf(fact_6745_even__not__iff,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 0.29/0.60        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_not_iff
% 0.29/0.60  thf(fact_6746_sgn__of__nat,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 0.29/0.60        = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_of_nat
% 0.29/0.60  thf(fact_6747_sgn__of__nat,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.60        = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_of_nat
% 0.29/0.60  thf(fact_6748_sgn__of__nat,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.60        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_of_nat
% 0.29/0.60  thf(fact_6749_sgn__of__nat,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 0.29/0.60        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_of_nat
% 0.29/0.60  thf(fact_6750_and__minus__numerals_I2_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.60        = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_minus_numerals(2)
% 0.29/0.60  thf(fact_6751_and__minus__numerals_I6_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 0.29/0.60        = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_minus_numerals(6)
% 0.29/0.60  thf(fact_6752_not__one__eq,axiom,
% 0.29/0.60      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 0.29/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_one_eq
% 0.29/0.60  thf(fact_6753_not__one__eq,axiom,
% 0.29/0.60      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 0.29/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_one_eq
% 0.29/0.60  thf(fact_6754_and__numerals_I4_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(4)
% 0.29/0.60  thf(fact_6755_and__numerals_I4_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.60        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(4)
% 0.29/0.60  thf(fact_6756_and__numerals_I6_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(6)
% 0.29/0.60  thf(fact_6757_and__numerals_I6_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.60        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(6)
% 0.29/0.60  thf(fact_6758_and__minus__numerals_I1_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_minus_numerals(1)
% 0.29/0.60  thf(fact_6759_and__minus__numerals_I5_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_minus_numerals(5)
% 0.29/0.60  thf(fact_6760_and__numerals_I7_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.29/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(7)
% 0.29/0.60  thf(fact_6761_and__numerals_I7_J,axiom,
% 0.29/0.60      ! [X4: num,Y: num] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.60        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_numerals(7)
% 0.29/0.60  thf(fact_6762_disjunctive__diff,axiom,
% 0.29/0.60      ! [B: int,A: int] :
% 0.29/0.60        ( ! [N3: nat] :
% 0.29/0.60            ( ( bit_se1146084159140164899it_int @ B @ N3 )
% 0.29/0.60           => ( bit_se1146084159140164899it_int @ A @ N3 ) )
% 0.29/0.60       => ( ( minus_minus_int @ A @ B )
% 0.29/0.60          = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % disjunctive_diff
% 0.29/0.60  thf(fact_6763_norm__exp,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X4 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_exp
% 0.29/0.60  thf(fact_6764_norm__exp,axiom,
% 0.29/0.60      ! [X4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X4 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_exp
% 0.29/0.60  thf(fact_6765_and__not__numerals_I1_J,axiom,
% 0.29/0.60      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.60      = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(1)
% 0.29/0.60  thf(fact_6766_take__bit__eq__mask,axiom,
% 0.29/0.60      ( bit_se2923211474154528505it_int
% 0.29/0.60      = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_eq_mask
% 0.29/0.60  thf(fact_6767_take__bit__eq__mask,axiom,
% 0.29/0.60      ( bit_se2925701944663578781it_nat
% 0.29/0.60      = ( ^ [N: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_eq_mask
% 0.29/0.60  thf(fact_6768_and_Oassoc,axiom,
% 0.29/0.60      ! [A: int,B: int,C: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.assoc
% 0.29/0.60  thf(fact_6769_and_Oassoc,axiom,
% 0.29/0.60      ! [A: nat,B: nat,C: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.assoc
% 0.29/0.60  thf(fact_6770_and_Ocommute,axiom,
% 0.29/0.60      ( bit_se725231765392027082nd_int
% 0.29/0.60      = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.commute
% 0.29/0.60  thf(fact_6771_and_Ocommute,axiom,
% 0.29/0.60      ( bit_se727722235901077358nd_nat
% 0.29/0.60      = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.commute
% 0.29/0.60  thf(fact_6772_and_Oleft__commute,axiom,
% 0.29/0.60      ! [B: int,A: int,C: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_commute
% 0.29/0.60  thf(fact_6773_and_Oleft__commute,axiom,
% 0.29/0.60      ! [B: nat,A: nat,C: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and.left_commute
% 0.29/0.60  thf(fact_6774_of__nat__mask__eq,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.29/0.60        = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % of_nat_mask_eq
% 0.29/0.60  thf(fact_6775_of__nat__mask__eq,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.29/0.60        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % of_nat_mask_eq
% 0.29/0.60  thf(fact_6776_of__nat__and__eq,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 0.29/0.60        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % of_nat_and_eq
% 0.29/0.60  thf(fact_6777_of__nat__and__eq,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 0.29/0.60        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % of_nat_and_eq
% 0.29/0.60  thf(fact_6778_exp__less__cancel,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 0.29/0.60       => ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_less_cancel
% 0.29/0.60  thf(fact_6779_sgn__0__0,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = zero_z3403309356797280102nteger )
% 0.29/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0_0
% 0.29/0.60  thf(fact_6780_sgn__0__0,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ A )
% 0.29/0.60          = zero_zero_real )
% 0.29/0.60        = ( A = zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0_0
% 0.29/0.60  thf(fact_6781_sgn__0__0,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = zero_zero_rat )
% 0.29/0.60        = ( A = zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0_0
% 0.29/0.60  thf(fact_6782_sgn__0__0,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ A )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60        = ( A = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_0_0
% 0.29/0.60  thf(fact_6783_sgn__eq__0__iff,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = zero_z3403309356797280102nteger )
% 0.29/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_eq_0_iff
% 0.29/0.60  thf(fact_6784_sgn__eq__0__iff,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( ( sgn_sgn_complex @ A )
% 0.29/0.60          = zero_zero_complex )
% 0.29/0.60        = ( A = zero_zero_complex ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_eq_0_iff
% 0.29/0.60  thf(fact_6785_sgn__eq__0__iff,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ A )
% 0.29/0.60          = zero_zero_real )
% 0.29/0.60        = ( A = zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_eq_0_iff
% 0.29/0.60  thf(fact_6786_sgn__eq__0__iff,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = zero_zero_rat )
% 0.29/0.60        = ( A = zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_eq_0_iff
% 0.29/0.60  thf(fact_6787_sgn__eq__0__iff,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ A )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60        = ( A = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_eq_0_iff
% 0.29/0.60  thf(fact_6788_sgn__mult,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.29/0.60        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult
% 0.29/0.60  thf(fact_6789_sgn__mult,axiom,
% 0.29/0.60      ! [A: rat,B: rat] :
% 0.29/0.60        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.60        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult
% 0.29/0.60  thf(fact_6790_sgn__mult,axiom,
% 0.29/0.60      ! [A: complex,B: complex] :
% 0.29/0.60        ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 0.29/0.60        = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult
% 0.29/0.60  thf(fact_6791_sgn__mult,axiom,
% 0.29/0.60      ! [A: real,B: real] :
% 0.29/0.60        ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 0.29/0.60        = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult
% 0.29/0.60  thf(fact_6792_sgn__mult,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 0.29/0.60        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult
% 0.29/0.60  thf(fact_6793_same__sgn__sgn__add,axiom,
% 0.29/0.60      ! [B: code_integer,A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.60          = ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60       => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.60          = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_sgn_add
% 0.29/0.60  thf(fact_6794_same__sgn__sgn__add,axiom,
% 0.29/0.60      ! [B: real,A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ B )
% 0.29/0.60          = ( sgn_sgn_real @ A ) )
% 0.29/0.60       => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 0.29/0.60          = ( sgn_sgn_real @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_sgn_add
% 0.29/0.60  thf(fact_6795_same__sgn__sgn__add,axiom,
% 0.29/0.60      ! [B: rat,A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ B )
% 0.29/0.60          = ( sgn_sgn_rat @ A ) )
% 0.29/0.60       => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.60          = ( sgn_sgn_rat @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_sgn_add
% 0.29/0.60  thf(fact_6796_same__sgn__sgn__add,axiom,
% 0.29/0.60      ! [B: int,A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ B )
% 0.29/0.60          = ( sgn_sgn_int @ A ) )
% 0.29/0.60       => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.60          = ( sgn_sgn_int @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_sgn_add
% 0.29/0.60  thf(fact_6797_take__bit__not__eq__mask__diff,axiom,
% 0.29/0.60      ! [N2: nat,A: int] :
% 0.29/0.60        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 0.29/0.60        = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_not_eq_mask_diff
% 0.29/0.60  thf(fact_6798_bit__and__iff,axiom,
% 0.29/0.60      ! [A: int,B: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N2 )
% 0.29/0.60        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 0.29/0.60          & ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_and_iff
% 0.29/0.60  thf(fact_6799_bit__and__iff,axiom,
% 0.29/0.60      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.60        ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N2 )
% 0.29/0.60        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 0.29/0.60          & ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_and_iff
% 0.29/0.60  thf(fact_6800_bit_Oconj__xor__distrib,axiom,
% 0.29/0.60      ! [X4: int,Y: int,Z: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_se6526347334894502574or_int @ Y @ Z ) )
% 0.29/0.60        = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se725231765392027082nd_int @ X4 @ Z ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_xor_distrib
% 0.29/0.60  thf(fact_6801_bit_Oconj__xor__distrib2,axiom,
% 0.29/0.60      ! [Y: int,Z: int,X4: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y @ Z ) @ X4 )
% 0.29/0.60        = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y @ X4 ) @ ( bit_se725231765392027082nd_int @ Z @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit.conj_xor_distrib2
% 0.29/0.60  thf(fact_6802_div__eq__sgn__abs,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ K )
% 0.29/0.60          = ( sgn_sgn_int @ L ) )
% 0.29/0.60       => ( ( divide_divide_int @ K @ L )
% 0.29/0.60          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % div_eq_sgn_abs
% 0.29/0.60  thf(fact_6803_take__bit__not__iff,axiom,
% 0.29/0.60      ! [N2: nat,A: int,B: int] :
% 0.29/0.60        ( ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 0.29/0.60          = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 0.29/0.60        = ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 0.29/0.60          = ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_not_iff
% 0.29/0.60  thf(fact_6804_take__bit__not__take__bit,axiom,
% 0.29/0.60      ! [N2: nat,A: int] :
% 0.29/0.60        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 0.29/0.60        = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_not_take_bit
% 0.29/0.60  thf(fact_6805_bit__not__int__iff,axiom,
% 0.29/0.60      ! [K: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_not_int_iff
% 0.29/0.60  thf(fact_6806_bit__and__int__iff,axiom,
% 0.29/0.60      ! [K: int,L: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N2 )
% 0.29/0.60        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 0.29/0.60          & ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_and_int_iff
% 0.29/0.60  thf(fact_6807_less__eq__mask,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % less_eq_mask
% 0.29/0.60  thf(fact_6808_and__not__numerals_I2_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.60        = one_one_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(2)
% 0.29/0.60  thf(fact_6809_and__not__numerals_I4_J,axiom,
% 0.29/0.60      ! [M: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(4)
% 0.29/0.60  thf(fact_6810_take__bit__not__mask__eq__0,axiom,
% 0.29/0.60      ! [M: nat,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.60       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) )
% 0.29/0.60          = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_not_mask_eq_0
% 0.29/0.60  thf(fact_6811_and__not__numerals_I5_J,axiom,
% 0.29/0.60      ! [M: num,N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(5)
% 0.29/0.60  thf(fact_6812_and__not__numerals_I7_J,axiom,
% 0.29/0.60      ! [M: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(7)
% 0.29/0.60  thf(fact_6813_and__not__numerals_I3_J,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.60        = zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(3)
% 0.29/0.60  thf(fact_6814_and__eq__minus__1__iff,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 0.29/0.60          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = ( ( A
% 0.29/0.60            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60          & ( B
% 0.29/0.60            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_eq_minus_1_iff
% 0.29/0.60  thf(fact_6815_and__eq__minus__1__iff,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 0.29/0.60          = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = ( ( A
% 0.29/0.60            = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60          & ( B
% 0.29/0.60            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_eq_minus_1_iff
% 0.29/0.60  thf(fact_6816_exp__total,axiom,
% 0.29/0.60      ! [Y: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.60       => ? [X5: real] :
% 0.29/0.60            ( ( exp_real @ X5 )
% 0.29/0.60            = Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_total
% 0.29/0.60  thf(fact_6817_exp__gt__zero,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_gt_zero
% 0.29/0.60  thf(fact_6818_not__exp__less__zero,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ~ ( ord_less_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % not_exp_less_zero
% 0.29/0.60  thf(fact_6819_exp__ge__zero,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ge_zero
% 0.29/0.60  thf(fact_6820_not__exp__le__zero,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ~ ( ord_less_eq_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 0.29/0.60  
% 0.29/0.60  % not_exp_le_zero
% 0.29/0.60  thf(fact_6821_sgn__not__eq__imp,axiom,
% 0.29/0.60      ! [B: real,A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ B )
% 0.29/0.60         != ( sgn_sgn_real @ A ) )
% 0.29/0.60       => ( ( ( sgn_sgn_real @ A )
% 0.29/0.60           != zero_zero_real )
% 0.29/0.60         => ( ( ( sgn_sgn_real @ B )
% 0.29/0.60             != zero_zero_real )
% 0.29/0.60           => ( ( sgn_sgn_real @ A )
% 0.29/0.60              = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_not_eq_imp
% 0.29/0.60  thf(fact_6822_sgn__not__eq__imp,axiom,
% 0.29/0.60      ! [B: int,A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ B )
% 0.29/0.60         != ( sgn_sgn_int @ A ) )
% 0.29/0.60       => ( ( ( sgn_sgn_int @ A )
% 0.29/0.60           != zero_zero_int )
% 0.29/0.60         => ( ( ( sgn_sgn_int @ B )
% 0.29/0.60             != zero_zero_int )
% 0.29/0.60           => ( ( sgn_sgn_int @ A )
% 0.29/0.60              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_not_eq_imp
% 0.29/0.60  thf(fact_6823_sgn__not__eq__imp,axiom,
% 0.29/0.60      ! [B: code_integer,A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.60         != ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60       => ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60           != zero_z3403309356797280102nteger )
% 0.29/0.60         => ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.60             != zero_z3403309356797280102nteger )
% 0.29/0.60           => ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_not_eq_imp
% 0.29/0.60  thf(fact_6824_sgn__not__eq__imp,axiom,
% 0.29/0.60      ! [B: rat,A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ B )
% 0.29/0.60         != ( sgn_sgn_rat @ A ) )
% 0.29/0.60       => ( ( ( sgn_sgn_rat @ A )
% 0.29/0.60           != zero_zero_rat )
% 0.29/0.60         => ( ( ( sgn_sgn_rat @ B )
% 0.29/0.60             != zero_zero_rat )
% 0.29/0.60           => ( ( sgn_sgn_rat @ A )
% 0.29/0.60              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_not_eq_imp
% 0.29/0.60  thf(fact_6825_sgn__minus__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.60      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_minus_1
% 0.29/0.60  thf(fact_6826_sgn__minus__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_minus_1
% 0.29/0.60  thf(fact_6827_sgn__minus__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.60      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_minus_1
% 0.29/0.60  thf(fact_6828_sgn__minus__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_minus_1
% 0.29/0.60  thf(fact_6829_sgn__minus__1,axiom,
% 0.29/0.60      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.60      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_minus_1
% 0.29/0.60  thf(fact_6830_AND__upper2_H,axiom,
% 0.29/0.60      ! [Y: int,Z: int,X4: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.60         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper2'
% 0.29/0.60  thf(fact_6831_AND__upper1_H,axiom,
% 0.29/0.60      ! [Y: int,Z: int,Ya: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.60         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper1'
% 0.29/0.60  thf(fact_6832_AND__upper2,axiom,
% 0.29/0.60      ! [Y: int,X4: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper2
% 0.29/0.60  thf(fact_6833_AND__upper1,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.60       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper1
% 0.29/0.60  thf(fact_6834_AND__lower,axiom,
% 0.29/0.60      ! [X4: int,Y: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.60       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_lower
% 0.29/0.60  thf(fact_6835_not__diff__distrib,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.60        = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_diff_distrib
% 0.29/0.60  thf(fact_6836_not__add__distrib,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.60        = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_add_distrib
% 0.29/0.60  thf(fact_6837_linordered__idom__class_Oabs__sgn,axiom,
% 0.29/0.60      ( abs_abs_Code_integer
% 0.29/0.60      = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % linordered_idom_class.abs_sgn
% 0.29/0.60  thf(fact_6838_linordered__idom__class_Oabs__sgn,axiom,
% 0.29/0.60      ( abs_abs_rat
% 0.29/0.60      = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % linordered_idom_class.abs_sgn
% 0.29/0.60  thf(fact_6839_linordered__idom__class_Oabs__sgn,axiom,
% 0.29/0.60      ( abs_abs_real
% 0.29/0.60      = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % linordered_idom_class.abs_sgn
% 0.29/0.60  thf(fact_6840_linordered__idom__class_Oabs__sgn,axiom,
% 0.29/0.60      ( abs_abs_int
% 0.29/0.60      = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % linordered_idom_class.abs_sgn
% 0.29/0.60  thf(fact_6841_abs__mult__sgn,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_sgn
% 0.29/0.60  thf(fact_6842_abs__mult__sgn,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_sgn
% 0.29/0.60  thf(fact_6843_abs__mult__sgn,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_sgn
% 0.29/0.60  thf(fact_6844_abs__mult__sgn,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_sgn
% 0.29/0.60  thf(fact_6845_abs__mult__sgn,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_mult_sgn
% 0.29/0.60  thf(fact_6846_sgn__mult__abs,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_abs
% 0.29/0.60  thf(fact_6847_sgn__mult__abs,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_abs
% 0.29/0.60  thf(fact_6848_sgn__mult__abs,axiom,
% 0.29/0.60      ! [A: complex] :
% 0.29/0.60        ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_abs
% 0.29/0.60  thf(fact_6849_sgn__mult__abs,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_abs
% 0.29/0.60  thf(fact_6850_sgn__mult__abs,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 0.29/0.60        = A ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mult_abs
% 0.29/0.60  thf(fact_6851_mult__sgn__abs,axiom,
% 0.29/0.60      ! [X4: code_integer] :
% 0.29/0.60        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ X4 ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_sgn_abs
% 0.29/0.60  thf(fact_6852_mult__sgn__abs,axiom,
% 0.29/0.60      ! [X4: rat] :
% 0.29/0.60        ( ( times_times_rat @ ( sgn_sgn_rat @ X4 ) @ ( abs_abs_rat @ X4 ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_sgn_abs
% 0.29/0.60  thf(fact_6853_mult__sgn__abs,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( times_times_real @ ( sgn_sgn_real @ X4 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_sgn_abs
% 0.29/0.60  thf(fact_6854_mult__sgn__abs,axiom,
% 0.29/0.60      ! [X4: int] :
% 0.29/0.60        ( ( times_times_int @ ( sgn_sgn_int @ X4 ) @ ( abs_abs_int @ X4 ) )
% 0.29/0.60        = X4 ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_sgn_abs
% 0.29/0.60  thf(fact_6855_same__sgn__abs__add,axiom,
% 0.29/0.60      ! [B: code_integer,A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ B )
% 0.29/0.60          = ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60       => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.29/0.60          = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_abs_add
% 0.29/0.60  thf(fact_6856_same__sgn__abs__add,axiom,
% 0.29/0.60      ! [B: real,A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ B )
% 0.29/0.60          = ( sgn_sgn_real @ A ) )
% 0.29/0.60       => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 0.29/0.60          = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_abs_add
% 0.29/0.60  thf(fact_6857_same__sgn__abs__add,axiom,
% 0.29/0.60      ! [B: rat,A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ B )
% 0.29/0.60          = ( sgn_sgn_rat @ A ) )
% 0.29/0.60       => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 0.29/0.60          = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_abs_add
% 0.29/0.60  thf(fact_6858_same__sgn__abs__add,axiom,
% 0.29/0.60      ! [B: int,A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ B )
% 0.29/0.60          = ( sgn_sgn_int @ A ) )
% 0.29/0.60       => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 0.29/0.60          = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % same_sgn_abs_add
% 0.29/0.60  thf(fact_6859_exp__add__commuting,axiom,
% 0.29/0.60      ! [X4: complex,Y: complex] :
% 0.29/0.60        ( ( ( times_times_complex @ X4 @ Y )
% 0.29/0.60          = ( times_times_complex @ Y @ X4 ) )
% 0.29/0.60       => ( ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.60          = ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_add_commuting
% 0.29/0.60  thf(fact_6860_exp__add__commuting,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ( times_times_real @ X4 @ Y )
% 0.29/0.60          = ( times_times_real @ Y @ X4 ) )
% 0.29/0.60       => ( ( exp_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.60          = ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_add_commuting
% 0.29/0.60  thf(fact_6861_mult__exp__exp,axiom,
% 0.29/0.60      ! [X4: complex,Y: complex] :
% 0.29/0.60        ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) )
% 0.29/0.60        = ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_exp_exp
% 0.29/0.60  thf(fact_6862_mult__exp__exp,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 0.29/0.60        = ( exp_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mult_exp_exp
% 0.29/0.60  thf(fact_6863_exp__diff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( exp_real @ ( minus_minus_real @ X4 @ Y ) )
% 0.29/0.60        = ( divide_divide_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_diff
% 0.29/0.60  thf(fact_6864_exp__diff,axiom,
% 0.29/0.60      ! [X4: complex,Y: complex] :
% 0.29/0.60        ( ( exp_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 0.29/0.60        = ( divide1717551699836669952omplex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_diff
% 0.29/0.60  thf(fact_6865_and__not__numerals_I6_J,axiom,
% 0.29/0.60      ! [M: num,N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(6)
% 0.29/0.60  thf(fact_6866_and__not__numerals_I9_J,axiom,
% 0.29/0.60      ! [M: num,N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(9)
% 0.29/0.60  thf(fact_6867_mask__nonnegative__int,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_nonnegative_int
% 0.29/0.60  thf(fact_6868_not__mask__negative__int,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 0.29/0.60  
% 0.29/0.60  % not_mask_negative_int
% 0.29/0.60  thf(fact_6869_minus__exp__eq__not__mask,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.60        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_exp_eq_not_mask
% 0.29/0.60  thf(fact_6870_minus__exp__eq__not__mask,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_exp_eq_not_mask
% 0.29/0.60  thf(fact_6871_exp__gt__one,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_gt_one
% 0.29/0.60  thf(fact_6872_sgn__1__pos,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = one_one_Code_integer )
% 0.29/0.60        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_pos
% 0.29/0.60  thf(fact_6873_sgn__1__pos,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ A )
% 0.29/0.60          = one_one_real )
% 0.29/0.60        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_pos
% 0.29/0.60  thf(fact_6874_sgn__1__pos,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = one_one_rat )
% 0.29/0.60        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_pos
% 0.29/0.60  thf(fact_6875_sgn__1__pos,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ A )
% 0.29/0.60          = one_one_int )
% 0.29/0.60        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_pos
% 0.29/0.60  thf(fact_6876_exp__ge__add__one__self,axiom,
% 0.29/0.60      ! [X4: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ge_add_one_self
% 0.29/0.60  thf(fact_6877_abs__sgn__eq,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( A = zero_z3403309356797280102nteger )
% 0.29/0.60         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60            = zero_z3403309356797280102nteger ) )
% 0.29/0.60        & ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.60         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.29/0.60            = one_one_Code_integer ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq
% 0.29/0.60  thf(fact_6878_abs__sgn__eq,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( A = zero_zero_real )
% 0.29/0.60         => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60            = zero_zero_real ) )
% 0.29/0.60        & ( ( A != zero_zero_real )
% 0.29/0.60         => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.60            = one_one_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq
% 0.29/0.60  thf(fact_6879_abs__sgn__eq,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( A = zero_zero_rat )
% 0.29/0.60         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60            = zero_zero_rat ) )
% 0.29/0.60        & ( ( A != zero_zero_rat )
% 0.29/0.60         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.60            = one_one_rat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq
% 0.29/0.60  thf(fact_6880_abs__sgn__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( A = zero_zero_int )
% 0.29/0.60         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60            = zero_zero_int ) )
% 0.29/0.60        & ( ( A != zero_zero_int )
% 0.29/0.60         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.29/0.60            = one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % abs_sgn_eq
% 0.29/0.60  thf(fact_6881_and__less__eq,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( ord_less_int @ L @ zero_zero_int )
% 0.29/0.60       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_less_eq
% 0.29/0.60  thf(fact_6882_AND__upper1_H_H,axiom,
% 0.29/0.60      ! [Y: int,Z: int,Ya: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.60         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper1''
% 0.29/0.60  thf(fact_6883_AND__upper2_H_H,axiom,
% 0.29/0.60      ! [Y: int,Z: int,X4: int] :
% 0.29/0.60        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.60       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.60         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % AND_upper2''
% 0.29/0.60  thf(fact_6884_minus__eq__not__plus__1,axiom,
% 0.29/0.60      ( uminus1351360451143612070nteger
% 0.29/0.60      = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_eq_not_plus_1
% 0.29/0.60  thf(fact_6885_minus__eq__not__plus__1,axiom,
% 0.29/0.60      ( uminus_uminus_int
% 0.29/0.60      = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_eq_not_plus_1
% 0.29/0.60  thf(fact_6886_not__eq__complement,axiom,
% 0.29/0.60      ( bit_ri7632146776885996613nteger
% 0.29/0.60      = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_eq_complement
% 0.29/0.60  thf(fact_6887_not__eq__complement,axiom,
% 0.29/0.60      ( bit_ri7919022796975470100ot_int
% 0.29/0.60      = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_eq_complement
% 0.29/0.60  thf(fact_6888_minus__eq__not__minus__1,axiom,
% 0.29/0.60      ( uminus1351360451143612070nteger
% 0.29/0.60      = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_eq_not_minus_1
% 0.29/0.60  thf(fact_6889_minus__eq__not__minus__1,axiom,
% 0.29/0.60      ( uminus_uminus_int
% 0.29/0.60      = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_eq_not_minus_1
% 0.29/0.60  thf(fact_6890_div__sgn__abs__cancel,axiom,
% 0.29/0.60      ! [V: int,K: int,L: int] :
% 0.29/0.60        ( ( V != zero_zero_int )
% 0.29/0.60       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 0.29/0.60          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % div_sgn_abs_cancel
% 0.29/0.60  thf(fact_6891_not__int__def,axiom,
% 0.29/0.60      ( bit_ri7919022796975470100ot_int
% 0.29/0.60      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_int_def
% 0.29/0.60  thf(fact_6892_exp__minus__inverse,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) )
% 0.29/0.60        = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_minus_inverse
% 0.29/0.60  thf(fact_6893_exp__minus__inverse,axiom,
% 0.29/0.60      ! [X4: complex] :
% 0.29/0.60        ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) )
% 0.29/0.60        = one_one_complex ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_minus_inverse
% 0.29/0.60  thf(fact_6894_exp__of__nat2__mult,axiom,
% 0.29/0.60      ! [X4: complex,N2: nat] :
% 0.29/0.60        ( ( exp_complex @ ( times_times_complex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 0.29/0.60        = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_of_nat2_mult
% 0.29/0.60  thf(fact_6895_exp__of__nat2__mult,axiom,
% 0.29/0.60      ! [X4: real,N2: nat] :
% 0.29/0.60        ( ( exp_real @ ( times_times_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.60        = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_of_nat2_mult
% 0.29/0.60  thf(fact_6896_exp__of__nat__mult,axiom,
% 0.29/0.60      ! [N2: nat,X4: complex] :
% 0.29/0.60        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X4 ) )
% 0.29/0.60        = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_of_nat_mult
% 0.29/0.60  thf(fact_6897_exp__of__nat__mult,axiom,
% 0.29/0.60      ! [N2: nat,X4: real] :
% 0.29/0.60        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) )
% 0.29/0.60        = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_of_nat_mult
% 0.29/0.60  thf(fact_6898_div__dvd__sgn__abs,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ L @ K )
% 0.29/0.60       => ( ( divide_divide_int @ K @ L )
% 0.29/0.60          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % div_dvd_sgn_abs
% 0.29/0.60  thf(fact_6899_sgn__mod,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( L != zero_zero_int )
% 0.29/0.60       => ( ~ ( dvd_dvd_int @ L @ K )
% 0.29/0.60         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 0.29/0.60            = ( sgn_sgn_int @ L ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_mod
% 0.29/0.60  thf(fact_6900_and__not__numerals_I8_J,axiom,
% 0.29/0.60      ! [M: num,N2: num] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.60        = ( 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 @ N2 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_not_numerals(8)
% 0.29/0.60  thf(fact_6901_minus__numeral__inc__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) )
% 0.29/0.60        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_numeral_inc_eq
% 0.29/0.60  thf(fact_6902_minus__numeral__inc__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % minus_numeral_inc_eq
% 0.29/0.60  thf(fact_6903_less__mask,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.60       => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % less_mask
% 0.29/0.60  thf(fact_6904_even__and__iff,axiom,
% 0.29/0.60      ! [A: code_integer,B: code_integer] :
% 0.29/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 0.29/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.29/0.60          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_and_iff
% 0.29/0.60  thf(fact_6905_even__and__iff,axiom,
% 0.29/0.60      ! [A: int,B: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.29/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.29/0.60          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_and_iff
% 0.29/0.60  thf(fact_6906_even__and__iff,axiom,
% 0.29/0.60      ! [A: nat,B: nat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.29/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.29/0.60          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_and_iff
% 0.29/0.60  thf(fact_6907_sgn__1__neg,axiom,
% 0.29/0.60      ! [A: real] :
% 0.29/0.60        ( ( ( sgn_sgn_real @ A )
% 0.29/0.60          = ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.60        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_neg
% 0.29/0.60  thf(fact_6908_sgn__1__neg,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ A )
% 0.29/0.60          = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.60        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_neg
% 0.29/0.60  thf(fact_6909_sgn__1__neg,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( ( sgn_sgn_Code_integer @ A )
% 0.29/0.60          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.60        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_neg
% 0.29/0.60  thf(fact_6910_sgn__1__neg,axiom,
% 0.29/0.60      ! [A: rat] :
% 0.29/0.60        ( ( ( sgn_sgn_rat @ A )
% 0.29/0.60          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.60        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_1_neg
% 0.29/0.60  thf(fact_6911_sgn__if,axiom,
% 0.29/0.60      ( sgn_sgn_real
% 0.29/0.60      = ( ^ [X: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_if
% 0.29/0.60  thf(fact_6912_sgn__if,axiom,
% 0.29/0.60      ( sgn_sgn_int
% 0.29/0.60      = ( ^ [X: int] : ( if_int @ ( X = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_if
% 0.29/0.60  thf(fact_6913_sgn__if,axiom,
% 0.29/0.60      ( sgn_sgn_Code_integer
% 0.29/0.60      = ( ^ [X: code_integer] : ( if_Code_integer @ ( X = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_if
% 0.29/0.60  thf(fact_6914_sgn__if,axiom,
% 0.29/0.60      ( sgn_sgn_rat
% 0.29/0.60      = ( ^ [X: rat] : ( if_rat @ ( X = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_if
% 0.29/0.60  thf(fact_6915_not__int__div__2,axiom,
% 0.29/0.60      ! [K: int] :
% 0.29/0.60        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_int_div_2
% 0.29/0.60  thf(fact_6916_even__not__iff__int,axiom,
% 0.29/0.60      ! [K: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.29/0.60        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_not_iff_int
% 0.29/0.60  thf(fact_6917_exp__ge__add__one__self__aux,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ge_add_one_self_aux
% 0.29/0.60  thf(fact_6918_even__and__iff__int,axiom,
% 0.29/0.60      ! [K: int,L: int] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.29/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.29/0.60          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % even_and_iff_int
% 0.29/0.60  thf(fact_6919_lemma__exp__total,axiom,
% 0.29/0.60      ! [Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ one_one_real @ Y )
% 0.29/0.60       => ? [X5: real] :
% 0.29/0.60            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 0.29/0.60            & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 0.29/0.60            & ( ( exp_real @ X5 )
% 0.29/0.60              = Y ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % lemma_exp_total
% 0.29/0.60  thf(fact_6920_ln__ge__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X4 ) )
% 0.29/0.60          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % ln_ge_iff
% 0.29/0.60  thf(fact_6921_zsgn__def,axiom,
% 0.29/0.60      ( sgn_sgn_int
% 0.29/0.60      = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zsgn_def
% 0.29/0.60  thf(fact_6922_ln__x__over__x__mono,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X4 )
% 0.29/0.60       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.60         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % ln_x_over_x_mono
% 0.29/0.60  thf(fact_6923_not__numeral__Bit0__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) )
% 0.29/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_numeral_Bit0_eq
% 0.29/0.60  thf(fact_6924_not__numeral__Bit0__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) )
% 0.29/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_numeral_Bit0_eq
% 0.29/0.60  thf(fact_6925_norm__sgn,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ( X4 = zero_zero_real )
% 0.29/0.60         => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 0.29/0.60            = zero_zero_real ) )
% 0.29/0.60        & ( ( X4 != zero_zero_real )
% 0.29/0.60         => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 0.29/0.60            = one_one_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_sgn
% 0.29/0.60  thf(fact_6926_norm__sgn,axiom,
% 0.29/0.60      ! [X4: complex] :
% 0.29/0.60        ( ( ( X4 = zero_zero_complex )
% 0.29/0.60         => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 0.29/0.60            = zero_zero_real ) )
% 0.29/0.60        & ( ( X4 != zero_zero_complex )
% 0.29/0.60         => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 0.29/0.60            = one_one_real ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % norm_sgn
% 0.29/0.60  thf(fact_6927_bit__minus__int__iff,axiom,
% 0.29/0.60      ! [K: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 0.29/0.60        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_minus_int_iff
% 0.29/0.60  thf(fact_6928_not__numeral__BitM__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N2 ) ) )
% 0.29/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_numeral_BitM_eq
% 0.29/0.60  thf(fact_6929_not__numeral__BitM__eq,axiom,
% 0.29/0.60      ! [N2: num] :
% 0.29/0.60        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N2 ) ) )
% 0.29/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_numeral_BitM_eq
% 0.29/0.60  thf(fact_6930_one__and__eq,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 0.29/0.60        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % one_and_eq
% 0.29/0.60  thf(fact_6931_one__and__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 0.29/0.60        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % one_and_eq
% 0.29/0.60  thf(fact_6932_one__and__eq,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 0.29/0.60        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % one_and_eq
% 0.29/0.60  thf(fact_6933_and__one__eq,axiom,
% 0.29/0.60      ! [A: code_integer] :
% 0.29/0.60        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 0.29/0.60        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_one_eq
% 0.29/0.60  thf(fact_6934_and__one__eq,axiom,
% 0.29/0.60      ! [A: int] :
% 0.29/0.60        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 0.29/0.60        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_one_eq
% 0.29/0.60  thf(fact_6935_and__one__eq,axiom,
% 0.29/0.60      ! [A: nat] :
% 0.29/0.60        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 0.29/0.60        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_one_eq
% 0.29/0.60  thf(fact_6936_exp__le,axiom,
% 0.29/0.60      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_le
% 0.29/0.60  thf(fact_6937_take__bit__eq__mask__iff,axiom,
% 0.29/0.60      ! [N2: nat,K: int] :
% 0.29/0.60        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.60          = ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.60        = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.29/0.60          = zero_zero_int ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_eq_mask_iff
% 0.29/0.60  thf(fact_6938_exp__divide__power__eq,axiom,
% 0.29/0.60      ! [N2: nat,X4: complex] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 0.29/0.60          = ( exp_complex @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_divide_power_eq
% 0.29/0.60  thf(fact_6939_exp__divide__power__eq,axiom,
% 0.29/0.60      ! [N2: nat,X4: real] :
% 0.29/0.60        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 0.29/0.60          = ( exp_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_divide_power_eq
% 0.29/0.60  thf(fact_6940_eucl__rel__int__remainderI,axiom,
% 0.29/0.60      ! [R3: int,L: int,K: int,Q3: int] :
% 0.29/0.60        ( ( ( sgn_sgn_int @ R3 )
% 0.29/0.60          = ( sgn_sgn_int @ L ) )
% 0.29/0.60       => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 0.29/0.60         => ( ( K
% 0.29/0.60              = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R3 ) )
% 0.29/0.60           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eucl_rel_int_remainderI
% 0.29/0.60  thf(fact_6941_tanh__altdef,axiom,
% 0.29/0.60      ( tanh_real
% 0.29/0.60      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_altdef
% 0.29/0.60  thf(fact_6942_tanh__altdef,axiom,
% 0.29/0.60      ( tanh_complex
% 0.29/0.60      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % tanh_altdef
% 0.29/0.60  thf(fact_6943_and__exp__eq__0__iff__not__bit,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.60          = zero_zero_int )
% 0.29/0.60        = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_exp_eq_0_iff_not_bit
% 0.29/0.60  thf(fact_6944_and__exp__eq__0__iff__not__bit,axiom,
% 0.29/0.60      ! [A: nat,N2: nat] :
% 0.29/0.60        ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.60          = zero_zero_nat )
% 0.29/0.60        = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_exp_eq_0_iff_not_bit
% 0.29/0.60  thf(fact_6945_exp__half__le2,axiom,
% 0.29/0.60      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_half_le2
% 0.29/0.60  thf(fact_6946_Suc__mask__eq__exp,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.29/0.60        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % Suc_mask_eq_exp
% 0.29/0.60  thf(fact_6947_mask__nat__less__exp,axiom,
% 0.29/0.60      ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_nat_less_exp
% 0.29/0.60  thf(fact_6948_bit__not__iff__eq,axiom,
% 0.29/0.60      ! [A: int,N2: nat] :
% 0.29/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N2 )
% 0.29/0.60        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.60           != zero_zero_int )
% 0.29/0.60          & ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % bit_not_iff_eq
% 0.29/0.60  thf(fact_6949_exp__double,axiom,
% 0.29/0.60      ! [Z: complex] :
% 0.29/0.60        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 0.29/0.60        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_double
% 0.29/0.60  thf(fact_6950_exp__double,axiom,
% 0.29/0.60      ! [Z: real] :
% 0.29/0.60        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 0.29/0.60        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_double
% 0.29/0.60  thf(fact_6951_eucl__rel__int_Osimps,axiom,
% 0.29/0.60      ( eucl_rel_int
% 0.29/0.60      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 0.29/0.60            ( ? [K3: int] :
% 0.29/0.60                ( ( A1 = K3 )
% 0.29/0.60                & ( A22 = zero_zero_int )
% 0.29/0.60                & ( A32
% 0.29/0.60                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 0.29/0.60            | ? [L2: int,K3: int,Q5: int] :
% 0.29/0.60                ( ( A1 = K3 )
% 0.29/0.60                & ( A22 = L2 )
% 0.29/0.60                & ( A32
% 0.29/0.60                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.29/0.60                & ( L2 != zero_zero_int )
% 0.29/0.60                & ( K3
% 0.29/0.60                  = ( times_times_int @ Q5 @ L2 ) ) )
% 0.29/0.60            | ? [R5: int,L2: int,K3: int,Q5: int] :
% 0.29/0.60                ( ( A1 = K3 )
% 0.29/0.60                & ( A22 = L2 )
% 0.29/0.60                & ( A32
% 0.29/0.60                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 0.29/0.60                & ( ( sgn_sgn_int @ R5 )
% 0.29/0.60                  = ( sgn_sgn_int @ L2 ) )
% 0.29/0.60                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 0.29/0.60                & ( K3
% 0.29/0.60                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eucl_rel_int.simps
% 0.29/0.60  thf(fact_6952_eucl__rel__int_Ocases,axiom,
% 0.29/0.60      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 0.29/0.60        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 0.29/0.60       => ( ( ( A23 = zero_zero_int )
% 0.29/0.60           => ( A33
% 0.29/0.60             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.29/0.60         => ( ! [Q2: int] :
% 0.29/0.60                ( ( A33
% 0.29/0.60                  = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 0.29/0.60               => ( ( A23 != zero_zero_int )
% 0.29/0.60                 => ( A12
% 0.29/0.60                   != ( times_times_int @ Q2 @ A23 ) ) ) )
% 0.29/0.60           => ~ ! [R2: int,Q2: int] :
% 0.29/0.60                  ( ( A33
% 0.29/0.60                    = ( product_Pair_int_int @ Q2 @ R2 ) )
% 0.29/0.60                 => ( ( ( sgn_sgn_int @ R2 )
% 0.29/0.60                      = ( sgn_sgn_int @ A23 ) )
% 0.29/0.60                   => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 0.29/0.60                     => ( A12
% 0.29/0.60                       != ( plus_plus_int @ ( times_times_int @ Q2 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % eucl_rel_int.cases
% 0.29/0.60  thf(fact_6953_div__noneq__sgn__abs,axiom,
% 0.29/0.60      ! [L: int,K: int] :
% 0.29/0.60        ( ( L != zero_zero_int )
% 0.29/0.60       => ( ( ( sgn_sgn_int @ K )
% 0.29/0.60           != ( sgn_sgn_int @ L ) )
% 0.29/0.60         => ( ( divide_divide_int @ K @ L )
% 0.29/0.60            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 0.29/0.60              @ ( zero_n2684676970156552555ol_int
% 0.29/0.60                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % div_noneq_sgn_abs
% 0.29/0.60  thf(fact_6954_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % semiring_bit_operations_class.even_mask_iff
% 0.29/0.60  thf(fact_6955_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % semiring_bit_operations_class.even_mask_iff
% 0.29/0.60  thf(fact_6956_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.60        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.60  
% 0.29/0.60  % semiring_bit_operations_class.even_mask_iff
% 0.29/0.60  thf(fact_6957_mask__half__int,axiom,
% 0.29/0.60      ! [N2: nat] :
% 0.29/0.60        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.60        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_half_int
% 0.29/0.60  thf(fact_6958_mask__nat__def,axiom,
% 0.29/0.60      ( bit_se2002935070580805687sk_nat
% 0.29/0.60      = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_nat_def
% 0.29/0.60  thf(fact_6959_mask__int__def,axiom,
% 0.29/0.60      ( bit_se2000444600071755411sk_int
% 0.29/0.60      = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_int_def
% 0.29/0.60  thf(fact_6960_exp__bound__half,axiom,
% 0.29/0.60      ! [Z: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.60       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_bound_half
% 0.29/0.60  thf(fact_6961_exp__bound__half,axiom,
% 0.29/0.60      ! [Z: complex] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.60       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_bound_half
% 0.29/0.60  thf(fact_6962_mask__eq__exp__minus__1,axiom,
% 0.29/0.60      ( bit_se2002935070580805687sk_nat
% 0.29/0.60      = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_eq_exp_minus_1
% 0.29/0.60  thf(fact_6963_mask__eq__exp__minus__1,axiom,
% 0.29/0.60      ( bit_se2000444600071755411sk_int
% 0.29/0.60      = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % mask_eq_exp_minus_1
% 0.29/0.60  thf(fact_6964_exp__bound,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.60         => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_bound
% 0.29/0.60  thf(fact_6965_not__int__rec,axiom,
% 0.29/0.60      ( bit_ri7919022796975470100ot_int
% 0.29/0.60      = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % not_int_rec
% 0.29/0.60  thf(fact_6966_and__int__rec,axiom,
% 0.29/0.60      ( bit_se725231765392027082nd_int
% 0.29/0.60      = ( ^ [K3: int,L2: int] :
% 0.29/0.60            ( plus_plus_int
% 0.29/0.60            @ ( zero_n2684676970156552555ol_int
% 0.29/0.60              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.29/0.60                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.29/0.60            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % and_int_rec
% 0.29/0.60  thf(fact_6967_real__exp__bound__lemma,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.60         => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % real_exp_bound_lemma
% 0.29/0.60  thf(fact_6968_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.29/0.60      ! [N2: nat,X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X4 )
% 0.29/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ge_one_plus_x_over_n_power_n
% 0.29/0.60  thf(fact_6969_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.29/0.60      ! [X4: real,N2: nat] :
% 0.29/0.60        ( ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.60         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_ge_one_minus_x_over_n_power_n
% 0.29/0.60  thf(fact_6970_exp__bound__lemma,axiom,
% 0.29/0.60      ! [Z: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.60       => ( 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 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_bound_lemma
% 0.29/0.60  thf(fact_6971_exp__bound__lemma,axiom,
% 0.29/0.60      ! [Z: complex] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.60       => ( 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 ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_bound_lemma
% 0.29/0.60  thf(fact_6972_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.29/0.60      ! [N2: nat,K: int] :
% 0.29/0.60        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 0.29/0.60          = ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.60        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % take_bit_eq_mask_iff_exp_dvd
% 0.29/0.60  thf(fact_6973_exp__lower__Taylor__quadratic,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( divide_divide_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X4 ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % exp_lower_Taylor_quadratic
% 0.29/0.60  thf(fact_6974_log__base__10__eq1,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.60          = ( 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 @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % log_base_10_eq1
% 0.29/0.60  thf(fact_6975_modulo__int__def,axiom,
% 0.29/0.60      ( modulo_modulo_int
% 0.29/0.60      = ( ^ [K3: int,L2: int] :
% 0.29/0.60            ( if_int @ ( L2 = zero_zero_int ) @ K3
% 0.29/0.60            @ ( if_int
% 0.29/0.60              @ ( ( sgn_sgn_int @ K3 )
% 0.29/0.60                = ( sgn_sgn_int @ L2 ) )
% 0.29/0.60              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 0.29/0.60              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.29/0.60                @ ( minus_minus_int
% 0.29/0.60                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 0.29/0.60                    @ ( zero_n2684676970156552555ol_int
% 0.29/0.60                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 0.29/0.60                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % modulo_int_def
% 0.29/0.60  thf(fact_6976_divide__int__def,axiom,
% 0.29/0.60      ( divide_divide_int
% 0.29/0.60      = ( ^ [K3: int,L2: int] :
% 0.29/0.60            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 0.29/0.60            @ ( if_int
% 0.29/0.60              @ ( ( sgn_sgn_int @ K3 )
% 0.29/0.60                = ( sgn_sgn_int @ L2 ) )
% 0.29/0.60              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 0.29/0.60              @ ( uminus_uminus_int
% 0.29/0.60                @ ( semiri1314217659103216013at_int
% 0.29/0.60                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 0.29/0.60                    @ ( zero_n2687167440665602831ol_nat
% 0.29/0.60                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % divide_int_def
% 0.29/0.60  thf(fact_6977_arctan__half,axiom,
% 0.29/0.60      ( arctan
% 0.29/0.60      = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % arctan_half
% 0.29/0.60  thf(fact_6978_log__base__10__eq2,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.60       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.60          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % log_base_10_eq2
% 0.29/0.60  thf(fact_6979_machin,axiom,
% 0.29/0.60      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.60      = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.60  
% 0.29/0.60  % machin
% 0.29/0.60  thf(fact_6980_zero__le__sgn__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X4 ) )
% 0.29/0.60        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.60  
% 0.29/0.60  % zero_le_sgn_iff
% 0.29/0.60  thf(fact_6981_sgn__le__0__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % sgn_le_0_iff
% 0.29/0.60  thf(fact_6982_real__sqrt__less__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 0.29/0.60        = ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % real_sqrt_less_iff
% 0.29/0.60  thf(fact_6983_real__sqrt__le__iff,axiom,
% 0.29/0.60      ! [X4: real,Y: real] :
% 0.29/0.60        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 0.29/0.60        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.60  
% 0.29/0.60  % real_sqrt_le_iff
% 0.29/0.60  thf(fact_6984_real__sqrt__one,axiom,
% 0.29/0.60      ( ( sqrt @ one_one_real )
% 0.29/0.60      = one_one_real ) ).
% 0.29/0.60  
% 0.29/0.60  % real_sqrt_one
% 0.29/0.60  thf(fact_6985_real__sqrt__eq__1__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ( sqrt @ X4 )
% 0.29/0.60          = one_one_real )
% 0.29/0.60        = ( X4 = one_one_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % real_sqrt_eq_1_iff
% 0.29/0.60  thf(fact_6986_real__sqrt__lt__0__iff,axiom,
% 0.29/0.60      ! [X4: real] :
% 0.29/0.60        ( ( ord_less_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 0.29/0.60        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.60  
% 0.29/0.60  % real_sqrt_lt_0_iff
% 0.29/0.60  thf(fact_6987_real__sqrt__gt__0__iff,axiom,
% 0.29/0.60      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.29/0.61        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_gt_0_iff
% 0.29/0.61  thf(fact_6988_nat__numeral,axiom,
% 0.29/0.61      ! [K: num] :
% 0.29/0.61        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.29/0.61        = ( numeral_numeral_nat @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_numeral
% 0.29/0.61  thf(fact_6989_real__sqrt__le__0__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_le_0_iff
% 0.29/0.61  thf(fact_6990_real__sqrt__ge__0__iff,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.29/0.61        = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_0_iff
% 0.29/0.61  thf(fact_6991_real__sqrt__lt__1__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( sqrt @ X4 ) @ one_one_real )
% 0.29/0.61        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_lt_1_iff
% 0.29/0.61  thf(fact_6992_real__sqrt__gt__1__iff,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 0.29/0.61        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_gt_1_iff
% 0.29/0.61  thf(fact_6993_real__sqrt__le__1__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ one_one_real )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_le_1_iff
% 0.29/0.61  thf(fact_6994_real__sqrt__ge__1__iff,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 0.29/0.61        = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_1_iff
% 0.29/0.61  thf(fact_6995_log__one,axiom,
% 0.29/0.61      ! [A: real] :
% 0.29/0.61        ( ( log @ A @ one_one_real )
% 0.29/0.61        = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % log_one
% 0.29/0.61  thf(fact_6996_real__sqrt__four,axiom,
% 0.29/0.61      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_four
% 0.29/0.61  thf(fact_6997_nat__1,axiom,
% 0.29/0.61      ( ( nat2 @ one_one_int )
% 0.29/0.61      = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_1
% 0.29/0.61  thf(fact_6998_nat__0__iff,axiom,
% 0.29/0.61      ! [I2: int] :
% 0.29/0.61        ( ( ( nat2 @ I2 )
% 0.29/0.61          = zero_zero_nat )
% 0.29/0.61        = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_0_iff
% 0.29/0.61  thf(fact_6999_nat__le__0,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.29/0.61       => ( ( nat2 @ Z )
% 0.29/0.61          = zero_zero_nat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_le_0
% 0.29/0.61  thf(fact_7000_zless__nat__conj,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.29/0.61        = ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.61          & ( ord_less_int @ W @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zless_nat_conj
% 0.29/0.61  thf(fact_7001_log__eq__one,axiom,
% 0.29/0.61      ! [A: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( log @ A @ A )
% 0.29/0.61            = one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_eq_one
% 0.29/0.61  thf(fact_7002_log__less__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61           => ( ( ord_less_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 0.29/0.61              = ( ord_less_real @ X4 @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_less_cancel_iff
% 0.29/0.61  thf(fact_7003_log__less__one__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ ( log @ A @ X4 ) @ one_one_real )
% 0.29/0.61            = ( ord_less_real @ X4 @ A ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_less_one_cancel_iff
% 0.29/0.61  thf(fact_7004_one__less__log__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X4 ) )
% 0.29/0.61            = ( ord_less_real @ A @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_log_cancel_iff
% 0.29/0.61  thf(fact_7005_log__less__zero__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 0.29/0.61            = ( ord_less_real @ X4 @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_less_zero_cancel_iff
% 0.29/0.61  thf(fact_7006_zero__less__log__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 0.29/0.61            = ( ord_less_real @ one_one_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_log_cancel_iff
% 0.29/0.61  thf(fact_7007_int__nat__eq,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.29/0.61            = Z ) )
% 0.29/0.61        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.29/0.61            = zero_zero_int ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % int_nat_eq
% 0.29/0.61  thf(fact_7008_zero__less__nat__eq,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 0.29/0.61        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_nat_eq
% 0.29/0.61  thf(fact_7009_zero__le__log__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 0.29/0.61            = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_le_log_cancel_iff
% 0.29/0.61  thf(fact_7010_log__le__zero__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 0.29/0.61            = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_le_zero_cancel_iff
% 0.29/0.61  thf(fact_7011_one__le__log__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X4 ) )
% 0.29/0.61            = ( ord_less_eq_real @ A @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_le_log_cancel_iff
% 0.29/0.61  thf(fact_7012_log__le__one__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ one_one_real )
% 0.29/0.61            = ( ord_less_eq_real @ X4 @ A ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_le_one_cancel_iff
% 0.29/0.61  thf(fact_7013_log__le__cancel__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 0.29/0.61              = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_le_cancel_iff
% 0.29/0.61  thf(fact_7014_diff__nat__numeral,axiom,
% 0.29/0.61      ! [V: num,V3: num] :
% 0.29/0.61        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 0.29/0.61        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % diff_nat_numeral
% 0.29/0.61  thf(fact_7015_and__nat__numerals_I3_J,axiom,
% 0.29/0.61      ! [X4: num] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.61        = zero_zero_nat ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_numerals(3)
% 0.29/0.61  thf(fact_7016_and__nat__numerals_I1_J,axiom,
% 0.29/0.61      ! [Y: num] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.61        = zero_zero_nat ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_numerals(1)
% 0.29/0.61  thf(fact_7017_nat__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( nat2 @ Y )
% 0.29/0.61          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_eq_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7018_numeral__power__eq__nat__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 0.29/0.61          = ( nat2 @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_eq_nat_cancel_iff
% 0.29/0.61  thf(fact_7019_one__less__nat__eq,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.29/0.61        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_nat_eq
% 0.29/0.61  thf(fact_7020_real__sqrt__abs,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( sqrt @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = ( abs_abs_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_abs
% 0.29/0.61  thf(fact_7021_log__pow__cancel,axiom,
% 0.29/0.61      ! [A: real,B: nat] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.29/0.61            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_pow_cancel
% 0.29/0.61  thf(fact_7022_and__nat__numerals_I2_J,axiom,
% 0.29/0.61      ! [Y: num] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.61        = one_one_nat ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_numerals(2)
% 0.29/0.61  thf(fact_7023_and__nat__numerals_I4_J,axiom,
% 0.29/0.61      ! [X4: num] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.61        = one_one_nat ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_numerals(4)
% 0.29/0.61  thf(fact_7024_real__sqrt__pow2,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_pow2
% 0.29/0.61  thf(fact_7025_real__sqrt__pow2__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_pow2_iff
% 0.29/0.61  thf(fact_7026_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real,Xa: real,Ya: real] :
% 0.29/0.61        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_mult_squared_eq
% 0.29/0.61  thf(fact_7027_nat__numeral__diff__1,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.29/0.61        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_numeral_diff_1
% 0.29/0.61  thf(fact_7028_nat__less__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_less_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7029_numeral__power__less__nat__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_less_nat_cancel_iff
% 0.29/0.61  thf(fact_7030_numeral__power__le__nat__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_le_nat_cancel_iff
% 0.29/0.61  thf(fact_7031_nat__le__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_le_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7032_Suc__0__and__eq,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.61        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Suc_0_and_eq
% 0.29/0.61  thf(fact_7033_and__Suc__0__eq,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.61        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % and_Suc_0_eq
% 0.29/0.61  thf(fact_7034_nat__mask__eq,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.61        = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mask_eq
% 0.29/0.61  thf(fact_7035_and__nat__def,axiom,
% 0.29/0.61      ( bit_se727722235901077358nd_nat
% 0.29/0.61      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_def
% 0.29/0.61  thf(fact_7036_real__sqrt__less__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.61       => ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_less_mono
% 0.29/0.61  thf(fact_7037_real__sqrt__le__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61       => ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_le_mono
% 0.29/0.61  thf(fact_7038_real__sqrt__power,axiom,
% 0.29/0.61      ! [X4: real,K: nat] :
% 0.29/0.61        ( ( sqrt @ ( power_power_real @ X4 @ K ) )
% 0.29/0.61        = ( power_power_real @ ( sqrt @ X4 ) @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_power
% 0.29/0.61  thf(fact_7039_real__sqrt__gt__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_gt_zero
% 0.29/0.61  thf(fact_7040_real__sqrt__eq__zero__cancel,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ( sqrt @ X4 )
% 0.29/0.61            = zero_zero_real )
% 0.29/0.61         => ( X4 = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_eq_zero_cancel
% 0.29/0.61  thf(fact_7041_real__sqrt__ge__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_zero
% 0.29/0.61  thf(fact_7042_real__sqrt__ge__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_one
% 0.29/0.61  thf(fact_7043_nat__numeral__as__int,axiom,
% 0.29/0.61      ( numeral_numeral_nat
% 0.29/0.61      = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_numeral_as_int
% 0.29/0.61  thf(fact_7044_nat__mono,axiom,
% 0.29/0.61      ! [X4: int,Y: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ X4 @ Y )
% 0.29/0.61       => ( ord_less_eq_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mono
% 0.29/0.61  thf(fact_7045_ex__nat,axiom,
% 0.29/0.61      ( ( ^ [P3: nat > $o] :
% 0.29/0.61          ? [X6: nat] : ( P3 @ X6 ) )
% 0.29/0.61      = ( ^ [P4: nat > $o] :
% 0.29/0.61          ? [X: int] :
% 0.29/0.61            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.61            & ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_nat
% 0.29/0.61  thf(fact_7046_all__nat,axiom,
% 0.29/0.61      ( ( ^ [P3: nat > $o] :
% 0.29/0.61          ! [X6: nat] : ( P3 @ X6 ) )
% 0.29/0.61      = ( ^ [P4: nat > $o] :
% 0.29/0.61          ! [X: int] :
% 0.29/0.61            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.29/0.61           => ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % all_nat
% 0.29/0.61  thf(fact_7047_eq__nat__nat__iff,axiom,
% 0.29/0.61      ! [Z: int,Z6: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.29/0.61         => ( ( ( nat2 @ Z )
% 0.29/0.61              = ( nat2 @ Z6 ) )
% 0.29/0.61            = ( Z = Z6 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % eq_nat_nat_iff
% 0.29/0.61  thf(fact_7048_nat__one__as__int,axiom,
% 0.29/0.61      ( one_one_nat
% 0.29/0.61      = ( nat2 @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_one_as_int
% 0.29/0.61  thf(fact_7049_pi__not__less__zero,axiom,
% 0.29/0.61      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_not_less_zero
% 0.29/0.61  thf(fact_7050_pi__gt__zero,axiom,
% 0.29/0.61      ord_less_real @ zero_zero_real @ pi ).
% 0.29/0.61  
% 0.29/0.61  % pi_gt_zero
% 0.29/0.61  thf(fact_7051_pi__ge__zero,axiom,
% 0.29/0.61      ord_less_eq_real @ zero_zero_real @ pi ).
% 0.29/0.61  
% 0.29/0.61  % pi_ge_zero
% 0.29/0.61  thf(fact_7052_unset__bit__nat__def,axiom,
% 0.29/0.61      ( bit_se4205575877204974255it_nat
% 0.29/0.61      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % unset_bit_nat_def
% 0.29/0.61  thf(fact_7053_real__div__sqrt,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( divide_divide_real @ X4 @ ( sqrt @ X4 ) )
% 0.29/0.61          = ( sqrt @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_div_sqrt
% 0.29/0.61  thf(fact_7054_sqrt__add__le__add__sqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_add_le_add_sqrt
% 0.29/0.61  thf(fact_7055_le__real__sqrt__sumsq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_real_sqrt_sumsq
% 0.29/0.61  thf(fact_7056_nat__mono__iff,axiom,
% 0.29/0.61      ! [Z: int,W: int] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mono_iff
% 0.29/0.61  thf(fact_7057_zless__nat__eq__int__zless,axiom,
% 0.29/0.61      ! [M: nat,Z: int] :
% 0.29/0.61        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 0.29/0.61        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zless_nat_eq_int_zless
% 0.29/0.61  thf(fact_7058_nat__le__iff,axiom,
% 0.29/0.61      ! [X4: int,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( nat2 @ X4 ) @ N2 )
% 0.29/0.61        = ( ord_less_eq_int @ X4 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_le_iff
% 0.29/0.61  thf(fact_7059_nat__0__le,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.29/0.61          = Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_0_le
% 0.29/0.61  thf(fact_7060_int__eq__iff,axiom,
% 0.29/0.61      ! [M: nat,Z: int] :
% 0.29/0.61        ( ( ( semiri1314217659103216013at_int @ M )
% 0.29/0.61          = Z )
% 0.29/0.61        = ( ( M
% 0.29/0.61            = ( nat2 @ Z ) )
% 0.29/0.61          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % int_eq_iff
% 0.29/0.61  thf(fact_7061_nat__int__add,axiom,
% 0.29/0.61      ! [A: nat,B: nat] :
% 0.29/0.61        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.29/0.61        = ( plus_plus_nat @ A @ B ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_int_add
% 0.29/0.61  thf(fact_7062_log__ln,axiom,
% 0.29/0.61      ( ln_ln_real
% 0.29/0.61      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_ln
% 0.29/0.61  thf(fact_7063_xor__nat__def,axiom,
% 0.29/0.61      ( bit_se6528837805403552850or_nat
% 0.29/0.61      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % xor_nat_def
% 0.29/0.61  thf(fact_7064_sqrt2__less__2,axiom,
% 0.29/0.61      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt2_less_2
% 0.29/0.61  thf(fact_7065_sgn__real__def,axiom,
% 0.29/0.61      ( sgn_sgn_real
% 0.29/0.61      = ( ^ [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 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sgn_real_def
% 0.29/0.61  thf(fact_7066_log__base__change,axiom,
% 0.29/0.61      ! [A: real,B: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( log @ B @ X4 )
% 0.29/0.61            = ( divide_divide_real @ ( log @ A @ X4 ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_base_change
% 0.29/0.61  thf(fact_7067_less__log__of__power,axiom,
% 0.29/0.61      ! [B: real,N2: nat,M: real] :
% 0.29/0.61        ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_log_of_power
% 0.29/0.61  thf(fact_7068_log__of__power__eq,axiom,
% 0.29/0.61      ! [M: nat,B: real,N2: nat] :
% 0.29/0.61        ( ( ( semiri5074537144036343181t_real @ M )
% 0.29/0.61          = ( power_power_real @ B @ N2 ) )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ( semiri5074537144036343181t_real @ N2 )
% 0.29/0.61            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_of_power_eq
% 0.29/0.61  thf(fact_7069_nat__less__eq__zless,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_less_eq_zless
% 0.29/0.61  thf(fact_7070_nat__le__eq__zle,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ( ord_less_int @ zero_zero_int @ W )
% 0.29/0.61          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.29/0.61       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_le_eq_zle
% 0.29/0.61  thf(fact_7071_nat__eq__iff,axiom,
% 0.29/0.61      ! [W: int,M: nat] :
% 0.29/0.61        ( ( ( nat2 @ W )
% 0.29/0.61          = M )
% 0.29/0.61        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61           => ( W
% 0.29/0.61              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.29/0.61          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61           => ( M = zero_zero_nat ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_eq_iff
% 0.29/0.61  thf(fact_7072_nat__eq__iff2,axiom,
% 0.29/0.61      ! [M: nat,W: int] :
% 0.29/0.61        ( ( M
% 0.29/0.61          = ( nat2 @ W ) )
% 0.29/0.61        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61           => ( W
% 0.29/0.61              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.29/0.61          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61           => ( M = zero_zero_nat ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_eq_iff2
% 0.29/0.61  thf(fact_7073_split__nat,axiom,
% 0.29/0.61      ! [P: nat > $o,I2: int] :
% 0.29/0.61        ( ( P @ ( nat2 @ I2 ) )
% 0.29/0.61        = ( ! [N: nat] :
% 0.29/0.61              ( ( I2
% 0.29/0.61                = ( semiri1314217659103216013at_int @ N ) )
% 0.29/0.61             => ( P @ N ) )
% 0.29/0.61          & ( ( ord_less_int @ I2 @ zero_zero_int )
% 0.29/0.61           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % split_nat
% 0.29/0.61  thf(fact_7074_le__nat__iff,axiom,
% 0.29/0.61      ! [K: int,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.61       => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 0.29/0.61          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_nat_iff
% 0.29/0.61  thf(fact_7075_nat__add__distrib,axiom,
% 0.29/0.61      ! [Z: int,Z6: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.29/0.61         => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 0.29/0.61            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_add_distrib
% 0.29/0.61  thf(fact_7076_nat__mult__distrib,axiom,
% 0.29/0.61      ! [Z: int,Z6: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 0.29/0.61          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mult_distrib
% 0.29/0.61  thf(fact_7077_Suc__as__int,axiom,
% 0.29/0.61      ( suc
% 0.29/0.61      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Suc_as_int
% 0.29/0.61  thf(fact_7078_nat__diff__distrib_H,axiom,
% 0.29/0.61      ! [X4: int,Y: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.61         => ( ( nat2 @ ( minus_minus_int @ X4 @ Y ) )
% 0.29/0.61            = ( minus_minus_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_diff_distrib'
% 0.29/0.61  thf(fact_7079_nat__diff__distrib,axiom,
% 0.29/0.61      ! [Z6: int,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.29/0.61       => ( ( ord_less_eq_int @ Z6 @ Z )
% 0.29/0.61         => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 0.29/0.61            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_diff_distrib
% 0.29/0.61  thf(fact_7080_nat__abs__triangle__ineq,axiom,
% 0.29/0.61      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_abs_triangle_ineq
% 0.29/0.61  thf(fact_7081_nat__div__distrib,axiom,
% 0.29/0.61      ! [X4: int,Y: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.61       => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 0.29/0.61          = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_div_distrib
% 0.29/0.61  thf(fact_7082_nat__div__distrib_H,axiom,
% 0.29/0.61      ! [Y: int,X4: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.61       => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 0.29/0.61          = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_div_distrib'
% 0.29/0.61  thf(fact_7083_nat__power__eq,axiom,
% 0.29/0.61      ! [Z: int,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 0.29/0.61          = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_power_eq
% 0.29/0.61  thf(fact_7084_nat__mod__distrib,axiom,
% 0.29/0.61      ! [X4: int,Y: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.61         => ( ( nat2 @ ( modulo_modulo_int @ X4 @ Y ) )
% 0.29/0.61            = ( modulo_modulo_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mod_distrib
% 0.29/0.61  thf(fact_7085_pi__less__4,axiom,
% 0.29/0.61      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_less_4
% 0.29/0.61  thf(fact_7086_pi__ge__two,axiom,
% 0.29/0.61      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 0.29/0.61  
% 0.29/0.61  % pi_ge_two
% 0.29/0.61  thf(fact_7087_div__abs__eq__div__nat,axiom,
% 0.29/0.61      ! [K: int,L: int] :
% 0.29/0.61        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.29/0.61        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % div_abs_eq_div_nat
% 0.29/0.61  thf(fact_7088_pi__half__neq__two,axiom,
% 0.29/0.61      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_neq_two
% 0.29/0.61  thf(fact_7089_mod__abs__eq__div__nat,axiom,
% 0.29/0.61      ! [K: int,L: int] :
% 0.29/0.61        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.29/0.61        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % mod_abs_eq_div_nat
% 0.29/0.61  thf(fact_7090_take__bit__nat__eq,axiom,
% 0.29/0.61      ! [K: int,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.61       => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 0.29/0.61          = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % take_bit_nat_eq
% 0.29/0.61  thf(fact_7091_nat__take__bit__eq,axiom,
% 0.29/0.61      ! [K: int,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.61       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 0.29/0.61          = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_take_bit_eq
% 0.29/0.61  thf(fact_7092_arctan__inverse,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( X4 != zero_zero_real )
% 0.29/0.61       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X4 ) )
% 0.29/0.61          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X4 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_inverse
% 0.29/0.61  thf(fact_7093_bit__nat__iff,axiom,
% 0.29/0.61      ! [K: int,N2: nat] :
% 0.29/0.61        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 0.29/0.61        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.61          & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % bit_nat_iff
% 0.29/0.61  thf(fact_7094_real__less__rsqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.29/0.61       => ( ord_less_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_less_rsqrt
% 0.29/0.61  thf(fact_7095_sqrt__le__D,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y )
% 0.29/0.61       => ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_le_D
% 0.29/0.61  thf(fact_7096_real__le__rsqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.29/0.61       => ( ord_less_eq_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_le_rsqrt
% 0.29/0.61  thf(fact_7097_nat__2,axiom,
% 0.29/0.61      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.61      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_2
% 0.29/0.61  thf(fact_7098_log__mult,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61             => ( ( log @ A @ ( times_times_real @ X4 @ Y ) )
% 0.29/0.61                = ( plus_plus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_mult
% 0.29/0.61  thf(fact_7099_sgn__power__injE,axiom,
% 0.29/0.61      ! [A: real,N2: nat,X4: real,B: real] :
% 0.29/0.61        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 0.29/0.61          = X4 )
% 0.29/0.61       => ( ( X4
% 0.29/0.61            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 0.29/0.61         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.61           => ( A = B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sgn_power_injE
% 0.29/0.61  thf(fact_7100_log__divide,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61             => ( ( log @ A @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.61                = ( minus_minus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_divide
% 0.29/0.61  thf(fact_7101_le__log__of__power,axiom,
% 0.29/0.61      ! [B: real,N2: nat,M: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_log_of_power
% 0.29/0.61  thf(fact_7102_log__base__pow,axiom,
% 0.29/0.61      ! [A: real,N2: nat,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( log @ ( power_power_real @ A @ N2 ) @ X4 )
% 0.29/0.61          = ( divide_divide_real @ ( log @ A @ X4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_base_pow
% 0.29/0.61  thf(fact_7103_log__nat__power,axiom,
% 0.29/0.61      ! [X4: real,B: real,N2: nat] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( log @ B @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.61          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_nat_power
% 0.29/0.61  thf(fact_7104_Suc__nat__eq__nat__zadd1,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( suc @ ( nat2 @ Z ) )
% 0.29/0.61          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Suc_nat_eq_nat_zadd1
% 0.29/0.61  thf(fact_7105_nat__less__iff,axiom,
% 0.29/0.61      ! [W: int,M: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.29/0.61       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.29/0.61          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_less_iff
% 0.29/0.61  thf(fact_7106_nat__mult__distrib__neg,axiom,
% 0.29/0.61      ! [Z: int,Z6: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.29/0.61       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 0.29/0.61          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_mult_distrib_neg
% 0.29/0.61  thf(fact_7107_nat__abs__int__diff,axiom,
% 0.29/0.61      ! [A: nat,B: nat] :
% 0.29/0.61        ( ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.61         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.29/0.61            = ( minus_minus_nat @ B @ A ) ) )
% 0.29/0.61        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.61         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.29/0.61            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_abs_int_diff
% 0.29/0.61  thf(fact_7108_pi__half__neq__zero,axiom,
% 0.29/0.61      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61     != zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_neq_zero
% 0.29/0.61  thf(fact_7109_pi__half__less__two,axiom,
% 0.29/0.61      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_less_two
% 0.29/0.61  thf(fact_7110_pi__half__le__two,axiom,
% 0.29/0.61      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_le_two
% 0.29/0.61  thf(fact_7111_real__le__lsqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_le_lsqrt
% 0.29/0.61  thf(fact_7112_real__sqrt__unique,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61          = X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( sqrt @ X4 )
% 0.29/0.61            = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_unique
% 0.29/0.61  thf(fact_7113_lemma__real__divide__sqrt__less,axiom,
% 0.29/0.61      ! [U: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ U )
% 0.29/0.61       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.29/0.61  
% 0.29/0.61  % lemma_real_divide_sqrt_less
% 0.29/0.61  thf(fact_7114_real__sqrt__sum__squares__eq__cancel,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61          = X4 )
% 0.29/0.61       => ( Y = zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_eq_cancel
% 0.29/0.61  thf(fact_7115_real__sqrt__sum__squares__eq__cancel2,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61          = Y )
% 0.29/0.61       => ( X4 = zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_eq_cancel2
% 0.29/0.61  thf(fact_7116_real__sqrt__sum__squares__ge1,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_ge1
% 0.29/0.61  thf(fact_7117_real__sqrt__sum__squares__ge2,axiom,
% 0.29/0.61      ! [Y: real,X4: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_ge2
% 0.29/0.61  thf(fact_7118_real__sqrt__sum__squares__triangle__ineq,axiom,
% 0.29/0.61      ! [A: real,C: real,B: real,D: 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 @ D ) @ ( 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 @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_triangle_ineq
% 0.29/0.61  thf(fact_7119_sqrt__ge__absD,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ Y ) )
% 0.29/0.61       => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_ge_absD
% 0.29/0.61  thf(fact_7120_log__of__power__less,axiom,
% 0.29/0.61      ! [M: nat,B: real,N2: nat] :
% 0.29/0.61        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.61           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_of_power_less
% 0.29/0.61  thf(fact_7121_log2__of__power__eq,axiom,
% 0.29/0.61      ! [M: nat,N2: nat] :
% 0.29/0.61        ( ( M
% 0.29/0.61          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.61       => ( ( semiri5074537144036343181t_real @ N2 )
% 0.29/0.61          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log2_of_power_eq
% 0.29/0.61  thf(fact_7122_log__eq__div__ln__mult__log,axiom,
% 0.29/0.61      ! [A: real,B: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.61           => ( ( B != one_one_real )
% 0.29/0.61             => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61               => ( ( log @ A @ X4 )
% 0.29/0.61                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X4 ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_eq_div_ln_mult_log
% 0.29/0.61  thf(fact_7123_nat__dvd__iff,axiom,
% 0.29/0.61      ! [Z: int,M: nat] :
% 0.29/0.61        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 0.29/0.61        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.29/0.61          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61           => ( M = zero_zero_nat ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_dvd_iff
% 0.29/0.61  thf(fact_7124_pi__half__gt__zero,axiom,
% 0.29/0.61      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_gt_zero
% 0.29/0.61  thf(fact_7125_pi__half__ge__zero,axiom,
% 0.29/0.61      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % pi_half_ge_zero
% 0.29/0.61  thf(fact_7126_m2pi__less__pi,axiom,
% 0.29/0.61      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.29/0.61  
% 0.29/0.61  % m2pi_less_pi
% 0.29/0.61  thf(fact_7127_arctan__ubound,axiom,
% 0.29/0.61      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_ubound
% 0.29/0.61  thf(fact_7128_arctan__one,axiom,
% 0.29/0.61      ( ( arctan @ one_one_real )
% 0.29/0.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_one
% 0.29/0.61  thf(fact_7129_real__less__lsqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( ord_less_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_less_lsqrt
% 0.29/0.61  thf(fact_7130_sqrt__sum__squares__le__sum,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_sum_squares_le_sum
% 0.29/0.61  thf(fact_7131_log__of__power__le,axiom,
% 0.29/0.61      ! [M: nat,B: real,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.61           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_of_power_le
% 0.29/0.61  thf(fact_7132_sqrt__sum__squares__le__sum__abs,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_sum_squares_le_sum_abs
% 0.29/0.61  thf(fact_7133_real__sqrt__ge__abs2,axiom,
% 0.29/0.61      ! [Y: real,X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_abs2
% 0.29/0.61  thf(fact_7134_real__sqrt__ge__abs1,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_ge_abs1
% 0.29/0.61  thf(fact_7135_ln__sqrt,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ln_ln_real @ ( sqrt @ X4 ) )
% 0.29/0.61          = ( divide_divide_real @ ( ln_ln_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ln_sqrt
% 0.29/0.61  thf(fact_7136_sqrt__even__pow2,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.61          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_even_pow2
% 0.29/0.61  thf(fact_7137_minus__pi__half__less__zero,axiom,
% 0.29/0.61      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.29/0.61  
% 0.29/0.61  % minus_pi_half_less_zero
% 0.29/0.61  thf(fact_7138_arctan__bounded,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.29/0.61        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_bounded
% 0.29/0.61  thf(fact_7139_arctan__lbound,axiom,
% 0.29/0.61      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_lbound
% 0.29/0.61  thf(fact_7140_and__nat__unfold,axiom,
% 0.29/0.61      ( bit_se727722235901077358nd_nat
% 0.29/0.61      = ( ^ [M6: nat,N: nat] :
% 0.29/0.61            ( if_nat
% 0.29/0.61            @ ( ( M6 = zero_zero_nat )
% 0.29/0.61              | ( N = zero_zero_nat ) )
% 0.29/0.61            @ zero_zero_nat
% 0.29/0.61            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_unfold
% 0.29/0.61  thf(fact_7141_arsinh__real__aux,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arsinh_real_aux
% 0.29/0.61  thf(fact_7142_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.29/0.61      ! [X4: real,Y: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_mult_ge_zero
% 0.29/0.61  thf(fact_7143_real__sqrt__power__even,axiom,
% 0.29/0.61      ! [N2: nat,X4: real] :
% 0.29/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( power_power_real @ ( sqrt @ X4 ) @ N2 )
% 0.29/0.61            = ( power_power_real @ X4 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_power_even
% 0.29/0.61  thf(fact_7144_arith__geo__mean__sqrt,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X4 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arith_geo_mean_sqrt
% 0.29/0.61  thf(fact_7145_less__log2__of__power,axiom,
% 0.29/0.61      ! [N2: nat,M: nat] :
% 0.29/0.61        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 0.29/0.61       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_log2_of_power
% 0.29/0.61  thf(fact_7146_le__log2__of__power,axiom,
% 0.29/0.61      ! [N2: nat,M: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 0.29/0.61       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_log2_of_power
% 0.29/0.61  thf(fact_7147_and__nat__rec,axiom,
% 0.29/0.61      ( bit_se727722235901077358nd_nat
% 0.29/0.61      = ( ^ [M6: nat,N: nat] :
% 0.29/0.61            ( plus_plus_nat
% 0.29/0.61            @ ( zero_n2687167440665602831ol_nat
% 0.29/0.61              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.29/0.61                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.61            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % and_nat_rec
% 0.29/0.61  thf(fact_7148_even__nat__iff,axiom,
% 0.29/0.61      ! [K: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.61       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.29/0.61          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % even_nat_iff
% 0.29/0.61  thf(fact_7149_log2__of__power__less,axiom,
% 0.29/0.61      ! [M: nat,N2: nat] :
% 0.29/0.61        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.61       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.61         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log2_of_power_less
% 0.29/0.61  thf(fact_7150_cos__x__y__le__one,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_x_y_le_one
% 0.29/0.61  thf(fact_7151_real__sqrt__sum__squares__less,axiom,
% 0.29/0.61      ! [X4: real,U: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_sqrt_sum_squares_less
% 0.29/0.61  thf(fact_7152_arcosh__real__def,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( arcosh_real @ X4 )
% 0.29/0.61          = ( ln_ln_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcosh_real_def
% 0.29/0.61  thf(fact_7153_sqrt__sum__squares__half__less,axiom,
% 0.29/0.61      ! [X4: real,U: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ X4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sqrt_sum_squares_half_less
% 0.29/0.61  thf(fact_7154_log2__of__power__le,axiom,
% 0.29/0.61      ! [M: nat,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.61       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.61         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log2_of_power_le
% 0.29/0.61  thf(fact_7155_machin__Euler,axiom,
% 0.29/0.61      ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % machin_Euler
% 0.29/0.61  thf(fact_7156_sin__cos__npi,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_npi
% 0.29/0.61  thf(fact_7157_ceiling__log__nat__eq__powr__iff,axiom,
% 0.29/0.61      ! [B: nat,K: nat,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.61       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.61         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.29/0.61              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 0.29/0.61            = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.29/0.61              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_log_nat_eq_powr_iff
% 0.29/0.61  thf(fact_7158_arsinh__real__def,axiom,
% 0.29/0.61      ( arsinh_real
% 0.29/0.61      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arsinh_real_def
% 0.29/0.61  thf(fact_7159_cos__pi__eq__zero,axiom,
% 0.29/0.61      ! [M: nat] :
% 0.29/0.61        ( ( 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 ) ) ) )
% 0.29/0.61        = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_pi_eq_zero
% 0.29/0.61  thf(fact_7160_ceiling__log__nat__eq__if,axiom,
% 0.29/0.61      ! [B: nat,N2: nat,K: nat] :
% 0.29/0.61        ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.29/0.61       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 0.29/0.61         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.61           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.29/0.61              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_log_nat_eq_if
% 0.29/0.61  thf(fact_7161_ceiling__log2__div2,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.61          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_log2_div2
% 0.29/0.61  thf(fact_7162_cos__zero,axiom,
% 0.29/0.61      ( ( cos_complex @ zero_zero_complex )
% 0.29/0.61      = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_zero
% 0.29/0.61  thf(fact_7163_cos__zero,axiom,
% 0.29/0.61      ( ( cos_real @ zero_zero_real )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_zero
% 0.29/0.61  thf(fact_7164_ceiling__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 0.29/0.61        = ( numeral_numeral_int @ V ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_numeral
% 0.29/0.61  thf(fact_7165_ceiling__one,axiom,
% 0.29/0.61      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.29/0.61      = one_one_int ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_one
% 0.29/0.61  thf(fact_7166_ceiling__one,axiom,
% 0.29/0.61      ( ( archim7802044766580827645g_real @ one_one_real )
% 0.29/0.61      = one_one_int ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_one
% 0.29/0.61  thf(fact_7167_cos__pi,axiom,
% 0.29/0.61      ( ( cos_real @ pi )
% 0.29/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_pi
% 0.29/0.61  thf(fact_7168_sin__cos__squared__add3,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ X4 ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ X4 ) ) )
% 0.29/0.61        = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add3
% 0.29/0.61  thf(fact_7169_sin__cos__squared__add3,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ X4 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ X4 ) ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add3
% 0.29/0.61  thf(fact_7170_ceiling__le__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_zero
% 0.29/0.61  thf(fact_7171_ceiling__le__zero,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_zero
% 0.29/0.61  thf(fact_7172_zero__less__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_ceiling
% 0.29/0.61  thf(fact_7173_zero__less__ceiling,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_ceiling
% 0.29/0.61  thf(fact_7174_ceiling__le__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_numeral
% 0.29/0.61  thf(fact_7175_ceiling__le__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_numeral
% 0.29/0.61  thf(fact_7176_ceiling__less__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_one
% 0.29/0.61  thf(fact_7177_ceiling__less__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_one
% 0.29/0.61  thf(fact_7178_one__le__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_le_ceiling
% 0.29/0.61  thf(fact_7179_one__le__ceiling,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_le_ceiling
% 0.29/0.61  thf(fact_7180_numeral__less__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_less_ceiling
% 0.29/0.61  thf(fact_7181_numeral__less__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_less_ceiling
% 0.29/0.61  thf(fact_7182_ceiling__le__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_one
% 0.29/0.61  thf(fact_7183_ceiling__le__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_one
% 0.29/0.61  thf(fact_7184_one__less__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ one_one_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_ceiling
% 0.29/0.61  thf(fact_7185_one__less__ceiling,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ one_one_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_ceiling
% 0.29/0.61  thf(fact_7186_ceiling__add__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_numeral
% 0.29/0.61  thf(fact_7187_ceiling__add__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_numeral
% 0.29/0.61  thf(fact_7188_ceiling__neg__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_neg_numeral
% 0.29/0.61  thf(fact_7189_ceiling__neg__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_neg_numeral
% 0.29/0.61  thf(fact_7190_ceiling__add__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_one
% 0.29/0.61  thf(fact_7191_ceiling__add__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_one
% 0.29/0.61  thf(fact_7192_ceiling__diff__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_diff_numeral
% 0.29/0.61  thf(fact_7193_ceiling__diff__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_diff_numeral
% 0.29/0.61  thf(fact_7194_ceiling__diff__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_diff_one
% 0.29/0.61  thf(fact_7195_ceiling__diff__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_diff_one
% 0.29/0.61  thf(fact_7196_ceiling__numeral__power,axiom,
% 0.29/0.61      ! [X4: num,N2: nat] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.61        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_numeral_power
% 0.29/0.61  thf(fact_7197_nat__ceiling__le__eq,axiom,
% 0.29/0.61      ! [X4: real,A: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) @ A )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nat_ceiling_le_eq
% 0.29/0.61  thf(fact_7198_ceiling__less__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_zero
% 0.29/0.61  thf(fact_7199_ceiling__less__zero,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_zero
% 0.29/0.61  thf(fact_7200_zero__le__ceiling,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_le_ceiling
% 0.29/0.61  thf(fact_7201_zero__le__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_le_ceiling
% 0.29/0.61  thf(fact_7202_ceiling__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [A: num,B: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7203_ceiling__less__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_numeral
% 0.29/0.61  thf(fact_7204_ceiling__less__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_numeral
% 0.29/0.61  thf(fact_7205_numeral__le__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_le_ceiling
% 0.29/0.61  thf(fact_7206_numeral__le__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_le_ceiling
% 0.29/0.61  thf(fact_7207_ceiling__le__neg__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_neg_numeral
% 0.29/0.61  thf(fact_7208_ceiling__le__neg__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_le_neg_numeral
% 0.29/0.61  thf(fact_7209_neg__numeral__less__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_less_ceiling
% 0.29/0.61  thf(fact_7210_neg__numeral__less__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_less_ceiling
% 0.29/0.61  thf(fact_7211_cos__pi__half,axiom,
% 0.29/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_pi_half
% 0.29/0.61  thf(fact_7212_sin__two__pi,axiom,
% 0.29/0.61      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61      = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_two_pi
% 0.29/0.61  thf(fact_7213_sin__pi__half,axiom,
% 0.29/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_pi_half
% 0.29/0.61  thf(fact_7214_cos__two__pi,axiom,
% 0.29/0.61      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_two_pi
% 0.29/0.61  thf(fact_7215_cos__periodic,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cos_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.29/0.61        = ( cos_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_periodic
% 0.29/0.61  thf(fact_7216_sin__periodic,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( sin_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.29/0.61        = ( sin_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_periodic
% 0.29/0.61  thf(fact_7217_cos__2pi__minus,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 0.29/0.61        = ( cos_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_2pi_minus
% 0.29/0.61  thf(fact_7218_cos__npi,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 0.29/0.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_npi
% 0.29/0.61  thf(fact_7219_cos__npi2,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.61        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_npi2
% 0.29/0.61  thf(fact_7220_ceiling__minus__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [A: num,B: num] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_minus_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7221_sin__cos__squared__add2,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add2
% 0.29/0.61  thf(fact_7222_sin__cos__squared__add2,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add2
% 0.29/0.61  thf(fact_7223_sin__cos__squared__add,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add
% 0.29/0.61  thf(fact_7224_sin__cos__squared__add,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_squared_add
% 0.29/0.61  thf(fact_7225_sin__2npi,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 0.29/0.61        = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_2npi
% 0.29/0.61  thf(fact_7226_cos__2npi,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_2npi
% 0.29/0.61  thf(fact_7227_sin__2pi__minus,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 0.29/0.61        = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_2pi_minus
% 0.29/0.61  thf(fact_7228_ceiling__less__neg__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_neg_numeral
% 0.29/0.61  thf(fact_7229_ceiling__less__neg__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_neg_numeral
% 0.29/0.61  thf(fact_7230_neg__numeral__le__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_le_ceiling
% 0.29/0.61  thf(fact_7231_neg__numeral__le__ceiling,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_le_ceiling
% 0.29/0.61  thf(fact_7232_cos__3over2__pi,axiom,
% 0.29/0.61      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.29/0.61      = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_3over2_pi
% 0.29/0.61  thf(fact_7233_sin__3over2__pi,axiom,
% 0.29/0.61      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.29/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_3over2_pi
% 0.29/0.61  thf(fact_7234_cos__one__sin__zero,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61          = one_one_complex )
% 0.29/0.61       => ( ( sin_complex @ X4 )
% 0.29/0.61          = zero_zero_complex ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_one_sin_zero
% 0.29/0.61  thf(fact_7235_cos__one__sin__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61          = one_one_real )
% 0.29/0.61       => ( ( sin_real @ X4 )
% 0.29/0.61          = zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_one_sin_zero
% 0.29/0.61  thf(fact_7236_sin__add,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_add
% 0.29/0.61  thf(fact_7237_sin__add,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( sin_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_add
% 0.29/0.61  thf(fact_7238_cos__diff,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_diff
% 0.29/0.61  thf(fact_7239_cos__diff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_diff
% 0.29/0.61  thf(fact_7240_cos__add,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.61        = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_add
% 0.29/0.61  thf(fact_7241_cos__add,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61        = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_add
% 0.29/0.61  thf(fact_7242_sin__zero__norm__cos__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( sin_real @ X4 )
% 0.29/0.61          = zero_zero_real )
% 0.29/0.61       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X4 ) )
% 0.29/0.61          = one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_norm_cos_one
% 0.29/0.61  thf(fact_7243_sin__zero__norm__cos__one,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( ( sin_complex @ X4 )
% 0.29/0.61          = zero_zero_complex )
% 0.29/0.61       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X4 ) )
% 0.29/0.61          = one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_norm_cos_one
% 0.29/0.61  thf(fact_7244_sin__zero__abs__cos__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( sin_real @ X4 )
% 0.29/0.61          = zero_zero_real )
% 0.29/0.61       => ( ( abs_abs_real @ ( cos_real @ X4 ) )
% 0.29/0.61          = one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_abs_cos_one
% 0.29/0.61  thf(fact_7245_sin__double,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X4 ) ) @ ( cos_complex @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_double
% 0.29/0.61  thf(fact_7246_sin__double,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X4 ) ) @ ( cos_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_double
% 0.29/0.61  thf(fact_7247_sincos__principal__value,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61      ? [Y3: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 0.29/0.61        & ( ord_less_eq_real @ Y3 @ pi )
% 0.29/0.61        & ( ( sin_real @ Y3 )
% 0.29/0.61          = ( sin_real @ X4 ) )
% 0.29/0.61        & ( ( cos_real @ Y3 )
% 0.29/0.61          = ( cos_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sincos_principal_value
% 0.29/0.61  thf(fact_7248_ceiling__mono,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.61       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_mono
% 0.29/0.61  thf(fact_7249_ceiling__mono,axiom,
% 0.29/0.61      ! [Y: rat,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ Y @ X4 )
% 0.29/0.61       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_mono
% 0.29/0.61  thf(fact_7250_sin__x__le__x,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ord_less_eq_real @ ( sin_real @ X4 ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_x_le_x
% 0.29/0.61  thf(fact_7251_ceiling__less__cancel,axiom,
% 0.29/0.61      ! [X4: rat,Y: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 0.29/0.61       => ( ord_less_rat @ X4 @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_cancel
% 0.29/0.61  thf(fact_7252_ceiling__less__cancel,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) )
% 0.29/0.61       => ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_less_cancel
% 0.29/0.61  thf(fact_7253_sin__le__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( sin_real @ X4 ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_le_one
% 0.29/0.61  thf(fact_7254_cos__le__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( cos_real @ X4 ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_le_one
% 0.29/0.61  thf(fact_7255_abs__sin__x__le__abs__x,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ ( abs_abs_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % abs_sin_x_le_abs_x
% 0.29/0.61  thf(fact_7256_sin__cos__le1,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_le1
% 0.29/0.61  thf(fact_7257_sin__squared__eq,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_squared_eq
% 0.29/0.61  thf(fact_7258_sin__squared__eq,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_squared_eq
% 0.29/0.61  thf(fact_7259_cos__squared__eq,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_squared_eq
% 0.29/0.61  thf(fact_7260_cos__squared__eq,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.61        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_squared_eq
% 0.29/0.61  thf(fact_7261_of__nat__ceiling,axiom,
% 0.29/0.61      ! [R3: real] : ( ord_less_eq_real @ R3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_ceiling
% 0.29/0.61  thf(fact_7262_of__nat__ceiling,axiom,
% 0.29/0.61      ! [R3: rat] : ( ord_less_eq_rat @ R3 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_ceiling
% 0.29/0.61  thf(fact_7263_sin__gt__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ pi )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_gt_zero
% 0.29/0.61  thf(fact_7264_sin__x__ge__neg__x,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ ( sin_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_x_ge_neg_x
% 0.29/0.61  thf(fact_7265_sin__ge__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_ge_zero
% 0.29/0.61  thf(fact_7266_ceiling__add__le,axiom,
% 0.29/0.61      ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_le
% 0.29/0.61  thf(fact_7267_ceiling__add__le,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_le
% 0.29/0.61  thf(fact_7268_real__nat__ceiling__ge,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_nat_ceiling_ge
% 0.29/0.61  thf(fact_7269_sin__ge__minus__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_ge_minus_one
% 0.29/0.61  thf(fact_7270_cos__inj__pi,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ pi )
% 0.29/0.61             => ( ( ( cos_real @ X4 )
% 0.29/0.61                  = ( cos_real @ Y ) )
% 0.29/0.61               => ( X4 = Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_inj_pi
% 0.29/0.61  thf(fact_7271_cos__mono__le__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ pi )
% 0.29/0.61             => ( ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 0.29/0.61                = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_mono_le_eq
% 0.29/0.61  thf(fact_7272_cos__monotone__0__pi__le,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61           => ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_monotone_0_pi_le
% 0.29/0.61  thf(fact_7273_cos__ge__minus__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_ge_minus_one
% 0.29/0.61  thf(fact_7274_abs__sin__le__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % abs_sin_le_one
% 0.29/0.61  thf(fact_7275_abs__cos__le__one,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X4 ) ) @ one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % abs_cos_le_one
% 0.29/0.61  thf(fact_7276_sin__times__sin,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_times_sin
% 0.29/0.61  thf(fact_7277_sin__times__sin,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.29/0.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_times_sin
% 0.29/0.61  thf(fact_7278_sin__times__cos,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_times_cos
% 0.29/0.61  thf(fact_7279_sin__times__cos,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 0.29/0.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_times_cos
% 0.29/0.61  thf(fact_7280_cos__times__sin,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_times_sin
% 0.29/0.61  thf(fact_7281_cos__times__sin,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 0.29/0.61        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_times_sin
% 0.29/0.61  thf(fact_7282_sin__plus__sin,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_plus_sin
% 0.29/0.61  thf(fact_7283_sin__plus__sin,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_plus_sin
% 0.29/0.61  thf(fact_7284_sin__diff__sin,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_diff_sin
% 0.29/0.61  thf(fact_7285_sin__diff__sin,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_diff_sin
% 0.29/0.61  thf(fact_7286_cos__diff__cos,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_diff_cos
% 0.29/0.61  thf(fact_7287_cos__diff__cos,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_diff_cos
% 0.29/0.61  thf(fact_7288_cos__double,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double
% 0.29/0.61  thf(fact_7289_cos__double,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double
% 0.29/0.61  thf(fact_7290_cos__double__sin,axiom,
% 0.29/0.61      ! [W: complex] :
% 0.29/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.29/0.61        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double_sin
% 0.29/0.61  thf(fact_7291_cos__double__sin,axiom,
% 0.29/0.61      ! [W: real] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double_sin
% 0.29/0.61  thf(fact_7292_cos__two__neq__zero,axiom,
% 0.29/0.61      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61     != zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_two_neq_zero
% 0.29/0.61  thf(fact_7293_cos__monotone__0__pi,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61           => ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_monotone_0_pi
% 0.29/0.61  thf(fact_7294_cos__mono__less__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ pi )
% 0.29/0.61             => ( ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 0.29/0.61                = ( ord_less_real @ Y @ X4 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_mono_less_eq
% 0.29/0.61  thf(fact_7295_sin__eq__0__pi,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ pi )
% 0.29/0.61         => ( ( ( sin_real @ X4 )
% 0.29/0.61              = zero_zero_real )
% 0.29/0.61           => ( X4 = zero_zero_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_eq_0_pi
% 0.29/0.61  thf(fact_7296_sin__zero__pi__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ pi )
% 0.29/0.61       => ( ( ( sin_real @ X4 )
% 0.29/0.61            = zero_zero_real )
% 0.29/0.61          = ( X4 = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_pi_iff
% 0.29/0.61  thf(fact_7297_cos__monotone__minus__pi__0_H,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.61           => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_monotone_minus_pi_0'
% 0.29/0.61  thf(fact_7298_sincos__total__pi,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61       => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61            = one_one_real )
% 0.29/0.61         => ? [T3: real] :
% 0.29/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.61              & ( ord_less_eq_real @ T3 @ pi )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( cos_real @ T3 ) )
% 0.29/0.61              & ( Y
% 0.29/0.61                = ( sin_real @ T3 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sincos_total_pi
% 0.29/0.61  thf(fact_7299_sin__cos__sqrt,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) )
% 0.29/0.61       => ( ( sin_real @ X4 )
% 0.29/0.61          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_sqrt
% 0.29/0.61  thf(fact_7300_sin__expansion__lemma,axiom,
% 0.29/0.61      ! [X4: real,M: nat] :
% 0.29/0.61        ( ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61        = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_expansion_lemma
% 0.29/0.61  thf(fact_7301_cos__expansion__lemma,axiom,
% 0.29/0.61      ! [X4: real,M: nat] :
% 0.29/0.61        ( ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_expansion_lemma
% 0.29/0.61  thf(fact_7302_mult__ceiling__le,axiom,
% 0.29/0.61      ! [A: real,B: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.61         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % mult_ceiling_le
% 0.29/0.61  thf(fact_7303_mult__ceiling__le,axiom,
% 0.29/0.61      ! [A: rat,B: rat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.61       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.61         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % mult_ceiling_le
% 0.29/0.61  thf(fact_7304_sin__gt__zero__02,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_gt_zero_02
% 0.29/0.61  thf(fact_7305_cos__two__less__zero,axiom,
% 0.29/0.61      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.29/0.61  
% 0.29/0.61  % cos_two_less_zero
% 0.29/0.61  thf(fact_7306_cos__is__zero,axiom,
% 0.29/0.61      ? [X5: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 0.29/0.61        & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61        & ( ( cos_real @ X5 )
% 0.29/0.61          = zero_zero_real )
% 0.29/0.61        & ! [Y4: real] :
% 0.29/0.61            ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 0.29/0.61              & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61              & ( ( cos_real @ Y4 )
% 0.29/0.61                = zero_zero_real ) )
% 0.29/0.61           => ( Y4 = X5 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_is_zero
% 0.29/0.61  thf(fact_7307_cos__two__le__zero,axiom,
% 0.29/0.61      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.29/0.61  
% 0.29/0.61  % cos_two_le_zero
% 0.29/0.61  thf(fact_7308_cos__monotone__minus__pi__0,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.61           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_monotone_minus_pi_0
% 0.29/0.61  thf(fact_7309_cos__total,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ? [X5: real] :
% 0.29/0.61              ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 0.29/0.61              & ( ord_less_eq_real @ X5 @ pi )
% 0.29/0.61              & ( ( cos_real @ X5 )
% 0.29/0.61                = Y )
% 0.29/0.61              & ! [Y4: real] :
% 0.29/0.61                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 0.29/0.61                    & ( ord_less_eq_real @ Y4 @ pi )
% 0.29/0.61                    & ( ( cos_real @ Y4 )
% 0.29/0.61                      = Y ) )
% 0.29/0.61                 => ( Y4 = X5 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_total
% 0.29/0.61  thf(fact_7310_sincos__total__pi__half,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61              = one_one_real )
% 0.29/0.61           => ? [T3: real] :
% 0.29/0.61                ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.61                & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61                & ( X4
% 0.29/0.61                  = ( cos_real @ T3 ) )
% 0.29/0.61                & ( Y
% 0.29/0.61                  = ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sincos_total_pi_half
% 0.29/0.61  thf(fact_7311_sincos__total__2pi__le,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61          = one_one_real )
% 0.29/0.61       => ? [T3: real] :
% 0.29/0.61            ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.61            & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61            & ( X4
% 0.29/0.61              = ( cos_real @ T3 ) )
% 0.29/0.61            & ( Y
% 0.29/0.61              = ( sin_real @ T3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sincos_total_2pi_le
% 0.29/0.61  thf(fact_7312_sincos__total__2pi,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.61          = one_one_real )
% 0.29/0.61       => ~ ! [T3: real] :
% 0.29/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61               => ( ( X4
% 0.29/0.61                    = ( cos_real @ T3 ) )
% 0.29/0.61                 => ( Y
% 0.29/0.61                   != ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sincos_total_2pi
% 0.29/0.61  thf(fact_7313_sin__pi__divide__n__ge__0,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( N2 != zero_zero_nat )
% 0.29/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_pi_divide_n_ge_0
% 0.29/0.61  thf(fact_7314_sin__45,axiom,
% 0.29/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_45
% 0.29/0.61  thf(fact_7315_cos__45,axiom,
% 0.29/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_45
% 0.29/0.61  thf(fact_7316_cos__times__cos,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_times_cos
% 0.29/0.61  thf(fact_7317_cos__times__cos,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.29/0.61        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_times_cos
% 0.29/0.61  thf(fact_7318_cos__plus__cos,axiom,
% 0.29/0.61      ! [W: real,Z: real] :
% 0.29/0.61        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_plus_cos
% 0.29/0.61  thf(fact_7319_cos__plus__cos,axiom,
% 0.29/0.61      ! [W: complex,Z: complex] :
% 0.29/0.61        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 0.29/0.61        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_plus_cos
% 0.29/0.61  thf(fact_7320_sin__gt__zero2,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_gt_zero2
% 0.29/0.61  thf(fact_7321_sin__lt__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ pi @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61         => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_lt_zero
% 0.29/0.61  thf(fact_7322_cos__double__less__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.61         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double_less_one
% 0.29/0.61  thf(fact_7323_sin__30,axiom,
% 0.29/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_30
% 0.29/0.61  thf(fact_7324_cos__gt__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_gt_zero
% 0.29/0.61  thf(fact_7325_sin__inj__pi,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ( sin_real @ X4 )
% 0.29/0.61                  = ( sin_real @ Y ) )
% 0.29/0.61               => ( X4 = Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_inj_pi
% 0.29/0.61  thf(fact_7326_sin__mono__le__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_eq_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 0.29/0.61                = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_mono_le_eq
% 0.29/0.61  thf(fact_7327_sin__monotone__2pi__le,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_monotone_2pi_le
% 0.29/0.61  thf(fact_7328_cos__60,axiom,
% 0.29/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_60
% 0.29/0.61  thf(fact_7329_sin__60,axiom,
% 0.29/0.61      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_60
% 0.29/0.61  thf(fact_7330_cos__30,axiom,
% 0.29/0.61      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_30
% 0.29/0.61  thf(fact_7331_cos__double__cos,axiom,
% 0.29/0.61      ! [W: complex] :
% 0.29/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 0.29/0.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double_cos
% 0.29/0.61  thf(fact_7332_cos__double__cos,axiom,
% 0.29/0.61      ! [W: real] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 0.29/0.61        = ( 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 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_double_cos
% 0.29/0.61  thf(fact_7333_cos__treble__cos,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_treble_cos
% 0.29/0.61  thf(fact_7334_cos__treble__cos,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X4 ) )
% 0.29/0.61        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_treble_cos
% 0.29/0.61  thf(fact_7335_sin__le__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ pi @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61         => ( ord_less_eq_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_le_zero
% 0.29/0.61  thf(fact_7336_sin__less__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.61         => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_less_zero
% 0.29/0.61  thf(fact_7337_sin__mono__less__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 0.29/0.61                = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_mono_less_eq
% 0.29/0.61  thf(fact_7338_sin__monotone__2pi,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_monotone_2pi
% 0.29/0.61  thf(fact_7339_sin__total,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ? [X5: real] :
% 0.29/0.61              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 0.29/0.61              & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61              & ( ( sin_real @ X5 )
% 0.29/0.61                = Y )
% 0.29/0.61              & ! [Y4: real] :
% 0.29/0.61                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 0.29/0.61                    & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61                    & ( ( sin_real @ Y4 )
% 0.29/0.61                      = Y ) )
% 0.29/0.61                 => ( Y4 = X5 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_total
% 0.29/0.61  thf(fact_7340_cos__gt__zero__pi,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_gt_zero_pi
% 0.29/0.61  thf(fact_7341_cos__ge__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_ge_zero
% 0.29/0.61  thf(fact_7342_cos__one__2pi,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61          = one_one_real )
% 0.29/0.61        = ( ? [X: nat] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.29/0.61          | ? [X: nat] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_one_2pi
% 0.29/0.61  thf(fact_7343_sin__pi__divide__n__gt__0,axiom,
% 0.29/0.61      ! [N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_pi_divide_n_gt_0
% 0.29/0.61  thf(fact_7344_sin__arctan,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( sin_real @ ( arctan @ X4 ) )
% 0.29/0.61        = ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_arctan
% 0.29/0.61  thf(fact_7345_cos__arctan,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cos_real @ ( arctan @ X4 ) )
% 0.29/0.61        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_arctan
% 0.29/0.61  thf(fact_7346_sin__zero__lemma,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ( sin_real @ X4 )
% 0.29/0.61            = zero_zero_real )
% 0.29/0.61         => ? [N3: nat] :
% 0.29/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_lemma
% 0.29/0.61  thf(fact_7347_sin__zero__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( sin_real @ X4 )
% 0.29/0.61          = zero_zero_real )
% 0.29/0.61        = ( ? [N: nat] :
% 0.29/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.61          | ? [N: nat] :
% 0.29/0.61              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_zero_iff
% 0.29/0.61  thf(fact_7348_cos__zero__lemma,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ( cos_real @ X4 )
% 0.29/0.61            = zero_zero_real )
% 0.29/0.61         => ? [N3: nat] :
% 0.29/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_zero_lemma
% 0.29/0.61  thf(fact_7349_cos__zero__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61          = zero_zero_real )
% 0.29/0.61        = ( ? [N: nat] :
% 0.29/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.61          | ? [N: nat] :
% 0.29/0.61              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.29/0.61              & ( X4
% 0.29/0.61                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_zero_iff
% 0.29/0.61  thf(fact_7350_tan__double,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61         != zero_zero_real )
% 0.29/0.61       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61           != zero_zero_real )
% 0.29/0.61         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X4 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_double
% 0.29/0.61  thf(fact_7351_tan__double,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61         != zero_zero_complex )
% 0.29/0.61       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61           != zero_zero_complex )
% 0.29/0.61         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.61            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_double
% 0.29/0.61  thf(fact_7352_sin__tan,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61       => ( ( sin_real @ X4 )
% 0.29/0.61          = ( divide_divide_real @ ( tan_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_tan
% 0.29/0.61  thf(fact_7353_cos__tan,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61       => ( ( cos_real @ X4 )
% 0.29/0.61          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_tan
% 0.29/0.61  thf(fact_7354_complex__unimodular__polar,axiom,
% 0.29/0.61      ! [Z: complex] :
% 0.29/0.61        ( ( ( real_V1022390504157884413omplex @ Z )
% 0.29/0.61          = one_one_real )
% 0.29/0.61       => ~ ! [T3: real] :
% 0.29/0.61              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.61             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.61               => ( Z
% 0.29/0.61                 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % complex_unimodular_polar
% 0.29/0.61  thf(fact_7355_ceiling__log__eq__powr__iff,axiom,
% 0.29/0.61      ! [X4: real,B: real,K: nat] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X4 ) )
% 0.29/0.61              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.29/0.61            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X4 )
% 0.29/0.61              & ( ord_less_eq_real @ X4 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_log_eq_powr_iff
% 0.29/0.61  thf(fact_7356_powr__one__eq__one,axiom,
% 0.29/0.61      ! [A: real] :
% 0.29/0.61        ( ( powr_real @ one_one_real @ A )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_one_eq_one
% 0.29/0.61  thf(fact_7357_powr__zero__eq__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( X4 = zero_zero_real )
% 0.29/0.61         => ( ( powr_real @ X4 @ zero_zero_real )
% 0.29/0.61            = zero_zero_real ) )
% 0.29/0.61        & ( ( X4 != zero_zero_real )
% 0.29/0.61         => ( ( powr_real @ X4 @ zero_zero_real )
% 0.29/0.61            = one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_zero_eq_one
% 0.29/0.61  thf(fact_7358_powr__gt__zero,axiom,
% 0.29/0.61      ! [X4: real,A: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X4 @ A ) )
% 0.29/0.61        = ( X4 != zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_gt_zero
% 0.29/0.61  thf(fact_7359_powr__nonneg__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( powr_real @ A @ X4 ) @ zero_zero_real )
% 0.29/0.61        = ( A = zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_nonneg_iff
% 0.29/0.61  thf(fact_7360_powr__less__cancel__iff,axiom,
% 0.29/0.61      ! [X4: real,A: real,B: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 0.29/0.61          = ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_cancel_iff
% 0.29/0.61  thf(fact_7361_powr__eq__one__iff,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ A )
% 0.29/0.61       => ( ( ( powr_real @ A @ X4 )
% 0.29/0.61            = one_one_real )
% 0.29/0.61          = ( X4 = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_eq_one_iff
% 0.29/0.61  thf(fact_7362_powr__one__gt__zero__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( powr_real @ X4 @ one_one_real )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_one_gt_zero_iff
% 0.29/0.61  thf(fact_7363_powr__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ one_one_real )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_one
% 0.29/0.61  thf(fact_7364_powr__le__cancel__iff,axiom,
% 0.29/0.61      ! [X4: real,A: real,B: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 0.29/0.61          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_le_cancel_iff
% 0.29/0.61  thf(fact_7365_numeral__powr__numeral__real,axiom,
% 0.29/0.61      ! [M: num,N2: num] :
% 0.29/0.61        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.61        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_powr_numeral_real
% 0.29/0.61  thf(fact_7366_log__powr__cancel,axiom,
% 0.29/0.61      ! [A: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 0.29/0.61            = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_powr_cancel
% 0.29/0.61  thf(fact_7367_powr__log__cancel,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( powr_real @ A @ ( log @ A @ X4 ) )
% 0.29/0.61              = X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_log_cancel
% 0.29/0.61  thf(fact_7368_tan__periodic__n,axiom,
% 0.29/0.61      ! [X4: real,N2: num] :
% 0.29/0.61        ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 0.29/0.61        = ( tan_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_periodic_n
% 0.29/0.61  thf(fact_7369_norm__cos__sin,axiom,
% 0.29/0.61      ! [T2: real] :
% 0.29/0.61        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T2 ) @ ( sin_real @ T2 ) ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_cos_sin
% 0.29/0.61  thf(fact_7370_powr__numeral,axiom,
% 0.29/0.61      ! [X4: real,N2: num] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.61          = ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_numeral
% 0.29/0.61  thf(fact_7371_tan__periodic,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.29/0.61        = ( tan_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_periodic
% 0.29/0.61  thf(fact_7372_square__powr__half,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( powr_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61        = ( abs_abs_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % square_powr_half
% 0.29/0.61  thf(fact_7373_powr__non__neg,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ~ ( ord_less_real @ ( powr_real @ A @ X4 ) @ zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_non_neg
% 0.29/0.61  thf(fact_7374_powr__less__mono2__neg,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.61           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_mono2_neg
% 0.29/0.61  thf(fact_7375_powr__ge__pzero,axiom,
% 0.29/0.61      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X4 @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_ge_pzero
% 0.29/0.61  thf(fact_7376_powr__mono2,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61           => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mono2
% 0.29/0.61  thf(fact_7377_powr__less__cancel,axiom,
% 0.29/0.61      ! [X4: real,A: real,B: real] :
% 0.29/0.61        ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61         => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_cancel
% 0.29/0.61  thf(fact_7378_powr__less__mono,axiom,
% 0.29/0.61      ! [A: real,B: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ A @ B )
% 0.29/0.61       => ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61         => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_mono
% 0.29/0.61  thf(fact_7379_powr__mono,axiom,
% 0.29/0.61      ! [A: real,B: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.61       => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61         => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mono
% 0.29/0.61  thf(fact_7380_one__complex_Ocode,axiom,
% 0.29/0.61      ( one_one_complex
% 0.29/0.61      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_complex.code
% 0.29/0.61  thf(fact_7381_Complex__eq__1,axiom,
% 0.29/0.61      ! [A: real,B: real] :
% 0.29/0.61        ( ( ( complex2 @ A @ B )
% 0.29/0.61          = one_one_complex )
% 0.29/0.61        = ( ( A = one_one_real )
% 0.29/0.61          & ( B = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Complex_eq_1
% 0.29/0.61  thf(fact_7382_Complex__eq__numeral,axiom,
% 0.29/0.61      ! [A: real,B: real,W: num] :
% 0.29/0.61        ( ( ( complex2 @ A @ B )
% 0.29/0.61          = ( numera6690914467698888265omplex @ W ) )
% 0.29/0.61        = ( ( A
% 0.29/0.61            = ( numeral_numeral_real @ W ) )
% 0.29/0.61          & ( B = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Complex_eq_numeral
% 0.29/0.61  thf(fact_7383_powr__mono2_H,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mono2'
% 0.29/0.61  thf(fact_7384_powr__less__mono2,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.61           => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_mono2
% 0.29/0.61  thf(fact_7385_powr__inj,axiom,
% 0.29/0.61      ! [A: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( A != one_one_real )
% 0.29/0.61         => ( ( ( powr_real @ A @ X4 )
% 0.29/0.61              = ( powr_real @ A @ Y ) )
% 0.29/0.61            = ( X4 = Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_inj
% 0.29/0.61  thf(fact_7386_gr__one__powr,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ord_less_real @ one_one_real @ ( powr_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % gr_one_powr
% 0.29/0.61  thf(fact_7387_ge__one__powr__ge__zero,axiom,
% 0.29/0.61      ! [X4: real,A: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.61         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ge_one_powr_ge_zero
% 0.29/0.61  thf(fact_7388_powr__mono__both,axiom,
% 0.29/0.61      ! [A: real,B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.61         => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61           => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61             => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mono_both
% 0.29/0.61  thf(fact_7389_powr__le1,axiom,
% 0.29/0.61      ! [A: real,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61           => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_le1
% 0.29/0.61  thf(fact_7390_powr__divide,axiom,
% 0.29/0.61      ! [X4: real,Y: real,A: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( powr_real @ ( divide_divide_real @ X4 @ Y ) @ A )
% 0.29/0.61            = ( divide_divide_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_divide
% 0.29/0.61  thf(fact_7391_powr__mult,axiom,
% 0.29/0.61      ! [X4: real,Y: real,A: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61         => ( ( powr_real @ ( times_times_real @ X4 @ Y ) @ A )
% 0.29/0.61            = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mult
% 0.29/0.61  thf(fact_7392_Complex__eq__neg__1,axiom,
% 0.29/0.61      ! [A: real,B: real] :
% 0.29/0.61        ( ( ( complex2 @ A @ B )
% 0.29/0.61          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.29/0.61        = ( ( A
% 0.29/0.61            = ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.61          & ( B = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Complex_eq_neg_1
% 0.29/0.61  thf(fact_7393_Complex__eq__neg__numeral,axiom,
% 0.29/0.61      ! [A: real,B: real,W: num] :
% 0.29/0.61        ( ( ( complex2 @ A @ B )
% 0.29/0.61          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.61        = ( ( A
% 0.29/0.61            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.61          & ( B = zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % Complex_eq_neg_numeral
% 0.29/0.61  thf(fact_7394_powr__add,axiom,
% 0.29/0.61      ! [X4: real,A: real,B: real] :
% 0.29/0.61        ( ( powr_real @ X4 @ ( plus_plus_real @ A @ B ) )
% 0.29/0.61        = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_add
% 0.29/0.61  thf(fact_7395_powr__diff,axiom,
% 0.29/0.61      ! [W: real,Z1: real,Z22: real] :
% 0.29/0.61        ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 0.29/0.61        = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_diff
% 0.29/0.61  thf(fact_7396_tan__def,axiom,
% 0.29/0.61      ( tan_real
% 0.29/0.61      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_def
% 0.29/0.61  thf(fact_7397_tan__def,axiom,
% 0.29/0.61      ( tan_complex
% 0.29/0.61      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_def
% 0.29/0.61  thf(fact_7398_powr__realpow,axiom,
% 0.29/0.61      ! [X4: real,N2: nat] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.29/0.61          = ( power_power_real @ X4 @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_realpow
% 0.29/0.61  thf(fact_7399_less__log__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ Y @ ( log @ B @ X4 ) )
% 0.29/0.61            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_log_iff
% 0.29/0.61  thf(fact_7400_log__less__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ ( log @ B @ X4 ) @ Y )
% 0.29/0.61            = ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_less_iff
% 0.29/0.61  thf(fact_7401_less__powr__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) )
% 0.29/0.61            = ( ord_less_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_powr_iff
% 0.29/0.61  thf(fact_7402_powr__less__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 )
% 0.29/0.61            = ( ord_less_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_less_iff
% 0.29/0.61  thf(fact_7403_powr__minus__divide,axiom,
% 0.29/0.61      ! [X4: real,A: real] :
% 0.29/0.61        ( ( powr_real @ X4 @ ( uminus_uminus_real @ A ) )
% 0.29/0.61        = ( divide_divide_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_minus_divide
% 0.29/0.61  thf(fact_7404_powr__neg__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.61          = ( divide_divide_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_neg_one
% 0.29/0.61  thf(fact_7405_powr__mult__base,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( times_times_real @ X4 @ ( powr_real @ X4 @ Y ) )
% 0.29/0.61          = ( powr_real @ X4 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_mult_base
% 0.29/0.61  thf(fact_7406_le__log__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) )
% 0.29/0.61            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_log_iff
% 0.29/0.61  thf(fact_7407_log__le__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y )
% 0.29/0.61            = ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_le_iff
% 0.29/0.61  thf(fact_7408_le__powr__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) )
% 0.29/0.61            = ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_powr_iff
% 0.29/0.61  thf(fact_7409_powr__le__iff,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 )
% 0.29/0.61            = ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_le_iff
% 0.29/0.61  thf(fact_7410_ln__powr__bound,axiom,
% 0.29/0.61      ! [X4: real,A: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61         => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( divide_divide_real @ ( powr_real @ X4 @ A ) @ A ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ln_powr_bound
% 0.29/0.61  thf(fact_7411_ln__powr__bound2,axiom,
% 0.29/0.61      ! [X4: real,A: real] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.61         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X4 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ln_powr_bound2
% 0.29/0.61  thf(fact_7412_tan__45,axiom,
% 0.29/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_45
% 0.29/0.61  thf(fact_7413_log__add__eq__powr,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.61       => ( ( B != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( plus_plus_real @ ( log @ B @ X4 ) @ Y )
% 0.29/0.61              = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_add_eq_powr
% 0.29/0.61  thf(fact_7414_add__log__eq__powr,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.61       => ( ( B != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( plus_plus_real @ Y @ ( log @ B @ X4 ) )
% 0.29/0.61              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % add_log_eq_powr
% 0.29/0.61  thf(fact_7415_minus__log__eq__powr,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.61       => ( ( B != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( minus_minus_real @ Y @ ( log @ B @ X4 ) )
% 0.29/0.61              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % minus_log_eq_powr
% 0.29/0.61  thf(fact_7416_tan__60,axiom,
% 0.29/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.29/0.61      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_60
% 0.29/0.61  thf(fact_7417_lemma__tan__total,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.29/0.61       => ? [X5: real] :
% 0.29/0.61            ( ( ord_less_real @ zero_zero_real @ X5 )
% 0.29/0.61            & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61            & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % lemma_tan_total
% 0.29/0.61  thf(fact_7418_tan__gt__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_gt_zero
% 0.29/0.61  thf(fact_7419_tan__total,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61      ? [X5: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 0.29/0.61        & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61        & ( ( tan_real @ X5 )
% 0.29/0.61          = Y )
% 0.29/0.61        & ! [Y4: real] :
% 0.29/0.61            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 0.29/0.61              & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61              & ( ( tan_real @ Y4 )
% 0.29/0.61                = Y ) )
% 0.29/0.61           => ( Y4 = X5 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_total
% 0.29/0.61  thf(fact_7420_tan__monotone,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.61         => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_monotone
% 0.29/0.61  thf(fact_7421_tan__monotone_H,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61           => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_real @ Y @ X4 )
% 0.29/0.61                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_monotone'
% 0.29/0.61  thf(fact_7422_tan__mono__lt__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 0.29/0.61                = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_mono_lt_eq
% 0.29/0.61  thf(fact_7423_lemma__tan__total1,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61      ? [X5: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 0.29/0.61        & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61        & ( ( tan_real @ X5 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % lemma_tan_total1
% 0.29/0.61  thf(fact_7424_tan__minus__45,axiom,
% 0.29/0.61      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_minus_45
% 0.29/0.61  thf(fact_7425_tan__inverse,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 0.29/0.61        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_inverse
% 0.29/0.61  thf(fact_7426_log__minus__eq__powr,axiom,
% 0.29/0.61      ! [B: real,X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.61       => ( ( B != one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61           => ( ( minus_minus_real @ ( log @ B @ X4 ) @ Y )
% 0.29/0.61              = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % log_minus_eq_powr
% 0.29/0.61  thf(fact_7427_complex__norm,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( real_V1022390504157884413omplex @ ( complex2 @ X4 @ Y ) )
% 0.29/0.61        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % complex_norm
% 0.29/0.61  thf(fact_7428_add__tan__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61         != zero_zero_real )
% 0.29/0.61       => ( ( ( cos_real @ Y )
% 0.29/0.61           != zero_zero_real )
% 0.29/0.61         => ( ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 0.29/0.61            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % add_tan_eq
% 0.29/0.61  thf(fact_7429_add__tan__eq,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61         != zero_zero_complex )
% 0.29/0.61       => ( ( ( cos_complex @ Y )
% 0.29/0.61           != zero_zero_complex )
% 0.29/0.61         => ( ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) )
% 0.29/0.61            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % add_tan_eq
% 0.29/0.61  thf(fact_7430_powr__half__sqrt,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61          = ( sqrt @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_half_sqrt
% 0.29/0.61  thf(fact_7431_powr__neg__numeral,axiom,
% 0.29/0.61      ! [X4: real,N2: num] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( powr_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.61          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % powr_neg_numeral
% 0.29/0.61  thf(fact_7432_tan__total__pos,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61       => ? [X5: real] :
% 0.29/0.61            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 0.29/0.61            & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61            & ( ( tan_real @ X5 )
% 0.29/0.61              = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_total_pos
% 0.29/0.61  thf(fact_7433_tan__pos__pi2__le,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_pos_pi2_le
% 0.29/0.61  thf(fact_7434_tan__less__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.61         => ( ord_less_real @ ( tan_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_less_zero
% 0.29/0.61  thf(fact_7435_tan__mono__le__eq,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 0.29/0.61                = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_mono_le_eq
% 0.29/0.61  thf(fact_7436_tan__mono__le,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61           => ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_mono_le
% 0.29/0.61  thf(fact_7437_tan__bound__pi2,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X4 ) ) @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_bound_pi2
% 0.29/0.61  thf(fact_7438_tan__30,axiom,
% 0.29/0.61      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.29/0.61      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_30
% 0.29/0.61  thf(fact_7439_arctan__unique,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( ( tan_real @ X4 )
% 0.29/0.61              = Y )
% 0.29/0.61           => ( ( arctan @ Y )
% 0.29/0.61              = X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_unique
% 0.29/0.61  thf(fact_7440_arctan__tan,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( arctan @ ( tan_real @ X4 ) )
% 0.29/0.61            = X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan_tan
% 0.29/0.61  thf(fact_7441_arctan,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.29/0.61        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61        & ( ( tan_real @ ( arctan @ Y ) )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arctan
% 0.29/0.61  thf(fact_7442_lemma__tan__add1,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61         != zero_zero_real )
% 0.29/0.61       => ( ( ( cos_real @ Y )
% 0.29/0.61           != zero_zero_real )
% 0.29/0.61         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) )
% 0.29/0.61            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % lemma_tan_add1
% 0.29/0.61  thf(fact_7443_lemma__tan__add1,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61         != zero_zero_complex )
% 0.29/0.61       => ( ( ( cos_complex @ Y )
% 0.29/0.61           != zero_zero_complex )
% 0.29/0.61         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) )
% 0.29/0.61            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % lemma_tan_add1
% 0.29/0.61  thf(fact_7444_tan__diff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61         != zero_zero_real )
% 0.29/0.61       => ( ( ( cos_real @ Y )
% 0.29/0.61           != zero_zero_real )
% 0.29/0.61         => ( ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 0.29/0.61             != zero_zero_real )
% 0.29/0.61           => ( ( tan_real @ ( minus_minus_real @ X4 @ Y ) )
% 0.29/0.61              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_diff
% 0.29/0.61  thf(fact_7445_tan__diff,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61         != zero_zero_complex )
% 0.29/0.61       => ( ( ( cos_complex @ Y )
% 0.29/0.61           != zero_zero_complex )
% 0.29/0.61         => ( ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 0.29/0.61             != zero_zero_complex )
% 0.29/0.61           => ( ( tan_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 0.29/0.61              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_diff
% 0.29/0.61  thf(fact_7446_tan__add,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( cos_real @ X4 )
% 0.29/0.61         != zero_zero_real )
% 0.29/0.61       => ( ( ( cos_real @ Y )
% 0.29/0.61           != zero_zero_real )
% 0.29/0.61         => ( ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61             != zero_zero_real )
% 0.29/0.61           => ( ( tan_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_add
% 0.29/0.61  thf(fact_7447_tan__add,axiom,
% 0.29/0.61      ! [X4: complex,Y: complex] :
% 0.29/0.61        ( ( ( cos_complex @ X4 )
% 0.29/0.61         != zero_zero_complex )
% 0.29/0.61       => ( ( ( cos_complex @ Y )
% 0.29/0.61           != zero_zero_complex )
% 0.29/0.61         => ( ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.61             != zero_zero_complex )
% 0.29/0.61           => ( ( tan_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.61              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_add
% 0.29/0.61  thf(fact_7448_tan__total__pi4,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ? [Z2: real] :
% 0.29/0.61            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 0.29/0.61            & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.29/0.61            & ( ( tan_real @ Z2 )
% 0.29/0.61              = X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_total_pi4
% 0.29/0.61  thf(fact_7449_tan__half,axiom,
% 0.29/0.61      ( tan_real
% 0.29/0.61      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_half
% 0.29/0.61  thf(fact_7450_tan__half,axiom,
% 0.29/0.61      ( tan_complex
% 0.29/0.61      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % tan_half
% 0.29/0.61  thf(fact_7451_arcosh__def,axiom,
% 0.29/0.61      ( arcosh_real
% 0.29/0.61      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcosh_def
% 0.29/0.61  thf(fact_7452_cos__arcsin,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( cos_real @ ( arcsin @ X4 ) )
% 0.29/0.61            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_arcsin
% 0.29/0.61  thf(fact_7453_sin__arccos__abs,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61       => ( ( sin_real @ ( arccos @ Y ) )
% 0.29/0.61          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_arccos_abs
% 0.29/0.61  thf(fact_7454_sin__arccos,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( sin_real @ ( arccos @ X4 ) )
% 0.29/0.61            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_arccos
% 0.29/0.61  thf(fact_7455_arsinh__def,axiom,
% 0.29/0.61      ( arsinh_real
% 0.29/0.61      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arsinh_def
% 0.29/0.61  thf(fact_7456_of__real__eq__1__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( real_V1803761363581548252l_real @ X4 )
% 0.29/0.61          = one_one_real )
% 0.29/0.61        = ( X4 = one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_eq_1_iff
% 0.29/0.61  thf(fact_7457_of__real__eq__1__iff,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( real_V4546457046886955230omplex @ X4 )
% 0.29/0.61          = one_one_complex )
% 0.29/0.61        = ( X4 = one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_eq_1_iff
% 0.29/0.61  thf(fact_7458_of__real__1,axiom,
% 0.29/0.61      ( ( real_V1803761363581548252l_real @ one_one_real )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_1
% 0.29/0.61  thf(fact_7459_of__real__1,axiom,
% 0.29/0.61      ( ( real_V4546457046886955230omplex @ one_one_real )
% 0.29/0.61      = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_1
% 0.29/0.61  thf(fact_7460_of__real__numeral,axiom,
% 0.29/0.61      ! [W: num] :
% 0.29/0.61        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.61        = ( numeral_numeral_real @ W ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_numeral
% 0.29/0.61  thf(fact_7461_of__real__numeral,axiom,
% 0.29/0.61      ! [W: num] :
% 0.29/0.61        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 0.29/0.61        = ( numera6690914467698888265omplex @ W ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_numeral
% 0.29/0.61  thf(fact_7462_of__real__divide,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.61        = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_divide
% 0.29/0.61  thf(fact_7463_of__real__divide,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.61        = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_divide
% 0.29/0.61  thf(fact_7464_of__real__add,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_add
% 0.29/0.61  thf(fact_7465_of__real__add,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.61        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_add
% 0.29/0.61  thf(fact_7466_of__real__power,axiom,
% 0.29/0.61      ! [X4: real,N2: nat] :
% 0.29/0.61        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.61        = ( power_power_real @ ( real_V1803761363581548252l_real @ X4 ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_power
% 0.29/0.61  thf(fact_7467_of__real__power,axiom,
% 0.29/0.61      ! [X4: real,N2: nat] :
% 0.29/0.61        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.61        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X4 ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_power
% 0.29/0.61  thf(fact_7468_arccos__1,axiom,
% 0.29/0.61      ( ( arccos @ one_one_real )
% 0.29/0.61      = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_1
% 0.29/0.61  thf(fact_7469_arccos__minus__1,axiom,
% 0.29/0.61      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.61      = pi ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_minus_1
% 0.29/0.61  thf(fact_7470_of__real__neg__numeral,axiom,
% 0.29/0.61      ! [W: num] :
% 0.29/0.61        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.61        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_neg_numeral
% 0.29/0.61  thf(fact_7471_of__real__neg__numeral,axiom,
% 0.29/0.61      ! [W: num] :
% 0.29/0.61        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.61        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_real_neg_numeral
% 0.29/0.61  thf(fact_7472_cos__of__real__pi,axiom,
% 0.29/0.61      ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 0.29/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_of_real_pi
% 0.29/0.61  thf(fact_7473_cos__of__real__pi,axiom,
% 0.29/0.61      ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 0.29/0.61      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_of_real_pi
% 0.29/0.61  thf(fact_7474_cos__arccos,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( cos_real @ ( arccos @ Y ) )
% 0.29/0.61            = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_arccos
% 0.29/0.61  thf(fact_7475_sin__arcsin,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( sin_real @ ( arcsin @ Y ) )
% 0.29/0.61            = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_arcsin
% 0.29/0.61  thf(fact_7476_norm__of__real__add1,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ one_one_real ) )
% 0.29/0.61        = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_add1
% 0.29/0.61  thf(fact_7477_norm__of__real__add1,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ one_one_complex ) )
% 0.29/0.61        = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_add1
% 0.29/0.61  thf(fact_7478_norm__of__real__addn,axiom,
% 0.29/0.61      ! [X4: real,B: num] :
% 0.29/0.61        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( numeral_numeral_real @ B ) ) )
% 0.29/0.61        = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_addn
% 0.29/0.61  thf(fact_7479_norm__of__real__addn,axiom,
% 0.29/0.61      ! [X4: real,B: num] :
% 0.29/0.61        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 0.29/0.61        = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_addn
% 0.29/0.61  thf(fact_7480_arccos__0,axiom,
% 0.29/0.61      ( ( arccos @ zero_zero_real )
% 0.29/0.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_0
% 0.29/0.61  thf(fact_7481_arcsin__1,axiom,
% 0.29/0.61      ( ( arcsin @ one_one_real )
% 0.29/0.61      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_1
% 0.29/0.61  thf(fact_7482_cos__of__real__pi__half,axiom,
% 0.29/0.61      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_of_real_pi_half
% 0.29/0.61  thf(fact_7483_cos__of__real__pi__half,axiom,
% 0.29/0.61      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = zero_zero_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_of_real_pi_half
% 0.29/0.61  thf(fact_7484_sin__of__real__pi__half,axiom,
% 0.29/0.61      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_of_real_pi_half
% 0.29/0.61  thf(fact_7485_sin__of__real__pi__half,axiom,
% 0.29/0.61      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.29/0.61      = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_of_real_pi_half
% 0.29/0.61  thf(fact_7486_arcsin__minus__1,axiom,
% 0.29/0.61      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 0.29/0.61      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_minus_1
% 0.29/0.61  thf(fact_7487_nonzero__of__real__divide,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( Y != zero_zero_real )
% 0.29/0.61       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.61          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nonzero_of_real_divide
% 0.29/0.61  thf(fact_7488_nonzero__of__real__divide,axiom,
% 0.29/0.61      ! [Y: real,X4: real] :
% 0.29/0.61        ( ( Y != zero_zero_real )
% 0.29/0.61       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 0.29/0.61          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % nonzero_of_real_divide
% 0.29/0.61  thf(fact_7489_arccos__le__arccos,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61           => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_le_arccos
% 0.29/0.61  thf(fact_7490_arccos__le__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 0.29/0.61            = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_le_mono
% 0.29/0.61  thf(fact_7491_arccos__eq__iff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61          & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 0.29/0.61       => ( ( ( arccos @ X4 )
% 0.29/0.61            = ( arccos @ Y ) )
% 0.29/0.61          = ( X4 = Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_eq_iff
% 0.29/0.61  thf(fact_7492_arcsin__minus,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( arcsin @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.61            = ( uminus_uminus_real @ ( arcsin @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_minus
% 0.29/0.61  thf(fact_7493_arcsin__le__arcsin,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61           => ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_le_arcsin
% 0.29/0.61  thf(fact_7494_arcsin__le__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 0.29/0.61            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_le_mono
% 0.29/0.61  thf(fact_7495_arcsin__eq__iff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61         => ( ( ( arcsin @ X4 )
% 0.29/0.61              = ( arcsin @ Y ) )
% 0.29/0.61            = ( X4 = Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_eq_iff
% 0.29/0.61  thf(fact_7496_norm__less__p1,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X4 ) ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_less_p1
% 0.29/0.61  thf(fact_7497_norm__less__p1,axiom,
% 0.29/0.61      ! [X4: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X4 ) ) @ one_one_complex ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_less_p1
% 0.29/0.61  thf(fact_7498_arccos__lbound,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_lbound
% 0.29/0.61  thf(fact_7499_arccos__less__arccos,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.61         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_less_arccos
% 0.29/0.61  thf(fact_7500_arccos__less__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 0.29/0.61            = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_less_mono
% 0.29/0.61  thf(fact_7501_arccos__ubound,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_ubound
% 0.29/0.61  thf(fact_7502_arccos__cos,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.61         => ( ( arccos @ ( cos_real @ X4 ) )
% 0.29/0.61            = X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_cos
% 0.29/0.61  thf(fact_7503_arcsin__less__arcsin,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.61         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61           => ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_less_arcsin
% 0.29/0.61  thf(fact_7504_arcsin__less__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 0.29/0.61            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_less_mono
% 0.29/0.61  thf(fact_7505_cos__arccos__abs,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.29/0.61       => ( ( cos_real @ ( arccos @ Y ) )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_arccos_abs
% 0.29/0.61  thf(fact_7506_norm__of__real__diff,axiom,
% 0.29/0.61      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_diff
% 0.29/0.61  thf(fact_7507_norm__of__real__diff,axiom,
% 0.29/0.61      ! [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 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % norm_of_real_diff
% 0.29/0.61  thf(fact_7508_arccos__cos__eq__abs,axiom,
% 0.29/0.61      ! [Theta: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 0.29/0.61       => ( ( arccos @ ( cos_real @ Theta ) )
% 0.29/0.61          = ( abs_abs_real @ Theta ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_cos_eq_abs
% 0.29/0.61  thf(fact_7509_arccos__lt__bounded,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.29/0.61            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_lt_bounded
% 0.29/0.61  thf(fact_7510_arccos__bounded,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.29/0.61            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_bounded
% 0.29/0.61  thf(fact_7511_sin__arccos__nonzero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( sin_real @ ( arccos @ X4 ) )
% 0.29/0.61           != zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_arccos_nonzero
% 0.29/0.61  thf(fact_7512_arccos__cos2,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.61       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 0.29/0.61         => ( ( arccos @ ( cos_real @ X4 ) )
% 0.29/0.61            = ( uminus_uminus_real @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_cos2
% 0.29/0.61  thf(fact_7513_arccos__minus,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.61            = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_minus
% 0.29/0.61  thf(fact_7514_cos__arcsin__nonzero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( cos_real @ ( arcsin @ X4 ) )
% 0.29/0.61           != zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_arcsin_nonzero
% 0.29/0.61  thf(fact_7515_arccos,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.29/0.61            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 0.29/0.61            & ( ( cos_real @ ( arccos @ Y ) )
% 0.29/0.61              = Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos
% 0.29/0.61  thf(fact_7516_arccos__minus__abs,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.61       => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.61          = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_minus_abs
% 0.29/0.61  thf(fact_7517_cos__sin__eq,axiom,
% 0.29/0.61      ( cos_real
% 0.29/0.61      = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_sin_eq
% 0.29/0.61  thf(fact_7518_cos__sin__eq,axiom,
% 0.29/0.61      ( cos_complex
% 0.29/0.61      = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_sin_eq
% 0.29/0.61  thf(fact_7519_sin__cos__eq,axiom,
% 0.29/0.61      ( sin_real
% 0.29/0.61      = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_eq
% 0.29/0.61  thf(fact_7520_sin__cos__eq,axiom,
% 0.29/0.61      ( sin_complex
% 0.29/0.61      = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_cos_eq
% 0.29/0.61  thf(fact_7521_minus__sin__cos__eq,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( uminus_uminus_real @ ( sin_real @ X4 ) )
% 0.29/0.61        = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % minus_sin_cos_eq
% 0.29/0.61  thf(fact_7522_minus__sin__cos__eq,axiom,
% 0.29/0.61      ! [X4: complex] :
% 0.29/0.61        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X4 ) )
% 0.29/0.61        = ( cos_complex @ ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % minus_sin_cos_eq
% 0.29/0.61  thf(fact_7523_arccos__le__pi2,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arccos_le_pi2
% 0.29/0.61  thf(fact_7524_arcsin__lt__bounded,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.29/0.61            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_lt_bounded
% 0.29/0.61  thf(fact_7525_arcsin__bounded,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.29/0.61            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_bounded
% 0.29/0.61  thf(fact_7526_arcsin__ubound,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_ubound
% 0.29/0.61  thf(fact_7527_arcsin__lbound,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_lbound
% 0.29/0.61  thf(fact_7528_arcsin__sin,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61         => ( ( arcsin @ ( sin_real @ X4 ) )
% 0.29/0.61            = X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_sin
% 0.29/0.61  thf(fact_7529_arcsin,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.29/0.61            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61            & ( ( sin_real @ ( arcsin @ Y ) )
% 0.29/0.61              = Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin
% 0.29/0.61  thf(fact_7530_arcsin__pi,axiom,
% 0.29/0.61      ! [Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.29/0.61       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.29/0.61            & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 0.29/0.61            & ( ( sin_real @ ( arcsin @ Y ) )
% 0.29/0.61              = Y ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_pi
% 0.29/0.61  thf(fact_7531_arcsin__le__iff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ Y )
% 0.29/0.61                = ( ord_less_eq_real @ X4 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % arcsin_le_iff
% 0.29/0.61  thf(fact_7532_le__arcsin__iff,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.61       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.61         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.29/0.61           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.61             => ( ( ord_less_eq_real @ Y @ ( arcsin @ X4 ) )
% 0.29/0.61                = ( ord_less_eq_real @ ( sin_real @ Y ) @ X4 ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_arcsin_iff
% 0.29/0.61  thf(fact_7533_floor__log__nat__eq__powr__iff,axiom,
% 0.29/0.61      ! [B: nat,K: nat,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.61       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.61         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.29/0.61              = ( semiri1314217659103216013at_int @ N2 ) )
% 0.29/0.61            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.29/0.61              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_log_nat_eq_powr_iff
% 0.29/0.61  thf(fact_7534_cos__npi__int,axiom,
% 0.29/0.61      ! [N2: int] :
% 0.29/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 0.29/0.61            = one_one_real ) )
% 0.29/0.61        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.61         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 0.29/0.61            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_npi_int
% 0.29/0.61  thf(fact_7535_cot__less__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.61         => ( ord_less_real @ ( cot_real @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cot_less_zero
% 0.29/0.61  thf(fact_7536_floor__log__nat__eq__if,axiom,
% 0.29/0.61      ! [B: nat,N2: nat,K: nat] :
% 0.29/0.61        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.29/0.61       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 0.29/0.61         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.29/0.61           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.29/0.61              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_log_nat_eq_if
% 0.29/0.61  thf(fact_7537_cot__periodic,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( cot_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.29/0.61        = ( cot_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % cot_periodic
% 0.29/0.61  thf(fact_7538_of__int__floor__cancel,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ? [N: int] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( ring_1_of_int_real @ N ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_floor_cancel
% 0.29/0.61  thf(fact_7539_of__int__floor__cancel,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ? [N: int] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_floor_cancel
% 0.29/0.61  thf(fact_7540_of__int__ceiling__cancel,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ? [N: int] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_ceiling_cancel
% 0.29/0.61  thf(fact_7541_of__int__ceiling__cancel,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.61          = X4 )
% 0.29/0.61        = ( ? [N: int] :
% 0.29/0.61              ( X4
% 0.29/0.61              = ( ring_1_of_int_real @ N ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_ceiling_cancel
% 0.29/0.61  thf(fact_7542_of__int__le__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_iff
% 0.29/0.61  thf(fact_7543_of__int__le__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_iff
% 0.29/0.61  thf(fact_7544_of__int__le__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_iff
% 0.29/0.61  thf(fact_7545_of__int__numeral,axiom,
% 0.29/0.61      ! [K: num] :
% 0.29/0.61        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.29/0.61        = ( numeral_numeral_rat @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral
% 0.29/0.61  thf(fact_7546_of__int__numeral,axiom,
% 0.29/0.61      ! [K: num] :
% 0.29/0.61        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 0.29/0.61        = ( numera6690914467698888265omplex @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral
% 0.29/0.61  thf(fact_7547_of__int__numeral,axiom,
% 0.29/0.61      ! [K: num] :
% 0.29/0.61        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 0.29/0.61        = ( numeral_numeral_real @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral
% 0.29/0.61  thf(fact_7548_of__int__numeral,axiom,
% 0.29/0.61      ! [K: num] :
% 0.29/0.61        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.29/0.61        = ( numeral_numeral_int @ K ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral
% 0.29/0.61  thf(fact_7549_of__int__eq__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ Z )
% 0.29/0.61          = ( numeral_numeral_rat @ N2 ) )
% 0.29/0.61        = ( Z
% 0.29/0.61          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_iff
% 0.29/0.61  thf(fact_7550_of__int__eq__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.29/0.61          = ( numera6690914467698888265omplex @ N2 ) )
% 0.29/0.61        = ( Z
% 0.29/0.61          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_iff
% 0.29/0.61  thf(fact_7551_of__int__eq__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ Z )
% 0.29/0.61          = ( numeral_numeral_real @ N2 ) )
% 0.29/0.61        = ( Z
% 0.29/0.61          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_iff
% 0.29/0.61  thf(fact_7552_of__int__eq__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ( ring_1_of_int_int @ Z )
% 0.29/0.61          = ( numeral_numeral_int @ N2 ) )
% 0.29/0.61        = ( Z
% 0.29/0.61          = ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_iff
% 0.29/0.61  thf(fact_7553_of__int__less__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_iff
% 0.29/0.61  thf(fact_7554_of__int__less__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_iff
% 0.29/0.61  thf(fact_7555_of__int__less__iff,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_int @ W @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_iff
% 0.29/0.61  thf(fact_7556_of__int__1,axiom,
% 0.29/0.61      ( ( ring_17405671764205052669omplex @ one_one_int )
% 0.29/0.61      = one_one_complex ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1
% 0.29/0.61  thf(fact_7557_of__int__1,axiom,
% 0.29/0.61      ( ( ring_1_of_int_int @ one_one_int )
% 0.29/0.61      = one_one_int ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1
% 0.29/0.61  thf(fact_7558_of__int__1,axiom,
% 0.29/0.61      ( ( ring_1_of_int_real @ one_one_int )
% 0.29/0.61      = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1
% 0.29/0.61  thf(fact_7559_of__int__1,axiom,
% 0.29/0.61      ( ( ring_1_of_int_rat @ one_one_int )
% 0.29/0.61      = one_one_rat ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1
% 0.29/0.61  thf(fact_7560_of__int__eq__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.29/0.61          = one_one_complex )
% 0.29/0.61        = ( Z = one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_1_iff
% 0.29/0.61  thf(fact_7561_of__int__eq__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ( ring_1_of_int_int @ Z )
% 0.29/0.61          = one_one_int )
% 0.29/0.61        = ( Z = one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_1_iff
% 0.29/0.61  thf(fact_7562_of__int__eq__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ Z )
% 0.29/0.61          = one_one_real )
% 0.29/0.61        = ( Z = one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_1_iff
% 0.29/0.61  thf(fact_7563_of__int__eq__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ Z )
% 0.29/0.61          = one_one_rat )
% 0.29/0.61        = ( Z = one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_1_iff
% 0.29/0.61  thf(fact_7564_of__int__add,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 0.29/0.61        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_add
% 0.29/0.61  thf(fact_7565_of__int__add,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 0.29/0.61        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_add
% 0.29/0.61  thf(fact_7566_of__int__add,axiom,
% 0.29/0.61      ! [W: int,Z: int] :
% 0.29/0.61        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 0.29/0.61        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_add
% 0.29/0.61  thf(fact_7567_floor__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 0.29/0.61        = ( numeral_numeral_int @ V ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_numeral
% 0.29/0.61  thf(fact_7568_floor__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 0.29/0.61        = ( numeral_numeral_int @ V ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_numeral
% 0.29/0.61  thf(fact_7569_floor__one,axiom,
% 0.29/0.61      ( ( archim6058952711729229775r_real @ one_one_real )
% 0.29/0.61      = one_one_int ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_one
% 0.29/0.61  thf(fact_7570_floor__one,axiom,
% 0.29/0.61      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.29/0.61      = one_one_int ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_one
% 0.29/0.61  thf(fact_7571_of__int__power,axiom,
% 0.29/0.61      ! [Z: int,N2: nat] :
% 0.29/0.61        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N2 ) )
% 0.29/0.61        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power
% 0.29/0.61  thf(fact_7572_of__int__power,axiom,
% 0.29/0.61      ! [Z: int,N2: nat] :
% 0.29/0.61        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 0.29/0.61        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power
% 0.29/0.61  thf(fact_7573_of__int__power,axiom,
% 0.29/0.61      ! [Z: int,N2: nat] :
% 0.29/0.61        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 0.29/0.61        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power
% 0.29/0.61  thf(fact_7574_of__int__power,axiom,
% 0.29/0.61      ! [Z: int,N2: nat] :
% 0.29/0.61        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 0.29/0.61        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power
% 0.29/0.61  thf(fact_7575_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 0.29/0.61          = ( ring_1_of_int_rat @ X4 ) )
% 0.29/0.61        = ( ( power_power_int @ B @ W )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7576_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 0.29/0.61          = ( ring_1_of_int_real @ X4 ) )
% 0.29/0.61        = ( ( power_power_int @ B @ W )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7577_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 0.29/0.61          = ( ring_1_of_int_int @ X4 ) )
% 0.29/0.61        = ( ( power_power_int @ B @ W )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7578_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 0.29/0.61          = ( ring_17405671764205052669omplex @ X4 ) )
% 0.29/0.61        = ( ( power_power_int @ B @ W )
% 0.29/0.61          = X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7579_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ X4 )
% 0.29/0.61          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.29/0.61        = ( X4
% 0.29/0.61          = ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7580_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ X4 )
% 0.29/0.61          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.29/0.61        = ( X4
% 0.29/0.61          = ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7581_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_int @ X4 )
% 0.29/0.61          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.29/0.61        = ( X4
% 0.29/0.61          = ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7582_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ( ring_17405671764205052669omplex @ X4 )
% 0.29/0.61          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 0.29/0.61        = ( X4
% 0.29/0.61          = ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7583_ceiling__add__of__int,axiom,
% 0.29/0.61      ! [X4: rat,Z: int] :
% 0.29/0.61        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_of_int
% 0.29/0.61  thf(fact_7584_ceiling__add__of__int,axiom,
% 0.29/0.61      ! [X4: real,Z: int] :
% 0.29/0.61        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 0.29/0.61        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ceiling_add_of_int
% 0.29/0.61  thf(fact_7585_of__nat__nat__take__bit__eq,axiom,
% 0.29/0.61      ! [N2: nat,K: int] :
% 0.29/0.61        ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 0.29/0.61        = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat_take_bit_eq
% 0.29/0.61  thf(fact_7586_of__nat__nat__take__bit__eq,axiom,
% 0.29/0.61      ! [N2: nat,K: int] :
% 0.29/0.61        ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 0.29/0.61        = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat_take_bit_eq
% 0.29/0.61  thf(fact_7587_of__nat__nat__take__bit__eq,axiom,
% 0.29/0.61      ! [N2: nat,K: int] :
% 0.29/0.61        ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 0.29/0.61        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat_take_bit_eq
% 0.29/0.61  thf(fact_7588_of__int__0__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_le_iff
% 0.29/0.61  thf(fact_7589_of__int__0__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_le_iff
% 0.29/0.61  thf(fact_7590_of__int__0__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_le_iff
% 0.29/0.61  thf(fact_7591_of__int__le__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_0_iff
% 0.29/0.61  thf(fact_7592_of__int__le__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_0_iff
% 0.29/0.61  thf(fact_7593_of__int__le__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_0_iff
% 0.29/0.61  thf(fact_7594_of__int__0__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_less_iff
% 0.29/0.61  thf(fact_7595_of__int__0__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_less_iff
% 0.29/0.61  thf(fact_7596_of__int__0__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_0_less_iff
% 0.29/0.61  thf(fact_7597_of__int__less__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.29/0.61        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_0_iff
% 0.29/0.61  thf(fact_7598_of__int__less__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.29/0.61        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_0_iff
% 0.29/0.61  thf(fact_7599_of__int__less__0__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_0_iff
% 0.29/0.61  thf(fact_7600_of__int__numeral__le__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_le_iff
% 0.29/0.61  thf(fact_7601_of__int__numeral__le__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_le_iff
% 0.29/0.61  thf(fact_7602_of__int__numeral__le__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_le_iff
% 0.29/0.61  thf(fact_7603_of__int__le__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_iff
% 0.29/0.61  thf(fact_7604_of__int__le__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_iff
% 0.29/0.61  thf(fact_7605_of__int__le__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_iff
% 0.29/0.61  thf(fact_7606_of__int__less__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_iff
% 0.29/0.61  thf(fact_7607_of__int__less__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_iff
% 0.29/0.61  thf(fact_7608_of__int__less__numeral__iff,axiom,
% 0.29/0.61      ! [Z: int,N2: num] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_iff
% 0.29/0.61  thf(fact_7609_of__int__numeral__less__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_less_iff
% 0.29/0.61  thf(fact_7610_of__int__numeral__less__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_less_iff
% 0.29/0.61  thf(fact_7611_of__int__numeral__less__iff,axiom,
% 0.29/0.61      ! [N2: num,Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_numeral_less_iff
% 0.29/0.61  thf(fact_7612_of__int__le__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_1_iff
% 0.29/0.61  thf(fact_7613_of__int__le__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_1_iff
% 0.29/0.61  thf(fact_7614_of__int__le__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.29/0.61        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_1_iff
% 0.29/0.61  thf(fact_7615_of__int__1__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_le_iff
% 0.29/0.61  thf(fact_7616_of__int__1__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_le_iff
% 0.29/0.61  thf(fact_7617_of__int__1__le__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_le_iff
% 0.29/0.61  thf(fact_7618_zero__le__floor,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_le_floor
% 0.29/0.61  thf(fact_7619_zero__le__floor,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ zero_zero_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_le_floor
% 0.29/0.61  thf(fact_7620_of__int__1__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.61        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_less_iff
% 0.29/0.61  thf(fact_7621_of__int__1__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.61        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_less_iff
% 0.29/0.61  thf(fact_7622_of__int__1__less__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.29/0.61        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_1_less_iff
% 0.29/0.61  thf(fact_7623_of__int__less__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.29/0.61        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_1_iff
% 0.29/0.61  thf(fact_7624_of__int__less__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.29/0.61        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_1_iff
% 0.29/0.61  thf(fact_7625_of__int__less__1__iff,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.29/0.61        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_1_iff
% 0.29/0.61  thf(fact_7626_floor__less__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_zero
% 0.29/0.61  thf(fact_7627_floor__less__zero,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_rat @ X4 @ zero_zero_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_zero
% 0.29/0.61  thf(fact_7628_numeral__le__floor,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_le_floor
% 0.29/0.61  thf(fact_7629_numeral__le__floor,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_le_floor
% 0.29/0.61  thf(fact_7630_zero__less__floor,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_floor
% 0.29/0.61  thf(fact_7631_zero__less__floor,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % zero_less_floor
% 0.29/0.61  thf(fact_7632_floor__le__zero,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_zero
% 0.29/0.61  thf(fact_7633_floor__le__zero,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 0.29/0.61        = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_zero
% 0.29/0.61  thf(fact_7634_floor__less__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_numeral
% 0.29/0.61  thf(fact_7635_floor__less__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_numeral
% 0.29/0.61  thf(fact_7636_one__le__floor,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_le_floor
% 0.29/0.61  thf(fact_7637_one__le__floor,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_le_floor
% 0.29/0.61  thf(fact_7638_floor__less__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_one
% 0.29/0.61  thf(fact_7639_floor__less__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_one
% 0.29/0.61  thf(fact_7640_floor__neg__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_neg_numeral
% 0.29/0.61  thf(fact_7641_floor__neg__numeral,axiom,
% 0.29/0.61      ! [V: num] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.29/0.61        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_neg_numeral
% 0.29/0.61  thf(fact_7642_floor__diff__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_diff_numeral
% 0.29/0.61  thf(fact_7643_floor__diff__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_diff_numeral
% 0.29/0.61  thf(fact_7644_of__int__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7645_of__int__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7646_of__int__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7647_of__int__le__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7648_of__int__le__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7649_of__int__le__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7650_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_rat @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7651_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 0.29/0.61          = ( ring_17405671764205052669omplex @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7652_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_real @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7653_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_int @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7654_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ Y )
% 0.29/0.61          = ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7655_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.29/0.61          = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7656_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ Y )
% 0.29/0.61          = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7657_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_int @ Y )
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7658_floor__diff__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_diff_one
% 0.29/0.61  thf(fact_7659_floor__diff__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 0.29/0.61        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_diff_one
% 0.29/0.61  thf(fact_7660_of__int__less__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7661_of__int__less__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7662_of__int__less__of__int__power__cancel__iff,axiom,
% 0.29/0.61      ! [B: int,W: nat,X4: int] :
% 0.29/0.61        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_of_int_power_cancel_iff
% 0.29/0.61  thf(fact_7663_of__int__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7664_of__int__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7665_of__int__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: int,B: int,W: nat] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.29/0.61        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7666_of__nat__nat,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat
% 0.29/0.61  thf(fact_7667_of__nat__nat,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat
% 0.29/0.61  thf(fact_7668_of__nat__nat,axiom,
% 0.29/0.61      ! [Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.61       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.29/0.61          = ( ring_1_of_int_int @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_nat_nat
% 0.29/0.61  thf(fact_7669_floor__numeral__power,axiom,
% 0.29/0.61      ! [X4: num,N2: nat] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.61        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_numeral_power
% 0.29/0.61  thf(fact_7670_floor__numeral__power,axiom,
% 0.29/0.61      ! [X4: num,N2: nat] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_numeral_power
% 0.29/0.61  thf(fact_7671_floor__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [A: num,B: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.29/0.61        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7672_numeral__less__floor,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_less_floor
% 0.29/0.61  thf(fact_7673_numeral__less__floor,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_less_floor
% 0.29/0.61  thf(fact_7674_floor__le__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_numeral
% 0.29/0.61  thf(fact_7675_floor__le__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_numeral
% 0.29/0.61  thf(fact_7676_one__less__floor,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_floor
% 0.29/0.61  thf(fact_7677_one__less__floor,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % one_less_floor
% 0.29/0.61  thf(fact_7678_floor__le__one,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_one
% 0.29/0.61  thf(fact_7679_floor__le__one,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_one
% 0.29/0.61  thf(fact_7680_neg__numeral__le__floor,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_le_floor
% 0.29/0.61  thf(fact_7681_neg__numeral__le__floor,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_le_floor
% 0.29/0.61  thf(fact_7682_floor__less__neg__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_neg_numeral
% 0.29/0.61  thf(fact_7683_floor__less__neg__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_neg_numeral
% 0.29/0.61  thf(fact_7684_numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7685_numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7686_numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7687_of__int__le__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7688_of__int__le__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7689_of__int__le__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7690_numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7691_numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7692_numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7693_of__int__less__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7694_of__int__less__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7695_of__int__less__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7696_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_real @ Y )
% 0.29/0.61          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7697_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_int @ Y )
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7698_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.29/0.61          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7699_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.29/0.61          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7700_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [Y: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ( ring_1_of_int_rat @ Y )
% 0.29/0.61          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( Y
% 0.29/0.61          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_eq_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7701_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_real @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7702_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_int @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7703_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 )
% 0.29/0.61          = ( ring_17405671764205052669omplex @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7704_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 )
% 0.29/0.61          = ( ring_18347121197199848620nteger @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7705_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,Y: int] :
% 0.29/0.61        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 )
% 0.29/0.61          = ( ring_1_of_int_rat @ Y ) )
% 0.29/0.61        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 0.29/0.61          = Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_eq_of_int_cancel_iff
% 0.29/0.61  thf(fact_7706_floor__one__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [B: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 0.29/0.61        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_one_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7707_floor__minus__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [A: num,B: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.29/0.61        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_minus_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7708_sin__int__2pin,axiom,
% 0.29/0.61      ! [N2: int] :
% 0.29/0.61        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 0.29/0.61        = zero_zero_real ) ).
% 0.29/0.61  
% 0.29/0.61  % sin_int_2pin
% 0.29/0.61  thf(fact_7709_cos__int__2pin,axiom,
% 0.29/0.61      ! [N2: int] :
% 0.29/0.61        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 0.29/0.61        = one_one_real ) ).
% 0.29/0.61  
% 0.29/0.61  % cos_int_2pin
% 0.29/0.61  thf(fact_7710_neg__numeral__less__floor,axiom,
% 0.29/0.61      ! [V: num,X4: real] :
% 0.29/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_less_floor
% 0.29/0.61  thf(fact_7711_neg__numeral__less__floor,axiom,
% 0.29/0.61      ! [V: num,X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_less_floor
% 0.29/0.61  thf(fact_7712_floor__le__neg__numeral,axiom,
% 0.29/0.61      ! [X4: real,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_neg_numeral
% 0.29/0.61  thf(fact_7713_floor__le__neg__numeral,axiom,
% 0.29/0.61      ! [X4: rat,V: num] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_neg_numeral
% 0.29/0.61  thf(fact_7714_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7715_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7716_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7717_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_le_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7718_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7719_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7720_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7721_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.29/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_le_of_int_cancel_iff
% 0.29/0.61  thf(fact_7722_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7723_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7724_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7725_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.29/0.61      ! [X4: num,N2: nat,A: int] :
% 0.29/0.61        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 0.29/0.61        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 0.29/0.61  
% 0.29/0.61  % neg_numeral_power_less_of_int_cancel_iff
% 0.29/0.61  thf(fact_7726_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7727_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7728_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7729_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.29/0.61      ! [A: int,X4: num,N2: nat] :
% 0.29/0.61        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 0.29/0.61        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_less_neg_numeral_power_cancel_iff
% 0.29/0.61  thf(fact_7730_floor__minus__one__divide__eq__div__numeral,axiom,
% 0.29/0.61      ! [B: num] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 0.29/0.61        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_minus_one_divide_eq_div_numeral
% 0.29/0.61  thf(fact_7731_ex__le__of__int,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_le_of_int
% 0.29/0.61  thf(fact_7732_ex__le__of__int,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_le_of_int
% 0.29/0.61  thf(fact_7733_ex__of__int__less,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X4 ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_of_int_less
% 0.29/0.61  thf(fact_7734_ex__of__int__less,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_of_int_less
% 0.29/0.61  thf(fact_7735_ex__less__of__int,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_less_of_int
% 0.29/0.61  thf(fact_7736_ex__less__of__int,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61      ? [Z2: int] : ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % ex_less_of_int
% 0.29/0.61  thf(fact_7737_int__add__floor,axiom,
% 0.29/0.61      ! [Z: int,X4: real] :
% 0.29/0.61        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % int_add_floor
% 0.29/0.61  thf(fact_7738_int__add__floor,axiom,
% 0.29/0.61      ! [Z: int,X4: rat] :
% 0.29/0.61        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % int_add_floor
% 0.29/0.61  thf(fact_7739_floor__add__int,axiom,
% 0.29/0.61      ! [X4: real,Z: int] :
% 0.29/0.61        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 0.29/0.61        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_add_int
% 0.29/0.61  thf(fact_7740_floor__add__int,axiom,
% 0.29/0.61      ! [X4: rat,Z: int] :
% 0.29/0.61        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 0.29/0.61        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_add_int
% 0.29/0.61  thf(fact_7741_floor__divide__of__int__eq,axiom,
% 0.29/0.61      ! [K: int,L: int] :
% 0.29/0.61        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 0.29/0.61        = ( divide_divide_int @ K @ L ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_of_int_eq
% 0.29/0.61  thf(fact_7742_floor__divide__of__int__eq,axiom,
% 0.29/0.61      ! [K: int,L: int] :
% 0.29/0.61        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 0.29/0.61        = ( divide_divide_int @ K @ L ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_of_int_eq
% 0.29/0.61  thf(fact_7743_of__int__floor__le,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_floor_le
% 0.29/0.61  thf(fact_7744_of__int__floor__le,axiom,
% 0.29/0.61      ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_floor_le
% 0.29/0.61  thf(fact_7745_floor__less__iff,axiom,
% 0.29/0.61      ! [X4: real,Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_iff
% 0.29/0.61  thf(fact_7746_floor__less__iff,axiom,
% 0.29/0.61      ! [X4: rat,Z: int] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_iff
% 0.29/0.61  thf(fact_7747_le__floor__iff,axiom,
% 0.29/0.61      ! [Z: int,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_floor_iff
% 0.29/0.61  thf(fact_7748_le__floor__iff,axiom,
% 0.29/0.61      ! [Z: int,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_floor_iff
% 0.29/0.61  thf(fact_7749_floor__power,axiom,
% 0.29/0.61      ! [X4: real,N2: nat] :
% 0.29/0.61        ( ( X4
% 0.29/0.61          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) )
% 0.29/0.61       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.61          = ( power_power_int @ ( archim6058952711729229775r_real @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_power
% 0.29/0.61  thf(fact_7750_floor__power,axiom,
% 0.29/0.61      ! [X4: rat,N2: nat] :
% 0.29/0.61        ( ( X4
% 0.29/0.61          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) )
% 0.29/0.61       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X4 @ N2 ) )
% 0.29/0.61          = ( power_power_int @ ( archim3151403230148437115or_rat @ X4 ) @ N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_power
% 0.29/0.61  thf(fact_7751_real__of__int__floor__add__one__gt,axiom,
% 0.29/0.61      ! [R3: real] : ( ord_less_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_of_int_floor_add_one_gt
% 0.29/0.61  thf(fact_7752_floor__eq,axiom,
% 0.29/0.61      ! [N2: int,X4: real] :
% 0.29/0.61        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 0.29/0.61         => ( ( archim6058952711729229775r_real @ X4 )
% 0.29/0.61            = N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_eq
% 0.29/0.61  thf(fact_7753_real__of__int__floor__add__one__ge,axiom,
% 0.29/0.61      ! [R3: real] : ( ord_less_eq_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_of_int_floor_add_one_ge
% 0.29/0.61  thf(fact_7754_real__of__int__floor__gt__diff__one,axiom,
% 0.29/0.61      ! [R3: real] : ( ord_less_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_of_int_floor_gt_diff_one
% 0.29/0.61  thf(fact_7755_real__of__int__floor__ge__diff__one,axiom,
% 0.29/0.61      ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % real_of_int_floor_ge_diff_one
% 0.29/0.61  thf(fact_7756_floor__split,axiom,
% 0.29/0.61      ! [P: int > $o,T2: real] :
% 0.29/0.61        ( ( P @ ( archim6058952711729229775r_real @ T2 ) )
% 0.29/0.61        = ( ! [I3: int] :
% 0.29/0.61              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T2 )
% 0.29/0.61                & ( ord_less_real @ T2 @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 0.29/0.61             => ( P @ I3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_split
% 0.29/0.61  thf(fact_7757_floor__split,axiom,
% 0.29/0.61      ! [P: int > $o,T2: rat] :
% 0.29/0.61        ( ( P @ ( archim3151403230148437115or_rat @ T2 ) )
% 0.29/0.61        = ( ! [I3: int] :
% 0.29/0.61              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T2 )
% 0.29/0.61                & ( ord_less_rat @ T2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 0.29/0.61             => ( P @ I3 ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_split
% 0.29/0.61  thf(fact_7758_floor__eq__iff,axiom,
% 0.29/0.61      ! [X4: real,A: int] :
% 0.29/0.61        ( ( ( archim6058952711729229775r_real @ X4 )
% 0.29/0.61          = A )
% 0.29/0.61        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X4 )
% 0.29/0.61          & ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_eq_iff
% 0.29/0.61  thf(fact_7759_floor__eq__iff,axiom,
% 0.29/0.61      ! [X4: rat,A: int] :
% 0.29/0.61        ( ( ( archim3151403230148437115or_rat @ X4 )
% 0.29/0.61          = A )
% 0.29/0.61        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X4 )
% 0.29/0.61          & ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_eq_iff
% 0.29/0.61  thf(fact_7760_floor__unique,axiom,
% 0.29/0.61      ! [Z: int,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 0.29/0.61         => ( ( archim6058952711729229775r_real @ X4 )
% 0.29/0.61            = Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_unique
% 0.29/0.61  thf(fact_7761_floor__unique,axiom,
% 0.29/0.61      ! [Z: int,X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 )
% 0.29/0.61       => ( ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 0.29/0.61         => ( ( archim3151403230148437115or_rat @ X4 )
% 0.29/0.61            = Z ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_unique
% 0.29/0.61  thf(fact_7762_less__floor__iff,axiom,
% 0.29/0.61      ! [Z: int,X4: real] :
% 0.29/0.61        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_floor_iff
% 0.29/0.61  thf(fact_7763_less__floor__iff,axiom,
% 0.29/0.61      ! [Z: int,X4: rat] :
% 0.29/0.61        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 0.29/0.61        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % less_floor_iff
% 0.29/0.61  thf(fact_7764_floor__le__iff,axiom,
% 0.29/0.61      ! [X4: real,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 0.29/0.61        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_iff
% 0.29/0.61  thf(fact_7765_floor__le__iff,axiom,
% 0.29/0.61      ! [X4: rat,Z: int] :
% 0.29/0.61        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 0.29/0.61        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_iff
% 0.29/0.61  thf(fact_7766_floor__correct,axiom,
% 0.29/0.61      ! [X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 )
% 0.29/0.61        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_correct
% 0.29/0.61  thf(fact_7767_floor__correct,axiom,
% 0.29/0.61      ! [X4: rat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 )
% 0.29/0.61        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_correct
% 0.29/0.61  thf(fact_7768_floor__eq2,axiom,
% 0.29/0.61      ! [N2: int,X4: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 0.29/0.61       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 0.29/0.61         => ( ( archim6058952711729229775r_real @ X4 )
% 0.29/0.61            = N2 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_eq2
% 0.29/0.61  thf(fact_7769_floor__divide__real__eq__div,axiom,
% 0.29/0.61      ! [B: int,A: real] :
% 0.29/0.61        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.29/0.61       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 0.29/0.61          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_real_eq_div
% 0.29/0.61  thf(fact_7770_floor__mono,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.61       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_mono
% 0.29/0.61  thf(fact_7771_floor__mono,axiom,
% 0.29/0.61      ! [X4: rat,Y: rat] :
% 0.29/0.61        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.61       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_mono
% 0.29/0.61  thf(fact_7772_floor__less__cancel,axiom,
% 0.29/0.61      ! [X4: real,Y: real] :
% 0.29/0.61        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) )
% 0.29/0.61       => ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_cancel
% 0.29/0.61  thf(fact_7773_floor__less__cancel,axiom,
% 0.29/0.61      ! [X4: rat,Y: rat] :
% 0.29/0.61        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 0.29/0.61       => ( ord_less_rat @ X4 @ Y ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_less_cancel
% 0.29/0.61  thf(fact_7774_floor__le__ceiling,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_ceiling
% 0.29/0.61  thf(fact_7775_floor__le__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_le_ceiling
% 0.29/0.61  thf(fact_7776_le__of__int__ceiling,axiom,
% 0.29/0.61      ! [X4: real] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_of_int_ceiling
% 0.29/0.61  thf(fact_7777_le__of__int__ceiling,axiom,
% 0.29/0.61      ! [X4: rat] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % le_of_int_ceiling
% 0.29/0.61  thf(fact_7778_floor__divide__lower,axiom,
% 0.29/0.61      ! [Q3: real,P2: real] :
% 0.29/0.61        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.29/0.61       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_lower
% 0.29/0.61  thf(fact_7779_floor__divide__lower,axiom,
% 0.29/0.61      ! [Q3: rat,P2: rat] :
% 0.29/0.61        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.29/0.61       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 0.29/0.61  
% 0.29/0.61  % floor_divide_lower
% 0.29/0.61  thf(fact_7780_take__bit__of__int,axiom,
% 0.29/0.61      ! [N2: nat,K: int] :
% 0.29/0.61        ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 0.29/0.61        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % take_bit_of_int
% 0.29/0.61  thf(fact_7781_of__int__and__eq,axiom,
% 0.29/0.61      ! [K: int,L: int] :
% 0.29/0.61        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.29/0.61        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 0.29/0.61  
% 0.29/0.61  % of_int_and_eq
% 0.29/0.62  thf(fact_7782_of__int__not__eq,axiom,
% 0.29/0.62      ! [K: int] :
% 0.29/0.62        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.29/0.62        = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_not_eq
% 0.29/0.62  thf(fact_7783_of__int__xor__eq,axiom,
% 0.29/0.62      ! [K: int,L: int] :
% 0.29/0.62        ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.29/0.62        = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_xor_eq
% 0.29/0.62  thf(fact_7784_of__int__mask__eq,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.62        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_mask_eq
% 0.29/0.62  thf(fact_7785_floor__divide__upper,axiom,
% 0.29/0.62      ! [Q3: real,P2: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.29/0.62       => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_divide_upper
% 0.29/0.62  thf(fact_7786_floor__divide__upper,axiom,
% 0.29/0.62      ! [Q3: rat,P2: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.29/0.62       => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_divide_upper
% 0.29/0.62  thf(fact_7787_le__floor__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_floor_add
% 0.29/0.62  thf(fact_7788_le__floor__add,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_floor_add
% 0.29/0.62  thf(fact_7789_ceiling__le,axiom,
% 0.29/0.62      ! [X4: real,A: int] :
% 0.29/0.62        ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) )
% 0.29/0.62       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_le
% 0.29/0.62  thf(fact_7790_ceiling__le,axiom,
% 0.29/0.62      ! [X4: rat,A: int] :
% 0.29/0.62        ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) )
% 0.29/0.62       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_le
% 0.29/0.62  thf(fact_7791_ceiling__le__iff,axiom,
% 0.29/0.62      ! [X4: real,Z: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 0.29/0.62        = ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_le_iff
% 0.29/0.62  thf(fact_7792_ceiling__le__iff,axiom,
% 0.29/0.62      ! [X4: rat,Z: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 0.29/0.62        = ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_le_iff
% 0.29/0.62  thf(fact_7793_less__ceiling__iff,axiom,
% 0.29/0.62      ! [Z: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.62        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_ceiling_iff
% 0.29/0.62  thf(fact_7794_less__ceiling__iff,axiom,
% 0.29/0.62      ! [Z: int,X4: real] :
% 0.29/0.62        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.62        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_ceiling_iff
% 0.29/0.62  thf(fact_7795_real__of__int__div4,axiom,
% 0.29/0.62      ! [N2: int,X4: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_of_int_div4
% 0.29/0.62  thf(fact_7796_real__of__int__div,axiom,
% 0.29/0.62      ! [D: int,N2: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ D @ N2 )
% 0.29/0.62       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 0.29/0.62          = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_of_int_div
% 0.29/0.62  thf(fact_7797_of__nat__floor,axiom,
% 0.29/0.62      ! [R3: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 0.29/0.62       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R3 ) ) ) @ R3 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_floor
% 0.29/0.62  thf(fact_7798_of__nat__floor,axiom,
% 0.29/0.62      ! [R3: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 0.29/0.62       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R3 ) ) ) @ R3 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_floor
% 0.29/0.62  thf(fact_7799_one__add__floor,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 0.29/0.62        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_add_floor
% 0.29/0.62  thf(fact_7800_one__add__floor,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 0.29/0.62        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_add_floor
% 0.29/0.62  thf(fact_7801_le__mult__nat__floor,axiom,
% 0.29/0.62      ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_nat_floor
% 0.29/0.62  thf(fact_7802_le__mult__nat__floor,axiom,
% 0.29/0.62      ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_nat_floor
% 0.29/0.62  thf(fact_7803_floor__divide__of__nat__eq,axiom,
% 0.29/0.62      ! [M: nat,N2: nat] :
% 0.29/0.62        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.62        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_divide_of_nat_eq
% 0.29/0.62  thf(fact_7804_floor__divide__of__nat__eq,axiom,
% 0.29/0.62      ! [M: nat,N2: nat] :
% 0.29/0.62        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) )
% 0.29/0.62        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_divide_of_nat_eq
% 0.29/0.62  thf(fact_7805_nat__floor__neg,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.62       => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.62          = zero_zero_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_floor_neg
% 0.29/0.62  thf(fact_7806_floor__log__eq__powr__iff,axiom,
% 0.29/0.62      ! [X4: real,B: real,K: int] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.62         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X4 ) )
% 0.29/0.62              = K )
% 0.29/0.62            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X4 )
% 0.29/0.62              & ( ord_less_real @ X4 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_log_eq_powr_iff
% 0.29/0.62  thf(fact_7807_of__int__nonneg,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_nonneg
% 0.29/0.62  thf(fact_7808_of__int__nonneg,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_nonneg
% 0.29/0.62  thf(fact_7809_of__int__nonneg,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_nonneg
% 0.29/0.62  thf(fact_7810_of__int__leD,axiom,
% 0.29/0.62      ! [N2: int,X4: code_integer] :
% 0.29/0.62        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_leD
% 0.29/0.62  thf(fact_7811_of__int__leD,axiom,
% 0.29/0.62      ! [N2: int,X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_leD
% 0.29/0.62  thf(fact_7812_of__int__leD,axiom,
% 0.29/0.62      ! [N2: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_leD
% 0.29/0.62  thf(fact_7813_of__int__leD,axiom,
% 0.29/0.62      ! [N2: int,X4: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_eq_int @ one_one_int @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_leD
% 0.29/0.62  thf(fact_7814_of__int__pos,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_pos
% 0.29/0.62  thf(fact_7815_of__int__pos,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_pos
% 0.29/0.62  thf(fact_7816_of__int__pos,axiom,
% 0.29/0.62      ! [Z: int] :
% 0.29/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.29/0.62       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_pos
% 0.29/0.62  thf(fact_7817_of__int__lessD,axiom,
% 0.29/0.62      ! [N2: int,X4: code_integer] :
% 0.29/0.62        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_lessD
% 0.29/0.62  thf(fact_7818_of__int__lessD,axiom,
% 0.29/0.62      ! [N2: int,X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_lessD
% 0.29/0.62  thf(fact_7819_of__int__lessD,axiom,
% 0.29/0.62      ! [N2: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_lessD
% 0.29/0.62  thf(fact_7820_of__int__lessD,axiom,
% 0.29/0.62      ! [N2: int,X4: int] :
% 0.29/0.62        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 0.29/0.62       => ( ( N2 = zero_zero_int )
% 0.29/0.62          | ( ord_less_int @ one_one_int @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_lessD
% 0.29/0.62  thf(fact_7821_floor__eq3,axiom,
% 0.29/0.62      ! [N2: nat,X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.29/0.62         => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.62            = N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_eq3
% 0.29/0.62  thf(fact_7822_le__nat__floor,axiom,
% 0.29/0.62      ! [X4: nat,A: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ A )
% 0.29/0.62       => ( ord_less_eq_nat @ X4 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_nat_floor
% 0.29/0.62  thf(fact_7823_floor__exists1,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62      ? [X5: int] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X4 )
% 0.29/0.62        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 0.29/0.62        & ! [Y4: int] :
% 0.29/0.62            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X4 )
% 0.29/0.62              & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 0.29/0.62           => ( Y4 = X5 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_exists1
% 0.29/0.62  thf(fact_7824_floor__exists1,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62      ? [X5: int] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X4 )
% 0.29/0.62        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 0.29/0.62        & ! [Y4: int] :
% 0.29/0.62            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X4 )
% 0.29/0.62              & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 0.29/0.62           => ( Y4 = X5 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_exists1
% 0.29/0.62  thf(fact_7825_floor__exists,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62      ? [Z2: int] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 0.29/0.62        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_exists
% 0.29/0.62  thf(fact_7826_floor__exists,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62      ? [Z2: int] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 0.29/0.62        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_exists
% 0.29/0.62  thf(fact_7827_of__int__ceiling__le__add__one,axiom,
% 0.29/0.62      ! [R3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ ( plus_plus_real @ R3 @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_ceiling_le_add_one
% 0.29/0.62  thf(fact_7828_of__int__ceiling__le__add__one,axiom,
% 0.29/0.62      ! [R3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ ( plus_plus_rat @ R3 @ one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_ceiling_le_add_one
% 0.29/0.62  thf(fact_7829_of__int__neg__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_neg_numeral
% 0.29/0.62  thf(fact_7830_of__int__neg__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_neg_numeral
% 0.29/0.62  thf(fact_7831_of__int__neg__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_neg_numeral
% 0.29/0.62  thf(fact_7832_of__int__neg__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_neg_numeral
% 0.29/0.62  thf(fact_7833_of__int__neg__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_neg_numeral
% 0.29/0.62  thf(fact_7834_of__int__ceiling__diff__one__le,axiom,
% 0.29/0.62      ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ one_one_real ) @ R3 ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_ceiling_diff_one_le
% 0.29/0.62  thf(fact_7835_of__int__ceiling__diff__one__le,axiom,
% 0.29/0.62      ! [R3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ one_one_rat ) @ R3 ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_ceiling_diff_one_le
% 0.29/0.62  thf(fact_7836_ceiling__diff__floor__le__1,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim6058952711729229775r_real @ X4 ) ) @ one_one_int ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_diff_floor_le_1
% 0.29/0.62  thf(fact_7837_ceiling__diff__floor__le__1,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim3151403230148437115or_rat @ X4 ) ) @ one_one_int ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_diff_floor_le_1
% 0.29/0.62  thf(fact_7838_of__nat__less__of__int__iff,axiom,
% 0.29/0.62      ! [N2: nat,X4: int] :
% 0.29/0.62        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X4 ) )
% 0.29/0.62        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_less_of_int_iff
% 0.29/0.62  thf(fact_7839_of__nat__less__of__int__iff,axiom,
% 0.29/0.62      ! [N2: nat,X4: int] :
% 0.29/0.62        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) )
% 0.29/0.62        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_less_of_int_iff
% 0.29/0.62  thf(fact_7840_of__nat__less__of__int__iff,axiom,
% 0.29/0.62      ! [N2: nat,X4: int] :
% 0.29/0.62        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X4 ) )
% 0.29/0.62        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_less_of_int_iff
% 0.29/0.62  thf(fact_7841_int__le__real__less,axiom,
% 0.29/0.62      ( ord_less_eq_int
% 0.29/0.62      = ( ^ [N: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % int_le_real_less
% 0.29/0.62  thf(fact_7842_int__less__real__le,axiom,
% 0.29/0.62      ( ord_less_int
% 0.29/0.62      = ( ^ [N: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % int_less_real_le
% 0.29/0.62  thf(fact_7843_of__int__not__numeral,axiom,
% 0.29/0.62      ! [K: num] :
% 0.29/0.62        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_not_numeral
% 0.29/0.62  thf(fact_7844_ceiling__divide__eq__div,axiom,
% 0.29/0.62      ! [A: int,B: int] :
% 0.29/0.62        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_eq_div
% 0.29/0.62  thf(fact_7845_ceiling__divide__eq__div,axiom,
% 0.29/0.62      ! [A: int,B: int] :
% 0.29/0.62        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_eq_div
% 0.29/0.62  thf(fact_7846_real__of__int__div__aux,axiom,
% 0.29/0.62      ! [X4: int,D: int] :
% 0.29/0.62        ( ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ D ) )
% 0.29/0.62        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X4 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X4 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_of_int_div_aux
% 0.29/0.62  thf(fact_7847_le__mult__floor,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.62         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor
% 0.29/0.62  thf(fact_7848_le__mult__floor,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.29/0.62         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor
% 0.29/0.62  thf(fact_7849_floor__eq4,axiom,
% 0.29/0.62      ! [N2: nat,X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.29/0.62         => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 0.29/0.62            = N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_eq4
% 0.29/0.62  thf(fact_7850_ceiling__split,axiom,
% 0.29/0.62      ! [P: int > $o,T2: real] :
% 0.29/0.62        ( ( P @ ( archim7802044766580827645g_real @ T2 ) )
% 0.29/0.62        = ( ! [I3: int] :
% 0.29/0.62              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T2 )
% 0.29/0.62                & ( ord_less_eq_real @ T2 @ ( ring_1_of_int_real @ I3 ) ) )
% 0.29/0.62             => ( P @ I3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_split
% 0.29/0.62  thf(fact_7851_ceiling__split,axiom,
% 0.29/0.62      ! [P: int > $o,T2: rat] :
% 0.29/0.62        ( ( P @ ( archim2889992004027027881ng_rat @ T2 ) )
% 0.29/0.62        = ( ! [I3: int] :
% 0.29/0.62              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T2 )
% 0.29/0.62                & ( ord_less_eq_rat @ T2 @ ( ring_1_of_int_rat @ I3 ) ) )
% 0.29/0.62             => ( P @ I3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_split
% 0.29/0.62  thf(fact_7852_ceiling__eq__iff,axiom,
% 0.29/0.62      ! [X4: real,A: int] :
% 0.29/0.62        ( ( ( archim7802044766580827645g_real @ X4 )
% 0.29/0.62          = A )
% 0.29/0.62        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X4 )
% 0.29/0.62          & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_eq_iff
% 0.29/0.62  thf(fact_7853_ceiling__eq__iff,axiom,
% 0.29/0.62      ! [X4: rat,A: int] :
% 0.29/0.62        ( ( ( archim2889992004027027881ng_rat @ X4 )
% 0.29/0.62          = A )
% 0.29/0.62        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X4 )
% 0.29/0.62          & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_eq_iff
% 0.29/0.62  thf(fact_7854_ceiling__unique,axiom,
% 0.29/0.62      ! [Z: int,X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) )
% 0.29/0.62         => ( ( archim7802044766580827645g_real @ X4 )
% 0.29/0.62            = Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_unique
% 0.29/0.62  thf(fact_7855_ceiling__unique,axiom,
% 0.29/0.62      ! [Z: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) )
% 0.29/0.62         => ( ( archim2889992004027027881ng_rat @ X4 )
% 0.29/0.62            = Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_unique
% 0.29/0.62  thf(fact_7856_ceiling__correct,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) @ one_one_real ) @ X4 )
% 0.29/0.62        & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_correct
% 0.29/0.62  thf(fact_7857_ceiling__correct,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) @ one_one_rat ) @ X4 )
% 0.29/0.62        & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_correct
% 0.29/0.62  thf(fact_7858_cot__def,axiom,
% 0.29/0.62      ( cot_real
% 0.29/0.62      = ( ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cot_def
% 0.29/0.62  thf(fact_7859_cot__def,axiom,
% 0.29/0.62      ( cot_complex
% 0.29/0.62      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X ) @ ( sin_complex @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cot_def
% 0.29/0.62  thf(fact_7860_ceiling__less__iff,axiom,
% 0.29/0.62      ! [X4: real,Z: int] :
% 0.29/0.62        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 0.29/0.62        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_less_iff
% 0.29/0.62  thf(fact_7861_ceiling__less__iff,axiom,
% 0.29/0.62      ! [X4: rat,Z: int] :
% 0.29/0.62        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 0.29/0.62        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_less_iff
% 0.29/0.62  thf(fact_7862_le__ceiling__iff,axiom,
% 0.29/0.62      ! [Z: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 0.29/0.62        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_ceiling_iff
% 0.29/0.62  thf(fact_7863_le__ceiling__iff,axiom,
% 0.29/0.62      ! [Z: int,X4: real] :
% 0.29/0.62        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 0.29/0.62        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_ceiling_iff
% 0.29/0.62  thf(fact_7864_real__of__int__div2,axiom,
% 0.29/0.62      ! [N2: int,X4: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_of_int_div2
% 0.29/0.62  thf(fact_7865_real__of__int__div3,axiom,
% 0.29/0.62      ! [N2: int,X4: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % real_of_int_div3
% 0.29/0.62  thf(fact_7866_ceiling__divide__upper,axiom,
% 0.29/0.62      ! [Q3: real,P2: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.29/0.62       => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_upper
% 0.29/0.62  thf(fact_7867_ceiling__divide__upper,axiom,
% 0.29/0.62      ! [Q3: rat,P2: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.29/0.62       => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_upper
% 0.29/0.62  thf(fact_7868_even__of__int__iff,axiom,
% 0.29/0.62      ! [K: int] :
% 0.29/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 0.29/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.29/0.62  
% 0.29/0.62  % even_of_int_iff
% 0.29/0.62  thf(fact_7869_even__of__int__iff,axiom,
% 0.29/0.62      ! [K: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 0.29/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.29/0.62  
% 0.29/0.62  % even_of_int_iff
% 0.29/0.62  thf(fact_7870_of__int__of__nat,axiom,
% 0.29/0.62      ( ring_17405671764205052669omplex
% 0.29/0.62      = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_of_nat
% 0.29/0.62  thf(fact_7871_of__int__of__nat,axiom,
% 0.29/0.62      ( ring_18347121197199848620nteger
% 0.29/0.62      = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_of_nat
% 0.29/0.62  thf(fact_7872_of__int__of__nat,axiom,
% 0.29/0.62      ( ring_1_of_int_rat
% 0.29/0.62      = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_of_nat
% 0.29/0.62  thf(fact_7873_of__int__of__nat,axiom,
% 0.29/0.62      ( ring_1_of_int_real
% 0.29/0.62      = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_of_nat
% 0.29/0.62  thf(fact_7874_of__int__of__nat,axiom,
% 0.29/0.62      ( ring_1_of_int_int
% 0.29/0.62      = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_of_nat
% 0.29/0.62  thf(fact_7875_ceiling__divide__lower,axiom,
% 0.29/0.62      ! [Q3: rat,P2: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 0.29/0.62       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_lower
% 0.29/0.62  thf(fact_7876_ceiling__divide__lower,axiom,
% 0.29/0.62      ! [Q3: real,P2: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 0.29/0.62       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_divide_lower
% 0.29/0.62  thf(fact_7877_ceiling__eq,axiom,
% 0.29/0.62      ! [N2: int,X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 0.29/0.62         => ( ( archim7802044766580827645g_real @ X4 )
% 0.29/0.62            = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_eq
% 0.29/0.62  thf(fact_7878_ceiling__eq,axiom,
% 0.29/0.62      ! [N2: int,X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N2 ) @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N2 ) @ one_one_rat ) )
% 0.29/0.62         => ( ( archim2889992004027027881ng_rat @ X4 )
% 0.29/0.62            = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_eq
% 0.29/0.62  thf(fact_7879_cos__one__2pi__int,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( cos_real @ X4 )
% 0.29/0.62          = one_one_real )
% 0.29/0.62        = ( ? [X: int] :
% 0.29/0.62              ( X4
% 0.29/0.62              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cos_one_2pi_int
% 0.29/0.62  thf(fact_7880_arccos__cos__eq__abs__2pi,axiom,
% 0.29/0.62      ! [Theta: real] :
% 0.29/0.62        ~ ! [K2: int] :
% 0.29/0.62            ( ( arccos @ ( cos_real @ Theta ) )
% 0.29/0.62           != ( 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 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % arccos_cos_eq_abs_2pi
% 0.29/0.62  thf(fact_7881_cot__gt__zero,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.62         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cot_gt_zero
% 0.29/0.62  thf(fact_7882_floor__log2__div2,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.62       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.62          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_log2_div2
% 0.29/0.62  thf(fact_7883_tan__cot_H,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 0.29/0.62        = ( cot_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tan_cot'
% 0.29/0.62  thf(fact_7884_cos__zero__iff__int,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( cos_real @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62        = ( ? [I3: int] :
% 0.29/0.62              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.62              & ( X4
% 0.29/0.62                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cos_zero_iff_int
% 0.29/0.62  thf(fact_7885_sin__zero__iff__int,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( sin_real @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62        = ( ? [I3: int] :
% 0.29/0.62              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.62              & ( X4
% 0.29/0.62                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sin_zero_iff_int
% 0.29/0.62  thf(fact_7886_powr__int,axiom,
% 0.29/0.62      ! [X4: real,I2: int] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.29/0.62           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 0.29/0.62              = ( power_power_real @ X4 @ ( nat2 @ I2 ) ) ) )
% 0.29/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.29/0.62           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 0.29/0.62              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % powr_int
% 0.29/0.62  thf(fact_7887_round__unique,axiom,
% 0.29/0.62      ! [X4: real,Y: int] :
% 0.29/0.62        ( ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 0.29/0.62       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62         => ( ( archim8280529875227126926d_real @ X4 )
% 0.29/0.62            = Y ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_unique
% 0.29/0.62  thf(fact_7888_round__unique,axiom,
% 0.29/0.62      ! [X4: rat,Y: int] :
% 0.29/0.62        ( ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 0.29/0.62       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62         => ( ( archim7778729529865785530nd_rat @ X4 )
% 0.29/0.62            = Y ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_unique
% 0.29/0.62  thf(fact_7889_round__unique_H,axiom,
% 0.29/0.62      ! [X4: rat,N2: int] :
% 0.29/0.62        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.29/0.62       => ( ( archim7778729529865785530nd_rat @ X4 )
% 0.29/0.62          = N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_unique'
% 0.29/0.62  thf(fact_7890_round__unique_H,axiom,
% 0.29/0.62      ! [X4: real,N2: int] :
% 0.29/0.62        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.62       => ( ( archim8280529875227126926d_real @ X4 )
% 0.29/0.62          = N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_unique'
% 0.29/0.62  thf(fact_7891_of__int__round__abs__le,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ X4 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_abs_le
% 0.29/0.62  thf(fact_7892_of__int__round__abs__le,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ X4 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_abs_le
% 0.29/0.62  thf(fact_7893_of__int__round__gt,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_gt
% 0.29/0.62  thf(fact_7894_of__int__round__gt,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_gt
% 0.29/0.62  thf(fact_7895_of__int__round__ge,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_ge
% 0.29/0.62  thf(fact_7896_of__int__round__ge,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_ge
% 0.29/0.62  thf(fact_7897_round__numeral,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 0.29/0.62        = ( numeral_numeral_int @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_numeral
% 0.29/0.62  thf(fact_7898_round__1,axiom,
% 0.29/0.62      ( ( archim8280529875227126926d_real @ one_one_real )
% 0.29/0.62      = one_one_int ) ).
% 0.29/0.62  
% 0.29/0.62  % round_1
% 0.29/0.62  thf(fact_7899_round__1,axiom,
% 0.29/0.62      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.29/0.62      = one_one_int ) ).
% 0.29/0.62  
% 0.29/0.62  % round_1
% 0.29/0.62  thf(fact_7900_round__neg__numeral,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_neg_numeral
% 0.29/0.62  thf(fact_7901_round__neg__numeral,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_neg_numeral
% 0.29/0.62  thf(fact_7902_round__mono,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ X4 @ Y )
% 0.29/0.62       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_mono
% 0.29/0.62  thf(fact_7903_floor__le__round,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim8280529875227126926d_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_le_round
% 0.29/0.62  thf(fact_7904_floor__le__round,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_le_round
% 0.29/0.62  thf(fact_7905_ceiling__ge__round,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ceiling_ge_round
% 0.29/0.62  thf(fact_7906_round__diff__minimal,axiom,
% 0.29/0.62      ! [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 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_diff_minimal
% 0.29/0.62  thf(fact_7907_round__diff__minimal,axiom,
% 0.29/0.62      ! [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 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_diff_minimal
% 0.29/0.62  thf(fact_7908_round__def,axiom,
% 0.29/0.62      ( archim8280529875227126926d_real
% 0.29/0.62      = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_def
% 0.29/0.62  thf(fact_7909_round__def,axiom,
% 0.29/0.62      ( archim7778729529865785530nd_rat
% 0.29/0.62      = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_def
% 0.29/0.62  thf(fact_7910_of__int__round__le,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_le
% 0.29/0.62  thf(fact_7911_of__int__round__le,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_round_le
% 0.29/0.62  thf(fact_7912_round__altdef,axiom,
% 0.29/0.62      ( archim8280529875227126926d_real
% 0.29/0.62      = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_altdef
% 0.29/0.62  thf(fact_7913_round__altdef,axiom,
% 0.29/0.62      ( archim7778729529865785530nd_rat
% 0.29/0.62      = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % round_altdef
% 0.29/0.62  thf(fact_7914_powr__real__of__int,axiom,
% 0.29/0.62      ! [X4: real,N2: int] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.29/0.62           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 0.29/0.62              = ( power_power_real @ X4 @ ( nat2 @ N2 ) ) ) )
% 0.29/0.62          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 0.29/0.62           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 0.29/0.62              = ( inverse_inverse_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % powr_real_of_int
% 0.29/0.62  thf(fact_7915_cis__2pi,axiom,
% 0.29/0.62      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.29/0.62      = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % cis_2pi
% 0.29/0.62  thf(fact_7916_i__even__power,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % i_even_power
% 0.29/0.62  thf(fact_7917_gbinomial__absorption_H,axiom,
% 0.29/0.62      ! [K: nat,A: rat] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_rat @ A @ K )
% 0.29/0.62          = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption'
% 0.29/0.62  thf(fact_7918_gbinomial__absorption_H,axiom,
% 0.29/0.62      ! [K: nat,A: complex] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_complex @ A @ K )
% 0.29/0.62          = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption'
% 0.29/0.62  thf(fact_7919_gbinomial__absorption_H,axiom,
% 0.29/0.62      ! [K: nat,A: real] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_real @ A @ K )
% 0.29/0.62          = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption'
% 0.29/0.62  thf(fact_7920_inverse__inverse__eq,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62        = A ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_inverse_eq
% 0.29/0.62  thf(fact_7921_inverse__inverse__eq,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 0.29/0.62        = A ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_inverse_eq
% 0.29/0.62  thf(fact_7922_inverse__eq__iff__eq,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ A )
% 0.29/0.62          = ( inverse_inverse_real @ B ) )
% 0.29/0.62        = ( A = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_iff_eq
% 0.29/0.62  thf(fact_7923_inverse__eq__iff__eq,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62        = ( A = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_iff_eq
% 0.29/0.62  thf(fact_7924_inverse__nonzero__iff__nonzero,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ( inverse_inverse_rat @ A )
% 0.29/0.62          = zero_zero_rat )
% 0.29/0.62        = ( A = zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonzero_iff_nonzero
% 0.29/0.62  thf(fact_7925_inverse__nonzero__iff__nonzero,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ A )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62        = ( A = zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonzero_iff_nonzero
% 0.29/0.62  thf(fact_7926_inverse__nonzero__iff__nonzero,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = zero_zero_complex )
% 0.29/0.62        = ( A = zero_zero_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonzero_iff_nonzero
% 0.29/0.62  thf(fact_7927_inverse__zero,axiom,
% 0.29/0.62      ( ( inverse_inverse_rat @ zero_zero_rat )
% 0.29/0.62      = zero_zero_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero
% 0.29/0.62  thf(fact_7928_inverse__zero,axiom,
% 0.29/0.62      ( ( inverse_inverse_real @ zero_zero_real )
% 0.29/0.62      = zero_zero_real ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero
% 0.29/0.62  thf(fact_7929_inverse__zero,axiom,
% 0.29/0.62      ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 0.29/0.62      = zero_zero_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero
% 0.29/0.62  thf(fact_7930_inverse__mult__distrib,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 0.29/0.62        = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_mult_distrib
% 0.29/0.62  thf(fact_7931_inverse__mult__distrib,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 0.29/0.62        = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_mult_distrib
% 0.29/0.62  thf(fact_7932_inverse__eq__1__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ( inverse_inverse_rat @ X4 )
% 0.29/0.62          = one_one_rat )
% 0.29/0.62        = ( X4 = one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_1_iff
% 0.29/0.62  thf(fact_7933_inverse__eq__1__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ X4 )
% 0.29/0.62          = one_one_real )
% 0.29/0.62        = ( X4 = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_1_iff
% 0.29/0.62  thf(fact_7934_inverse__eq__1__iff,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ X4 )
% 0.29/0.62          = one_one_complex )
% 0.29/0.62        = ( X4 = one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_1_iff
% 0.29/0.62  thf(fact_7935_inverse__1,axiom,
% 0.29/0.62      ( ( inverse_inverse_rat @ one_one_rat )
% 0.29/0.62      = one_one_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_1
% 0.29/0.62  thf(fact_7936_inverse__1,axiom,
% 0.29/0.62      ( ( inverse_inverse_real @ one_one_real )
% 0.29/0.62      = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_1
% 0.29/0.62  thf(fact_7937_inverse__1,axiom,
% 0.29/0.62      ( ( invers8013647133539491842omplex @ one_one_complex )
% 0.29/0.62      = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_1
% 0.29/0.62  thf(fact_7938_inverse__divide,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 0.29/0.62        = ( divide_divide_real @ B @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_divide
% 0.29/0.62  thf(fact_7939_inverse__divide,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.29/0.62        = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_divide
% 0.29/0.62  thf(fact_7940_inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.62        = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_minus_eq
% 0.29/0.62  thf(fact_7941_inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.62        = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_minus_eq
% 0.29/0.62  thf(fact_7942_inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.62        = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_minus_eq
% 0.29/0.62  thf(fact_7943_abs__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62        = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % abs_inverse
% 0.29/0.62  thf(fact_7944_abs__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62        = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % abs_inverse
% 0.29/0.62  thf(fact_7945_abs__inverse,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 0.29/0.62        = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % abs_inverse
% 0.29/0.62  thf(fact_7946_inverse__sgn,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 0.29/0.62        = ( sgn_sgn_rat @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_sgn
% 0.29/0.62  thf(fact_7947_inverse__sgn,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 0.29/0.62        = ( sgn_sgn_real @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_sgn
% 0.29/0.62  thf(fact_7948_sgn__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62        = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sgn_inverse
% 0.29/0.62  thf(fact_7949_sgn__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62        = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sgn_inverse
% 0.29/0.62  thf(fact_7950_sgn__inverse,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 0.29/0.62        = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sgn_inverse
% 0.29/0.62  thf(fact_7951_inverse__nonnegative__iff__nonnegative,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonnegative_iff_nonnegative
% 0.29/0.62  thf(fact_7952_inverse__nonnegative__iff__nonnegative,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonnegative_iff_nonnegative
% 0.29/0.62  thf(fact_7953_inverse__nonpositive__iff__nonpositive,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.29/0.62        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonpositive_iff_nonpositive
% 0.29/0.62  thf(fact_7954_inverse__nonpositive__iff__nonpositive,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.29/0.62        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_nonpositive_iff_nonpositive
% 0.29/0.62  thf(fact_7955_inverse__positive__iff__positive,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_positive_iff_positive
% 0.29/0.62  thf(fact_7956_inverse__positive__iff__positive,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_positive_iff_positive
% 0.29/0.62  thf(fact_7957_inverse__negative__iff__negative,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.29/0.62        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_negative_iff_negative
% 0.29/0.62  thf(fact_7958_inverse__negative__iff__negative,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.29/0.62        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_negative_iff_negative
% 0.29/0.62  thf(fact_7959_inverse__less__iff__less__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff_less_neg
% 0.29/0.62  thf(fact_7960_inverse__less__iff__less__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff_less_neg
% 0.29/0.62  thf(fact_7961_inverse__less__iff__less,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.62         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff_less
% 0.29/0.62  thf(fact_7962_inverse__less__iff__less,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.62         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff_less
% 0.29/0.62  thf(fact_7963_gbinomial__0_I2_J,axiom,
% 0.29/0.62      ! [K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 0.29/0.62        = zero_zero_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(2)
% 0.29/0.62  thf(fact_7964_gbinomial__0_I2_J,axiom,
% 0.29/0.62      ! [K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 0.29/0.62        = zero_zero_real ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(2)
% 0.29/0.62  thf(fact_7965_gbinomial__0_I2_J,axiom,
% 0.29/0.62      ! [K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 0.29/0.62        = zero_zero_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(2)
% 0.29/0.62  thf(fact_7966_gbinomial__0_I2_J,axiom,
% 0.29/0.62      ! [K: nat] :
% 0.29/0.62        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.29/0.62        = zero_zero_nat ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(2)
% 0.29/0.62  thf(fact_7967_gbinomial__0_I2_J,axiom,
% 0.29/0.62      ! [K: nat] :
% 0.29/0.62        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.29/0.62        = zero_zero_int ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(2)
% 0.29/0.62  thf(fact_7968_gbinomial__0_I1_J,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 0.29/0.62        = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(1)
% 0.29/0.62  thf(fact_7969_gbinomial__0_I1_J,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( gbinomial_real @ A @ zero_zero_nat )
% 0.29/0.62        = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(1)
% 0.29/0.62  thf(fact_7970_gbinomial__0_I1_J,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.29/0.62        = one_one_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(1)
% 0.29/0.62  thf(fact_7971_gbinomial__0_I1_J,axiom,
% 0.29/0.62      ! [A: nat] :
% 0.29/0.62        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.29/0.62        = one_one_nat ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(1)
% 0.29/0.62  thf(fact_7972_gbinomial__0_I1_J,axiom,
% 0.29/0.62      ! [A: int] :
% 0.29/0.62        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.29/0.62        = one_one_int ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_0(1)
% 0.29/0.62  thf(fact_7973_norm__ii,axiom,
% 0.29/0.62      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 0.29/0.62      = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % norm_ii
% 0.29/0.62  thf(fact_7974_norm__cis,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 0.29/0.62        = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % norm_cis
% 0.29/0.62  thf(fact_7975_inverse__le__iff__le__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff_le_neg
% 0.29/0.62  thf(fact_7976_inverse__le__iff__le__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff_le_neg
% 0.29/0.62  thf(fact_7977_inverse__le__iff__le,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.62         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff_le
% 0.29/0.62  thf(fact_7978_inverse__le__iff__le,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.62         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff_le
% 0.29/0.62  thf(fact_7979_right__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62          = one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % right_inverse
% 0.29/0.62  thf(fact_7980_right__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 0.29/0.62          = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % right_inverse
% 0.29/0.62  thf(fact_7981_right__inverse,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 0.29/0.62          = one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % right_inverse
% 0.29/0.62  thf(fact_7982_left__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 0.29/0.62          = one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % left_inverse
% 0.29/0.62  thf(fact_7983_left__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 0.29/0.62          = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % left_inverse
% 0.29/0.62  thf(fact_7984_left__inverse,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 0.29/0.62          = one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % left_inverse
% 0.29/0.62  thf(fact_7985_inverse__eq__divide__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.62        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_numeral
% 0.29/0.62  thf(fact_7986_inverse__eq__divide__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 0.29/0.62        = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_numeral
% 0.29/0.62  thf(fact_7987_inverse__eq__divide__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.29/0.62        = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_numeral
% 0.29/0.62  thf(fact_7988_inverse__eq__divide__neg__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.62        = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_neg_numeral
% 0.29/0.62  thf(fact_7989_inverse__eq__divide__neg__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.29/0.62        = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_neg_numeral
% 0.29/0.62  thf(fact_7990_inverse__eq__divide__neg__numeral,axiom,
% 0.29/0.62      ! [W: num] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.62        = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide_neg_numeral
% 0.29/0.62  thf(fact_7991_exp__two__pi__i_H,axiom,
% 0.29/0.62      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62      = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_two_pi_i'
% 0.29/0.62  thf(fact_7992_exp__two__pi__i,axiom,
% 0.29/0.62      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 0.29/0.62      = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_two_pi_i
% 0.29/0.62  thf(fact_7993_cis__pi__half,axiom,
% 0.29/0.62      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.62      = imaginary_unit ) ).
% 0.29/0.62  
% 0.29/0.62  % cis_pi_half
% 0.29/0.62  thf(fact_7994_power2__i,axiom,
% 0.29/0.62      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power2_i
% 0.29/0.62  thf(fact_7995_cis__minus__pi__half,axiom,
% 0.29/0.62      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cis_minus_pi_half
% 0.29/0.62  thf(fact_7996_mult__commute__imp__mult__inverse__commute,axiom,
% 0.29/0.62      ! [Y: real,X4: real] :
% 0.29/0.62        ( ( ( times_times_real @ Y @ X4 )
% 0.29/0.62          = ( times_times_real @ X4 @ Y ) )
% 0.29/0.62       => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X4 )
% 0.29/0.62          = ( times_times_real @ X4 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_commute_imp_mult_inverse_commute
% 0.29/0.62  thf(fact_7997_mult__commute__imp__mult__inverse__commute,axiom,
% 0.29/0.62      ! [Y: complex,X4: complex] :
% 0.29/0.62        ( ( ( times_times_complex @ Y @ X4 )
% 0.29/0.62          = ( times_times_complex @ X4 @ Y ) )
% 0.29/0.62       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X4 )
% 0.29/0.62          = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_commute_imp_mult_inverse_commute
% 0.29/0.62  thf(fact_7998_power__inverse,axiom,
% 0.29/0.62      ! [A: real,N2: nat] :
% 0.29/0.62        ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N2 )
% 0.29/0.62        = ( inverse_inverse_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_inverse
% 0.29/0.62  thf(fact_7999_power__inverse,axiom,
% 0.29/0.62      ! [A: complex,N2: nat] :
% 0.29/0.62        ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N2 )
% 0.29/0.62        = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_inverse
% 0.29/0.62  thf(fact_8000_inverse__eq__imp__eq,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ A )
% 0.29/0.62          = ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( A = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_imp_eq
% 0.29/0.62  thf(fact_8001_inverse__eq__imp__eq,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62       => ( A = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_imp_eq
% 0.29/0.62  thf(fact_8002_field__class_Ofield__inverse__zero,axiom,
% 0.29/0.62      ( ( inverse_inverse_rat @ zero_zero_rat )
% 0.29/0.62      = zero_zero_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse_zero
% 0.29/0.62  thf(fact_8003_field__class_Ofield__inverse__zero,axiom,
% 0.29/0.62      ( ( inverse_inverse_real @ zero_zero_real )
% 0.29/0.62      = zero_zero_real ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse_zero
% 0.29/0.62  thf(fact_8004_field__class_Ofield__inverse__zero,axiom,
% 0.29/0.62      ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 0.29/0.62      = zero_zero_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse_zero
% 0.29/0.62  thf(fact_8005_inverse__zero__imp__zero,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ( inverse_inverse_rat @ A )
% 0.29/0.62          = zero_zero_rat )
% 0.29/0.62       => ( A = zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero_imp_zero
% 0.29/0.62  thf(fact_8006_inverse__zero__imp__zero,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ A )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62       => ( A = zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero_imp_zero
% 0.29/0.62  thf(fact_8007_inverse__zero__imp__zero,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = zero_zero_complex )
% 0.29/0.62       => ( A = zero_zero_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_zero_imp_zero
% 0.29/0.62  thf(fact_8008_nonzero__inverse__eq__imp__eq,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ( inverse_inverse_rat @ A )
% 0.29/0.62          = ( inverse_inverse_rat @ B ) )
% 0.29/0.62       => ( ( A != zero_zero_rat )
% 0.29/0.62         => ( ( B != zero_zero_rat )
% 0.29/0.62           => ( A = B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_imp_eq
% 0.29/0.62  thf(fact_8009_nonzero__inverse__eq__imp__eq,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ( inverse_inverse_real @ A )
% 0.29/0.62          = ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( ( A != zero_zero_real )
% 0.29/0.62         => ( ( B != zero_zero_real )
% 0.29/0.62           => ( A = B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_imp_eq
% 0.29/0.62  thf(fact_8010_nonzero__inverse__eq__imp__eq,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62       => ( ( A != zero_zero_complex )
% 0.29/0.62         => ( ( B != zero_zero_complex )
% 0.29/0.62           => ( A = B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_imp_eq
% 0.29/0.62  thf(fact_8011_nonzero__inverse__inverse__eq,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62          = A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_inverse_eq
% 0.29/0.62  thf(fact_8012_nonzero__inverse__inverse__eq,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62          = A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_inverse_eq
% 0.29/0.62  thf(fact_8013_nonzero__inverse__inverse__eq,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 0.29/0.62          = A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_inverse_eq
% 0.29/0.62  thf(fact_8014_nonzero__imp__inverse__nonzero,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( inverse_inverse_rat @ A )
% 0.29/0.62         != zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_imp_inverse_nonzero
% 0.29/0.62  thf(fact_8015_nonzero__imp__inverse__nonzero,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( inverse_inverse_real @ A )
% 0.29/0.62         != zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_imp_inverse_nonzero
% 0.29/0.62  thf(fact_8016_nonzero__imp__inverse__nonzero,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62         != zero_zero_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_imp_inverse_nonzero
% 0.29/0.62  thf(fact_8017_norm__inverse__le__norm,axiom,
% 0.29/0.62      ! [R3: real,X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ R3 @ ( real_V7735802525324610683m_real @ X4 ) )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.29/0.62         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % norm_inverse_le_norm
% 0.29/0.62  thf(fact_8018_norm__inverse__le__norm,axiom,
% 0.29/0.62      ! [R3: real,X4: complex] :
% 0.29/0.62        ( ( ord_less_eq_real @ R3 @ ( real_V1022390504157884413omplex @ X4 ) )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.29/0.62         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % norm_inverse_le_norm
% 0.29/0.62  thf(fact_8019_positive__imp__inverse__positive,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % positive_imp_inverse_positive
% 0.29/0.62  thf(fact_8020_positive__imp__inverse__positive,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % positive_imp_inverse_positive
% 0.29/0.62  thf(fact_8021_negative__imp__inverse__negative,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.62       => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % negative_imp_inverse_negative
% 0.29/0.62  thf(fact_8022_negative__imp__inverse__negative,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.62       => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % negative_imp_inverse_negative
% 0.29/0.62  thf(fact_8023_inverse__positive__imp__positive,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62       => ( ( A != zero_zero_rat )
% 0.29/0.62         => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_positive_imp_positive
% 0.29/0.62  thf(fact_8024_inverse__positive__imp__positive,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62       => ( ( A != zero_zero_real )
% 0.29/0.62         => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_positive_imp_positive
% 0.29/0.62  thf(fact_8025_inverse__negative__imp__negative,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 0.29/0.62       => ( ( A != zero_zero_rat )
% 0.29/0.62         => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_negative_imp_negative
% 0.29/0.62  thf(fact_8026_inverse__negative__imp__negative,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.29/0.62       => ( ( A != zero_zero_real )
% 0.29/0.62         => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_negative_imp_negative
% 0.29/0.62  thf(fact_8027_less__imp__inverse__less__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ A @ B )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_imp_inverse_less_neg
% 0.29/0.62  thf(fact_8028_less__imp__inverse__less__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ A @ B )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_imp_inverse_less_neg
% 0.29/0.62  thf(fact_8029_inverse__less__imp__less__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_imp_less_neg
% 0.29/0.62  thf(fact_8030_inverse__less__imp__less__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_imp_less_neg
% 0.29/0.62  thf(fact_8031_less__imp__inverse__less,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ A @ B )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_imp_inverse_less
% 0.29/0.62  thf(fact_8032_less__imp__inverse__less,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ A @ B )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_imp_inverse_less
% 0.29/0.62  thf(fact_8033_inverse__less__imp__less,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62         => ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_imp_less
% 0.29/0.62  thf(fact_8034_inverse__less__imp__less,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62         => ( ord_less_real @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_imp_less
% 0.29/0.62  thf(fact_8035_nonzero__inverse__mult__distrib,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( B != zero_zero_rat )
% 0.29/0.62         => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.62            = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_mult_distrib
% 0.29/0.62  thf(fact_8036_nonzero__inverse__mult__distrib,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( B != zero_zero_real )
% 0.29/0.62         => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 0.29/0.62            = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_mult_distrib
% 0.29/0.62  thf(fact_8037_nonzero__inverse__mult__distrib,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( B != zero_zero_complex )
% 0.29/0.62         => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 0.29/0.62            = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_mult_distrib
% 0.29/0.62  thf(fact_8038_nonzero__inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.62          = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_minus_eq
% 0.29/0.62  thf(fact_8039_nonzero__inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 0.29/0.62          = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_minus_eq
% 0.29/0.62  thf(fact_8040_nonzero__inverse__minus__eq,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.29/0.62          = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_minus_eq
% 0.29/0.62  thf(fact_8041_inverse__unique,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ( times_times_rat @ A @ B )
% 0.29/0.62          = one_one_rat )
% 0.29/0.62       => ( ( inverse_inverse_rat @ A )
% 0.29/0.62          = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_unique
% 0.29/0.62  thf(fact_8042_inverse__unique,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ( times_times_real @ A @ B )
% 0.29/0.62          = one_one_real )
% 0.29/0.62       => ( ( inverse_inverse_real @ A )
% 0.29/0.62          = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_unique
% 0.29/0.62  thf(fact_8043_inverse__unique,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ( times_times_complex @ A @ B )
% 0.29/0.62          = one_one_complex )
% 0.29/0.62       => ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_unique
% 0.29/0.62  thf(fact_8044_inverse__numeral__1,axiom,
% 0.29/0.62      ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 0.29/0.62      = ( numeral_numeral_real @ one ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_numeral_1
% 0.29/0.62  thf(fact_8045_inverse__numeral__1,axiom,
% 0.29/0.62      ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.29/0.62      = ( numera6690914467698888265omplex @ one ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_numeral_1
% 0.29/0.62  thf(fact_8046_divide__inverse__commute,axiom,
% 0.29/0.62      ( divide_divide_real
% 0.29/0.62      = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % divide_inverse_commute
% 0.29/0.62  thf(fact_8047_divide__inverse__commute,axiom,
% 0.29/0.62      ( divide1717551699836669952omplex
% 0.29/0.62      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % divide_inverse_commute
% 0.29/0.62  thf(fact_8048_divide__inverse,axiom,
% 0.29/0.62      ( divide_divide_real
% 0.29/0.62      = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % divide_inverse
% 0.29/0.62  thf(fact_8049_divide__inverse,axiom,
% 0.29/0.62      ( divide1717551699836669952omplex
% 0.29/0.62      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % divide_inverse
% 0.29/0.62  thf(fact_8050_field__class_Ofield__divide__inverse,axiom,
% 0.29/0.62      ( divide_divide_real
% 0.29/0.62      = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_divide_inverse
% 0.29/0.62  thf(fact_8051_field__class_Ofield__divide__inverse,axiom,
% 0.29/0.62      ( divide1717551699836669952omplex
% 0.29/0.62      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_divide_inverse
% 0.29/0.62  thf(fact_8052_inverse__eq__divide,axiom,
% 0.29/0.62      ( inverse_inverse_rat
% 0.29/0.62      = ( divide_divide_rat @ one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide
% 0.29/0.62  thf(fact_8053_inverse__eq__divide,axiom,
% 0.29/0.62      ( inverse_inverse_real
% 0.29/0.62      = ( divide_divide_real @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide
% 0.29/0.62  thf(fact_8054_inverse__eq__divide,axiom,
% 0.29/0.62      ( invers8013647133539491842omplex
% 0.29/0.62      = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_eq_divide
% 0.29/0.62  thf(fact_8055_power__mult__inverse__distrib,axiom,
% 0.29/0.62      ! [X4: real,M: nat] :
% 0.29/0.62        ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( inverse_inverse_real @ X4 ) )
% 0.29/0.62        = ( times_times_real @ ( inverse_inverse_real @ X4 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_mult_inverse_distrib
% 0.29/0.62  thf(fact_8056_power__mult__inverse__distrib,axiom,
% 0.29/0.62      ! [X4: complex,M: nat] :
% 0.29/0.62        ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( invers8013647133539491842omplex @ X4 ) )
% 0.29/0.62        = ( times_times_complex @ ( invers8013647133539491842omplex @ X4 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_mult_inverse_distrib
% 0.29/0.62  thf(fact_8057_power__mult__power__inverse__commute,axiom,
% 0.29/0.62      ! [X4: real,M: nat,N2: nat] :
% 0.29/0.62        ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) )
% 0.29/0.62        = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_mult_power_inverse_commute
% 0.29/0.62  thf(fact_8058_power__mult__power__inverse__commute,axiom,
% 0.29/0.62      ! [X4: complex,M: nat,N2: nat] :
% 0.29/0.62        ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) )
% 0.29/0.62        = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_mult_power_inverse_commute
% 0.29/0.62  thf(fact_8059_mult__inverse__of__nat__commute,axiom,
% 0.29/0.62      ! [Xa: nat,X4: real] :
% 0.29/0.62        ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X4 )
% 0.29/0.62        = ( times_times_real @ X4 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_inverse_of_nat_commute
% 0.29/0.62  thf(fact_8060_mult__inverse__of__nat__commute,axiom,
% 0.29/0.62      ! [Xa: nat,X4: complex] :
% 0.29/0.62        ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X4 )
% 0.29/0.62        = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_inverse_of_nat_commute
% 0.29/0.62  thf(fact_8061_nonzero__abs__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 0.29/0.62          = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_abs_inverse
% 0.29/0.62  thf(fact_8062_nonzero__abs__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 0.29/0.62          = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_abs_inverse
% 0.29/0.62  thf(fact_8063_divide__real__def,axiom,
% 0.29/0.62      ( divide_divide_real
% 0.29/0.62      = ( ^ [X: real,Y5: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y5 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % divide_real_def
% 0.29/0.62  thf(fact_8064_frac__ge__0,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_ge_0
% 0.29/0.62  thf(fact_8065_frac__ge__0,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_ge_0
% 0.29/0.62  thf(fact_8066_frac__lt__1,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X4 ) @ one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_lt_1
% 0.29/0.62  thf(fact_8067_frac__lt__1,axiom,
% 0.29/0.62      ! [X4: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X4 ) @ one_one_rat ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_lt_1
% 0.29/0.62  thf(fact_8068_frac__1__eq,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 0.29/0.62        = ( archim2898591450579166408c_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_1_eq
% 0.29/0.62  thf(fact_8069_frac__1__eq,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 0.29/0.62        = ( archimedean_frac_rat @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_1_eq
% 0.29/0.62  thf(fact_8070_le__imp__inverse__le__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_imp_inverse_le_neg
% 0.29/0.62  thf(fact_8071_le__imp__inverse__le__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_imp_inverse_le_neg
% 0.29/0.62  thf(fact_8072_inverse__le__imp__le__neg,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_imp_le_neg
% 0.29/0.62  thf(fact_8073_inverse__le__imp__le__neg,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.29/0.62         => ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_imp_le_neg
% 0.29/0.62  thf(fact_8074_le__imp__inverse__le,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62         => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_imp_inverse_le
% 0.29/0.62  thf(fact_8075_le__imp__inverse__le,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62         => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_imp_inverse_le
% 0.29/0.62  thf(fact_8076_inverse__le__imp__le,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62         => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_imp_le
% 0.29/0.62  thf(fact_8077_inverse__le__imp__le,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62         => ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_imp_le
% 0.29/0.62  thf(fact_8078_inverse__le__1__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 0.29/0.62        = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.62          | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_1_iff
% 0.29/0.62  thf(fact_8079_inverse__le__1__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 0.29/0.62        = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.62          | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_1_iff
% 0.29/0.62  thf(fact_8080_one__less__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.29/0.62         => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_less_inverse
% 0.29/0.62  thf(fact_8081_one__less__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( ord_less_real @ A @ one_one_real )
% 0.29/0.62         => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_less_inverse
% 0.29/0.62  thf(fact_8082_one__less__inverse__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 0.29/0.62        = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.62          & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_less_inverse_iff
% 0.29/0.62  thf(fact_8083_one__less__inverse__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 0.29/0.62        = ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62          & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_less_inverse_iff
% 0.29/0.62  thf(fact_8084_field__class_Ofield__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 0.29/0.62          = one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse
% 0.29/0.62  thf(fact_8085_field__class_Ofield__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 0.29/0.62          = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse
% 0.29/0.62  thf(fact_8086_field__class_Ofield__inverse,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 0.29/0.62          = one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % field_class.field_inverse
% 0.29/0.62  thf(fact_8087_division__ring__inverse__add,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( B != zero_zero_rat )
% 0.29/0.62         => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_add
% 0.29/0.62  thf(fact_8088_division__ring__inverse__add,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( B != zero_zero_real )
% 0.29/0.62         => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_add
% 0.29/0.62  thf(fact_8089_division__ring__inverse__add,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( B != zero_zero_complex )
% 0.29/0.62         => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62            = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_add
% 0.29/0.62  thf(fact_8090_inverse__add,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( B != zero_zero_rat )
% 0.29/0.62         => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_add
% 0.29/0.62  thf(fact_8091_inverse__add,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( B != zero_zero_real )
% 0.29/0.62         => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_add
% 0.29/0.62  thf(fact_8092_inverse__add,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( B != zero_zero_complex )
% 0.29/0.62         => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62            = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_add
% 0.29/0.62  thf(fact_8093_division__ring__inverse__diff,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( B != zero_zero_rat )
% 0.29/0.62         => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_diff
% 0.29/0.62  thf(fact_8094_division__ring__inverse__diff,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( B != zero_zero_real )
% 0.29/0.62         => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_diff
% 0.29/0.62  thf(fact_8095_division__ring__inverse__diff,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( B != zero_zero_complex )
% 0.29/0.62         => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62            = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % division_ring_inverse_diff
% 0.29/0.62  thf(fact_8096_nonzero__inverse__eq__divide,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( inverse_inverse_rat @ A )
% 0.29/0.62          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_divide
% 0.29/0.62  thf(fact_8097_nonzero__inverse__eq__divide,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( inverse_inverse_real @ A )
% 0.29/0.62          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_divide
% 0.29/0.62  thf(fact_8098_nonzero__inverse__eq__divide,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( invers8013647133539491842omplex @ A )
% 0.29/0.62          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nonzero_inverse_eq_divide
% 0.29/0.62  thf(fact_8099_gbinomial__Suc__Suc,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_Suc_Suc
% 0.29/0.62  thf(fact_8100_gbinomial__Suc__Suc,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_Suc_Suc
% 0.29/0.62  thf(fact_8101_gbinomial__Suc__Suc,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_Suc_Suc
% 0.29/0.62  thf(fact_8102_gbinomial__of__nat__symmetric,axiom,
% 0.29/0.62      ! [K: nat,N2: nat] :
% 0.29/0.62        ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.62       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 0.29/0.62          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_of_nat_symmetric
% 0.29/0.62  thf(fact_8103_inverse__powr,axiom,
% 0.29/0.62      ! [Y: real,A: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.62       => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 0.29/0.62          = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_powr
% 0.29/0.62  thf(fact_8104_Complex__eq__i,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ( complex2 @ X4 @ Y )
% 0.29/0.62          = imaginary_unit )
% 0.29/0.62        = ( ( X4 = zero_zero_real )
% 0.29/0.62          & ( Y = one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Complex_eq_i
% 0.29/0.62  thf(fact_8105_imaginary__unit_Ocode,axiom,
% 0.29/0.62      ( imaginary_unit
% 0.29/0.62      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % imaginary_unit.code
% 0.29/0.62  thf(fact_8106_inverse__le__iff,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.62           => ( ord_less_eq_rat @ B @ A ) )
% 0.29/0.62          & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.62           => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff
% 0.29/0.62  thf(fact_8107_inverse__le__iff,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62        = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.62           => ( ord_less_eq_real @ B @ A ) )
% 0.29/0.62          & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.62           => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_le_iff
% 0.29/0.62  thf(fact_8108_inverse__less__iff,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62        = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.29/0.62           => ( ord_less_rat @ B @ A ) )
% 0.29/0.62          & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.29/0.62           => ( ord_less_rat @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff
% 0.29/0.62  thf(fact_8109_inverse__less__iff,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62        = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.29/0.62           => ( ord_less_real @ B @ A ) )
% 0.29/0.62          & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.29/0.62           => ( ord_less_real @ A @ B ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_iff
% 0.29/0.62  thf(fact_8110_one__le__inverse,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_le_inverse
% 0.29/0.62  thf(fact_8111_one__le__inverse,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.62         => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_le_inverse
% 0.29/0.62  thf(fact_8112_inverse__less__1__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 0.29/0.62        = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 0.29/0.62          | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_1_iff
% 0.29/0.62  thf(fact_8113_inverse__less__1__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 0.29/0.62        = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.62          | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_less_1_iff
% 0.29/0.62  thf(fact_8114_one__le__inverse__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 0.29/0.62        = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.62          & ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_le_inverse_iff
% 0.29/0.62  thf(fact_8115_one__le__inverse__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 0.29/0.62        = ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62          & ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % one_le_inverse_iff
% 0.29/0.62  thf(fact_8116_inverse__diff__inverse,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( A != zero_zero_rat )
% 0.29/0.62       => ( ( B != zero_zero_rat )
% 0.29/0.62         => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 0.29/0.62            = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_diff_inverse
% 0.29/0.62  thf(fact_8117_inverse__diff__inverse,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( A != zero_zero_real )
% 0.29/0.62       => ( ( B != zero_zero_real )
% 0.29/0.62         => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.29/0.62            = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_diff_inverse
% 0.29/0.62  thf(fact_8118_inverse__diff__inverse,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( A != zero_zero_complex )
% 0.29/0.62       => ( ( B != zero_zero_complex )
% 0.29/0.62         => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 0.29/0.62            = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_diff_inverse
% 0.29/0.62  thf(fact_8119_reals__Archimedean,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.62       => ? [N3: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % reals_Archimedean
% 0.29/0.62  thf(fact_8120_reals__Archimedean,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ? [N3: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % reals_Archimedean
% 0.29/0.62  thf(fact_8121_gbinomial__addition__formula,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_addition_formula
% 0.29/0.62  thf(fact_8122_gbinomial__addition__formula,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ A @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_addition_formula
% 0.29/0.62  thf(fact_8123_gbinomial__addition__formula,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.29/0.62        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_addition_formula
% 0.29/0.62  thf(fact_8124_gbinomial__absorb__comp,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 0.29/0.62        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorb_comp
% 0.29/0.62  thf(fact_8125_gbinomial__absorb__comp,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 0.29/0.62        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorb_comp
% 0.29/0.62  thf(fact_8126_gbinomial__absorb__comp,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 0.29/0.62        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorb_comp
% 0.29/0.62  thf(fact_8127_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.29/0.62      ! [K: nat,A: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 0.29/0.62       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_ge_n_over_k_pow_k
% 0.29/0.62  thf(fact_8128_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.29/0.62      ! [K: nat,A: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 0.29/0.62       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_ge_n_over_k_pow_k
% 0.29/0.62  thf(fact_8129_gbinomial__mult__1,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.29/0.62        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1
% 0.29/0.62  thf(fact_8130_gbinomial__mult__1,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 0.29/0.62        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1
% 0.29/0.62  thf(fact_8131_gbinomial__mult__1,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 0.29/0.62        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1
% 0.29/0.62  thf(fact_8132_gbinomial__mult__1_H,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.29/0.62        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1'
% 0.29/0.62  thf(fact_8133_gbinomial__mult__1_H,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 0.29/0.62        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1'
% 0.29/0.62  thf(fact_8134_gbinomial__mult__1_H,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 0.29/0.62        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_mult_1'
% 0.29/0.62  thf(fact_8135_forall__pos__mono__1,axiom,
% 0.29/0.62      ! [P: real > $o,E2: real] :
% 0.29/0.62        ( ! [D3: real,E: real] :
% 0.29/0.62            ( ( ord_less_real @ D3 @ E )
% 0.29/0.62           => ( ( P @ D3 )
% 0.29/0.62             => ( P @ E ) ) )
% 0.29/0.62       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.29/0.62         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.62           => ( P @ E2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % forall_pos_mono_1
% 0.29/0.62  thf(fact_8136_forall__pos__mono,axiom,
% 0.29/0.62      ! [P: real > $o,E2: real] :
% 0.29/0.62        ( ! [D3: real,E: real] :
% 0.29/0.62            ( ( ord_less_real @ D3 @ E )
% 0.29/0.62           => ( ( P @ D3 )
% 0.29/0.62             => ( P @ E ) ) )
% 0.29/0.62       => ( ! [N3: nat] :
% 0.29/0.62              ( ( N3 != zero_zero_nat )
% 0.29/0.62             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 0.29/0.62         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.62           => ( P @ E2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % forall_pos_mono
% 0.29/0.62  thf(fact_8137_real__arch__inverse,axiom,
% 0.29/0.62      ! [E2: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.62        = ( ? [N: nat] :
% 0.29/0.62              ( ( N != zero_zero_nat )
% 0.29/0.62              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.29/0.62              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_arch_inverse
% 0.29/0.62  thf(fact_8138_sqrt__divide__self__eq,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( divide_divide_real @ ( sqrt @ X4 ) @ X4 )
% 0.29/0.62          = ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sqrt_divide_self_eq
% 0.29/0.62  thf(fact_8139_ln__inverse,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ln_ln_real @ ( inverse_inverse_real @ X4 ) )
% 0.29/0.62          = ( uminus_uminus_real @ ( ln_ln_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ln_inverse
% 0.29/0.62  thf(fact_8140_ex__inverse__of__nat__less,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 0.29/0.62       => ? [N3: nat] :
% 0.29/0.62            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.62            & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N3 ) ) @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ex_inverse_of_nat_less
% 0.29/0.62  thf(fact_8141_ex__inverse__of__nat__less,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ? [N3: nat] :
% 0.29/0.62            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.29/0.62            & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ex_inverse_of_nat_less
% 0.29/0.62  thf(fact_8142_power__diff__conv__inverse,axiom,
% 0.29/0.62      ! [X4: rat,M: nat,N2: nat] :
% 0.29/0.62        ( ( X4 != zero_zero_rat )
% 0.29/0.62       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.62         => ( ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.62            = ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ M ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_diff_conv_inverse
% 0.29/0.62  thf(fact_8143_power__diff__conv__inverse,axiom,
% 0.29/0.62      ! [X4: real,M: nat,N2: nat] :
% 0.29/0.62        ( ( X4 != zero_zero_real )
% 0.29/0.62       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.62         => ( ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.62            = ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ M ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_diff_conv_inverse
% 0.29/0.62  thf(fact_8144_power__diff__conv__inverse,axiom,
% 0.29/0.62      ! [X4: complex,M: nat,N2: nat] :
% 0.29/0.62        ( ( X4 != zero_zero_complex )
% 0.29/0.62       => ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.62         => ( ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/0.62            = ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ M ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_diff_conv_inverse
% 0.29/0.62  thf(fact_8145_Suc__times__gbinomial,axiom,
% 0.29/0.62      ! [K: nat,A: rat] :
% 0.29/0.62        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Suc_times_gbinomial
% 0.29/0.62  thf(fact_8146_Suc__times__gbinomial,axiom,
% 0.29/0.62      ! [K: nat,A: complex] :
% 0.29/0.62        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Suc_times_gbinomial
% 0.29/0.62  thf(fact_8147_Suc__times__gbinomial,axiom,
% 0.29/0.62      ! [K: nat,A: real] :
% 0.29/0.62        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Suc_times_gbinomial
% 0.29/0.62  thf(fact_8148_gbinomial__absorption,axiom,
% 0.29/0.62      ! [K: nat,A: rat] :
% 0.29/0.62        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption
% 0.29/0.62  thf(fact_8149_gbinomial__absorption,axiom,
% 0.29/0.62      ! [K: nat,A: complex] :
% 0.29/0.62        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption
% 0.29/0.62  thf(fact_8150_gbinomial__absorption,axiom,
% 0.29/0.62      ! [K: nat,A: real] :
% 0.29/0.62        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 0.29/0.62        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_absorption
% 0.29/0.62  thf(fact_8151_gbinomial__trinomial__revision,axiom,
% 0.29/0.62      ! [K: nat,M: nat,A: rat] :
% 0.29/0.62        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.62       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 0.29/0.62          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_trinomial_revision
% 0.29/0.62  thf(fact_8152_gbinomial__trinomial__revision,axiom,
% 0.29/0.62      ! [K: nat,M: nat,A: complex] :
% 0.29/0.62        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.62       => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 0.29/0.62          = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_trinomial_revision
% 0.29/0.62  thf(fact_8153_gbinomial__trinomial__revision,axiom,
% 0.29/0.62      ! [K: nat,M: nat,A: real] :
% 0.29/0.62        ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.62       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 0.29/0.62          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_trinomial_revision
% 0.29/0.62  thf(fact_8154_log__inverse,axiom,
% 0.29/0.62      ! [A: real,X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( A != one_one_real )
% 0.29/0.62         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62           => ( ( log @ A @ ( inverse_inverse_real @ X4 ) )
% 0.29/0.62              = ( uminus_uminus_real @ ( log @ A @ X4 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % log_inverse
% 0.29/0.62  thf(fact_8155_frac__eq,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( archim2898591450579166408c_real @ X4 )
% 0.29/0.62          = X4 )
% 0.29/0.62        = ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62          & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_eq
% 0.29/0.62  thf(fact_8156_frac__eq,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ( archimedean_frac_rat @ X4 )
% 0.29/0.62          = X4 )
% 0.29/0.62        = ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 0.29/0.62          & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_eq
% 0.29/0.62  thf(fact_8157_frac__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.29/0.62         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 0.29/0.62        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.29/0.62         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_add
% 0.29/0.62  thf(fact_8158_frac__add,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] :
% 0.29/0.62        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.29/0.62         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 0.29/0.62        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.29/0.62         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 0.29/0.62            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_add
% 0.29/0.62  thf(fact_8159_gbinomial__rec,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_rec
% 0.29/0.62  thf(fact_8160_gbinomial__rec,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_rec
% 0.29/0.62  thf(fact_8161_gbinomial__rec,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_rec
% 0.29/0.62  thf(fact_8162_gbinomial__factors,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_factors
% 0.29/0.62  thf(fact_8163_gbinomial__factors,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_factors
% 0.29/0.62  thf(fact_8164_gbinomial__factors,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 0.29/0.62        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_factors
% 0.29/0.62  thf(fact_8165_gbinomial__negated__upper,axiom,
% 0.29/0.62      ( gbinomial_complex
% 0.29/0.62      = ( ^ [A3: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A3 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_negated_upper
% 0.29/0.62  thf(fact_8166_gbinomial__negated__upper,axiom,
% 0.29/0.62      ( gbinomial_rat
% 0.29/0.62      = ( ^ [A3: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A3 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_negated_upper
% 0.29/0.62  thf(fact_8167_gbinomial__negated__upper,axiom,
% 0.29/0.62      ( gbinomial_real
% 0.29/0.62      = ( ^ [A3: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A3 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_negated_upper
% 0.29/0.62  thf(fact_8168_gbinomial__index__swap,axiom,
% 0.29/0.62      ! [K: nat,N2: nat] :
% 0.29/0.62        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 0.29/0.62        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_index_swap
% 0.29/0.62  thf(fact_8169_gbinomial__index__swap,axiom,
% 0.29/0.62      ! [K: nat,N2: nat] :
% 0.29/0.62        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 0.29/0.62        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_index_swap
% 0.29/0.62  thf(fact_8170_gbinomial__index__swap,axiom,
% 0.29/0.62      ! [K: nat,N2: nat] :
% 0.29/0.62        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 0.29/0.62        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_index_swap
% 0.29/0.62  thf(fact_8171_exp__plus__inverse__exp,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_plus_inverse_exp
% 0.29/0.62  thf(fact_8172_cmod__unit__one,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 0.29/0.62        = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_unit_one
% 0.29/0.62  thf(fact_8173_gbinomial__minus,axiom,
% 0.29/0.62      ! [A: complex,K: nat] :
% 0.29/0.62        ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 0.29/0.62        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_minus
% 0.29/0.62  thf(fact_8174_gbinomial__minus,axiom,
% 0.29/0.62      ! [A: rat,K: nat] :
% 0.29/0.62        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 0.29/0.62        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_minus
% 0.29/0.62  thf(fact_8175_gbinomial__minus,axiom,
% 0.29/0.62      ! [A: real,K: nat] :
% 0.29/0.62        ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 0.29/0.62        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_minus
% 0.29/0.62  thf(fact_8176_plus__inverse__ge__2,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % plus_inverse_ge_2
% 0.29/0.62  thf(fact_8177_real__inv__sqrt__pow2,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62          = ( inverse_inverse_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_inv_sqrt_pow2
% 0.29/0.62  thf(fact_8178_gbinomial__reduce__nat,axiom,
% 0.29/0.62      ! [K: nat,A: complex] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_complex @ A @ K )
% 0.29/0.62          = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_reduce_nat
% 0.29/0.62  thf(fact_8179_gbinomial__reduce__nat,axiom,
% 0.29/0.62      ! [K: nat,A: real] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_real @ A @ K )
% 0.29/0.62          = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_reduce_nat
% 0.29/0.62  thf(fact_8180_gbinomial__reduce__nat,axiom,
% 0.29/0.62      ! [K: nat,A: rat] :
% 0.29/0.62        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.62       => ( ( gbinomial_rat @ A @ K )
% 0.29/0.62          = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_reduce_nat
% 0.29/0.62  thf(fact_8181_gbinomial__pochhammer,axiom,
% 0.29/0.62      ( gbinomial_complex
% 0.29/0.62      = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer
% 0.29/0.62  thf(fact_8182_gbinomial__pochhammer,axiom,
% 0.29/0.62      ( gbinomial_rat
% 0.29/0.62      = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer
% 0.29/0.62  thf(fact_8183_gbinomial__pochhammer,axiom,
% 0.29/0.62      ( gbinomial_real
% 0.29/0.62      = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer
% 0.29/0.62  thf(fact_8184_gbinomial__pochhammer_H,axiom,
% 0.29/0.62      ( gbinomial_rat
% 0.29/0.62      = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer'
% 0.29/0.62  thf(fact_8185_gbinomial__pochhammer_H,axiom,
% 0.29/0.62      ( gbinomial_complex
% 0.29/0.62      = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer'
% 0.29/0.62  thf(fact_8186_gbinomial__pochhammer_H,axiom,
% 0.29/0.62      ( gbinomial_real
% 0.29/0.62      = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_pochhammer'
% 0.29/0.62  thf(fact_8187_tan__cot,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 0.29/0.62        = ( inverse_inverse_real @ ( tan_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tan_cot
% 0.29/0.62  thf(fact_8188_floor__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.29/0.62         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 0.29/0.62        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.29/0.62         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_add
% 0.29/0.62  thf(fact_8189_floor__add,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] :
% 0.29/0.62        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.29/0.62         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 0.29/0.62        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.29/0.62         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 0.29/0.62            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_add
% 0.29/0.62  thf(fact_8190_real__le__x__sinh,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ord_less_eq_real @ X4 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_le_x_sinh
% 0.29/0.62  thf(fact_8191_real__le__abs__sinh,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % real_le_abs_sinh
% 0.29/0.62  thf(fact_8192_tan__sec,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( cos_real @ X4 )
% 0.29/0.62         != zero_zero_real )
% 0.29/0.62       => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62          = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tan_sec
% 0.29/0.62  thf(fact_8193_tan__sec,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( cos_complex @ X4 )
% 0.29/0.62         != zero_zero_complex )
% 0.29/0.62       => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62          = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tan_sec
% 0.29/0.62  thf(fact_8194_Arg__minus__ii,axiom,
% 0.29/0.62      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 0.29/0.62      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Arg_minus_ii
% 0.29/0.62  thf(fact_8195_csqrt__ii,axiom,
% 0.29/0.62      ( ( csqrt @ imaginary_unit )
% 0.29/0.62      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_ii
% 0.29/0.62  thf(fact_8196_Arg__ii,axiom,
% 0.29/0.62      ( ( arg @ imaginary_unit )
% 0.29/0.62      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Arg_ii
% 0.29/0.62  thf(fact_8197_sinh__ln__real,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( sinh_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.62          = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_ln_real
% 0.29/0.62  thf(fact_8198_cis__multiple__2pi,axiom,
% 0.29/0.62      ! [N2: real] :
% 0.29/0.62        ( ( member_real @ N2 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 0.29/0.62          = one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cis_multiple_2pi
% 0.29/0.62  thf(fact_8199_sinh__real__less__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 0.29/0.62        = ( ord_less_real @ X4 @ Y ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_less_iff
% 0.29/0.62  thf(fact_8200_sinh__real__le__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 0.29/0.62        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_le_iff
% 0.29/0.62  thf(fact_8201_sinh__real__neg__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 0.29/0.62        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_neg_iff
% 0.29/0.62  thf(fact_8202_sinh__real__pos__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 0.29/0.62        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_pos_iff
% 0.29/0.62  thf(fact_8203_sinh__real__nonneg__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 0.29/0.62        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_nonneg_iff
% 0.29/0.62  thf(fact_8204_sinh__real__nonpos__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 0.29/0.62        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_real_nonpos_iff
% 0.29/0.62  thf(fact_8205_floor__add2,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62          | ( member_real @ Y @ ring_1_Ints_real ) )
% 0.29/0.62       => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62          = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_add2
% 0.29/0.62  thf(fact_8206_floor__add2,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] :
% 0.29/0.62        ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62          | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 0.29/0.62       => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 0.29/0.62          = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % floor_add2
% 0.29/0.62  thf(fact_8207_frac__gt__0__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) )
% 0.29/0.62        = ( ~ ( member_real @ X4 @ ring_1_Ints_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_gt_0_iff
% 0.29/0.62  thf(fact_8208_frac__gt__0__iff,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) )
% 0.29/0.62        = ( ~ ( member_rat @ X4 @ ring_1_Ints_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_gt_0_iff
% 0.29/0.62  thf(fact_8209_power2__csqrt,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = Z ) ).
% 0.29/0.62  
% 0.29/0.62  % power2_csqrt
% 0.29/0.62  thf(fact_8210_Ints__power,axiom,
% 0.29/0.62      ! [A: real,N2: nat] :
% 0.29/0.62        ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62       => ( member_real @ ( power_power_real @ A @ N2 ) @ ring_1_Ints_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_power
% 0.29/0.62  thf(fact_8211_Ints__power,axiom,
% 0.29/0.62      ! [A: int,N2: nat] :
% 0.29/0.62        ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.62       => ( member_int @ ( power_power_int @ A @ N2 ) @ ring_1_Ints_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_power
% 0.29/0.62  thf(fact_8212_Ints__power,axiom,
% 0.29/0.62      ! [A: complex,N2: nat] :
% 0.29/0.62        ( ( member_complex @ A @ ring_1_Ints_complex )
% 0.29/0.62       => ( member_complex @ ( power_power_complex @ A @ N2 ) @ ring_1_Ints_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_power
% 0.29/0.62  thf(fact_8213_Ints__numeral,axiom,
% 0.29/0.62      ! [N2: num] : ( member_complex @ ( numera6690914467698888265omplex @ N2 ) @ ring_1_Ints_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_numeral
% 0.29/0.62  thf(fact_8214_Ints__numeral,axiom,
% 0.29/0.62      ! [N2: num] : ( member_real @ ( numeral_numeral_real @ N2 ) @ ring_1_Ints_real ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_numeral
% 0.29/0.62  thf(fact_8215_Ints__numeral,axiom,
% 0.29/0.62      ! [N2: num] : ( member_int @ ( numeral_numeral_int @ N2 ) @ ring_1_Ints_int ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_numeral
% 0.29/0.62  thf(fact_8216_Ints__1,axiom,
% 0.29/0.62      member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 0.29/0.62  
% 0.29/0.62  % Ints_1
% 0.29/0.62  thf(fact_8217_Ints__1,axiom,
% 0.29/0.62      member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 0.29/0.62  
% 0.29/0.62  % Ints_1
% 0.29/0.62  thf(fact_8218_Ints__1,axiom,
% 0.29/0.62      member_int @ one_one_int @ ring_1_Ints_int ).
% 0.29/0.62  
% 0.29/0.62  % Ints_1
% 0.29/0.62  thf(fact_8219_Ints__1,axiom,
% 0.29/0.62      member_real @ one_one_real @ ring_1_Ints_real ).
% 0.29/0.62  
% 0.29/0.62  % Ints_1
% 0.29/0.62  thf(fact_8220_Ints__add,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( member_complex @ A @ ring_1_Ints_complex )
% 0.29/0.62       => ( ( member_complex @ B @ ring_1_Ints_complex )
% 0.29/0.62         => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_add
% 0.29/0.62  thf(fact_8221_Ints__add,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62       => ( ( member_real @ B @ ring_1_Ints_real )
% 0.29/0.62         => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_add
% 0.29/0.62  thf(fact_8222_Ints__add,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 0.29/0.62         => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_add
% 0.29/0.62  thf(fact_8223_Ints__add,axiom,
% 0.29/0.62      ! [A: int,B: int] :
% 0.29/0.62        ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.62       => ( ( member_int @ B @ ring_1_Ints_int )
% 0.29/0.62         => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_add
% 0.29/0.62  thf(fact_8224_Ints__double__eq__0__iff,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( member_complex @ A @ ring_1_Ints_complex )
% 0.29/0.62       => ( ( ( plus_plus_complex @ A @ A )
% 0.29/0.62            = zero_zero_complex )
% 0.29/0.62          = ( A = zero_zero_complex ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_double_eq_0_iff
% 0.29/0.62  thf(fact_8225_Ints__double__eq__0__iff,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62       => ( ( ( plus_plus_real @ A @ A )
% 0.29/0.62            = zero_zero_real )
% 0.29/0.62          = ( A = zero_zero_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_double_eq_0_iff
% 0.29/0.62  thf(fact_8226_Ints__double__eq__0__iff,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( ( plus_plus_rat @ A @ A )
% 0.29/0.62            = zero_zero_rat )
% 0.29/0.62          = ( A = zero_zero_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_double_eq_0_iff
% 0.29/0.62  thf(fact_8227_Ints__double__eq__0__iff,axiom,
% 0.29/0.62      ! [A: int] :
% 0.29/0.62        ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.62       => ( ( ( plus_plus_int @ A @ A )
% 0.29/0.62            = zero_zero_int )
% 0.29/0.62          = ( A = zero_zero_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_double_eq_0_iff
% 0.29/0.62  thf(fact_8228_Ints__odd__nonzero,axiom,
% 0.29/0.62      ! [A: complex] :
% 0.29/0.62        ( ( member_complex @ A @ ring_1_Ints_complex )
% 0.29/0.62       => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 0.29/0.62         != zero_zero_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_nonzero
% 0.29/0.62  thf(fact_8229_Ints__odd__nonzero,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62       => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 0.29/0.62         != zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_nonzero
% 0.29/0.62  thf(fact_8230_Ints__odd__nonzero,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 0.29/0.62         != zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_nonzero
% 0.29/0.62  thf(fact_8231_Ints__odd__nonzero,axiom,
% 0.29/0.62      ! [A: int] :
% 0.29/0.62        ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.62       => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 0.29/0.62         != zero_zero_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_nonzero
% 0.29/0.62  thf(fact_8232_of__int__divide__in__Ints,axiom,
% 0.29/0.62      ! [B: int,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.62       => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_divide_in_Ints
% 0.29/0.62  thf(fact_8233_of__int__divide__in__Ints,axiom,
% 0.29/0.62      ! [B: int,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.62       => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_divide_in_Ints
% 0.29/0.62  thf(fact_8234_of__int__divide__in__Ints,axiom,
% 0.29/0.62      ! [B: int,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.62       => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_divide_in_Ints
% 0.29/0.62  thf(fact_8235_of__int__divide__in__Ints,axiom,
% 0.29/0.62      ! [B: int,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.62       => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_divide_in_Ints
% 0.29/0.62  thf(fact_8236_of__int__divide__in__Ints,axiom,
% 0.29/0.62      ! [B: int,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ B @ A )
% 0.29/0.62       => ( member_Code_integer @ ( divide6298287555418463151nteger @ ( ring_18347121197199848620nteger @ A ) @ ( ring_18347121197199848620nteger @ B ) ) @ ring_11222124179247155820nteger ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_divide_in_Ints
% 0.29/0.62  thf(fact_8237_Ints__odd__less__0,axiom,
% 0.29/0.62      ! [A: real] :
% 0.29/0.62        ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62       => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 0.29/0.62          = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_less_0
% 0.29/0.62  thf(fact_8238_Ints__odd__less__0,axiom,
% 0.29/0.62      ! [A: rat] :
% 0.29/0.62        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 0.29/0.62          = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_less_0
% 0.29/0.62  thf(fact_8239_Ints__odd__less__0,axiom,
% 0.29/0.62      ! [A: int] :
% 0.29/0.62        ( ( member_int @ A @ ring_1_Ints_int )
% 0.29/0.62       => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 0.29/0.62          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_odd_less_0
% 0.29/0.62  thf(fact_8240_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.62      ! [X4: code_integer] :
% 0.29/0.62        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 0.29/0.62       => ( ( X4 != zero_z3403309356797280102nteger )
% 0.29/0.62         => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_ge1
% 0.29/0.62  thf(fact_8241_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( X4 != zero_zero_real )
% 0.29/0.62         => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_ge1
% 0.29/0.62  thf(fact_8242_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( X4 != zero_zero_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_ge1
% 0.29/0.62  thf(fact_8243_Ints__nonzero__abs__ge1,axiom,
% 0.29/0.62      ! [X4: int] :
% 0.29/0.62        ( ( member_int @ X4 @ ring_1_Ints_int )
% 0.29/0.62       => ( ( X4 != zero_zero_int )
% 0.29/0.62         => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_ge1
% 0.29/0.62  thf(fact_8244_Ints__nonzero__abs__less1,axiom,
% 0.29/0.62      ! [X4: code_integer] :
% 0.29/0.62        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 0.29/0.62       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer )
% 0.29/0.62         => ( X4 = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_less1
% 0.29/0.62  thf(fact_8245_Ints__nonzero__abs__less1,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.62         => ( X4 = zero_zero_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_less1
% 0.29/0.62  thf(fact_8246_Ints__nonzero__abs__less1,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat )
% 0.29/0.62         => ( X4 = zero_zero_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_less1
% 0.29/0.62  thf(fact_8247_Ints__nonzero__abs__less1,axiom,
% 0.29/0.62      ! [X4: int] :
% 0.29/0.62        ( ( member_int @ X4 @ ring_1_Ints_int )
% 0.29/0.62       => ( ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int )
% 0.29/0.62         => ( X4 = zero_zero_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_nonzero_abs_less1
% 0.29/0.62  thf(fact_8248_Ints__eq__abs__less1,axiom,
% 0.29/0.62      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.62        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 0.29/0.62       => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 0.29/0.62         => ( ( X4 = Y )
% 0.29/0.62            = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_eq_abs_less1
% 0.29/0.62  thf(fact_8249_Ints__eq__abs__less1,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( member_real @ Y @ ring_1_Ints_real )
% 0.29/0.62         => ( ( X4 = Y )
% 0.29/0.62            = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y ) ) @ one_one_real ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_eq_abs_less1
% 0.29/0.62  thf(fact_8250_Ints__eq__abs__less1,axiom,
% 0.29/0.62      ! [X4: rat,Y: rat] :
% 0.29/0.62        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62       => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 0.29/0.62         => ( ( X4 = Y )
% 0.29/0.62            = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_eq_abs_less1
% 0.29/0.62  thf(fact_8251_Ints__eq__abs__less1,axiom,
% 0.29/0.62      ! [X4: int,Y: int] :
% 0.29/0.62        ( ( member_int @ X4 @ ring_1_Ints_int )
% 0.29/0.62       => ( ( member_int @ Y @ ring_1_Ints_int )
% 0.29/0.62         => ( ( X4 = Y )
% 0.29/0.62            = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ints_eq_abs_less1
% 0.29/0.62  thf(fact_8252_of__real__sqrt,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X4 ) )
% 0.29/0.62          = ( csqrt @ ( real_V4546457046886955230omplex @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_real_sqrt
% 0.29/0.62  thf(fact_8253_frac__neg,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62         => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.62            = zero_zero_real ) )
% 0.29/0.62        & ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 0.29/0.62         => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 0.29/0.62            = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X4 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_neg
% 0.29/0.62  thf(fact_8254_frac__neg,axiom,
% 0.29/0.62      ! [X4: rat] :
% 0.29/0.62        ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 0.29/0.62            = zero_zero_rat ) )
% 0.29/0.62        & ( ~ ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.29/0.62         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 0.29/0.62            = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X4 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_neg
% 0.29/0.62  thf(fact_8255_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8256_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8257_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8258_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8259_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8260_le__mult__floor__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % le_mult_floor_Ints
% 0.29/0.62  thf(fact_8261_frac__unique__iff,axiom,
% 0.29/0.62      ! [X4: real,A: real] :
% 0.29/0.62        ( ( ( archim2898591450579166408c_real @ X4 )
% 0.29/0.62          = A )
% 0.29/0.62        = ( ( member_real @ ( minus_minus_real @ X4 @ A ) @ ring_1_Ints_real )
% 0.29/0.62          & ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62          & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_unique_iff
% 0.29/0.62  thf(fact_8262_frac__unique__iff,axiom,
% 0.29/0.62      ! [X4: rat,A: rat] :
% 0.29/0.62        ( ( ( archimedean_frac_rat @ X4 )
% 0.29/0.62          = A )
% 0.29/0.62        = ( ( member_rat @ ( minus_minus_rat @ X4 @ A ) @ ring_1_Ints_rat )
% 0.29/0.62          & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62          & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % frac_unique_iff
% 0.29/0.62  thf(fact_8263_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8264_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8265_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.62       => ( ( member_real @ A @ ring_1_Ints_real )
% 0.29/0.62         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8266_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8267_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8268_mult__ceiling__le__Ints,axiom,
% 0.29/0.62      ! [A: rat,B: rat] :
% 0.29/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.62       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.29/0.62         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % mult_ceiling_le_Ints
% 0.29/0.62  thf(fact_8269_Arg__bounded,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.29/0.62        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Arg_bounded
% 0.29/0.62  thf(fact_8270_sin__integer__2pi,axiom,
% 0.29/0.62      ! [N2: real] :
% 0.29/0.62        ( ( member_real @ N2 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 0.29/0.62          = zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sin_integer_2pi
% 0.29/0.62  thf(fact_8271_cos__integer__2pi,axiom,
% 0.29/0.62      ! [N2: real] :
% 0.29/0.62        ( ( member_real @ N2 @ ring_1_Ints_real )
% 0.29/0.62       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 0.29/0.62          = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cos_integer_2pi
% 0.29/0.62  thf(fact_8272_complex__inverse,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 0.29/0.62        = ( 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 ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_inverse
% 0.29/0.62  thf(fact_8273_sinh__field__def,axiom,
% 0.29/0.62      ( sinh_real
% 0.29/0.62      = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_field_def
% 0.29/0.62  thf(fact_8274_sinh__field__def,axiom,
% 0.29/0.62      ( sinh_complex
% 0.29/0.62      = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_field_def
% 0.29/0.62  thf(fact_8275_cis__Arg__unique,axiom,
% 0.29/0.62      ! [Z: complex,X4: real] :
% 0.29/0.62        ( ( ( sgn_sgn_complex @ Z )
% 0.29/0.62          = ( cis @ X4 ) )
% 0.29/0.62       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 0.29/0.62         => ( ( ord_less_eq_real @ X4 @ pi )
% 0.29/0.62           => ( ( arg @ Z )
% 0.29/0.62              = X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cis_Arg_unique
% 0.29/0.62  thf(fact_8276_Arg__correct,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( Z != zero_zero_complex )
% 0.29/0.62       => ( ( ( sgn_sgn_complex @ Z )
% 0.29/0.62            = ( cis @ ( arg @ Z ) ) )
% 0.29/0.62          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.29/0.62          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Arg_correct
% 0.29/0.62  thf(fact_8277_cosh__ln__real,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( cosh_real @ ( ln_ln_real @ X4 ) )
% 0.29/0.62          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_ln_real
% 0.29/0.62  thf(fact_8278_cosh__double,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.62        = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_double
% 0.29/0.62  thf(fact_8279_cosh__double,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.62        = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_double
% 0.29/0.62  thf(fact_8280_horner__sum__of__bool__2__less,axiom,
% 0.29/0.62      ! [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 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % horner_sum_of_bool_2_less
% 0.29/0.62  thf(fact_8281_cosh__zero__iff,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ( cosh_real @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62        = ( ( power_power_real @ ( exp_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_zero_iff
% 0.29/0.62  thf(fact_8282_cosh__zero__iff,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( cosh_complex @ X4 )
% 0.29/0.62          = zero_zero_complex )
% 0.29/0.62        = ( ( power_power_complex @ ( exp_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_zero_iff
% 0.29/0.62  thf(fact_8283_push__bit__numeral__minus__1,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.62        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_numeral_minus_1
% 0.29/0.62  thf(fact_8284_push__bit__numeral__minus__1,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_numeral_minus_1
% 0.29/0.62  thf(fact_8285_push__bit__nonnegative__int__iff,axiom,
% 0.29/0.62      ! [N2: nat,K: int] :
% 0.29/0.62        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 0.29/0.62        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_nonnegative_int_iff
% 0.29/0.62  thf(fact_8286_push__bit__negative__int__iff,axiom,
% 0.29/0.62      ! [N2: nat,K: int] :
% 0.29/0.62        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.62        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_negative_int_iff
% 0.29/0.62  thf(fact_8287_push__bit__eq__0__iff,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( ( bit_se545348938243370406it_int @ N2 @ A )
% 0.29/0.62          = zero_zero_int )
% 0.29/0.62        = ( A = zero_zero_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_eq_0_iff
% 0.29/0.62  thf(fact_8288_push__bit__eq__0__iff,axiom,
% 0.29/0.62      ! [N2: nat,A: nat] :
% 0.29/0.62        ( ( ( bit_se547839408752420682it_nat @ N2 @ A )
% 0.29/0.62          = zero_zero_nat )
% 0.29/0.62        = ( A = zero_zero_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_eq_0_iff
% 0.29/0.62  thf(fact_8289_push__bit__of__0,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ zero_zero_int )
% 0.29/0.62        = zero_zero_int ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_0
% 0.29/0.62  thf(fact_8290_push__bit__of__0,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ zero_zero_nat )
% 0.29/0.62        = zero_zero_nat ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_0
% 0.29/0.62  thf(fact_8291_push__bit__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_push_bit
% 0.29/0.62  thf(fact_8292_push__bit__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_push_bit
% 0.29/0.62  thf(fact_8293_push__bit__and,axiom,
% 0.29/0.62      ! [N2: nat,A: int,B: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.29/0.62        = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_and
% 0.29/0.62  thf(fact_8294_push__bit__and,axiom,
% 0.29/0.62      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.29/0.62        = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_and
% 0.29/0.62  thf(fact_8295_push__bit__xor,axiom,
% 0.29/0.62      ! [N2: nat,A: int,B: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 0.29/0.62        = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_xor
% 0.29/0.62  thf(fact_8296_push__bit__xor,axiom,
% 0.29/0.62      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 0.29/0.62        = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_xor
% 0.29/0.62  thf(fact_8297_concat__bit__of__zero__1,axiom,
% 0.29/0.62      ! [N2: nat,L: int] :
% 0.29/0.62        ( ( bit_concat_bit @ N2 @ zero_zero_int @ L )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ N2 @ L ) ) ).
% 0.29/0.62  
% 0.29/0.62  % concat_bit_of_zero_1
% 0.29/0.62  thf(fact_8298_cosh__0,axiom,
% 0.29/0.62      ( ( cosh_complex @ zero_zero_complex )
% 0.29/0.62      = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_0
% 0.29/0.62  thf(fact_8299_cosh__0,axiom,
% 0.29/0.62      ( ( cosh_real @ zero_zero_real )
% 0.29/0.62      = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_0
% 0.29/0.62  thf(fact_8300_push__bit__Suc__numeral,axiom,
% 0.29/0.62      ! [N2: nat,K: num] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ K ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc_numeral
% 0.29/0.62  thf(fact_8301_push__bit__Suc__numeral,axiom,
% 0.29/0.62      ! [N2: nat,K: num] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc_numeral
% 0.29/0.62  thf(fact_8302_push__bit__Suc__minus__numeral,axiom,
% 0.29/0.62      ! [N2: nat,K: num] :
% 0.29/0.62        ( ( bit_se7788150548672797655nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.62        = ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc_minus_numeral
% 0.29/0.62  thf(fact_8303_push__bit__Suc__minus__numeral,axiom,
% 0.29/0.62      ! [N2: nat,K: num] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc_minus_numeral
% 0.29/0.62  thf(fact_8304_push__bit__numeral,axiom,
% 0.29/0.62      ! [L: num,K: num] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ K ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_numeral
% 0.29/0.62  thf(fact_8305_push__bit__numeral,axiom,
% 0.29/0.62      ! [L: num,K: num] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_numeral
% 0.29/0.62  thf(fact_8306_push__bit__minus__one__eq__not__mask,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.62        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus_one_eq_not_mask
% 0.29/0.62  thf(fact_8307_push__bit__minus__one__eq__not__mask,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.62        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus_one_eq_not_mask
% 0.29/0.62  thf(fact_8308_push__bit__Suc,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ A )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc
% 0.29/0.62  thf(fact_8309_push__bit__Suc,axiom,
% 0.29/0.62      ! [N2: nat,A: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ A )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_Suc
% 0.29/0.62  thf(fact_8310_push__bit__of__1,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ one_one_int )
% 0.29/0.62        = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_1
% 0.29/0.62  thf(fact_8311_push__bit__of__1,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ one_one_nat )
% 0.29/0.62        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_1
% 0.29/0.62  thf(fact_8312_push__bit__of__Suc__0,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.62        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_Suc_0
% 0.29/0.62  thf(fact_8313_even__push__bit__iff,axiom,
% 0.29/0.62      ! [N2: nat,A: code_integer] :
% 0.29/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N2 @ A ) )
% 0.29/0.62        = ( ( N2 != zero_zero_nat )
% 0.29/0.62          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % even_push_bit_iff
% 0.29/0.62  thf(fact_8314_even__push__bit__iff,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 0.29/0.62        = ( ( N2 != zero_zero_nat )
% 0.29/0.62          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % even_push_bit_iff
% 0.29/0.62  thf(fact_8315_even__push__bit__iff,axiom,
% 0.29/0.62      ! [N2: nat,A: nat] :
% 0.29/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 0.29/0.62        = ( ( N2 != zero_zero_nat )
% 0.29/0.62          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % even_push_bit_iff
% 0.29/0.62  thf(fact_8316_push__bit__minus__numeral,axiom,
% 0.29/0.62      ! [L: num,K: num] :
% 0.29/0.62        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.62        = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus_numeral
% 0.29/0.62  thf(fact_8317_push__bit__minus__numeral,axiom,
% 0.29/0.62      ! [L: num,K: num] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus_numeral
% 0.29/0.62  thf(fact_8318_push__bit__of__int,axiom,
% 0.29/0.62      ! [N2: nat,K: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 0.29/0.62        = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_int
% 0.29/0.62  thf(fact_8319_of__nat__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat] :
% 0.29/0.62        ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_push_bit
% 0.29/0.62  thf(fact_8320_of__nat__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat] :
% 0.29/0.62        ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_nat_push_bit
% 0.29/0.62  thf(fact_8321_push__bit__of__nat,axiom,
% 0.29/0.62      ! [N2: nat,M: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 0.29/0.62        = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_nat
% 0.29/0.62  thf(fact_8322_push__bit__of__nat,axiom,
% 0.29/0.62      ! [N2: nat,M: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 0.29/0.62        = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_of_nat
% 0.29/0.62  thf(fact_8323_push__bit__nat__eq,axiom,
% 0.29/0.62      ! [N2: nat,K: int] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 0.29/0.62        = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_nat_eq
% 0.29/0.62  thf(fact_8324_push__bit__minus,axiom,
% 0.29/0.62      ! [N2: nat,A: code_integer] :
% 0.29/0.62        ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.62        = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N2 @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus
% 0.29/0.62  thf(fact_8325_push__bit__minus,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ A ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus
% 0.29/0.62  thf(fact_8326_push__bit__add,axiom,
% 0.29/0.62      ! [N2: nat,A: int,B: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 0.29/0.62        = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_add
% 0.29/0.62  thf(fact_8327_push__bit__add,axiom,
% 0.29/0.62      ! [N2: nat,A: nat,B: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.62        = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_add
% 0.29/0.62  thf(fact_8328_cosh__real__pos,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_pos
% 0.29/0.62  thf(fact_8329_cosh__real__nonpos__le__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.62       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.29/0.62         => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 0.29/0.62            = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_nonpos_le_iff
% 0.29/0.62  thf(fact_8330_cosh__real__nonneg__le__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.62         => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 0.29/0.62            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_nonneg_le_iff
% 0.29/0.62  thf(fact_8331_cosh__real__nonneg,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_nonneg
% 0.29/0.62  thf(fact_8332_cosh__real__ge__1,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_ge_1
% 0.29/0.62  thf(fact_8333_push__bit__take__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 0.29/0.62        = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_take_bit
% 0.29/0.62  thf(fact_8334_push__bit__take__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 0.29/0.62        = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_take_bit
% 0.29/0.62  thf(fact_8335_take__bit__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 0.29/0.62        = ( bit_se545348938243370406it_int @ N2 @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % take_bit_push_bit
% 0.29/0.62  thf(fact_8336_take__bit__push__bit,axiom,
% 0.29/0.62      ! [M: nat,N2: nat,A: nat] :
% 0.29/0.62        ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 0.29/0.62        = ( bit_se547839408752420682it_nat @ N2 @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % take_bit_push_bit
% 0.29/0.62  thf(fact_8337_sinh__less__cosh__real,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_less_cosh_real
% 0.29/0.62  thf(fact_8338_sinh__le__cosh__real,axiom,
% 0.29/0.62      ! [X4: real] : ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_le_cosh_real
% 0.29/0.62  thf(fact_8339_flip__bit__nat__def,axiom,
% 0.29/0.62      ( bit_se2161824704523386999it_nat
% 0.29/0.62      = ( ^ [M6: nat,N: nat] : ( bit_se6528837805403552850or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % flip_bit_nat_def
% 0.29/0.62  thf(fact_8340_cosh__real__strict__mono,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.62         => ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_strict_mono
% 0.29/0.62  thf(fact_8341_cosh__real__nonneg__less__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.62         => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 0.29/0.62            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_nonneg_less_iff
% 0.29/0.62  thf(fact_8342_cosh__real__nonpos__less__iff,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.62       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.29/0.62         => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 0.29/0.62            = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_real_nonpos_less_iff
% 0.29/0.62  thf(fact_8343_bit__push__bit__iff__int,axiom,
% 0.29/0.62      ! [M: nat,K: int,N2: nat] :
% 0.29/0.62        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 0.29/0.62        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.62          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_push_bit_iff_int
% 0.29/0.62  thf(fact_8344_bit__push__bit__iff__nat,axiom,
% 0.29/0.62      ! [M: nat,Q3: nat,N2: nat] :
% 0.29/0.62        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N2 )
% 0.29/0.62        = ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.62          & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_push_bit_iff_nat
% 0.29/0.62  thf(fact_8345_concat__bit__eq,axiom,
% 0.29/0.62      ( bit_concat_bit
% 0.29/0.62      = ( ^ [N: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % concat_bit_eq
% 0.29/0.62  thf(fact_8346_arcosh__cosh__real,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( arcosh_real @ ( cosh_real @ X4 ) )
% 0.29/0.62          = X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % arcosh_cosh_real
% 0.29/0.62  thf(fact_8347_flip__bit__eq__xor,axiom,
% 0.29/0.62      ( bit_se2159334234014336723it_int
% 0.29/0.62      = ( ^ [N: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % flip_bit_eq_xor
% 0.29/0.62  thf(fact_8348_flip__bit__eq__xor,axiom,
% 0.29/0.62      ( bit_se2161824704523386999it_nat
% 0.29/0.62      = ( ^ [N: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % flip_bit_eq_xor
% 0.29/0.62  thf(fact_8349_cosh__add,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( cosh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.62        = ( plus_plus_complex @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_add
% 0.29/0.62  thf(fact_8350_cosh__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( cosh_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62        = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_add
% 0.29/0.62  thf(fact_8351_sinh__add,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( sinh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.62        = ( plus_plus_complex @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_add
% 0.29/0.62  thf(fact_8352_sinh__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( sinh_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62        = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_add
% 0.29/0.62  thf(fact_8353_cosh__plus__sinh,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( plus_plus_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ X4 ) )
% 0.29/0.62        = ( exp_complex @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_plus_sinh
% 0.29/0.62  thf(fact_8354_cosh__plus__sinh,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( plus_plus_real @ ( cosh_real @ X4 ) @ ( sinh_real @ X4 ) )
% 0.29/0.62        = ( exp_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_plus_sinh
% 0.29/0.62  thf(fact_8355_sinh__plus__cosh,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( plus_plus_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ X4 ) )
% 0.29/0.62        = ( exp_complex @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_plus_cosh
% 0.29/0.62  thf(fact_8356_sinh__plus__cosh,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( plus_plus_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) )
% 0.29/0.62        = ( exp_real @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_plus_cosh
% 0.29/0.62  thf(fact_8357_flip__bit__int__def,axiom,
% 0.29/0.62      ( bit_se2159334234014336723it_int
% 0.29/0.62      = ( ^ [N: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % flip_bit_int_def
% 0.29/0.62  thf(fact_8358_tanh__def,axiom,
% 0.29/0.62      ( tanh_real
% 0.29/0.62      = ( ^ [X: real] : ( divide_divide_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tanh_def
% 0.29/0.62  thf(fact_8359_tanh__def,axiom,
% 0.29/0.62      ( tanh_complex
% 0.29/0.62      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tanh_def
% 0.29/0.62  thf(fact_8360_push__bit__double,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = ( times_times_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_double
% 0.29/0.62  thf(fact_8361_push__bit__double,axiom,
% 0.29/0.62      ! [N2: nat,A: nat] :
% 0.29/0.62        ( ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_double
% 0.29/0.62  thf(fact_8362_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.29/0.62      ( bit_se1146084159140164899it_int
% 0.29/0.62      = ( ^ [A3: int,N: nat] :
% 0.29/0.62            ( ( bit_se725231765392027082nd_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 0.29/0.62           != zero_zero_int ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_iff_and_push_bit_not_eq_0
% 0.29/0.62  thf(fact_8363_bit__iff__and__push__bit__not__eq__0,axiom,
% 0.29/0.62      ( bit_se1148574629649215175it_nat
% 0.29/0.62      = ( ^ [A3: nat,N: nat] :
% 0.29/0.62            ( ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 0.29/0.62           != zero_zero_nat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_iff_and_push_bit_not_eq_0
% 0.29/0.62  thf(fact_8364_push__bit__mask__eq,axiom,
% 0.29/0.62      ! [M: nat,N2: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 0.29/0.62        = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_mask_eq
% 0.29/0.62  thf(fact_8365_unset__bit__eq__and__not,axiom,
% 0.29/0.62      ( bit_se4203085406695923979it_int
% 0.29/0.62      = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % unset_bit_eq_and_not
% 0.29/0.62  thf(fact_8366_unset__bit__int__def,axiom,
% 0.29/0.62      ( bit_se4203085406695923979it_int
% 0.29/0.62      = ( ^ [N: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % unset_bit_int_def
% 0.29/0.62  thf(fact_8367_push__bit__int__def,axiom,
% 0.29/0.62      ( bit_se545348938243370406it_int
% 0.29/0.62      = ( ^ [N: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_int_def
% 0.29/0.62  thf(fact_8368_push__bit__nat__def,axiom,
% 0.29/0.62      ( bit_se547839408752420682it_nat
% 0.29/0.62      = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_nat_def
% 0.29/0.62  thf(fact_8369_push__bit__eq__mult,axiom,
% 0.29/0.62      ( bit_se545348938243370406it_int
% 0.29/0.62      = ( ^ [N: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_eq_mult
% 0.29/0.62  thf(fact_8370_push__bit__eq__mult,axiom,
% 0.29/0.62      ( bit_se547839408752420682it_nat
% 0.29/0.62      = ( ^ [N: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_eq_mult
% 0.29/0.62  thf(fact_8371_exp__dvdE,axiom,
% 0.29/0.62      ! [N2: nat,A: code_integer] :
% 0.29/0.62        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A )
% 0.29/0.62       => ~ ! [B5: code_integer] :
% 0.29/0.62              ( A
% 0.29/0.62             != ( bit_se7788150548672797655nteger @ N2 @ B5 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_dvdE
% 0.29/0.62  thf(fact_8372_exp__dvdE,axiom,
% 0.29/0.62      ! [N2: nat,A: int] :
% 0.29/0.62        ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A )
% 0.29/0.62       => ~ ! [B5: int] :
% 0.29/0.62              ( A
% 0.29/0.62             != ( bit_se545348938243370406it_int @ N2 @ B5 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_dvdE
% 0.29/0.62  thf(fact_8373_exp__dvdE,axiom,
% 0.29/0.62      ! [N2: nat,A: nat] :
% 0.29/0.62        ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A )
% 0.29/0.62       => ~ ! [B5: nat] :
% 0.29/0.62              ( A
% 0.29/0.62             != ( bit_se547839408752420682it_nat @ N2 @ B5 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % exp_dvdE
% 0.29/0.62  thf(fact_8374_sinh__double,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.62        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X4 ) ) @ ( cosh_complex @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_double
% 0.29/0.62  thf(fact_8375_sinh__double,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 0.29/0.62        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X4 ) ) @ ( cosh_real @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_double
% 0.29/0.62  thf(fact_8376_push__bit__minus__one,axiom,
% 0.29/0.62      ! [N2: nat] :
% 0.29/0.62        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.62        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % push_bit_minus_one
% 0.29/0.62  thf(fact_8377_tanh__add,axiom,
% 0.29/0.62      ! [X4: real,Y: real] :
% 0.29/0.62        ( ( ( cosh_real @ X4 )
% 0.29/0.62         != zero_zero_real )
% 0.29/0.62       => ( ( ( cosh_real @ Y )
% 0.29/0.62           != zero_zero_real )
% 0.29/0.62         => ( ( tanh_real @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.62            = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tanh_add
% 0.29/0.62  thf(fact_8378_tanh__add,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( ( cosh_complex @ X4 )
% 0.29/0.62         != zero_zero_complex )
% 0.29/0.62       => ( ( ( cosh_complex @ Y )
% 0.29/0.62           != zero_zero_complex )
% 0.29/0.62         => ( ( tanh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 0.29/0.62            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % tanh_add
% 0.29/0.62  thf(fact_8379_cosh__field__def,axiom,
% 0.29/0.62      ( cosh_real
% 0.29/0.62      = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_field_def
% 0.29/0.62  thf(fact_8380_cosh__field__def,axiom,
% 0.29/0.62      ( cosh_complex
% 0.29/0.62      = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_field_def
% 0.29/0.62  thf(fact_8381_cosh__square__eq,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_square_eq
% 0.29/0.62  thf(fact_8382_cosh__square__eq,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cosh_square_eq
% 0.29/0.62  thf(fact_8383_sinh__square__eq,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_square_eq
% 0.29/0.62  thf(fact_8384_sinh__square__eq,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % sinh_square_eq
% 0.29/0.62  thf(fact_8385_hyperbolic__pythagoras,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = one_one_complex ) ).
% 0.29/0.62  
% 0.29/0.62  % hyperbolic_pythagoras
% 0.29/0.62  thf(fact_8386_hyperbolic__pythagoras,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % hyperbolic_pythagoras
% 0.29/0.62  thf(fact_8387_bit__horner__sum__bit__iff,axiom,
% 0.29/0.62      ! [Bs: list_o,N2: nat] :
% 0.29/0.62        ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 0.29/0.62        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 0.29/0.62          & ( nth_o @ Bs @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_horner_sum_bit_iff
% 0.29/0.62  thf(fact_8388_bit__horner__sum__bit__iff,axiom,
% 0.29/0.62      ! [Bs: list_o,N2: nat] :
% 0.29/0.62        ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 0.29/0.62        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 0.29/0.62          & ( nth_o @ Bs @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_horner_sum_bit_iff
% 0.29/0.62  thf(fact_8389_bit__horner__sum__bit__iff,axiom,
% 0.29/0.62      ! [Bs: list_o,N2: nat] :
% 0.29/0.62        ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 0.29/0.62        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 0.29/0.62          & ( nth_o @ Bs @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % bit_horner_sum_bit_iff
% 0.29/0.62  thf(fact_8390_Cauchy__iff2,axiom,
% 0.29/0.62      ( topolo4055970368930404560y_real
% 0.29/0.62      = ( ^ [X3: nat > real] :
% 0.29/0.62          ! [J3: nat] :
% 0.29/0.62          ? [M8: nat] :
% 0.29/0.62          ! [M6: nat] :
% 0.29/0.62            ( ( ord_less_eq_nat @ M8 @ M6 )
% 0.29/0.62           => ! [N: nat] :
% 0.29/0.62                ( ( ord_less_eq_nat @ M8 @ N )
% 0.29/0.62               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Cauchy_iff2
% 0.29/0.62  thf(fact_8391_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.62        ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.62       => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.62              ( X4
% 0.29/0.62             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.62         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.62                ( X4
% 0.29/0.62               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.29/0.62           => ( ! [Mi3: nat,Ma3: nat] :
% 0.29/0.62                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.62                      ( X4
% 0.29/0.62                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.62                 => ( ( Xa = Mi3 )
% 0.29/0.62                    | ( Xa = Ma3 ) ) )
% 0.29/0.62             => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                    ( ? [Vc: vEBT_VEBT] :
% 0.29/0.62                        ( X4
% 0.29/0.62                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.62                   => ( ( Xa = Mi3 )
% 0.29/0.62                      | ( Xa = Ma3 )
% 0.29/0.62                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.29/0.62               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                      ( ? [Vd: vEBT_VEBT] :
% 0.29/0.62                          ( X4
% 0.29/0.62                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.62                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.membermima.elims(3)
% 0.29/0.62  thf(fact_8392_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.62        ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.62          = Y )
% 0.29/0.62       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.29/0.62                ( X4
% 0.29/0.62                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.62           => Y )
% 0.29/0.62         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.62                  ( X4
% 0.29/0.62                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.29/0.62             => Y )
% 0.29/0.62           => ( ! [Mi3: nat,Ma3: nat] :
% 0.29/0.62                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.62                      ( X4
% 0.29/0.62                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.62                 => ( Y
% 0.29/0.62                    = ( ~ ( ( Xa = Mi3 )
% 0.29/0.62                          | ( Xa = Ma3 ) ) ) ) )
% 0.29/0.62             => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                    ( ? [Vc: vEBT_VEBT] :
% 0.29/0.62                        ( X4
% 0.29/0.62                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.62                   => ( Y
% 0.29/0.62                      = ( ~ ( ( Xa = Mi3 )
% 0.29/0.62                            | ( Xa = Ma3 )
% 0.29/0.62                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 0.29/0.62               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                      ( ? [Vd: vEBT_VEBT] :
% 0.29/0.62                          ( X4
% 0.29/0.62                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.62                     => ( Y
% 0.29/0.62                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.membermima.elims(1)
% 0.29/0.62  thf(fact_8393_csqrt_Osimps_I1_J,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( re @ ( csqrt @ Z ) )
% 0.29/0.62        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt.simps(1)
% 0.29/0.62  thf(fact_8394_complex__Re__numeral,axiom,
% 0.29/0.62      ! [V: num] :
% 0.29/0.62        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 0.29/0.62        = ( numeral_numeral_real @ V ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_Re_numeral
% 0.29/0.62  thf(fact_8395_Re__divide__numeral,axiom,
% 0.29/0.62      ! [Z: complex,W: num] :
% 0.29/0.62        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.62        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Re_divide_numeral
% 0.29/0.62  thf(fact_8396_lambda__zero,axiom,
% 0.29/0.62      ( ( ^ [H2: rat] : zero_zero_rat )
% 0.29/0.62      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_zero
% 0.29/0.62  thf(fact_8397_lambda__zero,axiom,
% 0.29/0.62      ( ( ^ [H2: complex] : zero_zero_complex )
% 0.29/0.62      = ( times_times_complex @ zero_zero_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_zero
% 0.29/0.62  thf(fact_8398_lambda__zero,axiom,
% 0.29/0.62      ( ( ^ [H2: real] : zero_zero_real )
% 0.29/0.62      = ( times_times_real @ zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_zero
% 0.29/0.62  thf(fact_8399_lambda__zero,axiom,
% 0.29/0.62      ( ( ^ [H2: nat] : zero_zero_nat )
% 0.29/0.62      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_zero
% 0.29/0.62  thf(fact_8400_lambda__zero,axiom,
% 0.29/0.62      ( ( ^ [H2: int] : zero_zero_int )
% 0.29/0.62      = ( times_times_int @ zero_zero_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_zero
% 0.29/0.62  thf(fact_8401_less__set__def,axiom,
% 0.29/0.62      ( ord_less_set_real
% 0.29/0.62      = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.62            ( ord_less_real_o
% 0.29/0.62            @ ^ [X: real] : ( member_real @ X @ A6 )
% 0.29/0.62            @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_set_def
% 0.29/0.62  thf(fact_8402_less__set__def,axiom,
% 0.29/0.62      ( ord_less_set_nat
% 0.29/0.62      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.62            ( ord_less_nat_o
% 0.29/0.62            @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 0.29/0.62            @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_set_def
% 0.29/0.62  thf(fact_8403_less__set__def,axiom,
% 0.29/0.62      ( ord_less_set_complex
% 0.29/0.62      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.29/0.62            ( ord_less_complex_o
% 0.29/0.62            @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 0.29/0.62            @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_set_def
% 0.29/0.62  thf(fact_8404_less__set__def,axiom,
% 0.29/0.62      ( ord_less_set_int
% 0.29/0.62      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.62            ( ord_less_int_o
% 0.29/0.62            @ ^ [X: int] : ( member_int @ X @ A6 )
% 0.29/0.62            @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_set_def
% 0.29/0.62  thf(fact_8405_less__set__def,axiom,
% 0.29/0.62      ( ord_le7866589430770878221at_nat
% 0.29/0.62      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.29/0.62            ( ord_le549003669493604880_nat_o
% 0.29/0.62            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 0.29/0.62            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_set_def
% 0.29/0.62  thf(fact_8406_less__eq__set__def,axiom,
% 0.29/0.62      ( ord_less_eq_set_real
% 0.29/0.62      = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.62            ( ord_less_eq_real_o
% 0.29/0.62            @ ^ [X: real] : ( member_real @ X @ A6 )
% 0.29/0.62            @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_eq_set_def
% 0.29/0.62  thf(fact_8407_less__eq__set__def,axiom,
% 0.29/0.62      ( ord_less_eq_set_nat
% 0.29/0.62      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.62            ( ord_less_eq_nat_o
% 0.29/0.62            @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 0.29/0.62            @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_eq_set_def
% 0.29/0.62  thf(fact_8408_less__eq__set__def,axiom,
% 0.29/0.62      ( ord_le211207098394363844omplex
% 0.29/0.62      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.29/0.62            ( ord_le4573692005234683329plex_o
% 0.29/0.62            @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 0.29/0.62            @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_eq_set_def
% 0.29/0.62  thf(fact_8409_less__eq__set__def,axiom,
% 0.29/0.62      ( ord_le3146513528884898305at_nat
% 0.29/0.62      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 0.29/0.62            ( ord_le704812498762024988_nat_o
% 0.29/0.62            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 0.29/0.62            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_eq_set_def
% 0.29/0.62  thf(fact_8410_less__eq__set__def,axiom,
% 0.29/0.62      ( ord_less_eq_set_int
% 0.29/0.62      = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.62            ( ord_less_eq_int_o
% 0.29/0.62            @ ^ [X: int] : ( member_int @ X @ A6 )
% 0.29/0.62            @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % less_eq_set_def
% 0.29/0.62  thf(fact_8411_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.62        ( ord_le3146513528884898305at_nat
% 0.29/0.62        @ ( collec3392354462482085612at_nat
% 0.29/0.62          @ ^ [X: product_prod_nat_nat] :
% 0.29/0.62              ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8412_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_complex,P: complex > $o] :
% 0.29/0.62        ( ord_le211207098394363844omplex
% 0.29/0.62        @ ( collect_complex
% 0.29/0.62          @ ^ [X: complex] :
% 0.29/0.62              ( ( member_complex @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8413_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_real,P: real > $o] :
% 0.29/0.62        ( ord_less_eq_set_real
% 0.29/0.62        @ ( collect_real
% 0.29/0.62          @ ^ [X: real] :
% 0.29/0.62              ( ( member_real @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8414_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_list_nat,P: list_nat > $o] :
% 0.29/0.62        ( ord_le6045566169113846134st_nat
% 0.29/0.62        @ ( collect_list_nat
% 0.29/0.62          @ ^ [X: list_nat] :
% 0.29/0.62              ( ( member_list_nat @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8415_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_nat,P: nat > $o] :
% 0.29/0.62        ( ord_less_eq_set_nat
% 0.29/0.62        @ ( collect_nat
% 0.29/0.62          @ ^ [X: nat] :
% 0.29/0.62              ( ( member_nat @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8416_Collect__subset,axiom,
% 0.29/0.62      ! [A2: set_int,P: int > $o] :
% 0.29/0.62        ( ord_less_eq_set_int
% 0.29/0.62        @ ( collect_int
% 0.29/0.62          @ ^ [X: int] :
% 0.29/0.62              ( ( member_int @ X @ A2 )
% 0.29/0.62              & ( P @ X ) ) )
% 0.29/0.62        @ A2 ) ).
% 0.29/0.62  
% 0.29/0.62  % Collect_subset
% 0.29/0.62  thf(fact_8417_subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ord_le211207098394363844omplex
% 0.29/0.62          @ ( collect_complex
% 0.29/0.62            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 0.29/0.62          @ ( collect_complex
% 0.29/0.62            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 0.29/0.62        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % subset_divisors_dvd
% 0.29/0.62  thf(fact_8418_subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_eq_set_real
% 0.29/0.62          @ ( collect_real
% 0.29/0.62            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 0.29/0.62          @ ( collect_real
% 0.29/0.62            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 0.29/0.62        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % subset_divisors_dvd
% 0.29/0.62  thf(fact_8419_subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: nat,B: nat] :
% 0.29/0.62        ( ( ord_less_eq_set_nat
% 0.29/0.62          @ ( collect_nat
% 0.29/0.62            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 0.29/0.62          @ ( collect_nat
% 0.29/0.62            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 0.29/0.62        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % subset_divisors_dvd
% 0.29/0.62  thf(fact_8420_subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: code_integer,B: code_integer] :
% 0.29/0.62        ( ( ord_le7084787975880047091nteger
% 0.29/0.62          @ ( collect_Code_integer
% 0.29/0.62            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 0.29/0.62          @ ( collect_Code_integer
% 0.29/0.62            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 0.29/0.62        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % subset_divisors_dvd
% 0.29/0.62  thf(fact_8421_subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: int,B: int] :
% 0.29/0.62        ( ( ord_less_eq_set_int
% 0.29/0.62          @ ( collect_int
% 0.29/0.62            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 0.29/0.62          @ ( collect_int
% 0.29/0.62            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 0.29/0.62        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % subset_divisors_dvd
% 0.29/0.62  thf(fact_8422_strict__subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: complex,B: complex] :
% 0.29/0.62        ( ( ord_less_set_complex
% 0.29/0.62          @ ( collect_complex
% 0.29/0.62            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 0.29/0.62          @ ( collect_complex
% 0.29/0.62            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 0.29/0.62        = ( ( dvd_dvd_complex @ A @ B )
% 0.29/0.62          & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % strict_subset_divisors_dvd
% 0.29/0.62  thf(fact_8423_strict__subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: real,B: real] :
% 0.29/0.62        ( ( ord_less_set_real
% 0.29/0.62          @ ( collect_real
% 0.29/0.62            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 0.29/0.62          @ ( collect_real
% 0.29/0.62            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 0.29/0.62        = ( ( dvd_dvd_real @ A @ B )
% 0.29/0.62          & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % strict_subset_divisors_dvd
% 0.29/0.62  thf(fact_8424_strict__subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: nat,B: nat] :
% 0.29/0.62        ( ( ord_less_set_nat
% 0.29/0.62          @ ( collect_nat
% 0.29/0.62            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 0.29/0.62          @ ( collect_nat
% 0.29/0.62            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 0.29/0.62        = ( ( dvd_dvd_nat @ A @ B )
% 0.29/0.62          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % strict_subset_divisors_dvd
% 0.29/0.62  thf(fact_8425_strict__subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: int,B: int] :
% 0.29/0.62        ( ( ord_less_set_int
% 0.29/0.62          @ ( collect_int
% 0.29/0.62            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 0.29/0.62          @ ( collect_int
% 0.29/0.62            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 0.29/0.62        = ( ( dvd_dvd_int @ A @ B )
% 0.29/0.62          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % strict_subset_divisors_dvd
% 0.29/0.62  thf(fact_8426_strict__subset__divisors__dvd,axiom,
% 0.29/0.62      ! [A: code_integer,B: code_integer] :
% 0.29/0.62        ( ( ord_le1307284697595431911nteger
% 0.29/0.62          @ ( collect_Code_integer
% 0.29/0.62            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 0.29/0.62          @ ( collect_Code_integer
% 0.29/0.62            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 0.29/0.62        = ( ( dvd_dvd_Code_integer @ A @ B )
% 0.29/0.62          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % strict_subset_divisors_dvd
% 0.29/0.62  thf(fact_8427_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8428_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8429_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8430_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8431_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8432_numeral__code_I2_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 0.29/0.62        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(2)
% 0.29/0.62  thf(fact_8433_lambda__one,axiom,
% 0.29/0.62      ( ( ^ [X: rat] : X )
% 0.29/0.62      = ( times_times_rat @ one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_one
% 0.29/0.62  thf(fact_8434_lambda__one,axiom,
% 0.29/0.62      ( ( ^ [X: complex] : X )
% 0.29/0.62      = ( times_times_complex @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_one
% 0.29/0.62  thf(fact_8435_lambda__one,axiom,
% 0.29/0.62      ( ( ^ [X: real] : X )
% 0.29/0.62      = ( times_times_real @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_one
% 0.29/0.62  thf(fact_8436_lambda__one,axiom,
% 0.29/0.62      ( ( ^ [X: nat] : X )
% 0.29/0.62      = ( times_times_nat @ one_one_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_one
% 0.29/0.62  thf(fact_8437_lambda__one,axiom,
% 0.29/0.62      ( ( ^ [X: int] : X )
% 0.29/0.62      = ( times_times_int @ one_one_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % lambda_one
% 0.29/0.62  thf(fact_8438_nat__less__as__int,axiom,
% 0.29/0.62      ( ord_less_nat
% 0.29/0.62      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_less_as_int
% 0.29/0.62  thf(fact_8439_nat__leq__as__int,axiom,
% 0.29/0.62      ( ord_less_eq_nat
% 0.29/0.62      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_leq_as_int
% 0.29/0.62  thf(fact_8440_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8441_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8442_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8443_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8444_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8445_numeral__code_I3_J,axiom,
% 0.29/0.62      ! [N2: num] :
% 0.29/0.62        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 0.29/0.62        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 0.29/0.62  
% 0.29/0.62  % numeral_code(3)
% 0.29/0.62  thf(fact_8446_power__numeral__even,axiom,
% 0.29/0.62      ! [Z: complex,W: num] :
% 0.29/0.62        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.62        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_even
% 0.29/0.62  thf(fact_8447_power__numeral__even,axiom,
% 0.29/0.62      ! [Z: real,W: num] :
% 0.29/0.62        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.62        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_even
% 0.29/0.62  thf(fact_8448_power__numeral__even,axiom,
% 0.29/0.62      ! [Z: nat,W: num] :
% 0.29/0.62        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.62        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_even
% 0.29/0.62  thf(fact_8449_power__numeral__even,axiom,
% 0.29/0.62      ! [Z: int,W: num] :
% 0.29/0.62        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.29/0.62        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_even
% 0.29/0.62  thf(fact_8450_power__numeral__odd,axiom,
% 0.29/0.62      ! [Z: complex,W: num] :
% 0.29/0.62        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.62        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_odd
% 0.29/0.62  thf(fact_8451_power__numeral__odd,axiom,
% 0.29/0.62      ! [Z: real,W: num] :
% 0.29/0.62        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.62        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_odd
% 0.29/0.62  thf(fact_8452_power__numeral__odd,axiom,
% 0.29/0.62      ! [Z: nat,W: num] :
% 0.29/0.62        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.62        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_odd
% 0.29/0.62  thf(fact_8453_power__numeral__odd,axiom,
% 0.29/0.62      ! [Z: int,W: num] :
% 0.29/0.62        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.29/0.62        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % power_numeral_odd
% 0.29/0.62  thf(fact_8454_nat__plus__as__int,axiom,
% 0.29/0.62      ( plus_plus_nat
% 0.29/0.62      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_plus_as_int
% 0.29/0.62  thf(fact_8455_nat__div__as__int,axiom,
% 0.29/0.62      ( divide_divide_nat
% 0.29/0.62      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_div_as_int
% 0.29/0.62  thf(fact_8456_nat__mod__as__int,axiom,
% 0.29/0.62      ( modulo_modulo_nat
% 0.29/0.62      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % nat_mod_as_int
% 0.29/0.62  thf(fact_8457_complex__Re__le__cmod,axiom,
% 0.29/0.62      ! [X4: complex] : ( ord_less_eq_real @ ( re @ X4 ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_Re_le_cmod
% 0.29/0.62  thf(fact_8458_one__complex_Osimps_I1_J,axiom,
% 0.29/0.62      ( ( re @ one_one_complex )
% 0.29/0.62      = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % one_complex.simps(1)
% 0.29/0.62  thf(fact_8459_set__conv__nth,axiom,
% 0.29/0.62      ( set_complex2
% 0.29/0.62      = ( ^ [Xs3: list_complex] :
% 0.29/0.62            ( collect_complex
% 0.29/0.62            @ ^ [Uu3: complex] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_complex @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8460_set__conv__nth,axiom,
% 0.29/0.62      ( set_real2
% 0.29/0.62      = ( ^ [Xs3: list_real] :
% 0.29/0.62            ( collect_real
% 0.29/0.62            @ ^ [Uu3: real] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_real @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8461_set__conv__nth,axiom,
% 0.29/0.62      ( set_list_nat2
% 0.29/0.62      = ( ^ [Xs3: list_list_nat] :
% 0.29/0.62            ( collect_list_nat
% 0.29/0.62            @ ^ [Uu3: list_nat] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_list_nat @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_s3023201423986296836st_nat @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8462_set__conv__nth,axiom,
% 0.29/0.62      ( set_VEBT_VEBT2
% 0.29/0.62      = ( ^ [Xs3: list_VEBT_VEBT] :
% 0.29/0.62            ( collect_VEBT_VEBT
% 0.29/0.62            @ ^ [Uu3: vEBT_VEBT] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_VEBT_VEBT @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8463_set__conv__nth,axiom,
% 0.29/0.62      ( set_o2
% 0.29/0.62      = ( ^ [Xs3: list_o] :
% 0.29/0.62            ( collect_o
% 0.29/0.62            @ ^ [Uu3: $o] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_o @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8464_set__conv__nth,axiom,
% 0.29/0.62      ( set_nat2
% 0.29/0.62      = ( ^ [Xs3: list_nat] :
% 0.29/0.62            ( collect_nat
% 0.29/0.62            @ ^ [Uu3: nat] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_nat @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8465_set__conv__nth,axiom,
% 0.29/0.62      ( set_int2
% 0.29/0.62      = ( ^ [Xs3: list_int] :
% 0.29/0.62            ( collect_int
% 0.29/0.62            @ ^ [Uu3: int] :
% 0.29/0.62              ? [I3: nat] :
% 0.29/0.62                ( ( Uu3
% 0.29/0.62                  = ( nth_int @ Xs3 @ I3 ) )
% 0.29/0.62                & ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_conv_nth
% 0.29/0.62  thf(fact_8466_diff__nat__eq__if,axiom,
% 0.29/0.62      ! [Z6: int,Z: int] :
% 0.29/0.62        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 0.29/0.62         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 0.29/0.62            = ( nat2 @ Z ) ) )
% 0.29/0.62        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 0.29/0.62         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 0.29/0.62            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % diff_nat_eq_if
% 0.29/0.62  thf(fact_8467_abs__Re__le__cmod,axiom,
% 0.29/0.62      ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % abs_Re_le_cmod
% 0.29/0.62  thf(fact_8468_Re__csqrt,axiom,
% 0.29/0.62      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Re_csqrt
% 0.29/0.62  thf(fact_8469_set__decode__def,axiom,
% 0.29/0.62      ( nat_set_decode
% 0.29/0.62      = ( ^ [X: nat] :
% 0.29/0.62            ( collect_nat
% 0.29/0.62            @ ^ [N: nat] :
% 0.29/0.62                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % set_decode_def
% 0.29/0.62  thf(fact_8470_signed__take__bit__code,axiom,
% 0.29/0.62      ( bit_ri6519982836138164636nteger
% 0.29/0.62      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % signed_take_bit_code
% 0.29/0.62  thf(fact_8471_signed__take__bit__code,axiom,
% 0.29/0.62      ( bit_ri631733984087533419it_int
% 0.29/0.62      = ( ^ [N: nat,A3: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % signed_take_bit_code
% 0.29/0.62  thf(fact_8472_pochhammer__code,axiom,
% 0.29/0.62      ( comm_s4028243227959126397er_rat
% 0.29/0.62      = ( ^ [A3: rat,N: nat] :
% 0.29/0.62            ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 0.29/0.62            @ ( set_fo1949268297981939178at_rat
% 0.29/0.62              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.29/0.62              @ zero_zero_nat
% 0.29/0.62              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.29/0.62              @ one_one_rat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pochhammer_code
% 0.29/0.62  thf(fact_8473_pochhammer__code,axiom,
% 0.29/0.62      ( comm_s2602460028002588243omplex
% 0.29/0.62      = ( ^ [A3: complex,N: nat] :
% 0.29/0.62            ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 0.29/0.62            @ ( set_fo1517530859248394432omplex
% 0.29/0.62              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 0.29/0.62              @ zero_zero_nat
% 0.29/0.62              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.29/0.62              @ one_one_complex ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pochhammer_code
% 0.29/0.62  thf(fact_8474_pochhammer__code,axiom,
% 0.29/0.62      ( comm_s7457072308508201937r_real
% 0.29/0.62      = ( ^ [A3: real,N: nat] :
% 0.29/0.62            ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 0.29/0.62            @ ( set_fo3111899725591712190t_real
% 0.29/0.62              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 0.29/0.62              @ zero_zero_nat
% 0.29/0.62              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.29/0.62              @ one_one_real ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pochhammer_code
% 0.29/0.62  thf(fact_8475_pochhammer__code,axiom,
% 0.29/0.62      ( comm_s4660882817536571857er_int
% 0.29/0.62      = ( ^ [A3: int,N: nat] :
% 0.29/0.62            ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 0.29/0.62            @ ( set_fo2581907887559384638at_int
% 0.29/0.62              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.29/0.62              @ zero_zero_nat
% 0.29/0.62              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.29/0.62              @ one_one_int ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pochhammer_code
% 0.29/0.62  thf(fact_8476_pochhammer__code,axiom,
% 0.29/0.62      ( comm_s4663373288045622133er_nat
% 0.29/0.62      = ( ^ [A3: nat,N: nat] :
% 0.29/0.62            ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 0.29/0.62            @ ( set_fo2584398358068434914at_nat
% 0.29/0.62              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.29/0.62              @ zero_zero_nat
% 0.29/0.62              @ ( minus_minus_nat @ N @ one_one_nat )
% 0.29/0.62              @ one_one_nat ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pochhammer_code
% 0.29/0.62  thf(fact_8477_cmod__plus__Re__le__0__iff,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 0.29/0.62        = ( ( re @ Z )
% 0.29/0.62          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_plus_Re_le_0_iff
% 0.29/0.62  thf(fact_8478_gbinomial__code,axiom,
% 0.29/0.62      ( gbinomial_rat
% 0.29/0.62      = ( ^ [A3: rat,K3: nat] :
% 0.29/0.62            ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 0.29/0.62            @ ( divide_divide_rat
% 0.29/0.62              @ ( set_fo1949268297981939178at_rat
% 0.29/0.62                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 0.29/0.62                @ zero_zero_nat
% 0.29/0.62                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.29/0.62                @ one_one_rat )
% 0.29/0.62              @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_code
% 0.29/0.62  thf(fact_8479_gbinomial__code,axiom,
% 0.29/0.62      ( gbinomial_complex
% 0.29/0.62      = ( ^ [A3: complex,K3: nat] :
% 0.29/0.62            ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 0.29/0.62            @ ( divide1717551699836669952omplex
% 0.29/0.62              @ ( set_fo1517530859248394432omplex
% 0.29/0.62                @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 0.29/0.62                @ zero_zero_nat
% 0.29/0.62                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.29/0.62                @ one_one_complex )
% 0.29/0.62              @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_code
% 0.29/0.62  thf(fact_8480_gbinomial__code,axiom,
% 0.29/0.62      ( gbinomial_real
% 0.29/0.62      = ( ^ [A3: real,K3: nat] :
% 0.29/0.62            ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 0.29/0.62            @ ( divide_divide_real
% 0.29/0.62              @ ( set_fo3111899725591712190t_real
% 0.29/0.62                @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 0.29/0.62                @ zero_zero_nat
% 0.29/0.62                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.29/0.62                @ one_one_real )
% 0.29/0.62              @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % gbinomial_code
% 0.29/0.62  thf(fact_8481_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.29/0.62      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 0.29/0.62        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X4 )
% 0.29/0.62        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.29/0.62           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62          & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.naive_member.simps(3)
% 0.29/0.62  thf(fact_8482_CauchyD,axiom,
% 0.29/0.62      ! [X8: nat > complex,E2: real] :
% 0.29/0.62        ( ( topolo6517432010174082258omplex @ X8 )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.62         => ? [M9: nat] :
% 0.29/0.62            ! [M2: nat] :
% 0.29/0.62              ( ( ord_less_eq_nat @ M9 @ M2 )
% 0.29/0.62             => ! [N6: nat] :
% 0.29/0.62                  ( ( ord_less_eq_nat @ M9 @ N6 )
% 0.29/0.62                 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % CauchyD
% 0.29/0.62  thf(fact_8483_CauchyD,axiom,
% 0.29/0.62      ! [X8: nat > real,E2: real] :
% 0.29/0.62        ( ( topolo4055970368930404560y_real @ X8 )
% 0.29/0.62       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.62         => ? [M9: nat] :
% 0.29/0.62            ! [M2: nat] :
% 0.29/0.62              ( ( ord_less_eq_nat @ M9 @ M2 )
% 0.29/0.62             => ! [N6: nat] :
% 0.29/0.62                  ( ( ord_less_eq_nat @ M9 @ N6 )
% 0.29/0.62                 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % CauchyD
% 0.29/0.62  thf(fact_8484_CauchyI,axiom,
% 0.29/0.62      ! [X8: nat > complex] :
% 0.29/0.62        ( ! [E: real] :
% 0.29/0.62            ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.62           => ? [M10: nat] :
% 0.29/0.62              ! [M5: nat] :
% 0.29/0.62                ( ( ord_less_eq_nat @ M10 @ M5 )
% 0.29/0.62               => ! [N3: nat] :
% 0.29/0.62                    ( ( ord_less_eq_nat @ M10 @ N3 )
% 0.29/0.62                   => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 0.29/0.62       => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % CauchyI
% 0.29/0.62  thf(fact_8485_CauchyI,axiom,
% 0.29/0.62      ! [X8: nat > real] :
% 0.29/0.62        ( ! [E: real] :
% 0.29/0.62            ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.62           => ? [M10: nat] :
% 0.29/0.62              ! [M5: nat] :
% 0.29/0.62                ( ( ord_less_eq_nat @ M10 @ M5 )
% 0.29/0.62               => ! [N3: nat] :
% 0.29/0.62                    ( ( ord_less_eq_nat @ M10 @ N3 )
% 0.29/0.62                   => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 0.29/0.62       => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % CauchyI
% 0.29/0.62  thf(fact_8486_Cauchy__iff,axiom,
% 0.29/0.62      ( topolo6517432010174082258omplex
% 0.29/0.62      = ( ^ [X3: nat > complex] :
% 0.29/0.62          ! [E3: real] :
% 0.29/0.62            ( ( ord_less_real @ zero_zero_real @ E3 )
% 0.29/0.62           => ? [M8: nat] :
% 0.29/0.62              ! [M6: nat] :
% 0.29/0.62                ( ( ord_less_eq_nat @ M8 @ M6 )
% 0.29/0.62               => ! [N: nat] :
% 0.29/0.62                    ( ( ord_less_eq_nat @ M8 @ N )
% 0.29/0.62                   => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Cauchy_iff
% 0.29/0.62  thf(fact_8487_Cauchy__iff,axiom,
% 0.29/0.62      ( topolo4055970368930404560y_real
% 0.29/0.62      = ( ^ [X3: nat > real] :
% 0.29/0.62          ! [E3: real] :
% 0.29/0.62            ( ( ord_less_real @ zero_zero_real @ E3 )
% 0.29/0.62           => ? [M8: nat] :
% 0.29/0.62              ! [M6: nat] :
% 0.29/0.62                ( ( ord_less_eq_nat @ M8 @ M6 )
% 0.29/0.62               => ! [N: nat] :
% 0.29/0.62                    ( ( ord_less_eq_nat @ M8 @ N )
% 0.29/0.62                   => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Cauchy_iff
% 0.29/0.62  thf(fact_8488_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.29/0.62      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 0.29/0.62        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X4 )
% 0.29/0.62        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.29/0.62           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62          & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.membermima.simps(5)
% 0.29/0.62  thf(fact_8489_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.29/0.62      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 0.29/0.62        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ X4 )
% 0.29/0.62        = ( ( X4 = Mi )
% 0.29/0.62          | ( X4 = Ma )
% 0.29/0.62          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.29/0.62             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62            & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.membermima.simps(4)
% 0.29/0.62  thf(fact_8490_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.62        ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.62          = Y )
% 0.29/0.62       => ( ! [A5: $o,B5: $o] :
% 0.29/0.62              ( ( X4
% 0.29/0.62                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.62             => ( Y
% 0.29/0.62                = ( ~ ( ( ( Xa = zero_zero_nat )
% 0.29/0.62                       => A5 )
% 0.29/0.62                      & ( ( Xa != zero_zero_nat )
% 0.29/0.62                       => ( ( ( Xa = one_one_nat )
% 0.29/0.62                           => B5 )
% 0.29/0.62                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 0.29/0.62         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.62                  ( X4
% 0.29/0.62                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.29/0.62             => Y )
% 0.29/0.62           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                  ( ? [S3: vEBT_VEBT] :
% 0.29/0.62                      ( X4
% 0.29/0.62                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.62                 => ( Y
% 0.29/0.62                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.naive_member.elims(1)
% 0.29/0.62  thf(fact_8491_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.62        ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.62       => ( ! [A5: $o,B5: $o] :
% 0.29/0.62              ( ( X4
% 0.29/0.62                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.62             => ~ ( ( ( Xa = zero_zero_nat )
% 0.29/0.62                   => A5 )
% 0.29/0.62                  & ( ( Xa != zero_zero_nat )
% 0.29/0.62                   => ( ( ( Xa = one_one_nat )
% 0.29/0.62                       => B5 )
% 0.29/0.62                      & ( Xa = one_one_nat ) ) ) ) )
% 0.29/0.62         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                ( ? [S3: vEBT_VEBT] :
% 0.29/0.62                    ( X4
% 0.29/0.62                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.62               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.naive_member.elims(2)
% 0.29/0.62  thf(fact_8492_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.62        ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.62       => ( ! [A5: $o,B5: $o] :
% 0.29/0.62              ( ( X4
% 0.29/0.62                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.62             => ( ( ( Xa = zero_zero_nat )
% 0.29/0.62                 => A5 )
% 0.29/0.62                & ( ( Xa != zero_zero_nat )
% 0.29/0.62                 => ( ( ( Xa = one_one_nat )
% 0.29/0.62                     => B5 )
% 0.29/0.62                    & ( Xa = one_one_nat ) ) ) ) )
% 0.29/0.62         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.62                ( X4
% 0.29/0.62               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.29/0.62           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                  ( ? [S3: vEBT_VEBT] :
% 0.29/0.62                      ( X4
% 0.29/0.62                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.62                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.naive_member.elims(3)
% 0.29/0.62  thf(fact_8493_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.29/0.62      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.62        ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.62       => ( ! [Mi3: nat,Ma3: nat] :
% 0.29/0.62              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.62                  ( X4
% 0.29/0.62                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.62             => ~ ( ( Xa = Mi3 )
% 0.29/0.62                  | ( Xa = Ma3 ) ) )
% 0.29/0.62         => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                ( ? [Vc: vEBT_VEBT] :
% 0.29/0.62                    ( X4
% 0.29/0.62                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.62               => ~ ( ( Xa = Mi3 )
% 0.29/0.62                    | ( Xa = Ma3 )
% 0.29/0.62                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.29/0.62           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.29/0.62                  ( ? [Vd: vEBT_VEBT] :
% 0.29/0.62                      ( X4
% 0.29/0.62                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.62                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.62                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.62                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % VEBT_internal.membermima.elims(2)
% 0.29/0.62  thf(fact_8494_of__int__code__if,axiom,
% 0.29/0.62      ( ring_1_of_int_real
% 0.29/0.62      = ( ^ [K3: int] :
% 0.29/0.62            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 0.29/0.62            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.62              @ ( if_real
% 0.29/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.62                  = zero_zero_int )
% 0.29/0.62                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62                @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_code_if
% 0.29/0.62  thf(fact_8495_of__int__code__if,axiom,
% 0.29/0.62      ( ring_1_of_int_int
% 0.29/0.62      = ( ^ [K3: int] :
% 0.29/0.62            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 0.29/0.62            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.62              @ ( if_int
% 0.29/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.62                  = zero_zero_int )
% 0.29/0.62                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62                @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_code_if
% 0.29/0.62  thf(fact_8496_of__int__code__if,axiom,
% 0.29/0.62      ( ring_17405671764205052669omplex
% 0.29/0.62      = ( ^ [K3: int] :
% 0.29/0.62            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 0.29/0.62            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.62              @ ( if_complex
% 0.29/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.62                  = zero_zero_int )
% 0.29/0.62                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_code_if
% 0.29/0.62  thf(fact_8497_of__int__code__if,axiom,
% 0.29/0.62      ( ring_18347121197199848620nteger
% 0.29/0.62      = ( ^ [K3: int] :
% 0.29/0.62            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.29/0.62            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.62              @ ( if_Code_integer
% 0.29/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.62                  = zero_zero_int )
% 0.29/0.62                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_code_if
% 0.29/0.62  thf(fact_8498_of__int__code__if,axiom,
% 0.29/0.62      ( ring_1_of_int_rat
% 0.29/0.62      = ( ^ [K3: int] :
% 0.29/0.62            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 0.29/0.62            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.62              @ ( if_rat
% 0.29/0.62                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.62                  = zero_zero_int )
% 0.29/0.62                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.62                @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % of_int_code_if
% 0.29/0.62  thf(fact_8499_monoseq__arctan__series,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.62       => ( topolo6980174941875973593q_real
% 0.29/0.62          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % monoseq_arctan_series
% 0.29/0.62  thf(fact_8500_csqrt_Ocode,axiom,
% 0.29/0.62      ( csqrt
% 0.29/0.62      = ( ^ [Z5: complex] :
% 0.29/0.62            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.62            @ ( times_times_real
% 0.29/0.62              @ ( if_real
% 0.29/0.62                @ ( ( im @ Z5 )
% 0.29/0.62                  = zero_zero_real )
% 0.29/0.62                @ one_one_real
% 0.29/0.62                @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 0.29/0.62              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt.code
% 0.29/0.62  thf(fact_8501_ln__series,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.62         => ( ( ln_ln_real @ X4 )
% 0.29/0.62            = ( suminf_real
% 0.29/0.62              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % ln_series
% 0.29/0.62  thf(fact_8502_powser__zero,axiom,
% 0.29/0.62      ! [F: nat > complex] :
% 0.29/0.62        ( ( suminf_complex
% 0.29/0.62          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 0.29/0.62        = ( F @ zero_zero_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % powser_zero
% 0.29/0.62  thf(fact_8503_powser__zero,axiom,
% 0.29/0.62      ! [F: nat > real] :
% 0.29/0.62        ( ( suminf_real
% 0.29/0.62          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 0.29/0.62        = ( F @ zero_zero_nat ) ) ).
% 0.29/0.62  
% 0.29/0.62  % powser_zero
% 0.29/0.62  thf(fact_8504_Re__power__real,axiom,
% 0.29/0.62      ! [X4: complex,N2: nat] :
% 0.29/0.62        ( ( ( im @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62       => ( ( re @ ( power_power_complex @ X4 @ N2 ) )
% 0.29/0.62          = ( power_power_real @ ( re @ X4 ) @ N2 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Re_power_real
% 0.29/0.62  thf(fact_8505_Im__divide__numeral,axiom,
% 0.29/0.62      ! [Z: complex,W: num] :
% 0.29/0.62        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.29/0.62        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Im_divide_numeral
% 0.29/0.62  thf(fact_8506_csqrt__of__real__nonneg,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( im @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) )
% 0.29/0.62         => ( ( csqrt @ X4 )
% 0.29/0.62            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X4 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_of_real_nonneg
% 0.29/0.62  thf(fact_8507_csqrt__minus,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( ord_less_real @ ( im @ X4 ) @ zero_zero_real )
% 0.29/0.62          | ( ( ( im @ X4 )
% 0.29/0.62              = zero_zero_real )
% 0.29/0.62            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) ) ) )
% 0.29/0.62       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X4 ) )
% 0.29/0.62          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_minus
% 0.29/0.62  thf(fact_8508_csqrt__of__real__nonpos,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( ( im @ X4 )
% 0.29/0.62          = zero_zero_real )
% 0.29/0.62       => ( ( ord_less_eq_real @ ( re @ X4 ) @ zero_zero_real )
% 0.29/0.62         => ( ( csqrt @ X4 )
% 0.29/0.62            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X4 ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_of_real_nonpos
% 0.29/0.62  thf(fact_8509_imaginary__unit_Osimps_I2_J,axiom,
% 0.29/0.62      ( ( im @ imaginary_unit )
% 0.29/0.62      = one_one_real ) ).
% 0.29/0.62  
% 0.29/0.62  % imaginary_unit.simps(2)
% 0.29/0.62  thf(fact_8510_abs__Im__le__cmod,axiom,
% 0.29/0.62      ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 0.29/0.62  
% 0.29/0.62  % abs_Im_le_cmod
% 0.29/0.62  thf(fact_8511_cmod__Im__le__iff,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( ( re @ X4 )
% 0.29/0.62          = ( re @ Y ) )
% 0.29/0.62       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 0.29/0.62          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_Im_le_iff
% 0.29/0.62  thf(fact_8512_cmod__Re__le__iff,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( ( im @ X4 )
% 0.29/0.62          = ( im @ Y ) )
% 0.29/0.62       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 0.29/0.62          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_Re_le_iff
% 0.29/0.62  thf(fact_8513_csqrt__principal,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 0.29/0.62        | ( ( ( re @ ( csqrt @ Z ) )
% 0.29/0.62            = zero_zero_real )
% 0.29/0.62          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_principal
% 0.29/0.62  thf(fact_8514_cmod__le,axiom,
% 0.29/0.62      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_le
% 0.29/0.62  thf(fact_8515_monoseq__realpow,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.62       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.62         => ( topolo6980174941875973593q_real @ ( power_power_real @ X4 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % monoseq_realpow
% 0.29/0.62  thf(fact_8516_cmod__power2,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % cmod_power2
% 0.29/0.62  thf(fact_8517_Im__power2,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( im @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X4 ) ) @ ( im @ X4 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Im_power2
% 0.29/0.62  thf(fact_8518_Re__power2,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( re @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62        = ( minus_minus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Re_power2
% 0.29/0.62  thf(fact_8519_complex__eq__0,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( Z = zero_zero_complex )
% 0.29/0.62        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62          = zero_zero_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_eq_0
% 0.29/0.62  thf(fact_8520_norm__complex__def,axiom,
% 0.29/0.62      ( real_V1022390504157884413omplex
% 0.29/0.62      = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % norm_complex_def
% 0.29/0.62  thf(fact_8521_inverse__complex_Osimps_I1_J,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( re @ ( invers8013647133539491842omplex @ X4 ) )
% 0.29/0.62        = ( divide_divide_real @ ( re @ X4 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_complex.simps(1)
% 0.29/0.62  thf(fact_8522_complex__neq__0,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( Z != zero_zero_complex )
% 0.29/0.62        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_neq_0
% 0.29/0.62  thf(fact_8523_Re__divide,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( re @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 0.29/0.62        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Re_divide
% 0.29/0.62  thf(fact_8524_csqrt__unique,axiom,
% 0.29/0.62      ! [W: complex,Z: complex] :
% 0.29/0.62        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.62          = Z )
% 0.29/0.62       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 0.29/0.62            | ( ( ( re @ W )
% 0.29/0.62                = zero_zero_real )
% 0.29/0.62              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 0.29/0.62         => ( ( csqrt @ Z )
% 0.29/0.62            = W ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_unique
% 0.29/0.62  thf(fact_8525_csqrt__square,axiom,
% 0.29/0.62      ! [B: complex] :
% 0.29/0.62        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 0.29/0.62          | ( ( ( re @ B )
% 0.29/0.62              = zero_zero_real )
% 0.29/0.62            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 0.29/0.62       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.62          = B ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt_square
% 0.29/0.62  thf(fact_8526_inverse__complex_Osimps_I2_J,axiom,
% 0.29/0.62      ! [X4: complex] :
% 0.29/0.62        ( ( im @ ( invers8013647133539491842omplex @ X4 ) )
% 0.29/0.62        = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X4 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_complex.simps(2)
% 0.29/0.62  thf(fact_8527_Im__divide,axiom,
% 0.29/0.62      ! [X4: complex,Y: complex] :
% 0.29/0.62        ( ( im @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 0.29/0.62        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Im_divide
% 0.29/0.62  thf(fact_8528_complex__abs__le__norm,axiom,
% 0.29/0.62      ! [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 ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_abs_le_norm
% 0.29/0.62  thf(fact_8529_complex__unit__circle,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( Z != zero_zero_complex )
% 0.29/0.62       => ( ( 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 ) ) ) )
% 0.29/0.62          = one_one_real ) ) ).
% 0.29/0.62  
% 0.29/0.62  % complex_unit_circle
% 0.29/0.62  thf(fact_8530_inverse__complex_Ocode,axiom,
% 0.29/0.62      ( invers8013647133539491842omplex
% 0.29/0.62      = ( ^ [X: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % inverse_complex.code
% 0.29/0.62  thf(fact_8531_Complex__divide,axiom,
% 0.29/0.62      ( divide1717551699836669952omplex
% 0.29/0.62      = ( ^ [X: complex,Y5: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Complex_divide
% 0.29/0.62  thf(fact_8532_pi__series,axiom,
% 0.29/0.62      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.29/0.62      = ( suminf_real
% 0.29/0.62        @ ^ [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 ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % pi_series
% 0.29/0.62  thf(fact_8533_csqrt_Osimps_I2_J,axiom,
% 0.29/0.62      ! [Z: complex] :
% 0.29/0.62        ( ( im @ ( csqrt @ Z ) )
% 0.29/0.62        = ( times_times_real
% 0.29/0.62          @ ( if_real
% 0.29/0.62            @ ( ( im @ Z )
% 0.29/0.62              = zero_zero_real )
% 0.29/0.62            @ one_one_real
% 0.29/0.62            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 0.29/0.62          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % csqrt.simps(2)
% 0.29/0.62  thf(fact_8534_arctan__series,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.62       => ( ( arctan @ X4 )
% 0.29/0.62          = ( suminf_real
% 0.29/0.62            @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % arctan_series
% 0.29/0.62  thf(fact_8535_suminf__geometric,axiom,
% 0.29/0.62      ! [C: real] :
% 0.29/0.62        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.29/0.62       => ( ( suminf_real @ ( power_power_real @ C ) )
% 0.29/0.62          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % suminf_geometric
% 0.29/0.62  thf(fact_8536_suminf__geometric,axiom,
% 0.29/0.62      ! [C: complex] :
% 0.29/0.62        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.29/0.62       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 0.29/0.62          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % suminf_geometric
% 0.29/0.62  thf(fact_8537_summable__arctan__series,axiom,
% 0.29/0.62      ! [X4: real] :
% 0.29/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.62       => ( summable_real
% 0.29/0.62          @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % summable_arctan_series
% 0.29/0.62  thf(fact_8538_vebt__buildup_Oelims,axiom,
% 0.29/0.62      ! [X4: nat,Y: vEBT_VEBT] :
% 0.29/0.62        ( ( ( vEBT_vebt_buildup @ X4 )
% 0.29/0.62          = Y )
% 0.29/0.62       => ( ( ( X4 = zero_zero_nat )
% 0.29/0.62           => ( Y
% 0.29/0.62             != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.29/0.62         => ( ( ( X4
% 0.29/0.62                = ( suc @ zero_zero_nat ) )
% 0.29/0.62             => ( Y
% 0.29/0.62               != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.29/0.62           => ~ ! [Va2: nat] :
% 0.29/0.62                  ( ( X4
% 0.29/0.62                    = ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.62                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.62                       => ( Y
% 0.29/0.62                          = ( 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 ) ) ) ) ) ) )
% 0.29/0.62                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.62                       => ( Y
% 0.29/0.62                          = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % vebt_buildup.elims
% 0.29/0.62  thf(fact_8539_Im__Reals__divide,axiom,
% 0.29/0.62      ! [R3: complex,Z: complex] :
% 0.29/0.62        ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 0.29/0.62       => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 0.29/0.62          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Im_Reals_divide
% 0.29/0.62  thf(fact_8540_intind,axiom,
% 0.29/0.62      ! [I2: nat,N2: nat,P: nat > $o,X4: nat] :
% 0.29/0.62        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.62       => ( ( P @ X4 )
% 0.29/0.62         => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % intind
% 0.29/0.62  thf(fact_8541_intind,axiom,
% 0.29/0.62      ! [I2: nat,N2: nat,P: int > $o,X4: int] :
% 0.29/0.62        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.62       => ( ( P @ X4 )
% 0.29/0.62         => ( P @ ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % intind
% 0.29/0.62  thf(fact_8542_intind,axiom,
% 0.29/0.62      ! [I2: nat,N2: nat,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 0.29/0.62        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.62       => ( ( P @ X4 )
% 0.29/0.62         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % intind
% 0.29/0.62  thf(fact_8543_replicate__eq__replicate,axiom,
% 0.29/0.62      ! [M: nat,X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 0.29/0.62        ( ( ( replicate_VEBT_VEBT @ M @ X4 )
% 0.29/0.62          = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 0.29/0.62        = ( ( M = N2 )
% 0.29/0.62          & ( ( M != zero_zero_nat )
% 0.29/0.62           => ( X4 = Y ) ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % replicate_eq_replicate
% 0.29/0.62  thf(fact_8544_length__replicate,axiom,
% 0.29/0.62      ! [N2: nat,X4: vEBT_VEBT] :
% 0.29/0.62        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) )
% 0.29/0.62        = N2 ) ).
% 0.29/0.62  
% 0.29/0.62  % length_replicate
% 0.29/0.62  thf(fact_8545_length__replicate,axiom,
% 0.29/0.62      ! [N2: nat,X4: $o] :
% 0.29/0.62        ( ( size_size_list_o @ ( replicate_o @ N2 @ X4 ) )
% 0.29/0.62        = N2 ) ).
% 0.29/0.62  
% 0.29/0.62  % length_replicate
% 0.29/0.62  thf(fact_8546_length__replicate,axiom,
% 0.29/0.62      ! [N2: nat,X4: nat] :
% 0.29/0.62        ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X4 ) )
% 0.29/0.62        = N2 ) ).
% 0.29/0.62  
% 0.29/0.62  % length_replicate
% 0.29/0.62  thf(fact_8547_length__replicate,axiom,
% 0.29/0.62      ! [N2: nat,X4: int] :
% 0.29/0.62        ( ( size_size_list_int @ ( replicate_int @ N2 @ X4 ) )
% 0.29/0.62        = N2 ) ).
% 0.29/0.62  
% 0.29/0.62  % length_replicate
% 0.29/0.62  thf(fact_8548_summable__iff__shift,axiom,
% 0.29/0.62      ! [F: nat > real,K: nat] :
% 0.29/0.62        ( ( summable_real
% 0.29/0.62          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.29/0.62        = ( summable_real @ F ) ) ).
% 0.29/0.62  
% 0.29/0.62  % summable_iff_shift
% 0.29/0.62  thf(fact_8549_Ball__set__replicate,axiom,
% 0.29/0.62      ! [N2: nat,A: int,P: int > $o] :
% 0.29/0.62        ( ( ! [X: int] :
% 0.29/0.62              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 0.29/0.62             => ( P @ X ) ) )
% 0.29/0.62        = ( ( P @ A )
% 0.29/0.62          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ball_set_replicate
% 0.29/0.62  thf(fact_8550_Ball__set__replicate,axiom,
% 0.29/0.62      ! [N2: nat,A: nat,P: nat > $o] :
% 0.29/0.62        ( ( ! [X: nat] :
% 0.29/0.62              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 0.29/0.62             => ( P @ X ) ) )
% 0.29/0.62        = ( ( P @ A )
% 0.29/0.62          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ball_set_replicate
% 0.29/0.62  thf(fact_8551_Ball__set__replicate,axiom,
% 0.29/0.62      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.29/0.62        ( ( ! [X: vEBT_VEBT] :
% 0.29/0.62              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 0.29/0.62             => ( P @ X ) ) )
% 0.29/0.62        = ( ( P @ A )
% 0.29/0.62          | ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.62  
% 0.29/0.62  % Ball_set_replicate
% 0.29/0.62  thf(fact_8552_Bex__set__replicate,axiom,
% 0.29/0.63      ! [N2: nat,A: int,P: int > $o] :
% 0.29/0.63        ( ( ? [X: int] :
% 0.29/0.63              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 0.29/0.63              & ( P @ X ) ) )
% 0.29/0.63        = ( ( P @ A )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Bex_set_replicate
% 0.29/0.63  thf(fact_8553_Bex__set__replicate,axiom,
% 0.29/0.63      ! [N2: nat,A: nat,P: nat > $o] :
% 0.29/0.63        ( ( ? [X: nat] :
% 0.29/0.63              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 0.29/0.63              & ( P @ X ) ) )
% 0.29/0.63        = ( ( P @ A )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Bex_set_replicate
% 0.29/0.63  thf(fact_8554_Bex__set__replicate,axiom,
% 0.29/0.63      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.29/0.63        ( ( ? [X: vEBT_VEBT] :
% 0.29/0.63              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 0.29/0.63              & ( P @ X ) ) )
% 0.29/0.63        = ( ( P @ A )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Bex_set_replicate
% 0.29/0.63  thf(fact_8555_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Y: real] :
% 0.29/0.63        ( ( member_real @ X4 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8556_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat,Y: complex] :
% 0.29/0.63        ( ( member_complex @ X4 @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8557_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: product_prod_nat_nat,N2: nat,Y: product_prod_nat_nat] :
% 0.29/0.63        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8558_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: int,N2: nat,Y: int] :
% 0.29/0.63        ( ( member_int @ X4 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8559_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: nat,N2: nat,Y: nat] :
% 0.29/0.63        ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8560_in__set__replicate,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 0.29/0.63        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 0.29/0.63        = ( ( X4 = Y )
% 0.29/0.63          & ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % in_set_replicate
% 0.29/0.63  thf(fact_8561_nth__replicate,axiom,
% 0.29/0.63      ! [I2: nat,N2: nat,X4: nat] :
% 0.29/0.63        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.63       => ( ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 )
% 0.29/0.63          = X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % nth_replicate
% 0.29/0.63  thf(fact_8562_nth__replicate,axiom,
% 0.29/0.63      ! [I2: nat,N2: nat,X4: int] :
% 0.29/0.63        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.63       => ( ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 )
% 0.29/0.63          = X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % nth_replicate
% 0.29/0.63  thf(fact_8563_nth__replicate,axiom,
% 0.29/0.63      ! [I2: nat,N2: nat,X4: vEBT_VEBT] :
% 0.29/0.63        ( ( ord_less_nat @ I2 @ N2 )
% 0.29/0.63       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 )
% 0.29/0.63          = X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % nth_replicate
% 0.29/0.63  thf(fact_8564_summable__divide__iff,axiom,
% 0.29/0.63      ! [F: nat > real,C: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 0.29/0.63        = ( ( C = zero_zero_real )
% 0.29/0.63          | ( summable_real @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_divide_iff
% 0.29/0.63  thf(fact_8565_summable__divide__iff,axiom,
% 0.29/0.63      ! [F: nat > complex,C: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 0.29/0.63        = ( ( C = zero_zero_complex )
% 0.29/0.63          | ( summable_complex @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_divide_iff
% 0.29/0.63  thf(fact_8566_summable__geometric__iff,axiom,
% 0.29/0.63      ! [C: real] :
% 0.29/0.63        ( ( summable_real @ ( power_power_real @ C ) )
% 0.29/0.63        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_geometric_iff
% 0.29/0.63  thf(fact_8567_summable__geometric__iff,axiom,
% 0.29/0.63      ! [C: complex] :
% 0.29/0.63        ( ( summable_complex @ ( power_power_complex @ C ) )
% 0.29/0.63        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_geometric_iff
% 0.29/0.63  thf(fact_8568_summable__comparison__test,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real] :
% 0.29/0.63        ( ? [N7: nat] :
% 0.29/0.63          ! [N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( summable_real @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_comparison_test
% 0.29/0.63  thf(fact_8569_summable__comparison__test,axiom,
% 0.29/0.63      ! [F: nat > complex,G: nat > real] :
% 0.29/0.63        ( ? [N7: nat] :
% 0.29/0.63          ! [N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( summable_complex @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_comparison_test
% 0.29/0.63  thf(fact_8570_summable__comparison__test_H,axiom,
% 0.29/0.63      ! [G: nat > real,N4: nat,F: nat > real] :
% 0.29/0.63        ( ( summable_real @ G )
% 0.29/0.63       => ( ! [N3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63         => ( summable_real @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_comparison_test'
% 0.29/0.63  thf(fact_8571_summable__comparison__test_H,axiom,
% 0.29/0.63      ! [G: nat > real,N4: nat,F: nat > complex] :
% 0.29/0.63        ( ( summable_real @ G )
% 0.29/0.63       => ( ! [N3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63         => ( summable_complex @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_comparison_test'
% 0.29/0.63  thf(fact_8572_suminf__le,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( summable_real @ F )
% 0.29/0.63         => ( ( summable_real @ G )
% 0.29/0.63           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le
% 0.29/0.63  thf(fact_8573_suminf__le,axiom,
% 0.29/0.63      ! [F: nat > nat,G: nat > nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( summable_nat @ F )
% 0.29/0.63         => ( ( summable_nat @ G )
% 0.29/0.63           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le
% 0.29/0.63  thf(fact_8574_suminf__le,axiom,
% 0.29/0.63      ! [F: nat > int,G: nat > int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( summable_int @ F )
% 0.29/0.63         => ( ( summable_int @ G )
% 0.29/0.63           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le
% 0.29/0.63  thf(fact_8575_Reals__power,axiom,
% 0.29/0.63      ! [A: real,N2: nat] :
% 0.29/0.63        ( ( member_real @ A @ real_V470468836141973256s_real )
% 0.29/0.63       => ( member_real @ ( power_power_real @ A @ N2 ) @ real_V470468836141973256s_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_power
% 0.29/0.63  thf(fact_8576_Reals__power,axiom,
% 0.29/0.63      ! [A: complex,N2: nat] :
% 0.29/0.63        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 0.29/0.63       => ( member_complex @ ( power_power_complex @ A @ N2 ) @ real_V2521375963428798218omplex ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_power
% 0.29/0.63  thf(fact_8577_Reals__divide,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( member_real @ A @ real_V470468836141973256s_real )
% 0.29/0.63       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 0.29/0.63         => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_divide
% 0.29/0.63  thf(fact_8578_Reals__divide,axiom,
% 0.29/0.63      ! [A: complex,B: complex] :
% 0.29/0.63        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 0.29/0.63       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 0.29/0.63         => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_divide
% 0.29/0.63  thf(fact_8579_Reals__add,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( member_real @ A @ real_V470468836141973256s_real )
% 0.29/0.63       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 0.29/0.63         => ( member_real @ ( plus_plus_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_add
% 0.29/0.63  thf(fact_8580_Reals__add,axiom,
% 0.29/0.63      ! [A: complex,B: complex] :
% 0.29/0.63        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 0.29/0.63       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 0.29/0.63         => ( member_complex @ ( plus_plus_complex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_add
% 0.29/0.63  thf(fact_8581_Reals__1,axiom,
% 0.29/0.63      member_real @ one_one_real @ real_V470468836141973256s_real ).
% 0.29/0.63  
% 0.29/0.63  % Reals_1
% 0.29/0.63  thf(fact_8582_Reals__1,axiom,
% 0.29/0.63      member_complex @ one_one_complex @ real_V2521375963428798218omplex ).
% 0.29/0.63  
% 0.29/0.63  % Reals_1
% 0.29/0.63  thf(fact_8583_Reals__numeral,axiom,
% 0.29/0.63      ! [W: num] : ( member_complex @ ( numera6690914467698888265omplex @ W ) @ real_V2521375963428798218omplex ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_numeral
% 0.29/0.63  thf(fact_8584_Reals__numeral,axiom,
% 0.29/0.63      ! [W: num] : ( member_real @ ( numeral_numeral_real @ W ) @ real_V470468836141973256s_real ) ).
% 0.29/0.63  
% 0.29/0.63  % Reals_numeral
% 0.29/0.63  thf(fact_8585_summable__divide,axiom,
% 0.29/0.63      ! [F: nat > real,C: real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_divide
% 0.29/0.63  thf(fact_8586_summable__divide,axiom,
% 0.29/0.63      ! [F: nat > complex,C: complex] :
% 0.29/0.63        ( ( summable_complex @ F )
% 0.29/0.63       => ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_divide
% 0.29/0.63  thf(fact_8587_summable__ignore__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > real,K: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_ignore_initial_segment
% 0.29/0.63  thf(fact_8588_summable__add,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_add
% 0.29/0.63  thf(fact_8589_summable__add,axiom,
% 0.29/0.63      ! [F: nat > nat,G: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ( summable_nat @ G )
% 0.29/0.63         => ( summable_nat
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_add
% 0.29/0.63  thf(fact_8590_summable__add,axiom,
% 0.29/0.63      ! [F: nat > int,G: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ( summable_int @ G )
% 0.29/0.63         => ( summable_int
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_add
% 0.29/0.63  thf(fact_8591_summable__Suc__iff,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 0.29/0.63        = ( summable_real @ F ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_Suc_iff
% 0.29/0.63  thf(fact_8592_summable__zero__power,axiom,
% 0.29/0.63      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power
% 0.29/0.63  thf(fact_8593_summable__zero__power,axiom,
% 0.29/0.63      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power
% 0.29/0.63  thf(fact_8594_summable__zero__power,axiom,
% 0.29/0.63      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power
% 0.29/0.63  thf(fact_8595_suminf__add,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 0.29/0.63            = ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_add
% 0.29/0.63  thf(fact_8596_suminf__add,axiom,
% 0.29/0.63      ! [F: nat > nat,G: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ( summable_nat @ G )
% 0.29/0.63         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 0.29/0.63            = ( suminf_nat
% 0.29/0.63              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_add
% 0.29/0.63  thf(fact_8597_suminf__add,axiom,
% 0.29/0.63      ! [F: nat > int,G: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ( summable_int @ G )
% 0.29/0.63         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 0.29/0.63            = ( suminf_int
% 0.29/0.63              @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_add
% 0.29/0.63  thf(fact_8598_suminf__divide,axiom,
% 0.29/0.63      ! [F: nat > real,C: real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 0.29/0.63          = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_divide
% 0.29/0.63  thf(fact_8599_suminf__divide,axiom,
% 0.29/0.63      ! [F: nat > complex,C: complex] :
% 0.29/0.63        ( ( summable_complex @ F )
% 0.29/0.63       => ( ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 0.29/0.63          = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_divide
% 0.29/0.63  thf(fact_8600_series__comparison__complex,axiom,
% 0.29/0.63      ! [G: nat > complex,N4: nat,F: nat > real] :
% 0.29/0.63        ( ( summable_complex @ G )
% 0.29/0.63       => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 0.29/0.63         => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 0.29/0.63           => ( ! [N3: nat] :
% 0.29/0.63                  ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63                 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 0.29/0.63             => ( summable_real @ F ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % series_comparison_complex
% 0.29/0.63  thf(fact_8601_series__comparison__complex,axiom,
% 0.29/0.63      ! [G: nat > complex,N4: nat,F: nat > complex] :
% 0.29/0.63        ( ( summable_complex @ G )
% 0.29/0.63       => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 0.29/0.63         => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 0.29/0.63           => ( ! [N3: nat] :
% 0.29/0.63                  ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63                 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 0.29/0.63             => ( summable_complex @ F ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % series_comparison_complex
% 0.29/0.63  thf(fact_8602_powser__insidea,axiom,
% 0.29/0.63      ! [F: nat > real,X4: real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_insidea
% 0.29/0.63  thf(fact_8603_powser__insidea,axiom,
% 0.29/0.63      ! [F: nat > complex,X4: complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_insidea
% 0.29/0.63  thf(fact_8604_suminf__nonneg,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_nonneg
% 0.29/0.63  thf(fact_8605_suminf__nonneg,axiom,
% 0.29/0.63      ! [F: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_nonneg
% 0.29/0.63  thf(fact_8606_suminf__nonneg,axiom,
% 0.29/0.63      ! [F: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_nonneg
% 0.29/0.63  thf(fact_8607_suminf__eq__zero__iff,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ( suminf_real @ F )
% 0.29/0.63              = zero_zero_real )
% 0.29/0.63            = ( ! [N: nat] :
% 0.29/0.63                  ( ( F @ N )
% 0.29/0.63                  = zero_zero_real ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_eq_zero_iff
% 0.29/0.63  thf(fact_8608_suminf__eq__zero__iff,axiom,
% 0.29/0.63      ! [F: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ( suminf_nat @ F )
% 0.29/0.63              = zero_zero_nat )
% 0.29/0.63            = ( ! [N: nat] :
% 0.29/0.63                  ( ( F @ N )
% 0.29/0.63                  = zero_zero_nat ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_eq_zero_iff
% 0.29/0.63  thf(fact_8609_suminf__eq__zero__iff,axiom,
% 0.29/0.63      ! [F: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ( suminf_int @ F )
% 0.29/0.63              = zero_zero_int )
% 0.29/0.63            = ( ! [N: nat] :
% 0.29/0.63                  ( ( F @ N )
% 0.29/0.63                  = zero_zero_int ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_eq_zero_iff
% 0.29/0.63  thf(fact_8610_suminf__pos,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos
% 0.29/0.63  thf(fact_8611_suminf__pos,axiom,
% 0.29/0.63      ! [F: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos
% 0.29/0.63  thf(fact_8612_suminf__pos,axiom,
% 0.29/0.63      ! [F: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos
% 0.29/0.63  thf(fact_8613_summable__0__powser,axiom,
% 0.29/0.63      ! [F: nat > complex] :
% 0.29/0.63        ( summable_complex
% 0.29/0.63        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_0_powser
% 0.29/0.63  thf(fact_8614_summable__0__powser,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_0_powser
% 0.29/0.63  thf(fact_8615_summable__zero__power_H,axiom,
% 0.29/0.63      ! [F: nat > complex] :
% 0.29/0.63        ( summable_complex
% 0.29/0.63        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power'
% 0.29/0.63  thf(fact_8616_summable__zero__power_H,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power'
% 0.29/0.63  thf(fact_8617_summable__zero__power_H,axiom,
% 0.29/0.63      ! [F: nat > int] :
% 0.29/0.63        ( summable_int
% 0.29/0.63        @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_zero_power'
% 0.29/0.63  thf(fact_8618_summable__powser__split__head,axiom,
% 0.29/0.63      ! [F: nat > complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63        = ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_powser_split_head
% 0.29/0.63  thf(fact_8619_summable__powser__split__head,axiom,
% 0.29/0.63      ! [F: nat > real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63        = ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_powser_split_head
% 0.29/0.63  thf(fact_8620_powser__split__head_I3_J,axiom,
% 0.29/0.63      ! [F: nat > complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63       => ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(3)
% 0.29/0.63  thf(fact_8621_powser__split__head_I3_J,axiom,
% 0.29/0.63      ! [F: nat > real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63       => ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(3)
% 0.29/0.63  thf(fact_8622_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_real,N2: nat,X4: real] :
% 0.29/0.63        ( ( ( size_size_list_real @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: real] :
% 0.29/0.63              ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_real @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8623_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_complex,N2: nat,X4: complex] :
% 0.29/0.63        ( ( ( size_s3451745648224563538omplex @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: complex] :
% 0.29/0.63              ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_complex @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8624_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_P6011104703257516679at_nat,N2: nat,X4: product_prod_nat_nat] :
% 0.29/0.63        ( ( ( size_s5460976970255530739at_nat @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: product_prod_nat_nat] :
% 0.29/0.63              ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replic4235873036481779905at_nat @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8625_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_VEBT_VEBT,N2: nat,X4: vEBT_VEBT] :
% 0.29/0.63        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: vEBT_VEBT] :
% 0.29/0.63              ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_VEBT_VEBT @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8626_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_o,N2: nat,X4: $o] :
% 0.29/0.63        ( ( ( size_size_list_o @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: $o] :
% 0.29/0.63              ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_o @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8627_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_nat,N2: nat,X4: nat] :
% 0.29/0.63        ( ( ( size_size_list_nat @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: nat] :
% 0.29/0.63              ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_nat @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8628_replicate__eqI,axiom,
% 0.29/0.63      ! [Xs: list_int,N2: nat,X4: int] :
% 0.29/0.63        ( ( ( size_size_list_int @ Xs )
% 0.29/0.63          = N2 )
% 0.29/0.63       => ( ! [Y3: int] :
% 0.29/0.63              ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 0.29/0.63             => ( Y3 = X4 ) )
% 0.29/0.63         => ( Xs
% 0.29/0.63            = ( replicate_int @ N2 @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_eqI
% 0.29/0.63  thf(fact_8629_replicate__length__same,axiom,
% 0.29/0.63      ! [Xs: list_VEBT_VEBT,X4: vEBT_VEBT] :
% 0.29/0.63        ( ! [X5: vEBT_VEBT] :
% 0.29/0.63            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.29/0.63           => ( X5 = X4 ) )
% 0.29/0.63       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X4 )
% 0.29/0.63          = Xs ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_length_same
% 0.29/0.63  thf(fact_8630_replicate__length__same,axiom,
% 0.29/0.63      ! [Xs: list_o,X4: $o] :
% 0.29/0.63        ( ! [X5: $o] :
% 0.29/0.63            ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 0.29/0.63           => ( X5 = X4 ) )
% 0.29/0.63       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X4 )
% 0.29/0.63          = Xs ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_length_same
% 0.29/0.63  thf(fact_8631_replicate__length__same,axiom,
% 0.29/0.63      ! [Xs: list_nat,X4: nat] :
% 0.29/0.63        ( ! [X5: nat] :
% 0.29/0.63            ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 0.29/0.63           => ( X5 = X4 ) )
% 0.29/0.63       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X4 )
% 0.29/0.63          = Xs ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_length_same
% 0.29/0.63  thf(fact_8632_replicate__length__same,axiom,
% 0.29/0.63      ! [Xs: list_int,X4: int] :
% 0.29/0.63        ( ! [X5: int] :
% 0.29/0.63            ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 0.29/0.63           => ( X5 = X4 ) )
% 0.29/0.63       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X4 )
% 0.29/0.63          = Xs ) ) ).
% 0.29/0.63  
% 0.29/0.63  % replicate_length_same
% 0.29/0.63  thf(fact_8633_summable__powser__ignore__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > complex,M: nat,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63        = ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_powser_ignore_initial_segment
% 0.29/0.63  thf(fact_8634_summable__powser__ignore__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > real,M: nat,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63        = ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_powser_ignore_initial_segment
% 0.29/0.63  thf(fact_8635_summable__norm__comparison__test,axiom,
% 0.29/0.63      ! [F: nat > complex,G: nat > real] :
% 0.29/0.63        ( ? [N7: nat] :
% 0.29/0.63          ! [N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_comparison_test
% 0.29/0.63  thf(fact_8636_summable__rabs__comparison__test,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real] :
% 0.29/0.63        ( ? [N7: nat] :
% 0.29/0.63          ! [N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.29/0.63       => ( ( summable_real @ G )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_rabs_comparison_test
% 0.29/0.63  thf(fact_8637_nonzero__Reals__divide,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( member_real @ A @ real_V470468836141973256s_real )
% 0.29/0.63       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 0.29/0.63         => ( ( B != zero_zero_real )
% 0.29/0.63           => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % nonzero_Reals_divide
% 0.29/0.63  thf(fact_8638_nonzero__Reals__divide,axiom,
% 0.29/0.63      ! [A: complex,B: complex] :
% 0.29/0.63        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 0.29/0.63       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 0.29/0.63         => ( ( B != zero_zero_complex )
% 0.29/0.63           => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % nonzero_Reals_divide
% 0.29/0.63  thf(fact_8639_summable__rabs,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 0.29/0.63          @ ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_rabs
% 0.29/0.63  thf(fact_8640_suminf__pos2,axiom,
% 0.29/0.63      ! [F: nat > real,I2: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.29/0.63           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos2
% 0.29/0.63  thf(fact_8641_suminf__pos2,axiom,
% 0.29/0.63      ! [F: nat > nat,I2: nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.29/0.63           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos2
% 0.29/0.63  thf(fact_8642_suminf__pos2,axiom,
% 0.29/0.63      ! [F: nat > int,I2: nat] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 0.29/0.63           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos2
% 0.29/0.63  thf(fact_8643_suminf__pos__iff,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 0.29/0.63            = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos_iff
% 0.29/0.63  thf(fact_8644_suminf__pos__iff,axiom,
% 0.29/0.63      ! [F: nat > nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 0.29/0.63            = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos_iff
% 0.29/0.63  thf(fact_8645_suminf__pos__iff,axiom,
% 0.29/0.63      ! [F: nat > int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 0.29/0.63            = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_pos_iff
% 0.29/0.63  thf(fact_8646_summable__geometric,axiom,
% 0.29/0.63      ! [C: real] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.29/0.63       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_geometric
% 0.29/0.63  thf(fact_8647_summable__geometric,axiom,
% 0.29/0.63      ! [C: complex] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.29/0.63       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_geometric
% 0.29/0.63  thf(fact_8648_complete__algebra__summable__geometric,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ one_one_real )
% 0.29/0.63       => ( summable_real @ ( power_power_real @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % complete_algebra_summable_geometric
% 0.29/0.63  thf(fact_8649_complete__algebra__summable__geometric,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ one_one_real )
% 0.29/0.63       => ( summable_complex @ ( power_power_complex @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % complete_algebra_summable_geometric
% 0.29/0.63  thf(fact_8650_suminf__split__head,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 0.29/0.63          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_split_head
% 0.29/0.63  thf(fact_8651_summable__norm,axiom,
% 0.29/0.63      ! [F: nat > real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 0.29/0.63          @ ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm
% 0.29/0.63  thf(fact_8652_summable__norm,axiom,
% 0.29/0.63      ! [F: nat > complex] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 0.29/0.63          @ ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm
% 0.29/0.63  thf(fact_8653_powser__inside,axiom,
% 0.29/0.63      ! [F: nat > real,X4: real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_inside
% 0.29/0.63  thf(fact_8654_powser__inside,axiom,
% 0.29/0.63      ! [F: nat > complex,X4: complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 0.29/0.63         => ( summable_complex
% 0.29/0.63            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_inside
% 0.29/0.63  thf(fact_8655_summable__exp,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( summable_complex
% 0.29/0.63        @ ^ [N: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_exp
% 0.29/0.63  thf(fact_8656_summable__exp,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_exp
% 0.29/0.63  thf(fact_8657_powser__split__head_I1_J,axiom,
% 0.29/0.63      ! [F: nat > complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63       => ( ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 0.29/0.63            @ ( times_times_complex
% 0.29/0.63              @ ( suminf_complex
% 0.29/0.63                @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63              @ Z ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(1)
% 0.29/0.63  thf(fact_8658_powser__split__head_I1_J,axiom,
% 0.29/0.63      ! [F: nat > real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63       => ( ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 0.29/0.63            @ ( times_times_real
% 0.29/0.63              @ ( suminf_real
% 0.29/0.63                @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63              @ Z ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(1)
% 0.29/0.63  thf(fact_8659_powser__split__head_I2_J,axiom,
% 0.29/0.63      ! [F: nat > complex,Z: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63       => ( ( times_times_complex
% 0.29/0.63            @ ( suminf_complex
% 0.29/0.63              @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63            @ Z )
% 0.29/0.63          = ( minus_minus_complex
% 0.29/0.63            @ ( suminf_complex
% 0.29/0.63              @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 0.29/0.63            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(2)
% 0.29/0.63  thf(fact_8660_powser__split__head_I2_J,axiom,
% 0.29/0.63      ! [F: nat > real,Z: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63       => ( ( times_times_real
% 0.29/0.63            @ ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63            @ Z )
% 0.29/0.63          = ( minus_minus_real
% 0.29/0.63            @ ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 0.29/0.63            @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_split_head(2)
% 0.29/0.63  thf(fact_8661_suminf__exist__split,axiom,
% 0.29/0.63      ! [R3: real,F: nat > real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.29/0.63       => ( ( summable_real @ F )
% 0.29/0.63         => ? [N8: nat] :
% 0.29/0.63            ! [N6: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N8 @ N6 )
% 0.29/0.63             => ( ord_less_real
% 0.29/0.63                @ ( real_V7735802525324610683m_real
% 0.29/0.63                  @ ( suminf_real
% 0.29/0.63                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 0.29/0.63                @ R3 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_exist_split
% 0.29/0.63  thf(fact_8662_suminf__exist__split,axiom,
% 0.29/0.63      ! [R3: real,F: nat > complex] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ R3 )
% 0.29/0.63       => ( ( summable_complex @ F )
% 0.29/0.63         => ? [N8: nat] :
% 0.29/0.63            ! [N6: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N8 @ N6 )
% 0.29/0.63             => ( ord_less_real
% 0.29/0.63                @ ( real_V1022390504157884413omplex
% 0.29/0.63                  @ ( suminf_complex
% 0.29/0.63                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 0.29/0.63                @ R3 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_exist_split
% 0.29/0.63  thf(fact_8663_summable__power__series,axiom,
% 0.29/0.63      ! [F: nat > real,Z: real] :
% 0.29/0.63        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 0.29/0.63       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.29/0.63         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 0.29/0.63           => ( ( ord_less_real @ Z @ one_one_real )
% 0.29/0.63             => ( summable_real
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_power_series
% 0.29/0.63  thf(fact_8664_Abel__lemma,axiom,
% 0.29/0.63      ! [R3: real,R0: real,A: nat > complex,M7: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 0.29/0.63       => ( ( ord_less_real @ R3 @ R0 )
% 0.29/0.63         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 0.29/0.63           => ( summable_real
% 0.29/0.63              @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R3 @ N ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Abel_lemma
% 0.29/0.63  thf(fact_8665_summable__ratio__test,axiom,
% 0.29/0.63      ! [C: real,N4: nat,F: nat > real] :
% 0.29/0.63        ( ( ord_less_real @ C @ one_one_real )
% 0.29/0.63       => ( ! [N3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 0.29/0.63         => ( summable_real @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_ratio_test
% 0.29/0.63  thf(fact_8666_summable__ratio__test,axiom,
% 0.29/0.63      ! [C: real,N4: nat,F: nat > complex] :
% 0.29/0.63        ( ( ord_less_real @ C @ one_one_real )
% 0.29/0.63       => ( ! [N3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N4 @ N3 )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 0.29/0.63         => ( summable_complex @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_ratio_test
% 0.29/0.63  thf(fact_8667_Re__Reals__divide,axiom,
% 0.29/0.63      ! [R3: complex,Z: complex] :
% 0.29/0.63        ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 0.29/0.63       => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 0.29/0.63          = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Re_Reals_divide
% 0.29/0.63  thf(fact_8668_vebt__buildup_Osimps_I3_J,axiom,
% 0.29/0.63      ! [Va: nat] :
% 0.29/0.63        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.63         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.63            = ( 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 ) ) ) ) ) ) )
% 0.29/0.63        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.63         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.29/0.63            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % vebt_buildup.simps(3)
% 0.29/0.63  thf(fact_8669_sin__paired,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.29/0.63        @ ( sin_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_paired
% 0.29/0.63  thf(fact_8670_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.63        ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.63          = Y )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.63               => ( ~ Y
% 0.29/0.63                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 0.29/0.63           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.29/0.63                 => ( ~ Y
% 0.29/0.63                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 0.29/0.63             => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.63                    ( ( X4
% 0.29/0.63                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.63                   => ( ( Y
% 0.29/0.63                        = ( ( Xa = Mi3 )
% 0.29/0.63                          | ( Xa = Ma3 ) ) )
% 0.29/0.63                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 0.29/0.63               => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.63                      ( ( X4
% 0.29/0.63                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.63                     => ( ( Y
% 0.29/0.63                          = ( ( Xa = Mi3 )
% 0.29/0.63                            | ( Xa = Ma3 )
% 0.29/0.63                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.29/0.63                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) ) ) )
% 0.29/0.63                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.29/0.63                        ( ( X4
% 0.29/0.63                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.63                       => ( ( Y
% 0.29/0.63                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.29/0.63                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.membermima.pelims(1)
% 0.29/0.63  thf(fact_8671_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.63        ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.63               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 0.29/0.63           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.29/0.63                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 0.29/0.63             => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.63                    ( ( X4
% 0.29/0.63                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.63                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 0.29/0.63                     => ( ( Xa = Mi3 )
% 0.29/0.63                        | ( Xa = Ma3 ) ) ) )
% 0.29/0.63               => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.63                      ( ( X4
% 0.29/0.63                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.63                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 0.29/0.63                       => ( ( Xa = Mi3 )
% 0.29/0.63                          | ( Xa = Ma3 )
% 0.29/0.63                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.29/0.63                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.29/0.63                        ( ( X4
% 0.29/0.63                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.63                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 0.29/0.63                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.membermima.pelims(3)
% 0.29/0.63  thf(fact_8672_geometric__deriv__sums,axiom,
% 0.29/0.63      ! [Z: real] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 0.29/0.63       => ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) )
% 0.29/0.63          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_deriv_sums
% 0.29/0.63  thf(fact_8673_geometric__deriv__sums,axiom,
% 0.29/0.63      ! [Z: complex] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.29/0.63       => ( sums_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) )
% 0.29/0.63          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_deriv_sums
% 0.29/0.63  thf(fact_8674_powser__sums__zero__iff,axiom,
% 0.29/0.63      ! [A: nat > complex,X4: complex] :
% 0.29/0.63        ( ( sums_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 0.29/0.63          @ X4 )
% 0.29/0.63        = ( ( A @ zero_zero_nat )
% 0.29/0.63          = X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_zero_iff
% 0.29/0.63  thf(fact_8675_powser__sums__zero__iff,axiom,
% 0.29/0.63      ! [A: nat > real,X4: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 0.29/0.63          @ X4 )
% 0.29/0.63        = ( ( A @ zero_zero_nat )
% 0.29/0.63          = X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_zero_iff
% 0.29/0.63  thf(fact_8676_sums__le,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real,S: real,T2: real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( sums_real @ F @ S )
% 0.29/0.63         => ( ( sums_real @ G @ T2 )
% 0.29/0.63           => ( ord_less_eq_real @ S @ T2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_le
% 0.29/0.63  thf(fact_8677_sums__le,axiom,
% 0.29/0.63      ! [F: nat > nat,G: nat > nat,S: nat,T2: nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( sums_nat @ F @ S )
% 0.29/0.63         => ( ( sums_nat @ G @ T2 )
% 0.29/0.63           => ( ord_less_eq_nat @ S @ T2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_le
% 0.29/0.63  thf(fact_8678_sums__le,axiom,
% 0.29/0.63      ! [F: nat > int,G: nat > int,S: int,T2: int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.63       => ( ( sums_int @ F @ S )
% 0.29/0.63         => ( ( sums_int @ G @ T2 )
% 0.29/0.63           => ( ord_less_eq_int @ S @ T2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_le
% 0.29/0.63  thf(fact_8679_sums__divide,axiom,
% 0.29/0.63      ! [F: nat > real,A: real,C: real] :
% 0.29/0.63        ( ( sums_real @ F @ A )
% 0.29/0.63       => ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C )
% 0.29/0.63          @ ( divide_divide_real @ A @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_divide
% 0.29/0.63  thf(fact_8680_sums__divide,axiom,
% 0.29/0.63      ! [F: nat > complex,A: complex,C: complex] :
% 0.29/0.63        ( ( sums_complex @ F @ A )
% 0.29/0.63       => ( sums_complex
% 0.29/0.63          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C )
% 0.29/0.63          @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_divide
% 0.29/0.63  thf(fact_8681_sums__add,axiom,
% 0.29/0.63      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 0.29/0.63        ( ( sums_real @ F @ A )
% 0.29/0.63       => ( ( sums_real @ G @ B )
% 0.29/0.63         => ( sums_real
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 0.29/0.63            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_add
% 0.29/0.63  thf(fact_8682_sums__add,axiom,
% 0.29/0.63      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 0.29/0.63        ( ( sums_nat @ F @ A )
% 0.29/0.63       => ( ( sums_nat @ G @ B )
% 0.29/0.63         => ( sums_nat
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 0.29/0.63            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_add
% 0.29/0.63  thf(fact_8683_sums__add,axiom,
% 0.29/0.63      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 0.29/0.63        ( ( sums_int @ F @ A )
% 0.29/0.63       => ( ( sums_int @ G @ B )
% 0.29/0.63         => ( sums_int
% 0.29/0.63            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 0.29/0.63            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_add
% 0.29/0.63  thf(fact_8684_sums__mult__D,axiom,
% 0.29/0.63      ! [C: real,F: nat > real,A: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 0.29/0.63          @ A )
% 0.29/0.63       => ( ( C != zero_zero_real )
% 0.29/0.63         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_mult_D
% 0.29/0.63  thf(fact_8685_sums__mult__D,axiom,
% 0.29/0.63      ! [C: complex,F: nat > complex,A: complex] :
% 0.29/0.63        ( ( sums_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 0.29/0.63          @ A )
% 0.29/0.63       => ( ( C != zero_zero_complex )
% 0.29/0.63         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_mult_D
% 0.29/0.63  thf(fact_8686_sums__Suc__imp,axiom,
% 0.29/0.63      ! [F: nat > complex,S: complex] :
% 0.29/0.63        ( ( ( F @ zero_zero_nat )
% 0.29/0.63          = zero_zero_complex )
% 0.29/0.63       => ( ( sums_complex
% 0.29/0.63            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63            @ S )
% 0.29/0.63         => ( sums_complex @ F @ S ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc_imp
% 0.29/0.63  thf(fact_8687_sums__Suc__imp,axiom,
% 0.29/0.63      ! [F: nat > real,S: real] :
% 0.29/0.63        ( ( ( F @ zero_zero_nat )
% 0.29/0.63          = zero_zero_real )
% 0.29/0.63       => ( ( sums_real
% 0.29/0.63            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63            @ S )
% 0.29/0.63         => ( sums_real @ F @ S ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc_imp
% 0.29/0.63  thf(fact_8688_sums__Suc__iff,axiom,
% 0.29/0.63      ! [F: nat > real,S: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63          @ S )
% 0.29/0.63        = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc_iff
% 0.29/0.63  thf(fact_8689_sums__Suc,axiom,
% 0.29/0.63      ! [F: nat > real,L: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63          @ L )
% 0.29/0.63       => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc
% 0.29/0.63  thf(fact_8690_sums__Suc,axiom,
% 0.29/0.63      ! [F: nat > nat,L: nat] :
% 0.29/0.63        ( ( sums_nat
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63          @ L )
% 0.29/0.63       => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc
% 0.29/0.63  thf(fact_8691_sums__Suc,axiom,
% 0.29/0.63      ! [F: nat > int,L: int] :
% 0.29/0.63        ( ( sums_int
% 0.29/0.63          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 0.29/0.63          @ L )
% 0.29/0.63       => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_Suc
% 0.29/0.63  thf(fact_8692_sums__zero__iff__shift,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > complex,S: complex] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ I4 @ N2 )
% 0.29/0.63           => ( ( F @ I4 )
% 0.29/0.63              = zero_zero_complex ) )
% 0.29/0.63       => ( ( sums_complex
% 0.29/0.63            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 0.29/0.63            @ S )
% 0.29/0.63          = ( sums_complex @ F @ S ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_zero_iff_shift
% 0.29/0.63  thf(fact_8693_sums__zero__iff__shift,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > real,S: real] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ I4 @ N2 )
% 0.29/0.63           => ( ( F @ I4 )
% 0.29/0.63              = zero_zero_real ) )
% 0.29/0.63       => ( ( sums_real
% 0.29/0.63            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 0.29/0.63            @ S )
% 0.29/0.63          = ( sums_real @ F @ S ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_zero_iff_shift
% 0.29/0.63  thf(fact_8694_powser__sums__if,axiom,
% 0.29/0.63      ! [M: nat,Z: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N ) )
% 0.29/0.63        @ ( power_power_complex @ Z @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_if
% 0.29/0.63  thf(fact_8695_powser__sums__if,axiom,
% 0.29/0.63      ! [M: nat,Z: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N ) )
% 0.29/0.63        @ ( power_power_real @ Z @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_if
% 0.29/0.63  thf(fact_8696_powser__sums__if,axiom,
% 0.29/0.63      ! [M: nat,Z: int] :
% 0.29/0.63        ( sums_int
% 0.29/0.63        @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N ) )
% 0.29/0.63        @ ( power_power_int @ Z @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_if
% 0.29/0.63  thf(fact_8697_powser__sums__zero,axiom,
% 0.29/0.63      ! [A: nat > complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 0.29/0.63        @ ( A @ zero_zero_nat ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_zero
% 0.29/0.63  thf(fact_8698_powser__sums__zero,axiom,
% 0.29/0.63      ! [A: nat > real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 0.29/0.63        @ ( A @ zero_zero_nat ) ) ).
% 0.29/0.63  
% 0.29/0.63  % powser_sums_zero
% 0.29/0.63  thf(fact_8699_geometric__sums,axiom,
% 0.29/0.63      ! [C: real] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 0.29/0.63       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_sums
% 0.29/0.63  thf(fact_8700_geometric__sums,axiom,
% 0.29/0.63      ! [C: complex] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 0.29/0.63       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_sums
% 0.29/0.63  thf(fact_8701_power__half__series,axiom,
% 0.29/0.63      ( sums_real
% 0.29/0.63      @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 0.29/0.63      @ one_one_real ) ).
% 0.29/0.63  
% 0.29/0.63  % power_half_series
% 0.29/0.63  thf(fact_8702_sums__if_H,axiom,
% 0.29/0.63      ! [G: nat > real,X4: real] :
% 0.29/0.63        ( ( sums_real @ G @ X4 )
% 0.29/0.63       => ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.63          @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_if'
% 0.29/0.63  thf(fact_8703_sums__if,axiom,
% 0.29/0.63      ! [G: nat > real,X4: real,F: nat > real,Y: real] :
% 0.29/0.63        ( ( sums_real @ G @ X4 )
% 0.29/0.63       => ( ( sums_real @ F @ Y )
% 0.29/0.63         => ( sums_real
% 0.29/0.63            @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( F @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.63            @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_if
% 0.29/0.63  thf(fact_8704_cos__paired,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_real @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.63        @ ( cos_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_paired
% 0.29/0.63  thf(fact_8705_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.63        ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.29/0.63               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 0.29/0.63                 => ~ ( ( Xa = Mi3 )
% 0.29/0.63                      | ( Xa = Ma3 ) ) ) )
% 0.29/0.63           => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 0.29/0.63                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 0.29/0.63                   => ~ ( ( Xa = Mi3 )
% 0.29/0.63                        | ( Xa = Ma3 )
% 0.29/0.63                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.29/0.63             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.29/0.63                    ( ( X4
% 0.29/0.63                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 0.29/0.63                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 0.29/0.63                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.membermima.pelims(2)
% 0.29/0.63  thf(fact_8706_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.63        ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [A5: $o,B5: $o] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.63               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 0.29/0.63                 => ( ( ( Xa = zero_zero_nat )
% 0.29/0.63                     => A5 )
% 0.29/0.63                    & ( ( Xa != zero_zero_nat )
% 0.29/0.63                     => ( ( ( Xa = one_one_nat )
% 0.29/0.63                         => B5 )
% 0.29/0.63                        & ( Xa = one_one_nat ) ) ) ) ) )
% 0.29/0.63           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.29/0.63                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 0.29/0.63             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.29/0.63                    ( ( X4
% 0.29/0.63                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.63                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 0.29/0.63                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.naive_member.pelims(3)
% 0.29/0.63  thf(fact_8707_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.63        ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [A5: $o,B5: $o] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.63               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 0.29/0.63                 => ~ ( ( ( Xa = zero_zero_nat )
% 0.29/0.63                       => A5 )
% 0.29/0.63                      & ( ( Xa != zero_zero_nat )
% 0.29/0.63                       => ( ( ( Xa = one_one_nat )
% 0.29/0.63                           => B5 )
% 0.29/0.63                          & ( Xa = one_one_nat ) ) ) ) ) )
% 0.29/0.63           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.63                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 0.29/0.63                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.naive_member.pelims(2)
% 0.29/0.63  thf(fact_8708_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.29/0.63      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.63        ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 0.29/0.63          = Y )
% 0.29/0.63       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.63         => ( ! [A5: $o,B5: $o] :
% 0.29/0.63                ( ( X4
% 0.29/0.63                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.29/0.63               => ( ( Y
% 0.29/0.63                    = ( ( ( Xa = zero_zero_nat )
% 0.29/0.63                       => A5 )
% 0.29/0.63                      & ( ( Xa != zero_zero_nat )
% 0.29/0.63                       => ( ( ( Xa = one_one_nat )
% 0.29/0.63                           => B5 )
% 0.29/0.63                          & ( Xa = one_one_nat ) ) ) ) )
% 0.29/0.63                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 0.29/0.63           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.63                  ( ( X4
% 0.29/0.63                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.29/0.63                 => ( ~ Y
% 0.29/0.63                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 0.29/0.63             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.29/0.63                    ( ( X4
% 0.29/0.63                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.29/0.63                   => ( ( Y
% 0.29/0.63                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.29/0.63                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.63                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.29/0.63                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % VEBT_internal.naive_member.pelims(1)
% 0.29/0.63  thf(fact_8709_diffs__equiv,axiom,
% 0.29/0.63      ! [C: nat > complex,X4: complex] :
% 0.29/0.63        ( ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 0.29/0.63       => ( sums_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.29/0.63          @ ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diffs_equiv
% 0.29/0.63  thf(fact_8710_diffs__equiv,axiom,
% 0.29/0.63      ! [C: nat > real,X4: real] :
% 0.29/0.63        ( ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 0.29/0.63       => ( sums_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.29/0.63          @ ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diffs_equiv
% 0.29/0.63  thf(fact_8711_diffs__def,axiom,
% 0.29/0.63      ( diffs_complex
% 0.29/0.63      = ( ^ [C2: nat > complex,N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diffs_def
% 0.29/0.63  thf(fact_8712_diffs__def,axiom,
% 0.29/0.63      ( diffs_real
% 0.29/0.63      = ( ^ [C2: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diffs_def
% 0.29/0.63  thf(fact_8713_diffs__def,axiom,
% 0.29/0.63      ( diffs_int
% 0.29/0.63      = ( ^ [C2: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diffs_def
% 0.29/0.63  thf(fact_8714_termdiff__converges__all,axiom,
% 0.29/0.63      ! [C: nat > complex,X4: complex] :
% 0.29/0.63        ( ! [X5: complex] :
% 0.29/0.63            ( summable_complex
% 0.29/0.63            @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) )
% 0.29/0.63       => ( summable_complex
% 0.29/0.63          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % termdiff_converges_all
% 0.29/0.63  thf(fact_8715_termdiff__converges__all,axiom,
% 0.29/0.63      ! [C: nat > real,X4: real] :
% 0.29/0.63        ( ! [X5: real] :
% 0.29/0.63            ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) )
% 0.29/0.63       => ( summable_real
% 0.29/0.63          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % termdiff_converges_all
% 0.29/0.63  thf(fact_8716_termdiff__converges,axiom,
% 0.29/0.63      ! [X4: real,K5: real,C: nat > real] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 0.29/0.63       => ( ! [X5: real] :
% 0.29/0.63              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 0.29/0.63             => ( summable_real
% 0.29/0.63                @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) ) )
% 0.29/0.63         => ( summable_real
% 0.29/0.63            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % termdiff_converges
% 0.29/0.63  thf(fact_8717_termdiff__converges,axiom,
% 0.29/0.63      ! [X4: complex,K5: real,C: nat > complex] :
% 0.29/0.63        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 0.29/0.63       => ( ! [X5: complex] :
% 0.29/0.63              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 0.29/0.63             => ( summable_complex
% 0.29/0.63                @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) ) )
% 0.29/0.63         => ( summable_complex
% 0.29/0.63            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % termdiff_converges
% 0.29/0.63  thf(fact_8718_exp__first__two__terms,axiom,
% 0.29/0.63      ( exp_real
% 0.29/0.63      = ( ^ [X: real] :
% 0.29/0.63            ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X )
% 0.29/0.63            @ ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_first_two_terms
% 0.29/0.63  thf(fact_8719_exp__first__two__terms,axiom,
% 0.29/0.63      ( exp_complex
% 0.29/0.63      = ( ^ [X: complex] :
% 0.29/0.63            ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ X )
% 0.29/0.63            @ ( suminf_complex
% 0.29/0.63              @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_first_two_terms
% 0.29/0.63  thf(fact_8720_monoseq__def,axiom,
% 0.29/0.63      ( topolo6980174941875973593q_real
% 0.29/0.63      = ( ^ [X3: nat > real] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8721_monoseq__def,axiom,
% 0.29/0.63      ( topolo3100542954746470799et_int
% 0.29/0.63      = ( ^ [X3: nat > set_int] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_set_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8722_monoseq__def,axiom,
% 0.29/0.63      ( topolo4267028734544971653eq_rat
% 0.29/0.63      = ( ^ [X3: nat > rat] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_rat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8723_monoseq__def,axiom,
% 0.29/0.63      ( topolo1459490580787246023eq_num
% 0.29/0.63      = ( ^ [X3: nat > num] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_num @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8724_monoseq__def,axiom,
% 0.29/0.63      ( topolo4902158794631467389eq_nat
% 0.29/0.63      = ( ^ [X3: nat > nat] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_nat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8725_monoseq__def,axiom,
% 0.29/0.63      ( topolo4899668324122417113eq_int
% 0.29/0.63      = ( ^ [X3: nat > int] :
% 0.29/0.63            ( ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 0.29/0.63            | ! [M6: nat,N: nat] :
% 0.29/0.63                ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.63               => ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_def
% 0.29/0.63  thf(fact_8726_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > real] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8727_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > set_int] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8728_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > rat] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8729_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > num] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8730_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > nat] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8731_monoI2,axiom,
% 0.29/0.63      ! [X8: nat > int] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 0.29/0.63       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI2
% 0.29/0.63  thf(fact_8732_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > real] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8733_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > set_int] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_set_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8734_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > rat] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8735_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > num] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8736_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > nat] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8737_monoI1,axiom,
% 0.29/0.63      ! [X8: nat > int] :
% 0.29/0.63        ( ! [M5: nat,N3: nat] :
% 0.29/0.63            ( ( ord_less_eq_nat @ M5 @ N3 )
% 0.29/0.63           => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 0.29/0.63       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoI1
% 0.29/0.63  thf(fact_8738_scaleR__eq__iff,axiom,
% 0.29/0.63      ! [B: real,U: real,A: real] :
% 0.29/0.63        ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 0.29/0.63          = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 0.29/0.63        = ( ( A = B )
% 0.29/0.63          | ( U = one_one_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_eq_iff
% 0.29/0.63  thf(fact_8739_scaleR__power,axiom,
% 0.29/0.63      ! [X4: real,Y: real,N2: nat] :
% 0.29/0.63        ( ( power_power_real @ ( real_V1485227260804924795R_real @ X4 @ Y ) @ N2 )
% 0.29/0.63        = ( real_V1485227260804924795R_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_power
% 0.29/0.63  thf(fact_8740_scaleR__power,axiom,
% 0.29/0.63      ! [X4: real,Y: complex,N2: nat] :
% 0.29/0.63        ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X4 @ Y ) @ N2 )
% 0.29/0.63        = ( real_V2046097035970521341omplex @ ( power_power_real @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_power
% 0.29/0.63  thf(fact_8741_scaleR__minus1__left,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.63        = ( uminus_uminus_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_minus1_left
% 0.29/0.63  thf(fact_8742_scaleR__minus1__left,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.63        = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_minus1_left
% 0.29/0.63  thf(fact_8743_scaleR__collapse,axiom,
% 0.29/0.63      ! [U: real,A: real] :
% 0.29/0.63        ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 0.29/0.63        = A ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_collapse
% 0.29/0.63  thf(fact_8744_scaleR__times,axiom,
% 0.29/0.63      ! [U: num,W: num,A: complex] :
% 0.29/0.63        ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.29/0.63        = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_times
% 0.29/0.63  thf(fact_8745_scaleR__times,axiom,
% 0.29/0.63      ! [U: num,W: num,A: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.29/0.63        = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_times
% 0.29/0.63  thf(fact_8746_inverse__scaleR__times,axiom,
% 0.29/0.63      ! [V: num,W: num,A: complex] :
% 0.29/0.63        ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.29/0.63        = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % inverse_scaleR_times
% 0.29/0.63  thf(fact_8747_inverse__scaleR__times,axiom,
% 0.29/0.63      ! [V: num,W: num,A: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.29/0.63        = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % inverse_scaleR_times
% 0.29/0.63  thf(fact_8748_fraction__scaleR__times,axiom,
% 0.29/0.63      ! [U: num,V: num,W: num,A: complex] :
% 0.29/0.63        ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.29/0.63        = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % fraction_scaleR_times
% 0.29/0.63  thf(fact_8749_fraction__scaleR__times,axiom,
% 0.29/0.63      ! [U: num,V: num,W: num,A: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.29/0.63        = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % fraction_scaleR_times
% 0.29/0.63  thf(fact_8750_scaleR__half__double,axiom,
% 0.29/0.63      ! [A: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 0.29/0.63        = A ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_half_double
% 0.29/0.63  thf(fact_8751_scaleR__right__distrib,axiom,
% 0.29/0.63      ! [A: real,X4: real,Y: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X4 @ Y ) )
% 0.29/0.63        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_right_distrib
% 0.29/0.63  thf(fact_8752_scaleR__left__distrib,axiom,
% 0.29/0.63      ! [A: real,B: real,X4: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X4 )
% 0.29/0.63        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_left_distrib
% 0.29/0.63  thf(fact_8753_scaleR__left_Oadd,axiom,
% 0.29/0.63      ! [X4: real,Y: real,Xa: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X4 @ Y ) @ Xa )
% 0.29/0.63        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X4 @ Xa ) @ ( real_V1485227260804924795R_real @ Y @ Xa ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_left.add
% 0.29/0.63  thf(fact_8754_of__real__def,axiom,
% 0.29/0.63      ( real_V1803761363581548252l_real
% 0.29/0.63      = ( ^ [R5: real] : ( real_V1485227260804924795R_real @ R5 @ one_one_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_real_def
% 0.29/0.63  thf(fact_8755_of__real__def,axiom,
% 0.29/0.63      ( real_V4546457046886955230omplex
% 0.29/0.63      = ( ^ [R5: real] : ( real_V2046097035970521341omplex @ R5 @ one_one_complex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_real_def
% 0.29/0.63  thf(fact_8756_scaleR__right__mono,axiom,
% 0.29/0.63      ! [A: real,B: real,X4: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.63       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.63         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_right_mono
% 0.29/0.63  thf(fact_8757_scaleR__right__mono__neg,axiom,
% 0.29/0.63      ! [B: real,A: real,C: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ B @ A )
% 0.29/0.63       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.29/0.63         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_right_mono_neg
% 0.29/0.63  thf(fact_8758_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 0.29/0.63      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 0.29/0.63        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Real_Vector_Spaces.le_add_iff2
% 0.29/0.63  thf(fact_8759_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 0.29/0.63      ! [A: real,E2: real,C: real,B: real,D: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 0.29/0.63        = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Real_Vector_Spaces.le_add_iff1
% 0.29/0.63  thf(fact_8760_zero__le__scaleR__iff,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 0.29/0.63        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.63            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.63          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.63            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.63          | ( A = zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % zero_le_scaleR_iff
% 0.29/0.63  thf(fact_8761_scaleR__le__0__iff,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 0.29/0.63        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.63            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.29/0.63          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.29/0.63            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.63          | ( A = zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_le_0_iff
% 0.29/0.63  thf(fact_8762_scaleR__nonpos__nonpos,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.29/0.63         => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_nonpos_nonpos
% 0.29/0.63  thf(fact_8763_scaleR__nonpos__nonneg,axiom,
% 0.29/0.63      ! [A: real,X4: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.63         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_nonpos_nonneg
% 0.29/0.63  thf(fact_8764_scaleR__nonneg__nonpos,axiom,
% 0.29/0.63      ! [A: real,X4: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.63       => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.63         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_nonneg_nonpos
% 0.29/0.63  thf(fact_8765_scaleR__nonneg__nonneg,axiom,
% 0.29/0.63      ! [A: real,X4: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.63       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.63         => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X4 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_nonneg_nonneg
% 0.29/0.63  thf(fact_8766_split__scaleR__pos__le,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.63            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.29/0.63          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.63            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % split_scaleR_pos_le
% 0.29/0.63  thf(fact_8767_split__scaleR__neg__le,axiom,
% 0.29/0.63      ! [A: real,X4: real] :
% 0.29/0.63        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.63            & ( ord_less_eq_real @ X4 @ zero_zero_real ) )
% 0.29/0.63          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.29/0.63            & ( ord_less_eq_real @ zero_zero_real @ X4 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % split_scaleR_neg_le
% 0.29/0.63  thf(fact_8768_scaleR__mono_H,axiom,
% 0.29/0.63      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.63       => ( ( ord_less_eq_real @ C @ D )
% 0.29/0.63         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.63           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_mono'
% 0.29/0.63  thf(fact_8769_scaleR__mono,axiom,
% 0.29/0.63      ! [A: real,B: real,X4: real,Y: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.63       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.63         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.29/0.63           => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.63             => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ Y ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_mono
% 0.29/0.63  thf(fact_8770_scaleR__left__le__one__le,axiom,
% 0.29/0.63      ! [X4: real,A: real] :
% 0.29/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.63       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.29/0.63         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_left_le_one_le
% 0.29/0.63  thf(fact_8771_scaleR__2,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.63        = ( plus_plus_real @ X4 @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % scaleR_2
% 0.29/0.63  thf(fact_8772_real__vector__affinity__eq,axiom,
% 0.29/0.63      ! [M: real,X4: real,C: real,Y: real] :
% 0.29/0.63        ( ( M != zero_zero_real )
% 0.29/0.63       => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C )
% 0.29/0.63            = Y )
% 0.29/0.63          = ( X4
% 0.29/0.63            = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_vector_affinity_eq
% 0.29/0.63  thf(fact_8773_real__vector__eq__affinity,axiom,
% 0.29/0.63      ! [M: real,Y: real,X4: real,C: real] :
% 0.29/0.63        ( ( M != zero_zero_real )
% 0.29/0.63       => ( ( Y
% 0.29/0.63            = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C ) )
% 0.29/0.63          = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 0.29/0.63            = X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_vector_eq_affinity
% 0.29/0.63  thf(fact_8774_neg__less__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 0.29/0.63          = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_less_divideR_eq
% 0.29/0.63  thf(fact_8775_neg__divideR__less__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 0.29/0.63          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_divideR_less_eq
% 0.29/0.63  thf(fact_8776_pos__less__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 0.29/0.63          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_less_divideR_eq
% 0.29/0.63  thf(fact_8777_pos__divideR__less__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 0.29/0.63          = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_divideR_less_eq
% 0.29/0.63  thf(fact_8778_summable__exp__generic,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_exp_generic
% 0.29/0.63  thf(fact_8779_summable__exp__generic,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( summable_complex
% 0.29/0.63        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_exp_generic
% 0.29/0.63  thf(fact_8780_sin__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 0.29/0.63        @ ( sin_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_converges
% 0.29/0.63  thf(fact_8781_sin__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 0.29/0.63        @ ( sin_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_converges
% 0.29/0.63  thf(fact_8782_sin__def,axiom,
% 0.29/0.63      ( sin_real
% 0.29/0.63      = ( ^ [X: real] :
% 0.29/0.63            ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_def
% 0.29/0.63  thf(fact_8783_sin__def,axiom,
% 0.29/0.63      ( sin_complex
% 0.29/0.63      = ( ^ [X: complex] :
% 0.29/0.63            ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_def
% 0.29/0.63  thf(fact_8784_cos__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 0.29/0.63        @ ( cos_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_converges
% 0.29/0.63  thf(fact_8785_cos__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 0.29/0.63        @ ( cos_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_converges
% 0.29/0.63  thf(fact_8786_cos__def,axiom,
% 0.29/0.63      ( cos_real
% 0.29/0.63      = ( ^ [X: real] :
% 0.29/0.63            ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_def
% 0.29/0.63  thf(fact_8787_cos__def,axiom,
% 0.29/0.63      ( cos_complex
% 0.29/0.63      = ( ^ [X: complex] :
% 0.29/0.63            ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_def
% 0.29/0.63  thf(fact_8788_summable__norm__sin,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_sin
% 0.29/0.63  thf(fact_8789_summable__norm__sin,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_sin
% 0.29/0.63  thf(fact_8790_summable__norm__cos,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_cos
% 0.29/0.63  thf(fact_8791_summable__norm__cos,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_cos
% 0.29/0.63  thf(fact_8792_pos__le__minus__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 0.29/0.63          = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_le_minus_divideR_eq
% 0.29/0.63  thf(fact_8793_pos__minus__divideR__le__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 0.29/0.63          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_minus_divideR_le_eq
% 0.29/0.63  thf(fact_8794_neg__le__minus__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 0.29/0.63          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_le_minus_divideR_eq
% 0.29/0.63  thf(fact_8795_neg__minus__divideR__le__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 0.29/0.63          = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_minus_divideR_le_eq
% 0.29/0.63  thf(fact_8796_neg__minus__divideR__less__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 0.29/0.63          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_minus_divideR_less_eq
% 0.29/0.63  thf(fact_8797_neg__less__minus__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ C @ zero_zero_real )
% 0.29/0.63       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 0.29/0.63          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % neg_less_minus_divideR_eq
% 0.29/0.63  thf(fact_8798_pos__minus__divideR__less__eq,axiom,
% 0.29/0.63      ! [C: real,B: real,A: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 0.29/0.63          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_minus_divideR_less_eq
% 0.29/0.63  thf(fact_8799_pos__less__minus__divideR__eq,axiom,
% 0.29/0.63      ! [C: real,A: real,B: real] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.63       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 0.29/0.63          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pos_less_minus_divideR_eq
% 0.29/0.63  thf(fact_8800_exp__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) )
% 0.29/0.63        @ ( exp_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_converges
% 0.29/0.63  thf(fact_8801_exp__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) )
% 0.29/0.63        @ ( exp_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_converges
% 0.29/0.63  thf(fact_8802_exp__def,axiom,
% 0.29/0.63      ( exp_real
% 0.29/0.63      = ( ^ [X: real] :
% 0.29/0.63            ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_def
% 0.29/0.63  thf(fact_8803_exp__def,axiom,
% 0.29/0.63      ( exp_complex
% 0.29/0.63      = ( ^ [X: complex] :
% 0.29/0.63            ( suminf_complex
% 0.29/0.63            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_def
% 0.29/0.63  thf(fact_8804_summable__norm__exp,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_exp
% 0.29/0.63  thf(fact_8805_summable__norm__exp,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( summable_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summable_norm_exp
% 0.29/0.63  thf(fact_8806_sin__minus__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) ) )
% 0.29/0.63        @ ( sin_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_minus_converges
% 0.29/0.63  thf(fact_8807_sin__minus__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) ) )
% 0.29/0.63        @ ( sin_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_minus_converges
% 0.29/0.63  thf(fact_8808_cos__minus__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) )
% 0.29/0.63        @ ( cos_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_minus_converges
% 0.29/0.63  thf(fact_8809_cos__minus__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) )
% 0.29/0.63        @ ( cos_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_minus_converges
% 0.29/0.63  thf(fact_8810_cosh__def,axiom,
% 0.29/0.63      ( cosh_real
% 0.29/0.63      = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cosh_def
% 0.29/0.63  thf(fact_8811_cosh__def,axiom,
% 0.29/0.63      ( cosh_complex
% 0.29/0.63      = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cosh_def
% 0.29/0.63  thf(fact_8812_sinh__def,axiom,
% 0.29/0.63      ( sinh_real
% 0.29/0.63      = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sinh_def
% 0.29/0.63  thf(fact_8813_sinh__def,axiom,
% 0.29/0.63      ( sinh_complex
% 0.29/0.63      = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sinh_def
% 0.29/0.63  thf(fact_8814_exp__first__term,axiom,
% 0.29/0.63      ( exp_real
% 0.29/0.63      = ( ^ [X: real] :
% 0.29/0.63            ( plus_plus_real @ one_one_real
% 0.29/0.63            @ ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_first_term
% 0.29/0.63  thf(fact_8815_exp__first__term,axiom,
% 0.29/0.63      ( exp_complex
% 0.29/0.63      = ( ^ [X: complex] :
% 0.29/0.63            ( plus_plus_complex @ one_one_complex
% 0.29/0.63            @ ( suminf_complex
% 0.29/0.63              @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_first_term
% 0.29/0.63  thf(fact_8816_cosh__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) @ zero_zero_real )
% 0.29/0.63        @ ( cosh_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cosh_converges
% 0.29/0.63  thf(fact_8817_cosh__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) @ zero_zero_complex )
% 0.29/0.63        @ ( cosh_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cosh_converges
% 0.29/0.63  thf(fact_8818_sinh__converges,axiom,
% 0.29/0.63      ! [X4: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) )
% 0.29/0.63        @ ( sinh_real @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sinh_converges
% 0.29/0.63  thf(fact_8819_sinh__converges,axiom,
% 0.29/0.63      ! [X4: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) )
% 0.29/0.63        @ ( sinh_complex @ X4 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sinh_converges
% 0.29/0.63  thf(fact_8820_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8821_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > set_int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8822_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > rat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8823_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > num] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8824_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8825_mono__SucI1,axiom,
% 0.29/0.63      ! [X8: nat > int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 0.29/0.63       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI1
% 0.29/0.63  thf(fact_8826_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8827_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > set_int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8828_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > rat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8829_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > num] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8830_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8831_mono__SucI2,axiom,
% 0.29/0.63      ! [X8: nat > int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 0.29/0.63       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mono_SucI2
% 0.29/0.63  thf(fact_8832_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo6980174941875973593q_real
% 0.29/0.63      = ( ^ [X3: nat > real] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_real @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8833_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo3100542954746470799et_int
% 0.29/0.63      = ( ^ [X3: nat > set_int] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8834_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo4267028734544971653eq_rat
% 0.29/0.63      = ( ^ [X3: nat > rat] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8835_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo1459490580787246023eq_num
% 0.29/0.63      = ( ^ [X3: nat > num] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_num @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8836_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo4902158794631467389eq_nat
% 0.29/0.63      = ( ^ [X3: nat > nat] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8837_monoseq__Suc,axiom,
% 0.29/0.63      ( topolo4899668324122417113eq_int
% 0.29/0.63      = ( ^ [X3: nat > int] :
% 0.29/0.63            ( ! [N: nat] : ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 0.29/0.63            | ! [N: nat] : ( ord_less_eq_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % monoseq_Suc
% 0.29/0.63  thf(fact_8838_of__nat__code,axiom,
% 0.29/0.63      ( semiri8010041392384452111omplex
% 0.29/0.63      = ( ^ [N: nat] :
% 0.29/0.63            ( semiri2816024913162550771omplex
% 0.29/0.63            @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 0.29/0.63            @ N
% 0.29/0.63            @ zero_zero_complex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_code
% 0.29/0.63  thf(fact_8839_of__nat__code,axiom,
% 0.29/0.63      ( semiri681578069525770553at_rat
% 0.29/0.63      = ( ^ [N: nat] :
% 0.29/0.63            ( semiri7787848453975740701ux_rat
% 0.29/0.63            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 0.29/0.63            @ N
% 0.29/0.63            @ zero_zero_rat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_code
% 0.29/0.63  thf(fact_8840_of__nat__code,axiom,
% 0.29/0.63      ( semiri5074537144036343181t_real
% 0.29/0.63      = ( ^ [N: nat] :
% 0.29/0.63            ( semiri7260567687927622513x_real
% 0.29/0.63            @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 0.29/0.63            @ N
% 0.29/0.63            @ zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_code
% 0.29/0.63  thf(fact_8841_of__nat__code,axiom,
% 0.29/0.63      ( semiri1314217659103216013at_int
% 0.29/0.63      = ( ^ [N: nat] :
% 0.29/0.63            ( semiri8420488043553186161ux_int
% 0.29/0.63            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 0.29/0.63            @ N
% 0.29/0.63            @ zero_zero_int ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_code
% 0.29/0.63  thf(fact_8842_of__nat__code,axiom,
% 0.29/0.63      ( semiri1316708129612266289at_nat
% 0.29/0.63      = ( ^ [N: nat] :
% 0.29/0.63            ( semiri8422978514062236437ux_nat
% 0.29/0.63            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 0.29/0.63            @ N
% 0.29/0.63            @ zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_code
% 0.29/0.63  thf(fact_8843_Arg__def,axiom,
% 0.29/0.63      ( arg
% 0.29/0.63      = ( ^ [Z5: complex] :
% 0.29/0.63            ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 0.29/0.63            @ ( fChoice_real
% 0.29/0.63              @ ^ [A3: real] :
% 0.29/0.63                  ( ( ( sgn_sgn_complex @ Z5 )
% 0.29/0.63                    = ( cis @ A3 ) )
% 0.29/0.63                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 0.29/0.63                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Arg_def
% 0.29/0.63  thf(fact_8844_set__vebt__def,axiom,
% 0.29/0.63      ( vEBT_set_vebt
% 0.29/0.63      = ( ^ [T: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % set_vebt_def
% 0.29/0.63  thf(fact_8845_sin__x__sin__y,axiom,
% 0.29/0.63      ! [X4: complex,Y: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [N: nat] :
% 0.29/0.63                ( if_complex
% 0.29/0.63                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 0.29/0.63                  & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.63                @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 0.29/0.63                @ zero_zero_complex )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_x_sin_y
% 0.29/0.63  thf(fact_8846_sin__x__sin__y,axiom,
% 0.29/0.63      ! [X4: real,Y: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [N: nat] :
% 0.29/0.63                ( if_real
% 0.29/0.63                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 0.29/0.63                  & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.63                @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 0.29/0.63                @ zero_zero_real )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sin_x_sin_y
% 0.29/0.63  thf(fact_8847_atMost__eq__iff,axiom,
% 0.29/0.63      ! [X4: nat,Y: nat] :
% 0.29/0.63        ( ( ( set_ord_atMost_nat @ X4 )
% 0.29/0.63          = ( set_ord_atMost_nat @ Y ) )
% 0.29/0.63        = ( X4 = Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_eq_iff
% 0.29/0.63  thf(fact_8848_atMost__eq__iff,axiom,
% 0.29/0.63      ! [X4: int,Y: int] :
% 0.29/0.63        ( ( ( set_ord_atMost_int @ X4 )
% 0.29/0.63          = ( set_ord_atMost_int @ Y ) )
% 0.29/0.63        = ( X4 = Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_eq_iff
% 0.29/0.63  thf(fact_8849_atMost__iff,axiom,
% 0.29/0.63      ! [I2: real,K: real] :
% 0.29/0.63        ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 0.29/0.63        = ( ord_less_eq_real @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8850_atMost__iff,axiom,
% 0.29/0.63      ! [I2: set_int,K: set_int] :
% 0.29/0.63        ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 0.29/0.63        = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8851_atMost__iff,axiom,
% 0.29/0.63      ! [I2: rat,K: rat] :
% 0.29/0.63        ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 0.29/0.63        = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8852_atMost__iff,axiom,
% 0.29/0.63      ! [I2: num,K: num] :
% 0.29/0.63        ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 0.29/0.63        = ( ord_less_eq_num @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8853_atMost__iff,axiom,
% 0.29/0.63      ! [I2: nat,K: nat] :
% 0.29/0.63        ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 0.29/0.63        = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8854_atMost__iff,axiom,
% 0.29/0.63      ! [I2: int,K: int] :
% 0.29/0.63        ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 0.29/0.63        = ( ord_less_eq_int @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_iff
% 0.29/0.63  thf(fact_8855_atMost__subset__iff,axiom,
% 0.29/0.63      ! [X4: set_int,Y: set_int] :
% 0.29/0.63        ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X4 ) @ ( set_or58775011639299419et_int @ Y ) )
% 0.29/0.63        = ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_subset_iff
% 0.29/0.63  thf(fact_8856_atMost__subset__iff,axiom,
% 0.29/0.63      ! [X4: rat,Y: rat] :
% 0.29/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X4 ) @ ( set_ord_atMost_rat @ Y ) )
% 0.29/0.63        = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_subset_iff
% 0.29/0.63  thf(fact_8857_atMost__subset__iff,axiom,
% 0.29/0.63      ! [X4: num,Y: num] :
% 0.29/0.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X4 ) @ ( set_ord_atMost_num @ Y ) )
% 0.29/0.63        = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_subset_iff
% 0.29/0.63  thf(fact_8858_atMost__subset__iff,axiom,
% 0.29/0.63      ! [X4: nat,Y: nat] :
% 0.29/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X4 ) @ ( set_ord_atMost_nat @ Y ) )
% 0.29/0.63        = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_subset_iff
% 0.29/0.63  thf(fact_8859_atMost__subset__iff,axiom,
% 0.29/0.63      ! [X4: int,Y: int] :
% 0.29/0.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X4 ) @ ( set_ord_atMost_int @ Y ) )
% 0.29/0.63        = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_subset_iff
% 0.29/0.63  thf(fact_8860_sum_OatMost__Suc,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc
% 0.29/0.63  thf(fact_8861_sum_OatMost__Suc,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc
% 0.29/0.63  thf(fact_8862_sum_OatMost__Suc,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc
% 0.29/0.63  thf(fact_8863_sum_OatMost__Suc,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc
% 0.29/0.63  thf(fact_8864_norm__sum,axiom,
% 0.29/0.63      ! [F: nat > complex,A2: set_nat] :
% 0.29/0.63        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 0.29/0.63        @ ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % norm_sum
% 0.29/0.63  thf(fact_8865_norm__sum,axiom,
% 0.29/0.63      ! [F: nat > real,A2: set_nat] :
% 0.29/0.63        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.29/0.63        @ ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % norm_sum
% 0.29/0.63  thf(fact_8866_norm__sum,axiom,
% 0.29/0.63      ! [F: complex > complex,A2: set_complex] :
% 0.29/0.63        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 0.29/0.63        @ ( groups5808333547571424918x_real
% 0.29/0.63          @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % norm_sum
% 0.29/0.63  thf(fact_8867_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_real,F: real > complex,G: real > real] :
% 0.29/0.63        ( ! [X5: real] :
% 0.29/0.63            ( ( member_real @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8868_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_int,F: int > complex,G: int > real] :
% 0.29/0.63        ( ! [X5: int] :
% 0.29/0.63            ( ( member_int @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8869_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 0.29/0.63        ( ! [X5: product_prod_nat_nat] :
% 0.29/0.63            ( ( member8440522571783428010at_nat @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8870_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 0.29/0.63        ( ! [X5: nat] :
% 0.29/0.63            ( ( member_nat @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8871_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 0.29/0.63        ( ! [X5: nat] :
% 0.29/0.63            ( ( member_nat @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8872_sum__norm__le,axiom,
% 0.29/0.63      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 0.29/0.63        ( ! [X5: complex] :
% 0.29/0.63            ( ( member_complex @ X5 @ S2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 0.29/0.63       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_norm_le
% 0.29/0.63  thf(fact_8873_sum__choose__upper,axiom,
% 0.29/0.63      ! [M: nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_choose_upper
% 0.29/0.63  thf(fact_8874_mod__sum__eq,axiom,
% 0.29/0.63      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.29/0.63        ( ( modulo_modulo_nat
% 0.29/0.63          @ ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 0.29/0.63            @ A2 )
% 0.29/0.63          @ A )
% 0.29/0.63        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mod_sum_eq
% 0.29/0.63  thf(fact_8875_mod__sum__eq,axiom,
% 0.29/0.63      ! [F: int > int,A: int,A2: set_int] :
% 0.29/0.63        ( ( modulo_modulo_int
% 0.29/0.63          @ ( groups4538972089207619220nt_int
% 0.29/0.63            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.29/0.63            @ A2 )
% 0.29/0.63          @ A )
% 0.29/0.63        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mod_sum_eq
% 0.29/0.63  thf(fact_8876_sum_OatMost__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc_shift
% 0.29/0.63  thf(fact_8877_sum_OatMost__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc_shift
% 0.29/0.63  thf(fact_8878_sum_OatMost__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc_shift
% 0.29/0.63  thf(fact_8879_sum_OatMost__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_Suc_shift
% 0.29/0.63  thf(fact_8880_sum__telescope,axiom,
% 0.29/0.63      ! [F: nat > rat,I2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ I2 ) )
% 0.29/0.63        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_telescope
% 0.29/0.63  thf(fact_8881_sum__telescope,axiom,
% 0.29/0.63      ! [F: nat > int,I2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ I2 ) )
% 0.29/0.63        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_telescope
% 0.29/0.63  thf(fact_8882_sum__telescope,axiom,
% 0.29/0.63      ! [F: nat > real,I2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ I2 ) )
% 0.29/0.63        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_telescope
% 0.29/0.63  thf(fact_8883_polyfun__eq__coeffs,axiom,
% 0.29/0.63      ! [C: nat > complex,N2: nat,D: nat > complex] :
% 0.29/0.63        ( ( ! [X: complex] :
% 0.29/0.63              ( ( groups2073611262835488442omplex
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63              = ( groups2073611262835488442omplex
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 0.29/0.63        = ( ! [I3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.29/0.63             => ( ( C @ I3 )
% 0.29/0.63                = ( D @ I3 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_eq_coeffs
% 0.29/0.63  thf(fact_8884_polyfun__eq__coeffs,axiom,
% 0.29/0.63      ! [C: nat > real,N2: nat,D: nat > real] :
% 0.29/0.63        ( ( ! [X: real] :
% 0.29/0.63              ( ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63              = ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 0.29/0.63        = ( ! [I3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.29/0.63             => ( ( C @ I3 )
% 0.29/0.63                = ( D @ I3 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_eq_coeffs
% 0.29/0.63  thf(fact_8885_bounded__imp__summable,axiom,
% 0.29/0.63      ! [A: nat > int,B3: int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 0.29/0.63         => ( summable_int @ A ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % bounded_imp_summable
% 0.29/0.63  thf(fact_8886_bounded__imp__summable,axiom,
% 0.29/0.63      ! [A: nat > nat,B3: nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 0.29/0.63         => ( summable_nat @ A ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % bounded_imp_summable
% 0.29/0.63  thf(fact_8887_bounded__imp__summable,axiom,
% 0.29/0.63      ! [A: nat > real,B3: real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 0.29/0.63         => ( summable_real @ A ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % bounded_imp_summable
% 0.29/0.63  thf(fact_8888_atMost__def,axiom,
% 0.29/0.63      ( set_ord_atMost_real
% 0.29/0.63      = ( ^ [U2: real] :
% 0.29/0.63            ( collect_real
% 0.29/0.63            @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8889_atMost__def,axiom,
% 0.29/0.63      ( set_or58775011639299419et_int
% 0.29/0.63      = ( ^ [U2: set_int] :
% 0.29/0.63            ( collect_set_int
% 0.29/0.63            @ ^ [X: set_int] : ( ord_less_eq_set_int @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8890_atMost__def,axiom,
% 0.29/0.63      ( set_ord_atMost_rat
% 0.29/0.63      = ( ^ [U2: rat] :
% 0.29/0.63            ( collect_rat
% 0.29/0.63            @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8891_atMost__def,axiom,
% 0.29/0.63      ( set_ord_atMost_num
% 0.29/0.63      = ( ^ [U2: num] :
% 0.29/0.63            ( collect_num
% 0.29/0.63            @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8892_atMost__def,axiom,
% 0.29/0.63      ( set_ord_atMost_nat
% 0.29/0.63      = ( ^ [U2: nat] :
% 0.29/0.63            ( collect_nat
% 0.29/0.63            @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8893_atMost__def,axiom,
% 0.29/0.63      ( set_ord_atMost_int
% 0.29/0.63      = ( ^ [U2: int] :
% 0.29/0.63            ( collect_int
% 0.29/0.63            @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % atMost_def
% 0.29/0.63  thf(fact_8894_sum__choose__lower,axiom,
% 0.29/0.63      ! [R3: nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N2 ) ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_choose_lower
% 0.29/0.63  thf(fact_8895_choose__rising__sum_I2_J,axiom,
% 0.29/0.63      ! [N2: nat,M: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_rising_sum(2)
% 0.29/0.63  thf(fact_8896_choose__rising__sum_I1_J,axiom,
% 0.29/0.63      ! [N2: nat,M: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_rising_sum(1)
% 0.29/0.63  thf(fact_8897_polyfun__eq__0,axiom,
% 0.29/0.63      ! [C: nat > complex,N2: nat] :
% 0.29/0.63        ( ( ! [X: complex] :
% 0.29/0.63              ( ( groups2073611262835488442omplex
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63              = zero_zero_complex ) )
% 0.29/0.63        = ( ! [I3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.29/0.63             => ( ( C @ I3 )
% 0.29/0.63                = zero_zero_complex ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_eq_0
% 0.29/0.63  thf(fact_8898_polyfun__eq__0,axiom,
% 0.29/0.63      ! [C: nat > real,N2: nat] :
% 0.29/0.63        ( ( ! [X: real] :
% 0.29/0.63              ( ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63              = zero_zero_real ) )
% 0.29/0.63        = ( ! [I3: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ I3 @ N2 )
% 0.29/0.63             => ( ( C @ I3 )
% 0.29/0.63                = zero_zero_real ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_eq_0
% 0.29/0.63  thf(fact_8899_zero__polynom__imp__zero__coeffs,axiom,
% 0.29/0.63      ! [C: nat > complex,N2: nat,K: nat] :
% 0.29/0.63        ( ! [W2: complex] :
% 0.29/0.63            ( ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W2 @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_complex )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.63         => ( ( C @ K )
% 0.29/0.63            = zero_zero_complex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % zero_polynom_imp_zero_coeffs
% 0.29/0.63  thf(fact_8900_zero__polynom__imp__zero__coeffs,axiom,
% 0.29/0.63      ! [C: nat > real,N2: nat,K: nat] :
% 0.29/0.63        ( ! [W2: real] :
% 0.29/0.63            ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W2 @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_real )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/0.63         => ( ( C @ K )
% 0.29/0.63            = zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % zero_polynom_imp_zero_coeffs
% 0.29/0.63  thf(fact_8901_gbinomial__parallel__sum,axiom,
% 0.29/0.63      ! [A: complex,N2: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_parallel_sum
% 0.29/0.63  thf(fact_8902_gbinomial__parallel__sum,axiom,
% 0.29/0.63      ! [A: rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_parallel_sum
% 0.29/0.63  thf(fact_8903_gbinomial__parallel__sum,axiom,
% 0.29/0.63      ! [A: real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_parallel_sum
% 0.29/0.63  thf(fact_8904_sum__choose__diagonal,axiom,
% 0.29/0.63      ! [M: nat,N2: nat] :
% 0.29/0.63        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.63       => ( ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63          = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_choose_diagonal
% 0.29/0.63  thf(fact_8905_vandermonde,axiom,
% 0.29/0.63      ! [M: nat,N2: nat,R3: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ R3 ) )
% 0.29/0.63        = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R3 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % vandermonde
% 0.29/0.63  thf(fact_8906_sum__gp__basic,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_basic
% 0.29/0.63  thf(fact_8907_sum__gp__basic,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_basic
% 0.29/0.63  thf(fact_8908_sum__gp__basic,axiom,
% 0.29/0.63      ! [X4: int,N2: nat] :
% 0.29/0.63        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_basic
% 0.29/0.63  thf(fact_8909_sum__gp__basic,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_basic
% 0.29/0.63  thf(fact_8910_choose__row__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_row_sum
% 0.29/0.63  thf(fact_8911_binomial,axiom,
% 0.29/0.63      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.63        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial
% 0.29/0.63  thf(fact_8912_sum_Oin__pairs__0,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [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 ) ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.in_pairs_0
% 0.29/0.63  thf(fact_8913_sum_Oin__pairs__0,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.63        = ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [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 ) ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.in_pairs_0
% 0.29/0.63  thf(fact_8914_sum_Oin__pairs__0,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.63        = ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [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 ) ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.in_pairs_0
% 0.29/0.63  thf(fact_8915_sum_Oin__pairs__0,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [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 ) ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.in_pairs_0
% 0.29/0.63  thf(fact_8916_polynomial__product,axiom,
% 0.29/0.63      ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X4: rat] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ M @ I4 )
% 0.29/0.63           => ( ( A @ I4 )
% 0.29/0.63              = zero_zero_rat ) )
% 0.29/0.63       => ( ! [J2: nat] :
% 0.29/0.63              ( ( ord_less_nat @ N2 @ J2 )
% 0.29/0.63             => ( ( B @ J2 )
% 0.29/0.63                = zero_zero_rat ) )
% 0.29/0.63         => ( ( times_times_rat
% 0.29/0.63              @ ( groups2906978787729119204at_rat
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63              @ ( groups2906978787729119204at_rat
% 0.29/0.63                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X4 @ J3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63            = ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [R5: nat] :
% 0.29/0.63                  ( times_times_rat
% 0.29/0.63                  @ ( groups2906978787729119204at_rat
% 0.29/0.63                    @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.29/0.63                  @ ( power_power_rat @ X4 @ R5 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polynomial_product
% 0.29/0.63  thf(fact_8917_polynomial__product,axiom,
% 0.29/0.63      ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X4: complex] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ M @ I4 )
% 0.29/0.63           => ( ( A @ I4 )
% 0.29/0.63              = zero_zero_complex ) )
% 0.29/0.63       => ( ! [J2: nat] :
% 0.29/0.63              ( ( ord_less_nat @ N2 @ J2 )
% 0.29/0.63             => ( ( B @ J2 )
% 0.29/0.63                = zero_zero_complex ) )
% 0.29/0.63         => ( ( times_times_complex
% 0.29/0.63              @ ( groups2073611262835488442omplex
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63              @ ( groups2073611262835488442omplex
% 0.29/0.63                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X4 @ J3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63            = ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [R5: nat] :
% 0.29/0.63                  ( times_times_complex
% 0.29/0.63                  @ ( groups2073611262835488442omplex
% 0.29/0.63                    @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.29/0.63                  @ ( power_power_complex @ X4 @ R5 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polynomial_product
% 0.29/0.63  thf(fact_8918_polynomial__product,axiom,
% 0.29/0.63      ! [M: nat,A: nat > int,N2: nat,B: nat > int,X4: int] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ M @ I4 )
% 0.29/0.63           => ( ( A @ I4 )
% 0.29/0.63              = zero_zero_int ) )
% 0.29/0.63       => ( ! [J2: nat] :
% 0.29/0.63              ( ( ord_less_nat @ N2 @ J2 )
% 0.29/0.63             => ( ( B @ J2 )
% 0.29/0.63                = zero_zero_int ) )
% 0.29/0.63         => ( ( times_times_int
% 0.29/0.63              @ ( groups3539618377306564664at_int
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63              @ ( groups3539618377306564664at_int
% 0.29/0.63                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X4 @ J3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63            = ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [R5: nat] :
% 0.29/0.63                  ( times_times_int
% 0.29/0.63                  @ ( groups3539618377306564664at_int
% 0.29/0.63                    @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.29/0.63                  @ ( power_power_int @ X4 @ R5 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polynomial_product
% 0.29/0.63  thf(fact_8919_polynomial__product,axiom,
% 0.29/0.63      ! [M: nat,A: nat > real,N2: nat,B: nat > real,X4: real] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ M @ I4 )
% 0.29/0.63           => ( ( A @ I4 )
% 0.29/0.63              = zero_zero_real ) )
% 0.29/0.63       => ( ! [J2: nat] :
% 0.29/0.63              ( ( ord_less_nat @ N2 @ J2 )
% 0.29/0.63             => ( ( B @ J2 )
% 0.29/0.63                = zero_zero_real ) )
% 0.29/0.63         => ( ( times_times_real
% 0.29/0.63              @ ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63              @ ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X4 @ J3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63            = ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [R5: nat] :
% 0.29/0.63                  ( times_times_real
% 0.29/0.63                  @ ( groups6591440286371151544t_real
% 0.29/0.63                    @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.29/0.63                  @ ( power_power_real @ X4 @ R5 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polynomial_product
% 0.29/0.63  thf(fact_8920_gbinomial__sum__lower__neg,axiom,
% 0.29/0.63      ! [A: complex,M: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_sum_lower_neg
% 0.29/0.63  thf(fact_8921_gbinomial__sum__lower__neg,axiom,
% 0.29/0.63      ! [A: rat,M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_sum_lower_neg
% 0.29/0.63  thf(fact_8922_gbinomial__sum__lower__neg,axiom,
% 0.29/0.63      ! [A: real,M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_sum_lower_neg
% 0.29/0.63  thf(fact_8923_binomial__ring,axiom,
% 0.29/0.63      ! [A: rat,B: rat,N2: nat] :
% 0.29/0.63        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_ring
% 0.29/0.63  thf(fact_8924_binomial__ring,axiom,
% 0.29/0.63      ! [A: complex,B: complex,N2: nat] :
% 0.29/0.63        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_ring
% 0.29/0.63  thf(fact_8925_binomial__ring,axiom,
% 0.29/0.63      ! [A: int,B: int,N2: nat] :
% 0.29/0.63        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_ring
% 0.29/0.63  thf(fact_8926_binomial__ring,axiom,
% 0.29/0.63      ! [A: nat,B: nat,N2: nat] :
% 0.29/0.63        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_ring
% 0.29/0.63  thf(fact_8927_binomial__ring,axiom,
% 0.29/0.63      ! [A: real,B: real,N2: nat] :
% 0.29/0.63        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_ring
% 0.29/0.63  thf(fact_8928_polynomial__product__nat,axiom,
% 0.29/0.63      ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X4: nat] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( ord_less_nat @ M @ I4 )
% 0.29/0.63           => ( ( A @ I4 )
% 0.29/0.63              = zero_zero_nat ) )
% 0.29/0.63       => ( ! [J2: nat] :
% 0.29/0.63              ( ( ord_less_nat @ N2 @ J2 )
% 0.29/0.63             => ( ( B @ J2 )
% 0.29/0.63                = zero_zero_nat ) )
% 0.29/0.63         => ( ( times_times_nat
% 0.29/0.63              @ ( groups3542108847815614940at_nat
% 0.29/0.63                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X4 @ I3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63              @ ( groups3542108847815614940at_nat
% 0.29/0.63                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X4 @ J3 ) )
% 0.29/0.63                @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63            = ( groups3542108847815614940at_nat
% 0.29/0.63              @ ^ [R5: nat] :
% 0.29/0.63                  ( times_times_nat
% 0.29/0.63                  @ ( groups3542108847815614940at_nat
% 0.29/0.63                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.29/0.63                  @ ( power_power_nat @ X4 @ R5 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polynomial_product_nat
% 0.29/0.63  thf(fact_8929_choose__square__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_square_sum
% 0.29/0.63  thf(fact_8930_pochhammer__binomial__sum,axiom,
% 0.29/0.63      ! [A: rat,B: rat,N2: nat] :
% 0.29/0.63        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pochhammer_binomial_sum
% 0.29/0.63  thf(fact_8931_pochhammer__binomial__sum,axiom,
% 0.29/0.63      ! [A: complex,B: complex,N2: nat] :
% 0.29/0.63        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pochhammer_binomial_sum
% 0.29/0.63  thf(fact_8932_pochhammer__binomial__sum,axiom,
% 0.29/0.63      ! [A: int,B: int,N2: nat] :
% 0.29/0.63        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pochhammer_binomial_sum
% 0.29/0.63  thf(fact_8933_pochhammer__binomial__sum,axiom,
% 0.29/0.63      ! [A: real,B: real,N2: nat] :
% 0.29/0.63        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % pochhammer_binomial_sum
% 0.29/0.63  thf(fact_8934_sum__power__add,axiom,
% 0.29/0.63      ! [X4: complex,M: nat,I5: set_nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 0.29/0.63          @ I5 )
% 0.29/0.63        = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ I5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_power_add
% 0.29/0.63  thf(fact_8935_sum__power__add,axiom,
% 0.29/0.63      ! [X4: int,M: nat,I5: set_nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [I3: nat] : ( power_power_int @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 0.29/0.63          @ I5 )
% 0.29/0.63        = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ I5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_power_add
% 0.29/0.63  thf(fact_8936_sum__power__add,axiom,
% 0.29/0.63      ! [X4: real,M: nat,I5: set_nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( power_power_real @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 0.29/0.63          @ I5 )
% 0.29/0.63        = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ I5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_power_add
% 0.29/0.63  thf(fact_8937_sum_Ozero__middle,axiom,
% 0.29/0.63      ! [P2: nat,K: nat,G: nat > complex,H: nat > complex] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ P2 )
% 0.29/0.63         => ( ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ P2 ) )
% 0.29/0.63            = ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.zero_middle
% 0.29/0.63  thf(fact_8938_sum_Ozero__middle,axiom,
% 0.29/0.63      ! [P2: nat,K: nat,G: nat > rat,H: nat > rat] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ P2 )
% 0.29/0.63         => ( ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ P2 ) )
% 0.29/0.63            = ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.zero_middle
% 0.29/0.63  thf(fact_8939_sum_Ozero__middle,axiom,
% 0.29/0.63      ! [P2: nat,K: nat,G: nat > int,H: nat > int] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ P2 )
% 0.29/0.63         => ( ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ P2 ) )
% 0.29/0.63            = ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.zero_middle
% 0.29/0.63  thf(fact_8940_sum_Ozero__middle,axiom,
% 0.29/0.63      ! [P2: nat,K: nat,G: nat > nat,H: nat > nat] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ P2 )
% 0.29/0.63         => ( ( groups3542108847815614940at_nat
% 0.29/0.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ P2 ) )
% 0.29/0.63            = ( groups3542108847815614940at_nat
% 0.29/0.63              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.zero_middle
% 0.29/0.63  thf(fact_8941_sum_Ozero__middle,axiom,
% 0.29/0.63      ! [P2: nat,K: nat,G: nat > real,H: nat > real] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 0.29/0.63       => ( ( ord_less_eq_nat @ K @ P2 )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ P2 ) )
% 0.29/0.63            = ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.zero_middle
% 0.29/0.63  thf(fact_8942_gbinomial__partial__sum__poly,axiom,
% 0.29/0.63      ! [M: nat,A: complex,X4: complex,Y: complex] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly
% 0.29/0.63  thf(fact_8943_gbinomial__partial__sum__poly,axiom,
% 0.29/0.63      ! [M: nat,A: rat,X4: rat,Y: rat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly
% 0.29/0.63  thf(fact_8944_gbinomial__partial__sum__poly,axiom,
% 0.29/0.63      ! [M: nat,A: real,X4: real,Y: real] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly
% 0.29/0.63  thf(fact_8945_exp__series__add__commuting,axiom,
% 0.29/0.63      ! [X4: complex,Y: complex,N2: nat] :
% 0.29/0.63        ( ( ( times_times_complex @ X4 @ Y )
% 0.29/0.63          = ( times_times_complex @ Y @ X4 ) )
% 0.29/0.63       => ( ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ N2 ) )
% 0.29/0.63          = ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_complex @ X4 @ I3 ) ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_series_add_commuting
% 0.29/0.63  thf(fact_8946_exp__series__add__commuting,axiom,
% 0.29/0.63      ! [X4: real,Y: real,N2: nat] :
% 0.29/0.63        ( ( ( times_times_real @ X4 @ Y )
% 0.29/0.63          = ( times_times_real @ Y @ X4 ) )
% 0.29/0.63       => ( ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ N2 ) )
% 0.29/0.63          = ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_real @ X4 @ I3 ) ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % exp_series_add_commuting
% 0.29/0.63  thf(fact_8947_root__polyfun,axiom,
% 0.29/0.63      ! [N2: nat,Z: int,A: int] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( ( power_power_int @ Z @ N2 )
% 0.29/0.63            = A )
% 0.29/0.63          = ( ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_int @ ( if_int @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I3 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_int ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % root_polyfun
% 0.29/0.63  thf(fact_8948_root__polyfun,axiom,
% 0.29/0.63      ! [N2: nat,Z: complex,A: complex] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( ( power_power_complex @ Z @ N2 )
% 0.29/0.63            = A )
% 0.29/0.63          = ( ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_complex @ ( if_complex @ ( I3 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I3 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_complex ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % root_polyfun
% 0.29/0.63  thf(fact_8949_root__polyfun,axiom,
% 0.29/0.63      ! [N2: nat,Z: code_integer,A: code_integer] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( ( power_8256067586552552935nteger @ Z @ N2 )
% 0.29/0.63            = A )
% 0.29/0.63          = ( ( groups7501900531339628137nteger
% 0.29/0.63              @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I3 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % root_polyfun
% 0.29/0.63  thf(fact_8950_root__polyfun,axiom,
% 0.29/0.63      ! [N2: nat,Z: rat,A: rat] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( ( power_power_rat @ Z @ N2 )
% 0.29/0.63            = A )
% 0.29/0.63          = ( ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_rat @ ( if_rat @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I3 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_rat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % root_polyfun
% 0.29/0.63  thf(fact_8951_root__polyfun,axiom,
% 0.29/0.63      ! [N2: nat,Z: real,A: real] :
% 0.29/0.63        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( ( power_power_real @ Z @ N2 )
% 0.29/0.63            = A )
% 0.29/0.63          = ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_real @ ( if_real @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I3 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I3 ) )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = zero_zero_real ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % root_polyfun
% 0.29/0.63  thf(fact_8952_sum__gp0,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_rat )
% 0.29/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.29/0.63        & ( ( X4 != one_one_rat )
% 0.29/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp0
% 0.29/0.63  thf(fact_8953_sum__gp0,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_complex )
% 0.29/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.29/0.63        & ( ( X4 != one_one_complex )
% 0.29/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp0
% 0.29/0.63  thf(fact_8954_sum__gp0,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_real )
% 0.29/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 0.29/0.63        & ( ( X4 != one_one_real )
% 0.29/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp0
% 0.29/0.63  thf(fact_8955_choose__alternating__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( N2 != one_one_nat )
% 0.29/0.63       => ( ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_complex ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_linear_sum
% 0.29/0.63  thf(fact_8956_choose__alternating__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( N2 != one_one_nat )
% 0.29/0.63       => ( ( groups7501900531339628137nteger
% 0.29/0.63            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_linear_sum
% 0.29/0.63  thf(fact_8957_choose__alternating__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( N2 != one_one_nat )
% 0.29/0.63       => ( ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_rat ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_linear_sum
% 0.29/0.63  thf(fact_8958_choose__alternating__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( N2 != one_one_nat )
% 0.29/0.63       => ( ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_int ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_linear_sum
% 0.29/0.63  thf(fact_8959_choose__alternating__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( N2 != one_one_nat )
% 0.29/0.63       => ( ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ I3 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_linear_sum
% 0.29/0.63  thf(fact_8960_gbinomial__sum__nat__pow2,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_sum_nat_pow2
% 0.29/0.63  thf(fact_8961_gbinomial__sum__nat__pow2,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_sum_nat_pow2
% 0.29/0.63  thf(fact_8962_gbinomial__partial__sum__poly__xpos,axiom,
% 0.29/0.63      ! [M: nat,A: rat,X4: rat,Y: rat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly_xpos
% 0.29/0.63  thf(fact_8963_gbinomial__partial__sum__poly__xpos,axiom,
% 0.29/0.63      ! [M: nat,A: complex,X4: complex,Y: complex] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly_xpos
% 0.29/0.63  thf(fact_8964_gbinomial__partial__sum__poly__xpos,axiom,
% 0.29/0.63      ! [M: nat,A: real,X4: real,Y: real] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_sum_poly_xpos
% 0.29/0.63  thf(fact_8965_binomial__r__part__sum,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % binomial_r_part_sum
% 0.29/0.63  thf(fact_8966_choose__linear__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_linear_sum
% 0.29/0.63  thf(fact_8967_choose__alternating__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_complex ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_sum
% 0.29/0.63  thf(fact_8968_choose__alternating__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( groups7501900531339628137nteger
% 0.29/0.63            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_sum
% 0.29/0.63  thf(fact_8969_choose__alternating__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_rat ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_sum
% 0.29/0.63  thf(fact_8970_choose__alternating__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_int ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_sum
% 0.29/0.63  thf(fact_8971_choose__alternating__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_real ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_alternating_sum
% 0.29/0.63  thf(fact_8972_polyfun__extremal__lemma,axiom,
% 0.29/0.63      ! [E2: real,C: nat > complex,N2: nat] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.63       => ? [M9: real] :
% 0.29/0.63          ! [Z3: complex] :
% 0.29/0.63            ( ( ord_less_eq_real @ M9 @ ( real_V1022390504157884413omplex @ Z3 ) )
% 0.29/0.63           => ( ord_less_eq_real
% 0.29/0.63              @ ( real_V1022390504157884413omplex
% 0.29/0.63                @ ( groups2073611262835488442omplex
% 0.29/0.63                  @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 0.29/0.63                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_extremal_lemma
% 0.29/0.63  thf(fact_8973_polyfun__extremal__lemma,axiom,
% 0.29/0.63      ! [E2: real,C: nat > real,N2: nat] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.63       => ? [M9: real] :
% 0.29/0.63          ! [Z3: real] :
% 0.29/0.63            ( ( ord_less_eq_real @ M9 @ ( real_V7735802525324610683m_real @ Z3 ) )
% 0.29/0.63           => ( ord_less_eq_real
% 0.29/0.63              @ ( real_V7735802525324610683m_real
% 0.29/0.63                @ ( groups6591440286371151544t_real
% 0.29/0.63                  @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 0.29/0.63                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_extremal_lemma
% 0.29/0.63  thf(fact_8974_gbinomial__r__part__sum,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_r_part_sum
% 0.29/0.63  thf(fact_8975_gbinomial__r__part__sum,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_r_part_sum
% 0.29/0.63  thf(fact_8976_gbinomial__r__part__sum,axiom,
% 0.29/0.63      ! [M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_r_part_sum
% 0.29/0.63  thf(fact_8977_choose__odd__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [I3: nat] :
% 0.29/0.63                  ( if_rat
% 0.29/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.63                  @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) )
% 0.29/0.63                  @ zero_zero_rat )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_odd_sum
% 0.29/0.63  thf(fact_8978_choose__odd__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [I3: nat] :
% 0.29/0.63                  ( if_complex
% 0.29/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.63                  @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) )
% 0.29/0.63                  @ zero_zero_complex )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_odd_sum
% 0.29/0.63  thf(fact_8979_choose__odd__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [I3: nat] :
% 0.29/0.63                  ( if_int
% 0.29/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.63                  @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) )
% 0.29/0.63                  @ zero_zero_int )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_odd_sum
% 0.29/0.63  thf(fact_8980_choose__odd__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [I3: nat] :
% 0.29/0.63                  ( if_real
% 0.29/0.63                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.29/0.63                  @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) )
% 0.29/0.63                  @ zero_zero_real )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_odd_sum
% 0.29/0.63  thf(fact_8981_choose__even__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) @ zero_zero_rat )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_even_sum
% 0.29/0.63  thf(fact_8982_choose__even__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) @ zero_zero_complex )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_even_sum
% 0.29/0.63  thf(fact_8983_choose__even__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) @ zero_zero_int )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_even_sum
% 0.29/0.63  thf(fact_8984_choose__even__sum,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.29/0.63            @ ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) @ zero_zero_real )
% 0.29/0.63              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.63          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % choose_even_sum
% 0.29/0.63  thf(fact_8985_gbinomial__partial__row__sum,axiom,
% 0.29/0.63      ! [A: rat,M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_row_sum
% 0.29/0.63  thf(fact_8986_gbinomial__partial__row__sum,axiom,
% 0.29/0.63      ! [A: complex,M: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_row_sum
% 0.29/0.63  thf(fact_8987_gbinomial__partial__row__sum,axiom,
% 0.29/0.63      ! [A: real,M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ M ) )
% 0.29/0.63        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % gbinomial_partial_row_sum
% 0.29/0.63  thf(fact_8988_mask__eq__sum__exp,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 0.29/0.63        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.63          @ ( collect_nat
% 0.29/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mask_eq_sum_exp
% 0.29/0.63  thf(fact_8989_mask__eq__sum__exp,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 0.29/0.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.63          @ ( collect_nat
% 0.29/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mask_eq_sum_exp
% 0.29/0.63  thf(fact_8990_mask__eq__sum__exp__nat,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.63        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.63          @ ( collect_nat
% 0.29/0.63            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % mask_eq_sum_exp_nat
% 0.29/0.63  thf(fact_8991_cos__x__cos__y,axiom,
% 0.29/0.63      ! [X4: complex,Y: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [N: nat] :
% 0.29/0.63                ( if_complex
% 0.29/0.63                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 0.29/0.63                  & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.63                @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 0.29/0.63                @ zero_zero_complex )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_x_cos_y
% 0.29/0.63  thf(fact_8992_cos__x__cos__y,axiom,
% 0.29/0.63      ! [X4: real,Y: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [N: nat] :
% 0.29/0.63                ( if_real
% 0.29/0.63                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 0.29/0.63                  & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.29/0.63                @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 0.29/0.63                @ zero_zero_real )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % cos_x_cos_y
% 0.29/0.63  thf(fact_8993_sums__cos__x__plus__y,axiom,
% 0.29/0.63      ! [X4: complex,Y: complex] :
% 0.29/0.63        ( sums_complex
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_complex )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_cos_x_plus_y
% 0.29/0.63  thf(fact_8994_sums__cos__x__plus__y,axiom,
% 0.29/0.63      ! [X4: real,Y: real] :
% 0.29/0.63        ( sums_real
% 0.29/0.63        @ ^ [P5: nat] :
% 0.29/0.63            ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_real )
% 0.29/0.63            @ ( set_ord_atMost_nat @ P5 ) )
% 0.29/0.63        @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_cos_x_plus_y
% 0.29/0.63  thf(fact_8995_sum__abs__ge__zero,axiom,
% 0.29/0.63      ! [F: nat > real,A2: set_nat] :
% 0.29/0.63        ( ord_less_eq_real @ zero_zero_real
% 0.29/0.63        @ ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_abs_ge_zero
% 0.29/0.63  thf(fact_8996_sum__abs__ge__zero,axiom,
% 0.29/0.63      ! [F: int > int,A2: set_int] :
% 0.29/0.63        ( ord_less_eq_int @ zero_zero_int
% 0.29/0.63        @ ( groups4538972089207619220nt_int
% 0.29/0.63          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_abs_ge_zero
% 0.29/0.63  thf(fact_8997_sum__abs,axiom,
% 0.29/0.63      ! [F: nat > real,A2: set_nat] :
% 0.29/0.63        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.29/0.63        @ ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_abs
% 0.29/0.63  thf(fact_8998_sum__abs,axiom,
% 0.29/0.63      ! [F: int > int,A2: set_int] :
% 0.29/0.63        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.29/0.63        @ ( groups4538972089207619220nt_int
% 0.29/0.63          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_abs
% 0.29/0.63  thf(fact_8999_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_real,X4: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ I5 )
% 0.29/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups7713935264441627589nteger @ X4 @ I5 )
% 0.29/0.63            = one_one_Code_integer )
% 0.29/0.63         => ( ! [I4: real] :
% 0.29/0.63                ( ( member_real @ I4 @ I5 )
% 0.29/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_le3102999989581377725nteger
% 0.29/0.63              @ ( abs_abs_Code_integer
% 0.29/0.63                @ ( minus_8373710615458151222nteger
% 0.29/0.63                  @ ( groups7713935264441627589nteger
% 0.29/0.63                    @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9000_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_nat,X4: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( member_nat @ I4 @ I5 )
% 0.29/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups7501900531339628137nteger @ X4 @ I5 )
% 0.29/0.63            = one_one_Code_integer )
% 0.29/0.63         => ( ! [I4: nat] :
% 0.29/0.63                ( ( member_nat @ I4 @ I5 )
% 0.29/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_le3102999989581377725nteger
% 0.29/0.63              @ ( abs_abs_Code_integer
% 0.29/0.63                @ ( minus_8373710615458151222nteger
% 0.29/0.63                  @ ( groups7501900531339628137nteger
% 0.29/0.63                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9001_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_complex,X4: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ I5 )
% 0.29/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups6621422865394947399nteger @ X4 @ I5 )
% 0.29/0.63            = one_one_Code_integer )
% 0.29/0.63         => ( ! [I4: complex] :
% 0.29/0.63                ( ( member_complex @ I4 @ I5 )
% 0.29/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_le3102999989581377725nteger
% 0.29/0.63              @ ( abs_abs_Code_integer
% 0.29/0.63                @ ( minus_8373710615458151222nteger
% 0.29/0.63                  @ ( groups6621422865394947399nteger
% 0.29/0.63                    @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9002_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_int,X4: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.29/0.63        ( ! [I4: int] :
% 0.29/0.63            ( ( member_int @ I4 @ I5 )
% 0.29/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups7873554091576472773nteger @ X4 @ I5 )
% 0.29/0.63            = one_one_Code_integer )
% 0.29/0.63         => ( ! [I4: int] :
% 0.29/0.63                ( ( member_int @ I4 @ I5 )
% 0.29/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_le3102999989581377725nteger
% 0.29/0.63              @ ( abs_abs_Code_integer
% 0.29/0.63                @ ( minus_8373710615458151222nteger
% 0.29/0.63                  @ ( groups7873554091576472773nteger
% 0.29/0.63                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9003_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_real,X4: real > real,A: real > real,B: real,Delta: real] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups8097168146408367636l_real @ X4 @ I5 )
% 0.29/0.63            = one_one_real )
% 0.29/0.63         => ( ! [I4: real] :
% 0.29/0.63                ( ( member_real @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_real
% 0.29/0.63              @ ( abs_abs_real
% 0.29/0.63                @ ( minus_minus_real
% 0.29/0.63                  @ ( groups8097168146408367636l_real
% 0.29/0.63                    @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9004_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_complex,X4: complex > real,A: complex > real,B: real,Delta: real] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups5808333547571424918x_real @ X4 @ I5 )
% 0.29/0.63            = one_one_real )
% 0.29/0.63         => ( ! [I4: complex] :
% 0.29/0.63                ( ( member_complex @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_real
% 0.29/0.63              @ ( abs_abs_real
% 0.29/0.63                @ ( minus_minus_real
% 0.29/0.63                  @ ( groups5808333547571424918x_real
% 0.29/0.63                    @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9005_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_int,X4: int > real,A: int > real,B: real,Delta: real] :
% 0.29/0.63        ( ! [I4: int] :
% 0.29/0.63            ( ( member_int @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups8778361861064173332t_real @ X4 @ I5 )
% 0.29/0.63            = one_one_real )
% 0.29/0.63         => ( ! [I4: int] :
% 0.29/0.63                ( ( member_int @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_real
% 0.29/0.63              @ ( abs_abs_real
% 0.29/0.63                @ ( minus_minus_real
% 0.29/0.63                  @ ( groups8778361861064173332t_real
% 0.29/0.63                    @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9006_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_real,X4: real > rat,A: real > rat,B: rat,Delta: rat] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups1300246762558778688al_rat @ X4 @ I5 )
% 0.29/0.63            = one_one_rat )
% 0.29/0.63         => ( ! [I4: real] :
% 0.29/0.63                ( ( member_real @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_rat
% 0.29/0.63              @ ( abs_abs_rat
% 0.29/0.63                @ ( minus_minus_rat
% 0.29/0.63                  @ ( groups1300246762558778688al_rat
% 0.29/0.63                    @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9007_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_nat,X4: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( member_nat @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups2906978787729119204at_rat @ X4 @ I5 )
% 0.29/0.63            = one_one_rat )
% 0.29/0.63         => ( ! [I4: nat] :
% 0.29/0.63                ( ( member_nat @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_rat
% 0.29/0.63              @ ( abs_abs_rat
% 0.29/0.63                @ ( minus_minus_rat
% 0.29/0.63                  @ ( groups2906978787729119204at_rat
% 0.29/0.63                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9008_convex__sum__bound__le,axiom,
% 0.29/0.63      ! [I5: set_complex,X4: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ I5 )
% 0.29/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 0.29/0.63       => ( ( ( groups5058264527183730370ex_rat @ X4 @ I5 )
% 0.29/0.63            = one_one_rat )
% 0.29/0.63         => ( ! [I4: complex] :
% 0.29/0.63                ( ( member_complex @ I4 @ I5 )
% 0.29/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.29/0.63           => ( ord_less_eq_rat
% 0.29/0.63              @ ( abs_abs_rat
% 0.29/0.63                @ ( minus_minus_rat
% 0.29/0.63                  @ ( groups5058264527183730370ex_rat
% 0.29/0.63                    @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 0.29/0.63                    @ I5 )
% 0.29/0.63                  @ B ) )
% 0.29/0.63              @ Delta ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % convex_sum_bound_le
% 0.29/0.63  thf(fact_9009_Maclaurin__minus__cos__expansion,axiom,
% 0.29/0.63      ! [N2: nat,X4: real] :
% 0.29/0.63        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.63       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.63         => ? [T3: real] :
% 0.29/0.63              ( ( ord_less_real @ X4 @ T3 )
% 0.29/0.63              & ( ord_less_real @ T3 @ zero_zero_real )
% 0.29/0.63              & ( ( cos_real @ X4 )
% 0.29/0.63                = ( plus_plus_real
% 0.29/0.63                  @ ( groups6591440286371151544t_real
% 0.29/0.63                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_minus_cos_expansion
% 0.29/0.63  thf(fact_9010_lessThan__eq__iff,axiom,
% 0.29/0.63      ! [X4: nat,Y: nat] :
% 0.29/0.63        ( ( ( set_ord_lessThan_nat @ X4 )
% 0.29/0.63          = ( set_ord_lessThan_nat @ Y ) )
% 0.29/0.63        = ( X4 = Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_eq_iff
% 0.29/0.63  thf(fact_9011_lessThan__eq__iff,axiom,
% 0.29/0.63      ! [X4: int,Y: int] :
% 0.29/0.63        ( ( ( set_ord_lessThan_int @ X4 )
% 0.29/0.63          = ( set_ord_lessThan_int @ Y ) )
% 0.29/0.63        = ( X4 = Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_eq_iff
% 0.29/0.63  thf(fact_9012_lessThan__eq__iff,axiom,
% 0.29/0.63      ! [X4: real,Y: real] :
% 0.29/0.63        ( ( ( set_or5984915006950818249n_real @ X4 )
% 0.29/0.63          = ( set_or5984915006950818249n_real @ Y ) )
% 0.29/0.63        = ( X4 = Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_eq_iff
% 0.29/0.63  thf(fact_9013_of__nat__id,axiom,
% 0.29/0.63      ( semiri1316708129612266289at_nat
% 0.29/0.63      = ( ^ [N: nat] : N ) ) ).
% 0.29/0.63  
% 0.29/0.63  % of_nat_id
% 0.29/0.63  thf(fact_9014_lessThan__iff,axiom,
% 0.29/0.63      ! [I2: rat,K: rat] :
% 0.29/0.63        ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 0.29/0.63        = ( ord_less_rat @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_iff
% 0.29/0.63  thf(fact_9015_lessThan__iff,axiom,
% 0.29/0.63      ! [I2: num,K: num] :
% 0.29/0.63        ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 0.29/0.63        = ( ord_less_num @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_iff
% 0.29/0.63  thf(fact_9016_lessThan__iff,axiom,
% 0.29/0.63      ! [I2: nat,K: nat] :
% 0.29/0.63        ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 0.29/0.63        = ( ord_less_nat @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_iff
% 0.29/0.63  thf(fact_9017_lessThan__iff,axiom,
% 0.29/0.63      ! [I2: int,K: int] :
% 0.29/0.63        ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 0.29/0.63        = ( ord_less_int @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_iff
% 0.29/0.63  thf(fact_9018_lessThan__iff,axiom,
% 0.29/0.63      ! [I2: real,K: real] :
% 0.29/0.63        ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 0.29/0.63        = ( ord_less_real @ I2 @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_iff
% 0.29/0.63  thf(fact_9019_lessThan__subset__iff,axiom,
% 0.29/0.63      ! [X4: rat,Y: rat] :
% 0.29/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X4 ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.29/0.63        = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_subset_iff
% 0.29/0.63  thf(fact_9020_lessThan__subset__iff,axiom,
% 0.29/0.63      ! [X4: num,Y: num] :
% 0.29/0.63        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X4 ) @ ( set_ord_lessThan_num @ Y ) )
% 0.29/0.63        = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_subset_iff
% 0.29/0.63  thf(fact_9021_lessThan__subset__iff,axiom,
% 0.29/0.63      ! [X4: nat,Y: nat] :
% 0.29/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X4 ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.29/0.63        = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_subset_iff
% 0.29/0.63  thf(fact_9022_lessThan__subset__iff,axiom,
% 0.29/0.63      ! [X4: int,Y: int] :
% 0.29/0.63        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X4 ) @ ( set_ord_lessThan_int @ Y ) )
% 0.29/0.63        = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_subset_iff
% 0.29/0.63  thf(fact_9023_lessThan__subset__iff,axiom,
% 0.29/0.63      ! [X4: real,Y: real] :
% 0.29/0.63        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X4 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 0.29/0.63        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_subset_iff
% 0.29/0.63  thf(fact_9024_sum_OlessThan__Suc,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc
% 0.29/0.63  thf(fact_9025_sum_OlessThan__Suc,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc
% 0.29/0.63  thf(fact_9026_sum_OlessThan__Suc,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc
% 0.29/0.63  thf(fact_9027_sum_OlessThan__Suc,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc
% 0.29/0.63  thf(fact_9028_sumr__cos__zero__one,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = one_one_real ) ).
% 0.29/0.63  
% 0.29/0.63  % sumr_cos_zero_one
% 0.29/0.63  thf(fact_9029_sum__diff__distrib,axiom,
% 0.29/0.63      ! [Q: int > nat,P: int > nat,N2: int] :
% 0.29/0.63        ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 0.29/0.63       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 0.29/0.63          = ( groups4541462559716669496nt_nat
% 0.29/0.63            @ ^ [X: int] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 0.29/0.63            @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_diff_distrib
% 0.29/0.63  thf(fact_9030_sum__diff__distrib,axiom,
% 0.29/0.63      ! [Q: real > nat,P: real > nat,N2: real] :
% 0.29/0.63        ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 0.29/0.63       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 0.29/0.63          = ( groups1935376822645274424al_nat
% 0.29/0.63            @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 0.29/0.63            @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_diff_distrib
% 0.29/0.63  thf(fact_9031_sum__diff__distrib,axiom,
% 0.29/0.63      ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 0.29/0.63        ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 0.29/0.63       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.29/0.63          = ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_diff_distrib
% 0.29/0.63  thf(fact_9032_lessThan__def,axiom,
% 0.29/0.63      ( set_ord_lessThan_rat
% 0.29/0.63      = ( ^ [U2: rat] :
% 0.29/0.63            ( collect_rat
% 0.29/0.63            @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_def
% 0.29/0.63  thf(fact_9033_lessThan__def,axiom,
% 0.29/0.63      ( set_ord_lessThan_num
% 0.29/0.63      = ( ^ [U2: num] :
% 0.29/0.63            ( collect_num
% 0.29/0.63            @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_def
% 0.29/0.63  thf(fact_9034_lessThan__def,axiom,
% 0.29/0.63      ( set_ord_lessThan_nat
% 0.29/0.63      = ( ^ [U2: nat] :
% 0.29/0.63            ( collect_nat
% 0.29/0.63            @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_def
% 0.29/0.63  thf(fact_9035_lessThan__def,axiom,
% 0.29/0.63      ( set_ord_lessThan_int
% 0.29/0.63      = ( ^ [U2: int] :
% 0.29/0.63            ( collect_int
% 0.29/0.63            @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_def
% 0.29/0.63  thf(fact_9036_lessThan__def,axiom,
% 0.29/0.63      ( set_or5984915006950818249n_real
% 0.29/0.63      = ( ^ [U2: real] :
% 0.29/0.63            ( collect_real
% 0.29/0.63            @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_def
% 0.29/0.63  thf(fact_9037_sum__subtractf__nat,axiom,
% 0.29/0.63      ! [A2: set_real,G: real > nat,F: real > nat] :
% 0.29/0.63        ( ! [X5: real] :
% 0.29/0.63            ( ( member_real @ X5 @ A2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 0.29/0.63       => ( ( groups1935376822645274424al_nat
% 0.29/0.63            @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.63            @ A2 )
% 0.29/0.63          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_subtractf_nat
% 0.29/0.63  thf(fact_9038_sum__subtractf__nat,axiom,
% 0.29/0.63      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 0.29/0.63        ( ! [X5: complex] :
% 0.29/0.63            ( ( member_complex @ X5 @ A2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 0.29/0.63       => ( ( groups5693394587270226106ex_nat
% 0.29/0.63            @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.63            @ A2 )
% 0.29/0.63          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_subtractf_nat
% 0.29/0.63  thf(fact_9039_sum__subtractf__nat,axiom,
% 0.29/0.63      ! [A2: set_int,G: int > nat,F: int > nat] :
% 0.29/0.63        ( ! [X5: int] :
% 0.29/0.63            ( ( member_int @ X5 @ A2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 0.29/0.63       => ( ( groups4541462559716669496nt_nat
% 0.29/0.63            @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.63            @ A2 )
% 0.29/0.63          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_subtractf_nat
% 0.29/0.63  thf(fact_9040_sum__subtractf__nat,axiom,
% 0.29/0.63      ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 0.29/0.63        ( ! [X5: product_prod_nat_nat] :
% 0.29/0.63            ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 0.29/0.63       => ( ( groups977919841031483927at_nat
% 0.29/0.63            @ ^ [X: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.63            @ A2 )
% 0.29/0.63          = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_subtractf_nat
% 0.29/0.63  thf(fact_9041_sum__subtractf__nat,axiom,
% 0.29/0.63      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.29/0.63        ( ! [X5: nat] :
% 0.29/0.63            ( ( member_nat @ X5 @ A2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 0.29/0.63       => ( ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.63            @ A2 )
% 0.29/0.63          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_subtractf_nat
% 0.29/0.63  thf(fact_9042_sum__SucD,axiom,
% 0.29/0.63      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 0.29/0.63        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.29/0.63          = ( suc @ N2 ) )
% 0.29/0.63       => ? [X5: nat] :
% 0.29/0.63            ( ( member_nat @ X5 @ A2 )
% 0.29/0.63            & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_SucD
% 0.29/0.63  thf(fact_9043_lessThan__strict__subset__iff,axiom,
% 0.29/0.63      ! [M: rat,N2: rat] :
% 0.29/0.63        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 0.29/0.63        = ( ord_less_rat @ M @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_strict_subset_iff
% 0.29/0.63  thf(fact_9044_lessThan__strict__subset__iff,axiom,
% 0.29/0.63      ! [M: num,N2: num] :
% 0.29/0.63        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 0.29/0.63        = ( ord_less_num @ M @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_strict_subset_iff
% 0.29/0.63  thf(fact_9045_lessThan__strict__subset__iff,axiom,
% 0.29/0.63      ! [M: nat,N2: nat] :
% 0.29/0.63        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_strict_subset_iff
% 0.29/0.63  thf(fact_9046_lessThan__strict__subset__iff,axiom,
% 0.29/0.63      ! [M: int,N2: int] :
% 0.29/0.63        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 0.29/0.63        = ( ord_less_int @ M @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_strict_subset_iff
% 0.29/0.63  thf(fact_9047_lessThan__strict__subset__iff,axiom,
% 0.29/0.63      ! [M: real,N2: real] :
% 0.29/0.63        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 0.29/0.63        = ( ord_less_real @ M @ N2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_strict_subset_iff
% 0.29/0.63  thf(fact_9048_lessThan__Suc__atMost,axiom,
% 0.29/0.63      ! [K: nat] :
% 0.29/0.63        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.29/0.63        = ( set_ord_atMost_nat @ K ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lessThan_Suc_atMost
% 0.29/0.63  thf(fact_9049_Iic__subset__Iio__iff,axiom,
% 0.29/0.63      ! [A: rat,B: rat] :
% 0.29/0.63        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 0.29/0.63        = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Iic_subset_Iio_iff
% 0.29/0.63  thf(fact_9050_Iic__subset__Iio__iff,axiom,
% 0.29/0.63      ! [A: num,B: num] :
% 0.29/0.63        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 0.29/0.63        = ( ord_less_num @ A @ B ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Iic_subset_Iio_iff
% 0.29/0.63  thf(fact_9051_Iic__subset__Iio__iff,axiom,
% 0.29/0.63      ! [A: nat,B: nat] :
% 0.29/0.63        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 0.29/0.63        = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Iic_subset_Iio_iff
% 0.29/0.63  thf(fact_9052_Iic__subset__Iio__iff,axiom,
% 0.29/0.63      ! [A: int,B: int] :
% 0.29/0.63        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 0.29/0.63        = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Iic_subset_Iio_iff
% 0.29/0.63  thf(fact_9053_Iic__subset__Iio__iff,axiom,
% 0.29/0.63      ! [A: real,B: real] :
% 0.29/0.63        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 0.29/0.63        = ( ord_less_real @ A @ B ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Iic_subset_Iio_iff
% 0.29/0.63  thf(fact_9054_sum_Onat__diff__reindex,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.nat_diff_reindex
% 0.29/0.63  thf(fact_9055_sum_Onat__diff__reindex,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.nat_diff_reindex
% 0.29/0.63  thf(fact_9056_suminf__le__const,axiom,
% 0.29/0.63      ! [F: nat > int,X4: int] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le_const
% 0.29/0.63  thf(fact_9057_suminf__le__const,axiom,
% 0.29/0.63      ! [F: nat > nat,X4: nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le_const
% 0.29/0.63  thf(fact_9058_suminf__le__const,axiom,
% 0.29/0.63      ! [F: nat > real,X4: real] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X4 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_le_const
% 0.29/0.63  thf(fact_9059_sum_OlessThan__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc_shift
% 0.29/0.63  thf(fact_9060_sum_OlessThan__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc_shift
% 0.29/0.63  thf(fact_9061_sum_OlessThan__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc_shift
% 0.29/0.63  thf(fact_9062_sum_OlessThan__Suc__shift,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.lessThan_Suc_shift
% 0.29/0.63  thf(fact_9063_sum__lessThan__telescope_H,axiom,
% 0.29/0.63      ! [F: nat > rat,M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope'
% 0.29/0.63  thf(fact_9064_sum__lessThan__telescope_H,axiom,
% 0.29/0.63      ! [F: nat > int,M: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope'
% 0.29/0.63  thf(fact_9065_sum__lessThan__telescope_H,axiom,
% 0.29/0.63      ! [F: nat > real,M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope'
% 0.29/0.63  thf(fact_9066_sum__lessThan__telescope,axiom,
% 0.29/0.63      ! [F: nat > rat,M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope
% 0.29/0.63  thf(fact_9067_sum__lessThan__telescope,axiom,
% 0.29/0.63      ! [F: nat > int,M: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope
% 0.29/0.63  thf(fact_9068_sum__lessThan__telescope,axiom,
% 0.29/0.63      ! [F: nat > real,M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_lessThan_telescope
% 0.29/0.63  thf(fact_9069_summableI__nonneg__bounded,axiom,
% 0.29/0.63      ! [F: nat > int,X4: int] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( summable_int @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summableI_nonneg_bounded
% 0.29/0.63  thf(fact_9070_summableI__nonneg__bounded,axiom,
% 0.29/0.63      ! [F: nat > nat,X4: nat] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( summable_nat @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summableI_nonneg_bounded
% 0.29/0.63  thf(fact_9071_summableI__nonneg__bounded,axiom,
% 0.29/0.63      ! [F: nat > real,X4: real] :
% 0.29/0.63        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 0.29/0.63       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 0.29/0.63         => ( summable_real @ F ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % summableI_nonneg_bounded
% 0.29/0.63  thf(fact_9072_sums__iff__shift,axiom,
% 0.29/0.63      ! [F: nat > real,N2: nat,S: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 0.29/0.63          @ S )
% 0.29/0.63        = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_iff_shift
% 0.29/0.63  thf(fact_9073_sums__iff__shift_H,axiom,
% 0.29/0.63      ! [F: nat > real,N2: nat,S: real] :
% 0.29/0.63        ( ( sums_real
% 0.29/0.63          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 0.29/0.63          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 0.29/0.63        = ( sums_real @ F @ S ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_iff_shift'
% 0.29/0.63  thf(fact_9074_sums__split__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > real,S: real,N2: nat] :
% 0.29/0.63        ( ( sums_real @ F @ S )
% 0.29/0.63       => ( sums_real
% 0.29/0.63          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 0.29/0.63          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sums_split_initial_segment
% 0.29/0.63  thf(fact_9075_sum__nth__roots,axiom,
% 0.29/0.63      ! [N2: nat,C: complex] :
% 0.29/0.63        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( groups7754918857620584856omplex
% 0.29/0.63            @ ^ [X: complex] : X
% 0.29/0.63            @ ( collect_complex
% 0.29/0.63              @ ^ [Z5: complex] :
% 0.29/0.63                  ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.63                  = C ) ) )
% 0.29/0.63          = zero_zero_complex ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_nth_roots
% 0.29/0.63  thf(fact_9076_power__diff__1__eq,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat )
% 0.29/0.63        = ( times_times_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_1_eq
% 0.29/0.63  thf(fact_9077_power__diff__1__eq,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex )
% 0.29/0.63        = ( times_times_complex @ ( minus_minus_complex @ X4 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_1_eq
% 0.29/0.63  thf(fact_9078_power__diff__1__eq,axiom,
% 0.29/0.63      ! [X4: int,N2: nat] :
% 0.29/0.63        ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ one_one_int )
% 0.29/0.63        = ( times_times_int @ ( minus_minus_int @ X4 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_1_eq
% 0.29/0.63  thf(fact_9079_power__diff__1__eq,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real )
% 0.29/0.63        = ( times_times_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_1_eq
% 0.29/0.63  thf(fact_9080_one__diff__power__eq,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq
% 0.29/0.63  thf(fact_9081_one__diff__power__eq,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq
% 0.29/0.63  thf(fact_9082_one__diff__power__eq,axiom,
% 0.29/0.63      ! [X4: int,N2: nat] :
% 0.29/0.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq
% 0.29/0.63  thf(fact_9083_one__diff__power__eq,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq
% 0.29/0.63  thf(fact_9084_geometric__sum,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( X4 != one_one_rat )
% 0.29/0.63       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_sum
% 0.29/0.63  thf(fact_9085_geometric__sum,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( X4 != one_one_complex )
% 0.29/0.63       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_sum
% 0.29/0.63  thf(fact_9086_geometric__sum,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( X4 != one_one_real )
% 0.29/0.63       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % geometric_sum
% 0.29/0.63  thf(fact_9087_sum_OatMost__shift,axiom,
% 0.29/0.63      ! [G: nat > rat,N2: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_shift
% 0.29/0.63  thf(fact_9088_sum_OatMost__shift,axiom,
% 0.29/0.63      ! [G: nat > int,N2: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_shift
% 0.29/0.63  thf(fact_9089_sum_OatMost__shift,axiom,
% 0.29/0.63      ! [G: nat > nat,N2: nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups3542108847815614940at_nat
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_shift
% 0.29/0.63  thf(fact_9090_sum_OatMost__shift,axiom,
% 0.29/0.63      ! [G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.atMost_shift
% 0.29/0.63  thf(fact_9091_suminf__split__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > real,K: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( suminf_real @ F )
% 0.29/0.63          = ( plus_plus_real
% 0.29/0.63            @ ( suminf_real
% 0.29/0.63              @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.29/0.63            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_split_initial_segment
% 0.29/0.63  thf(fact_9092_suminf__minus__initial__segment,axiom,
% 0.29/0.63      ! [F: nat > real,K: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ( suminf_real
% 0.29/0.63            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 0.29/0.63          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % suminf_minus_initial_segment
% 0.29/0.63  thf(fact_9093_sum__roots__unity,axiom,
% 0.29/0.63      ! [N2: nat] :
% 0.29/0.63        ( ( ord_less_nat @ one_one_nat @ N2 )
% 0.29/0.63       => ( ( groups7754918857620584856omplex
% 0.29/0.63            @ ^ [X: complex] : X
% 0.29/0.63            @ ( collect_complex
% 0.29/0.63              @ ^ [Z5: complex] :
% 0.29/0.63                  ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.63                  = one_one_complex ) ) )
% 0.29/0.63          = zero_zero_complex ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_roots_unity
% 0.29/0.63  thf(fact_9094_sum__less__suminf,axiom,
% 0.29/0.63      ! [F: nat > int,N2: nat] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf
% 0.29/0.63  thf(fact_9095_sum__less__suminf,axiom,
% 0.29/0.63      ! [F: nat > nat,N2: nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf
% 0.29/0.63  thf(fact_9096_sum__less__suminf,axiom,
% 0.29/0.63      ! [F: nat > real,N2: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf
% 0.29/0.63  thf(fact_9097_sum__gp__strict,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_rat )
% 0.29/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( semiri681578069525770553at_rat @ N2 ) ) )
% 0.29/0.63        & ( ( X4 != one_one_rat )
% 0.29/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_strict
% 0.29/0.63  thf(fact_9098_sum__gp__strict,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_complex )
% 0.29/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( semiri8010041392384452111omplex @ N2 ) ) )
% 0.29/0.63        & ( ( X4 != one_one_complex )
% 0.29/0.63         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_strict
% 0.29/0.63  thf(fact_9099_sum__gp__strict,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( ( X4 = one_one_real )
% 0.29/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.63        & ( ( X4 != one_one_real )
% 0.29/0.63         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_gp_strict
% 0.29/0.63  thf(fact_9100_lemma__termdiff1,axiom,
% 0.29/0.63      ! [Z: rat,H: rat,M: nat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lemma_termdiff1
% 0.29/0.63  thf(fact_9101_lemma__termdiff1,axiom,
% 0.29/0.63      ! [Z: complex,H: complex,M: nat] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lemma_termdiff1
% 0.29/0.63  thf(fact_9102_lemma__termdiff1,axiom,
% 0.29/0.63      ! [Z: int,H: int,M: nat] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lemma_termdiff1
% 0.29/0.63  thf(fact_9103_lemma__termdiff1,axiom,
% 0.29/0.63      ! [Z: real,H: real,M: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % lemma_termdiff1
% 0.29/0.63  thf(fact_9104_diff__power__eq__sum,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat,Y: rat] :
% 0.29/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X4 @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diff_power_eq_sum
% 0.29/0.63  thf(fact_9105_diff__power__eq__sum,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat,Y: complex] :
% 0.29/0.63        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 0.29/0.63          @ ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X4 @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diff_power_eq_sum
% 0.29/0.63  thf(fact_9106_diff__power__eq__sum,axiom,
% 0.29/0.63      ! [X4: int,N2: nat,Y: int] :
% 0.29/0.63        ( ( minus_minus_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X4 @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diff_power_eq_sum
% 0.29/0.63  thf(fact_9107_diff__power__eq__sum,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Y: real] :
% 0.29/0.63        ( ( minus_minus_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 0.29/0.63        = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X4 @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % diff_power_eq_sum
% 0.29/0.63  thf(fact_9108_power__diff__sumr2,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat,Y: rat] :
% 0.29/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 0.29/0.63        = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X4 @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_sumr2
% 0.29/0.63  thf(fact_9109_power__diff__sumr2,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat,Y: complex] :
% 0.29/0.63        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 0.29/0.63        = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 0.29/0.63          @ ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X4 @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_sumr2
% 0.29/0.63  thf(fact_9110_power__diff__sumr2,axiom,
% 0.29/0.63      ! [X4: int,N2: nat,Y: int] :
% 0.29/0.63        ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 0.29/0.63        = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X4 @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_sumr2
% 0.29/0.63  thf(fact_9111_power__diff__sumr2,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Y: real] :
% 0.29/0.63        ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 0.29/0.63        = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_real @ X4 @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % power_diff_sumr2
% 0.29/0.63  thf(fact_9112_polyfun__linear__factor__root,axiom,
% 0.29/0.63      ! [C: nat > rat,A: rat,N2: nat] :
% 0.29/0.63        ( ( ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_rat )
% 0.29/0.63       => ~ ! [B5: nat > rat] :
% 0.29/0.63              ~ ! [Z3: rat] :
% 0.29/0.63                  ( ( groups2906978787729119204at_rat
% 0.29/0.63                    @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63                  = ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 0.29/0.63                    @ ( groups2906978787729119204at_rat
% 0.29/0.63                      @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 0.29/0.63                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor_root
% 0.29/0.63  thf(fact_9113_polyfun__linear__factor__root,axiom,
% 0.29/0.63      ! [C: nat > complex,A: complex,N2: nat] :
% 0.29/0.63        ( ( ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_complex )
% 0.29/0.63       => ~ ! [B5: nat > complex] :
% 0.29/0.63              ~ ! [Z3: complex] :
% 0.29/0.63                  ( ( groups2073611262835488442omplex
% 0.29/0.63                    @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63                  = ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 0.29/0.63                    @ ( groups2073611262835488442omplex
% 0.29/0.63                      @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 0.29/0.63                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor_root
% 0.29/0.63  thf(fact_9114_polyfun__linear__factor__root,axiom,
% 0.29/0.63      ! [C: nat > int,A: int,N2: nat] :
% 0.29/0.63        ( ( ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_int )
% 0.29/0.63       => ~ ! [B5: nat > int] :
% 0.29/0.63              ~ ! [Z3: int] :
% 0.29/0.63                  ( ( groups3539618377306564664at_int
% 0.29/0.63                    @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63                  = ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 0.29/0.63                    @ ( groups3539618377306564664at_int
% 0.29/0.63                      @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 0.29/0.63                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor_root
% 0.29/0.63  thf(fact_9115_polyfun__linear__factor__root,axiom,
% 0.29/0.63      ! [C: nat > real,A: real,N2: nat] :
% 0.29/0.63        ( ( ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63          = zero_zero_real )
% 0.29/0.63       => ~ ! [B5: nat > real] :
% 0.29/0.63              ~ ! [Z3: real] :
% 0.29/0.63                  ( ( groups6591440286371151544t_real
% 0.29/0.63                    @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 0.29/0.63                    @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63                  = ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 0.29/0.63                    @ ( groups6591440286371151544t_real
% 0.29/0.63                      @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 0.29/0.63                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor_root
% 0.29/0.63  thf(fact_9116_polyfun__linear__factor,axiom,
% 0.29/0.63      ! [C: nat > rat,N2: nat,A: rat] :
% 0.29/0.63      ? [B5: nat > rat] :
% 0.29/0.63      ! [Z3: rat] :
% 0.29/0.63        ( ( groups2906978787729119204at_rat
% 0.29/0.63          @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_rat
% 0.29/0.63          @ ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 0.29/0.63            @ ( groups2906978787729119204at_rat
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor
% 0.29/0.63  thf(fact_9117_polyfun__linear__factor,axiom,
% 0.29/0.63      ! [C: nat > complex,N2: nat,A: complex] :
% 0.29/0.63      ? [B5: nat > complex] :
% 0.29/0.63      ! [Z3: complex] :
% 0.29/0.63        ( ( groups2073611262835488442omplex
% 0.29/0.63          @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_complex
% 0.29/0.63          @ ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 0.29/0.63            @ ( groups2073611262835488442omplex
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.29/0.63          @ ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor
% 0.29/0.63  thf(fact_9118_polyfun__linear__factor,axiom,
% 0.29/0.63      ! [C: nat > int,N2: nat,A: int] :
% 0.29/0.63      ? [B5: nat > int] :
% 0.29/0.63      ! [Z3: int] :
% 0.29/0.63        ( ( groups3539618377306564664at_int
% 0.29/0.63          @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_int
% 0.29/0.63          @ ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 0.29/0.63            @ ( groups3539618377306564664at_int
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor
% 0.29/0.63  thf(fact_9119_polyfun__linear__factor,axiom,
% 0.29/0.63      ! [C: nat > real,N2: nat,A: real] :
% 0.29/0.63      ? [B5: nat > real] :
% 0.29/0.63      ! [Z3: real] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 0.29/0.63          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.63        = ( plus_plus_real
% 0.29/0.63          @ ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 0.29/0.63            @ ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 0.29/0.63            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % polyfun_linear_factor
% 0.29/0.63  thf(fact_9120_real__sum__nat__ivl__bounded2,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 0.29/0.63        ( ! [P7: nat] :
% 0.29/0.63            ( ( ord_less_nat @ P7 @ N2 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 0.29/0.63       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.29/0.63         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_sum_nat_ivl_bounded2
% 0.29/0.63  thf(fact_9121_real__sum__nat__ivl__bounded2,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 0.29/0.63        ( ! [P7: nat] :
% 0.29/0.63            ( ( ord_less_nat @ P7 @ N2 )
% 0.29/0.63           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 0.29/0.63       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.29/0.63         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_sum_nat_ivl_bounded2
% 0.29/0.63  thf(fact_9122_real__sum__nat__ivl__bounded2,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 0.29/0.63        ( ! [P7: nat] :
% 0.29/0.63            ( ( ord_less_nat @ P7 @ N2 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 0.29/0.63       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.29/0.63         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_sum_nat_ivl_bounded2
% 0.29/0.63  thf(fact_9123_real__sum__nat__ivl__bounded2,axiom,
% 0.29/0.63      ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 0.29/0.63        ( ! [P7: nat] :
% 0.29/0.63            ( ( ord_less_nat @ P7 @ N2 )
% 0.29/0.63           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 0.29/0.63       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.29/0.63         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % real_sum_nat_ivl_bounded2
% 0.29/0.63  thf(fact_9124_sum__less__suminf2,axiom,
% 0.29/0.63      ! [F: nat > int,N2: nat,I2: nat] :
% 0.29/0.63        ( ( summable_int @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 0.29/0.63           => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 0.29/0.63             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf2
% 0.29/0.63  thf(fact_9125_sum__less__suminf2,axiom,
% 0.29/0.63      ! [F: nat > nat,N2: nat,I2: nat] :
% 0.29/0.63        ( ( summable_nat @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 0.29/0.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 0.29/0.63             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf2
% 0.29/0.63  thf(fact_9126_sum__less__suminf2,axiom,
% 0.29/0.63      ! [F: nat > real,N2: nat,I2: nat] :
% 0.29/0.63        ( ( summable_real @ F )
% 0.29/0.63       => ( ! [M5: nat] :
% 0.29/0.63              ( ( ord_less_eq_nat @ N2 @ M5 )
% 0.29/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 0.29/0.63         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 0.29/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 0.29/0.63             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_less_suminf2
% 0.29/0.63  thf(fact_9127_one__diff__power__eq_H,axiom,
% 0.29/0.63      ! [X4: rat,N2: nat] :
% 0.29/0.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 )
% 0.29/0.63          @ ( groups2906978787729119204at_rat
% 0.29/0.63            @ ^ [I3: nat] : ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq'
% 0.29/0.63  thf(fact_9128_one__diff__power__eq_H,axiom,
% 0.29/0.63      ! [X4: complex,N2: nat] :
% 0.29/0.63        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 )
% 0.29/0.63          @ ( groups2073611262835488442omplex
% 0.29/0.63            @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq'
% 0.29/0.63  thf(fact_9129_one__diff__power__eq_H,axiom,
% 0.29/0.63      ! [X4: int,N2: nat] :
% 0.29/0.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 )
% 0.29/0.63          @ ( groups3539618377306564664at_int
% 0.29/0.63            @ ^ [I3: nat] : ( power_power_int @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq'
% 0.29/0.63  thf(fact_9130_one__diff__power__eq_H,axiom,
% 0.29/0.63      ! [X4: real,N2: nat] :
% 0.29/0.63        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.63        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % one_diff_power_eq'
% 0.29/0.63  thf(fact_9131_Maclaurin__zero,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Diff: nat > complex > real] :
% 0.29/0.63        ( ( X4 = zero_zero_real )
% 0.29/0.63       => ( ( N2 != zero_zero_nat )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_zero
% 0.29/0.63  thf(fact_9132_Maclaurin__zero,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Diff: nat > real > real] :
% 0.29/0.63        ( ( X4 = zero_zero_real )
% 0.29/0.63       => ( ( N2 != zero_zero_nat )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_zero
% 0.29/0.63  thf(fact_9133_Maclaurin__zero,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Diff: nat > rat > real] :
% 0.29/0.63        ( ( X4 = zero_zero_real )
% 0.29/0.63       => ( ( N2 != zero_zero_nat )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_zero
% 0.29/0.63  thf(fact_9134_Maclaurin__zero,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Diff: nat > nat > real] :
% 0.29/0.63        ( ( X4 = zero_zero_real )
% 0.29/0.63       => ( ( N2 != zero_zero_nat )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_zero
% 0.29/0.63  thf(fact_9135_Maclaurin__zero,axiom,
% 0.29/0.63      ! [X4: real,N2: nat,Diff: nat > int > real] :
% 0.29/0.63        ( ( X4 = zero_zero_real )
% 0.29/0.63       => ( ( N2 != zero_zero_nat )
% 0.29/0.63         => ( ( groups6591440286371151544t_real
% 0.29/0.63              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.63              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63            = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_zero
% 0.29/0.63  thf(fact_9136_Maclaurin__lemma,axiom,
% 0.29/0.63      ! [H: real,F: real > real,J: nat > real,N2: nat] :
% 0.29/0.63        ( ( ord_less_real @ zero_zero_real @ H )
% 0.29/0.63       => ? [B7: real] :
% 0.29/0.63            ( ( F @ H )
% 0.29/0.63            = ( plus_plus_real
% 0.29/0.63              @ ( groups6591440286371151544t_real
% 0.29/0.63                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.29/0.63                @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63              @ ( times_times_real @ B7 @ ( divide_divide_real @ ( power_power_real @ H @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % Maclaurin_lemma
% 0.29/0.63  thf(fact_9137_sum__split__even__odd,axiom,
% 0.29/0.63      ! [F: nat > real,G: nat > real,N2: nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 0.29/0.63          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.63        = ( plus_plus_real
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.63          @ ( groups6591440286371151544t_real
% 0.29/0.63            @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 0.29/0.63            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_split_even_odd
% 0.29/0.63  thf(fact_9138_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_real,F: real > rat,G: real > rat] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9139_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( member_nat @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9140_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9141_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_int,F: int > rat,G: int > rat] :
% 0.29/0.63        ( ! [I4: int] :
% 0.29/0.63            ( ( member_int @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9142_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_real,F: real > nat,G: real > nat] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9143_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9144_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_int,F: int > nat,G: int > nat] :
% 0.29/0.63        ( ! [I4: int] :
% 0.29/0.63            ( ( member_int @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9145_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_real,F: real > int,G: real > int] :
% 0.29/0.63        ( ! [I4: real] :
% 0.29/0.63            ( ( member_real @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9146_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 0.29/0.63        ( ! [I4: nat] :
% 0.29/0.63            ( ( member_nat @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9147_sum__mono,axiom,
% 0.29/0.63      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 0.29/0.63        ( ! [I4: complex] :
% 0.29/0.63            ( ( member_complex @ I4 @ K5 )
% 0.29/0.63           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.29/0.63       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_mono
% 0.29/0.63  thf(fact_9148_sum_Odistrib,axiom,
% 0.29/0.63      ! [G: nat > nat,H: nat > nat,A2: set_nat] :
% 0.29/0.63        ( ( groups3542108847815614940at_nat
% 0.29/0.63          @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H @ X ) )
% 0.29/0.63          @ A2 )
% 0.29/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H @ A2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.distrib
% 0.29/0.63  thf(fact_9149_sum_Odistrib,axiom,
% 0.29/0.63      ! [G: nat > real,H: nat > real,A2: set_nat] :
% 0.29/0.63        ( ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H @ X ) )
% 0.29/0.63          @ A2 )
% 0.29/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H @ A2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.distrib
% 0.29/0.63  thf(fact_9150_sum_Odistrib,axiom,
% 0.29/0.63      ! [G: complex > complex,H: complex > complex,A2: set_complex] :
% 0.29/0.63        ( ( groups7754918857620584856omplex
% 0.29/0.63          @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H @ X ) )
% 0.29/0.63          @ A2 )
% 0.29/0.63        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H @ A2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.distrib
% 0.29/0.63  thf(fact_9151_sum_Odistrib,axiom,
% 0.29/0.63      ! [G: int > int,H: int > int,A2: set_int] :
% 0.29/0.63        ( ( groups4538972089207619220nt_int
% 0.29/0.63          @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H @ X ) )
% 0.29/0.63          @ A2 )
% 0.29/0.63        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H @ A2 ) ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum.distrib
% 0.29/0.63  thf(fact_9152_sum__divide__distrib,axiom,
% 0.29/0.63      ! [F: nat > real,A2: set_nat,R3: real] :
% 0.29/0.63        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R3 )
% 0.29/0.63        = ( groups6591440286371151544t_real
% 0.29/0.63          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ R3 )
% 0.29/0.63          @ A2 ) ) ).
% 0.29/0.63  
% 0.29/0.63  % sum_divide_distrib
% 0.29/0.63  thf(fact_9153_sum__divide__distrib,axiom,
% 0.29/0.63      ! [F: complex > complex,A2: set_complex,R3: complex] :
% 0.29/0.63        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R3 )
% 0.29/0.63        = ( groups7754918857620584856omplex
% 0.29/0.64          @ ^ [N: complex] : ( divide1717551699836669952omplex @ ( F @ N ) @ R3 )
% 0.29/0.64          @ A2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_divide_distrib
% 0.29/0.64  thf(fact_9154_Maclaurin__exp__le,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64      ? [T3: real] :
% 0.29/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.64        & ( ( exp_real @ X4 )
% 0.29/0.64          = ( plus_plus_real
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_exp_le
% 0.29/0.64  thf(fact_9155_polyfun__diff__alt,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_rat
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( groups2906978787729119204at_rat
% 0.29/0.64                  @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X4 @ J3 ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff_alt
% 0.29/0.64  thf(fact_9156_polyfun__diff__alt,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_complex
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( groups2073611262835488442omplex
% 0.29/0.64                  @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X4 @ J3 ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff_alt
% 0.29/0.64  thf(fact_9157_polyfun__diff__alt,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_int
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( groups3539618377306564664at_int
% 0.29/0.64                  @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X4 @ J3 ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff_alt
% 0.29/0.64  thf(fact_9158_polyfun__diff__alt,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_real
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( groups6591440286371151544t_real
% 0.29/0.64                  @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X4 @ J3 ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff_alt
% 0.29/0.64  thf(fact_9159_exp__first__terms,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( exp_complex
% 0.29/0.64        = ( ^ [X: complex] :
% 0.29/0.64              ( plus_plus_complex
% 0.29/0.64              @ ( groups2073611262835488442omplex
% 0.29/0.64                @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) )
% 0.29/0.64                @ ( set_ord_lessThan_nat @ K ) )
% 0.29/0.64              @ ( suminf_complex
% 0.29/0.64                @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % exp_first_terms
% 0.29/0.64  thf(fact_9160_exp__first__terms,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( exp_real
% 0.29/0.64        = ( ^ [X: real] :
% 0.29/0.64              ( plus_plus_real
% 0.29/0.64              @ ( groups6591440286371151544t_real
% 0.29/0.64                @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) )
% 0.29/0.64                @ ( set_ord_lessThan_nat @ K ) )
% 0.29/0.64              @ ( suminf_real
% 0.29/0.64                @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % exp_first_terms
% 0.29/0.64  thf(fact_9161_Maclaurin__sin__bound,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64        ( ord_less_eq_real
% 0.29/0.64        @ ( abs_abs_real
% 0.29/0.64          @ ( minus_minus_real @ ( sin_real @ X4 )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 0.29/0.64        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X4 ) @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_sin_bound
% 0.29/0.64  thf(fact_9162_sum__pos__lt__pair,axiom,
% 0.29/0.64      ! [F: nat > real,K: nat] :
% 0.29/0.64        ( ( summable_real @ F )
% 0.29/0.64       => ( ! [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 ) ) ) ) )
% 0.29/0.64         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_pos_lt_pair
% 0.29/0.64  thf(fact_9163_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > real] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 0.29/0.64       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9164_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > real] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 0.29/0.64       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9165_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > real] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 0.29/0.64       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9166_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > rat] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 0.29/0.64       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9167_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > rat] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 0.29/0.64       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9168_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > rat] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 0.29/0.64       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9169_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > rat] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 0.29/0.64       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9170_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > nat] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 0.29/0.64       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9171_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > nat] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 0.29/0.64       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9172_sum__nonpos,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > nat] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 0.29/0.64       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonpos
% 0.29/0.64  thf(fact_9173_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > real] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9174_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > real] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9175_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > real] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9176_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > rat] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9177_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > rat] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9178_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > rat] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9179_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > rat] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9180_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_real,F: real > nat] :
% 0.29/0.64        ( ! [X5: real] :
% 0.29/0.64            ( ( member_real @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9181_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_complex,F: complex > nat] :
% 0.29/0.64        ( ! [X5: complex] :
% 0.29/0.64            ( ( member_complex @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9182_sum__nonneg,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > nat] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_nonneg
% 0.29/0.64  thf(fact_9183_sum__cong__Suc,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.29/0.64        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.29/0.64       => ( ! [X5: nat] :
% 0.29/0.64              ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 0.29/0.64             => ( ( F @ ( suc @ X5 ) )
% 0.29/0.64                = ( G @ ( suc @ X5 ) ) ) )
% 0.29/0.64         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.29/0.64            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_cong_Suc
% 0.29/0.64  thf(fact_9184_sum__cong__Suc,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.29/0.64        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.29/0.64       => ( ! [X5: nat] :
% 0.29/0.64              ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 0.29/0.64             => ( ( F @ ( suc @ X5 ) )
% 0.29/0.64                = ( G @ ( suc @ X5 ) ) ) )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 0.29/0.64            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_cong_Suc
% 0.29/0.64  thf(fact_9185_Maclaurin__exp__lt,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64        ( ( X4 != zero_zero_real )
% 0.29/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ? [T3: real] :
% 0.29/0.64              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 0.29/0.64              & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.64              & ( ( exp_real @ X4 )
% 0.29/0.64                = ( plus_plus_real
% 0.29/0.64                  @ ( groups6591440286371151544t_real
% 0.29/0.64                    @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.29/0.64                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_exp_lt
% 0.29/0.64  thf(fact_9186_lemma__termdiff2,axiom,
% 0.29/0.64      ! [H: rat,Z: rat,N2: nat] :
% 0.29/0.64        ( ( H != zero_zero_rat )
% 0.29/0.64       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ N2 ) @ ( power_power_rat @ Z @ N2 ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.64          = ( times_times_rat @ H
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [P5: nat] :
% 0.29/0.64                  ( groups2906978787729119204at_rat
% 0.29/0.64                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lemma_termdiff2
% 0.29/0.64  thf(fact_9187_lemma__termdiff2,axiom,
% 0.29/0.64      ! [H: complex,Z: complex,N2: nat] :
% 0.29/0.64        ( ( H != zero_zero_complex )
% 0.29/0.64       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.64          = ( times_times_complex @ H
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [P5: nat] :
% 0.29/0.64                  ( groups2073611262835488442omplex
% 0.29/0.64                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lemma_termdiff2
% 0.29/0.64  thf(fact_9188_lemma__termdiff2,axiom,
% 0.29/0.64      ! [H: real,Z: real,N2: nat] :
% 0.29/0.64        ( ( H != zero_zero_real )
% 0.29/0.64       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.29/0.64          = ( times_times_real @ H
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [P5: nat] :
% 0.29/0.64                  ( groups6591440286371151544t_real
% 0.29/0.64                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lemma_termdiff2
% 0.29/0.64  thf(fact_9189_Maclaurin__sin__expansion,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64      ? [T3: real] :
% 0.29/0.64        ( ( sin_real @ X4 )
% 0.29/0.64        = ( plus_plus_real
% 0.29/0.64          @ ( groups6591440286371151544t_real
% 0.29/0.64            @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64            @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_sin_expansion
% 0.29/0.64  thf(fact_9190_Maclaurin__sin__expansion2,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64      ? [T3: real] :
% 0.29/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.64        & ( ( sin_real @ X4 )
% 0.29/0.64          = ( plus_plus_real
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_sin_expansion2
% 0.29/0.64  thf(fact_9191_Maclaurin__cos__expansion,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64      ? [T3: real] :
% 0.29/0.64        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.64        & ( ( cos_real @ X4 )
% 0.29/0.64          = ( plus_plus_real
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_cos_expansion
% 0.29/0.64  thf(fact_9192_Maclaurin__sin__expansion4,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64       => ? [T3: real] :
% 0.29/0.64            ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.29/0.64            & ( ord_less_eq_real @ T3 @ X4 )
% 0.29/0.64            & ( ( sin_real @ X4 )
% 0.29/0.64              = ( plus_plus_real
% 0.29/0.64                @ ( groups6591440286371151544t_real
% 0.29/0.64                  @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64                  @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_sin_expansion4
% 0.29/0.64  thf(fact_9193_Maclaurin__sin__expansion3,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ? [T3: real] :
% 0.29/0.64              ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.29/0.64              & ( ord_less_real @ T3 @ X4 )
% 0.29/0.64              & ( ( sin_real @ X4 )
% 0.29/0.64                = ( plus_plus_real
% 0.29/0.64                  @ ( groups6591440286371151544t_real
% 0.29/0.64                    @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_sin_expansion3
% 0.29/0.64  thf(fact_9194_Maclaurin__cos__expansion2,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ? [T3: real] :
% 0.29/0.64              ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.29/0.64              & ( ord_less_real @ T3 @ X4 )
% 0.29/0.64              & ( ( cos_real @ X4 )
% 0.29/0.64                = ( plus_plus_real
% 0.29/0.64                  @ ( groups6591440286371151544t_real
% 0.29/0.64                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.64                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.64                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Maclaurin_cos_expansion2
% 0.29/0.64  thf(fact_9195_bij__betw__roots__unity,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( bij_betw_nat_complex
% 0.29/0.64          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ N2 )
% 0.29/0.64          @ ( collect_complex
% 0.29/0.64            @ ^ [Z5: complex] :
% 0.29/0.64                ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                = one_one_complex ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bij_betw_roots_unity
% 0.29/0.64  thf(fact_9196_sum__gp,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,X4: rat] :
% 0.29/0.64        ( ( ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_rat ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( ( X4 = one_one_rat )
% 0.29/0.64             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.29/0.64            & ( ( X4 != one_one_rat )
% 0.29/0.64             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp
% 0.29/0.64  thf(fact_9197_sum__gp,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,X4: complex] :
% 0.29/0.64        ( ( ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_complex ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( ( X4 = one_one_complex )
% 0.29/0.64             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.29/0.64            & ( ( X4 != one_one_complex )
% 0.29/0.64             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp
% 0.29/0.64  thf(fact_9198_sum__gp,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,X4: real] :
% 0.29/0.64        ( ( ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_real ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ N2 @ M )
% 0.29/0.64         => ( ( ( X4 = one_one_real )
% 0.29/0.64             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 0.29/0.64            & ( ( X4 != one_one_real )
% 0.29/0.64             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp
% 0.29/0.64  thf(fact_9199_gchoose__row__sum__weighted,axiom,
% 0.29/0.64      ! [R3: rat,M: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat
% 0.29/0.64          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.29/0.64        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gchoose_row_sum_weighted
% 0.29/0.64  thf(fact_9200_gchoose__row__sum__weighted,axiom,
% 0.29/0.64      ! [R3: complex,M: nat] :
% 0.29/0.64        ( ( groups2073611262835488442omplex
% 0.29/0.64          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.29/0.64        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gchoose_row_sum_weighted
% 0.29/0.64  thf(fact_9201_gchoose__row__sum__weighted,axiom,
% 0.29/0.64      ! [R3: real,M: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.29/0.64        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gchoose_row_sum_weighted
% 0.29/0.64  thf(fact_9202_gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9203_gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9204_gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9205_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: set_int,L: set_int,U: set_int] :
% 0.29/0.64        ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_set_int @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9206_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: rat,L: rat,U: rat] :
% 0.29/0.64        ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_rat @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9207_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: num,L: num,U: num] :
% 0.29/0.64        ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_num @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9208_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: nat,L: nat,U: nat] :
% 0.29/0.64        ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_nat @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9209_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: int,L: int,U: int] :
% 0.29/0.64        ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_int @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9210_atLeastAtMost__iff,axiom,
% 0.29/0.64      ! [I2: real,L: real,U: real] :
% 0.29/0.64        ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.29/0.64        = ( ( ord_less_eq_real @ L @ I2 )
% 0.29/0.64          & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_iff
% 0.29/0.64  thf(fact_9211_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: set_int,H: set_int,L3: set_int,H3: set_int] :
% 0.29/0.64        ( ( ( set_or370866239135849197et_int @ L @ H )
% 0.29/0.64          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_set_int @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9212_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: rat,H: rat,L3: rat,H3: rat] :
% 0.29/0.64        ( ( ( set_or633870826150836451st_rat @ L @ H )
% 0.29/0.64          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_rat @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9213_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: num,H: num,L3: num,H3: num] :
% 0.29/0.64        ( ( ( set_or7049704709247886629st_num @ L @ H )
% 0.29/0.64          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_num @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9214_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: nat,H: nat,L3: nat,H3: nat] :
% 0.29/0.64        ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 0.29/0.64          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_nat @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9215_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: int,H: int,L3: int,H3: int] :
% 0.29/0.64        ( ( ( set_or1266510415728281911st_int @ L @ H )
% 0.29/0.64          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_int @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9216_Icc__eq__Icc,axiom,
% 0.29/0.64      ! [L: real,H: real,L3: real,H3: real] :
% 0.29/0.64        ( ( ( set_or1222579329274155063t_real @ L @ H )
% 0.29/0.64          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.29/0.64        = ( ( ( L = L3 )
% 0.29/0.64            & ( H = H3 ) )
% 0.29/0.64          | ( ~ ( ord_less_eq_real @ L @ H )
% 0.29/0.64            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_Icc
% 0.29/0.64  thf(fact_9217_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.29/0.64        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_set_int @ C @ A )
% 0.29/0.64            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9218_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.64        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_rat @ C @ A )
% 0.29/0.64            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9219_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: num,B: num,C: num,D: num] :
% 0.29/0.64        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_num @ C @ A )
% 0.29/0.64            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9220_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.64            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9221_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.64        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_int @ C @ A )
% 0.29/0.64            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9222_atLeastatMost__subset__iff,axiom,
% 0.29/0.64      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.64        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.64          | ( ( ord_less_eq_real @ C @ A )
% 0.29/0.64            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_subset_iff
% 0.29/0.64  thf(fact_9223_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: set_int,H: set_int,H3: set_int] :
% 0.29/0.64        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H ) @ ( set_or58775011639299419et_int @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_set_int @ L @ H )
% 0.29/0.64          | ( ord_less_eq_set_int @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9224_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: rat,H: rat,H3: rat] :
% 0.29/0.64        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_rat @ L @ H )
% 0.29/0.64          | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9225_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: num,H: num,H3: num] :
% 0.29/0.64        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_num @ L @ H )
% 0.29/0.64          | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9226_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: nat,H: nat,H3: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_nat @ L @ H )
% 0.29/0.64          | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9227_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: int,H: int,H3: int] :
% 0.29/0.64        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_int @ L @ H )
% 0.29/0.64          | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9228_Icc__subset__Iic__iff,axiom,
% 0.29/0.64      ! [L: real,H: real,H3: real] :
% 0.29/0.64        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 0.29/0.64        = ( ~ ( ord_less_eq_real @ L @ H )
% 0.29/0.64          | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_subset_Iic_iff
% 0.29/0.64  thf(fact_9229_sum_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > complex] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = zero_zero_complex ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.cl_ivl_Suc
% 0.29/0.64  thf(fact_9230_sum_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > rat] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = zero_zero_rat ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.cl_ivl_Suc
% 0.29/0.64  thf(fact_9231_sum_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > int] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = zero_zero_int ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.cl_ivl_Suc
% 0.29/0.64  thf(fact_9232_sum_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > nat] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = zero_zero_nat ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.cl_ivl_Suc
% 0.29/0.64  thf(fact_9233_sum_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > real] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = zero_zero_real ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.cl_ivl_Suc
% 0.29/0.64  thf(fact_9234_not__Iic__eq__Icc,axiom,
% 0.29/0.64      ! [H3: int,L: int,H: int] :
% 0.29/0.64        ( ( set_ord_atMost_int @ H3 )
% 0.29/0.64       != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 0.29/0.64  
% 0.29/0.64  % not_Iic_eq_Icc
% 0.29/0.64  thf(fact_9235_not__Iic__eq__Icc,axiom,
% 0.29/0.64      ! [H3: real,L: real,H: real] :
% 0.29/0.64        ( ( set_ord_atMost_real @ H3 )
% 0.29/0.64       != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 0.29/0.64  
% 0.29/0.64  % not_Iic_eq_Icc
% 0.29/0.64  thf(fact_9236_not__Iic__le__Icc,axiom,
% 0.29/0.64      ! [H: int,L3: int,H3: int] :
% 0.29/0.64        ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % not_Iic_le_Icc
% 0.29/0.64  thf(fact_9237_not__Iic__le__Icc,axiom,
% 0.29/0.64      ! [H: real,L3: real,H3: real] :
% 0.29/0.64        ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % not_Iic_le_Icc
% 0.29/0.64  thf(fact_9238_all__nat__less,axiom,
% 0.29/0.64      ! [N2: nat,P: nat > $o] :
% 0.29/0.64        ( ( ! [M6: nat] :
% 0.29/0.64              ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.29/0.64             => ( P @ M6 ) ) )
% 0.29/0.64        = ( ! [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64             => ( P @ X ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % all_nat_less
% 0.29/0.64  thf(fact_9239_ex__nat__less,axiom,
% 0.29/0.64      ! [N2: nat,P: nat > $o] :
% 0.29/0.64        ( ( ? [M6: nat] :
% 0.29/0.64              ( ( ord_less_eq_nat @ M6 @ N2 )
% 0.29/0.64              & ( P @ M6 ) ) )
% 0.29/0.64        = ( ? [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64              & ( P @ X ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % ex_nat_less
% 0.29/0.64  thf(fact_9240_atMost__atLeast0,axiom,
% 0.29/0.64      ( set_ord_atMost_nat
% 0.29/0.64      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atMost_atLeast0
% 0.29/0.64  thf(fact_9241_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.29/0.64      ! [G: nat > nat,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.shift_bounds_cl_Suc_ivl
% 0.29/0.64  thf(fact_9242_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.29/0.64      ! [G: nat > real,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.shift_bounds_cl_Suc_ivl
% 0.29/0.64  thf(fact_9243_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.29/0.64      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.shift_bounds_cl_nat_ivl
% 0.29/0.64  thf(fact_9244_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.29/0.64      ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.shift_bounds_cl_nat_ivl
% 0.29/0.64  thf(fact_9245_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.29/0.64        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_set_int @ C @ A )
% 0.29/0.64              & ( ord_less_eq_set_int @ B @ D )
% 0.29/0.64              & ( ( ord_less_set_int @ C @ A )
% 0.29/0.64                | ( ord_less_set_int @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9246_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.29/0.64        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_rat @ C @ A )
% 0.29/0.64              & ( ord_less_eq_rat @ B @ D )
% 0.29/0.64              & ( ( ord_less_rat @ C @ A )
% 0.29/0.64                | ( ord_less_rat @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9247_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: num,B: num,C: num,D: num] :
% 0.29/0.64        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_num @ C @ A )
% 0.29/0.64              & ( ord_less_eq_num @ B @ D )
% 0.29/0.64              & ( ( ord_less_num @ C @ A )
% 0.29/0.64                | ( ord_less_num @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9248_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.64        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.64              & ( ord_less_eq_nat @ B @ D )
% 0.29/0.64              & ( ( ord_less_nat @ C @ A )
% 0.29/0.64                | ( ord_less_nat @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9249_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: int,B: int,C: int,D: int] :
% 0.29/0.64        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_int @ C @ A )
% 0.29/0.64              & ( ord_less_eq_int @ B @ D )
% 0.29/0.64              & ( ( ord_less_int @ C @ A )
% 0.29/0.64                | ( ord_less_int @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9250_atLeastatMost__psubset__iff,axiom,
% 0.29/0.64      ! [A: real,B: real,C: real,D: real] :
% 0.29/0.64        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.29/0.64        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.64            | ( ( ord_less_eq_real @ C @ A )
% 0.29/0.64              & ( ord_less_eq_real @ B @ D )
% 0.29/0.64              & ( ( ord_less_real @ C @ A )
% 0.29/0.64                | ( ord_less_real @ B @ D ) ) ) )
% 0.29/0.64          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastatMost_psubset_iff
% 0.29/0.64  thf(fact_9251_sum_OatLeastAtMost__rev,axiom,
% 0.29/0.64      ! [G: nat > nat,N2: nat,M: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeastAtMost_rev
% 0.29/0.64  thf(fact_9252_sum_OatLeastAtMost__rev,axiom,
% 0.29/0.64      ! [G: nat > real,N2: nat,M: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeastAtMost_rev
% 0.29/0.64  thf(fact_9253_sum__shift__lb__Suc0__0,axiom,
% 0.29/0.64      ! [F: nat > complex,K: nat] :
% 0.29/0.64        ( ( ( F @ zero_zero_nat )
% 0.29/0.64          = zero_zero_complex )
% 0.29/0.64       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.29/0.64          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_shift_lb_Suc0_0
% 0.29/0.64  thf(fact_9254_sum__shift__lb__Suc0__0,axiom,
% 0.29/0.64      ! [F: nat > rat,K: nat] :
% 0.29/0.64        ( ( ( F @ zero_zero_nat )
% 0.29/0.64          = zero_zero_rat )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.29/0.64          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_shift_lb_Suc0_0
% 0.29/0.64  thf(fact_9255_sum__shift__lb__Suc0__0,axiom,
% 0.29/0.64      ! [F: nat > int,K: nat] :
% 0.29/0.64        ( ( ( F @ zero_zero_nat )
% 0.29/0.64          = zero_zero_int )
% 0.29/0.64       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.29/0.64          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_shift_lb_Suc0_0
% 0.29/0.64  thf(fact_9256_sum__shift__lb__Suc0__0,axiom,
% 0.29/0.64      ! [F: nat > nat,K: nat] :
% 0.29/0.64        ( ( ( F @ zero_zero_nat )
% 0.29/0.64          = zero_zero_nat )
% 0.29/0.64       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.29/0.64          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_shift_lb_Suc0_0
% 0.29/0.64  thf(fact_9257_sum__shift__lb__Suc0__0,axiom,
% 0.29/0.64      ! [F: nat > real,K: nat] :
% 0.29/0.64        ( ( ( F @ zero_zero_nat )
% 0.29/0.64          = zero_zero_real )
% 0.29/0.64       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.29/0.64          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_shift_lb_Suc0_0
% 0.29/0.64  thf(fact_9258_sum_OatLeast0__atMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > rat,N2: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast0_atMost_Suc
% 0.29/0.64  thf(fact_9259_sum_OatLeast0__atMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > int,N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast0_atMost_Suc
% 0.29/0.64  thf(fact_9260_sum_OatLeast0__atMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast0_atMost_Suc
% 0.29/0.64  thf(fact_9261_sum_OatLeast0__atMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > real,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast0_atMost_Suc
% 0.29/0.64  thf(fact_9262_sum_OatLeast__Suc__atMost,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast_Suc_atMost
% 0.29/0.64  thf(fact_9263_sum_OatLeast__Suc__atMost,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast_Suc_atMost
% 0.29/0.64  thf(fact_9264_sum_OatLeast__Suc__atMost,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast_Suc_atMost
% 0.29/0.64  thf(fact_9265_sum_OatLeast__Suc__atMost,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast_Suc_atMost
% 0.29/0.64  thf(fact_9266_sum_Onat__ivl__Suc_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nat_ivl_Suc'
% 0.29/0.64  thf(fact_9267_sum_Onat__ivl__Suc_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nat_ivl_Suc'
% 0.29/0.64  thf(fact_9268_sum_Onat__ivl__Suc_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nat_ivl_Suc'
% 0.29/0.64  thf(fact_9269_sum_Onat__ivl__Suc_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nat_ivl_Suc'
% 0.29/0.64  thf(fact_9270_sum_OSuc__reindex__ivl,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_rat @ ( G @ M )
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.Suc_reindex_ivl
% 0.29/0.64  thf(fact_9271_sum_OSuc__reindex__ivl,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_int @ ( G @ M )
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.Suc_reindex_ivl
% 0.29/0.64  thf(fact_9272_sum_OSuc__reindex__ivl,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_nat @ ( G @ M )
% 0.29/0.64            @ ( groups3542108847815614940at_nat
% 0.29/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.Suc_reindex_ivl
% 0.29/0.64  thf(fact_9273_sum_OSuc__reindex__ivl,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 0.29/0.64          = ( plus_plus_real @ ( G @ M )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.Suc_reindex_ivl
% 0.29/0.64  thf(fact_9274_sum__Suc__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat
% 0.29/0.64            @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_Suc_diff
% 0.29/0.64  thf(fact_9275_sum__Suc__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups3539618377306564664at_int
% 0.29/0.64            @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_Suc_diff
% 0.29/0.64  thf(fact_9276_sum__Suc__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( groups6591440286371151544t_real
% 0.29/0.64            @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_Suc_diff
% 0.29/0.64  thf(fact_9277_sum_OatLeast1__atMost__eq,axiom,
% 0.29/0.64      ! [G: nat > nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast1_atMost_eq
% 0.29/0.64  thf(fact_9278_sum_OatLeast1__atMost__eq,axiom,
% 0.29/0.64      ! [G: nat > real,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.atLeast1_atMost_eq
% 0.29/0.64  thf(fact_9279_sum__bounds__lt__plus1,axiom,
% 0.29/0.64      ! [F: nat > nat,Mm: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ Mm ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_bounds_lt_plus1
% 0.29/0.64  thf(fact_9280_sum__bounds__lt__plus1,axiom,
% 0.29/0.64      ! [F: nat > real,Mm: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ Mm ) )
% 0.29/0.64        = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_bounds_lt_plus1
% 0.29/0.64  thf(fact_9281_sum_Onested__swap_H,axiom,
% 0.29/0.64      ! [A: nat > nat > nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.29/0.64          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [J3: nat] :
% 0.29/0.64              ( groups3542108847815614940at_nat
% 0.29/0.64              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nested_swap'
% 0.29/0.64  thf(fact_9282_sum_Onested__swap_H,axiom,
% 0.29/0.64      ! [A: nat > nat > real,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.29/0.64          @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [J3: nat] :
% 0.29/0.64              ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.nested_swap'
% 0.29/0.64  thf(fact_9283_sum__atLeastAtMost__code,axiom,
% 0.29/0.64      ! [F: nat > complex,A: nat,B: nat] :
% 0.29/0.64        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.64        = ( set_fo1517530859248394432omplex
% 0.29/0.64          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 0.29/0.64          @ A
% 0.29/0.64          @ B
% 0.29/0.64          @ zero_zero_complex ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_atLeastAtMost_code
% 0.29/0.64  thf(fact_9284_sum__atLeastAtMost__code,axiom,
% 0.29/0.64      ! [F: nat > rat,A: nat,B: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.64        = ( set_fo1949268297981939178at_rat
% 0.29/0.64          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 0.29/0.64          @ A
% 0.29/0.64          @ B
% 0.29/0.64          @ zero_zero_rat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_atLeastAtMost_code
% 0.29/0.64  thf(fact_9285_sum__atLeastAtMost__code,axiom,
% 0.29/0.64      ! [F: nat > int,A: nat,B: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.64        = ( set_fo2581907887559384638at_int
% 0.29/0.64          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 0.29/0.64          @ A
% 0.29/0.64          @ B
% 0.29/0.64          @ zero_zero_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_atLeastAtMost_code
% 0.29/0.64  thf(fact_9286_sum__atLeastAtMost__code,axiom,
% 0.29/0.64      ! [F: nat > nat,A: nat,B: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.64        = ( set_fo2584398358068434914at_nat
% 0.29/0.64          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 0.29/0.64          @ A
% 0.29/0.64          @ B
% 0.29/0.64          @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_atLeastAtMost_code
% 0.29/0.64  thf(fact_9287_sum__atLeastAtMost__code,axiom,
% 0.29/0.64      ! [F: nat > real,A: nat,B: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.64        = ( set_fo3111899725591712190t_real
% 0.29/0.64          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 0.29/0.64          @ A
% 0.29/0.64          @ B
% 0.29/0.64          @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_atLeastAtMost_code
% 0.29/0.64  thf(fact_9288_sum_Oub__add__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 0.29/0.64          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.ub_add_nat
% 0.29/0.64  thf(fact_9289_sum_Oub__add__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.29/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 0.29/0.64          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.ub_add_nat
% 0.29/0.64  thf(fact_9290_sum_Oub__add__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.29/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 0.29/0.64          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.ub_add_nat
% 0.29/0.64  thf(fact_9291_sum_Oub__add__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 0.29/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 0.29/0.64          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.ub_add_nat
% 0.29/0.64  thf(fact_9292_sum__up__index__split,axiom,
% 0.29/0.64      ! [F: nat > rat,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_up_index_split
% 0.29/0.64  thf(fact_9293_sum__up__index__split,axiom,
% 0.29/0.64      ! [F: nat > int,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_up_index_split
% 0.29/0.64  thf(fact_9294_sum__up__index__split,axiom,
% 0.29/0.64      ! [F: nat > nat,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_up_index_split
% 0.29/0.64  thf(fact_9295_sum__up__index__split,axiom,
% 0.29/0.64      ! [F: nat > real,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64        = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_up_index_split
% 0.29/0.64  thf(fact_9296_sum__natinterval__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > complex] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_natinterval_diff
% 0.29/0.64  thf(fact_9297_sum__natinterval__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > rat] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_rat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_natinterval_diff
% 0.29/0.64  thf(fact_9298_sum__natinterval__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > int] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_natinterval_diff
% 0.29/0.64  thf(fact_9299_sum__natinterval__diff,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > real] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64            = zero_zero_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_natinterval_diff
% 0.29/0.64  thf(fact_9300_sum__telescope_H_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups2906978787729119204at_rat
% 0.29/0.64            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.29/0.64          = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_telescope''
% 0.29/0.64  thf(fact_9301_sum__telescope_H_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups3539618377306564664at_int
% 0.29/0.64            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.29/0.64          = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_telescope''
% 0.29/0.64  thf(fact_9302_sum__telescope_H_H,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,F: nat > real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups6591440286371151544t_real
% 0.29/0.64            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.29/0.64          = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_telescope''
% 0.29/0.64  thf(fact_9303_sum__power__shift,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: complex] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_power_shift
% 0.29/0.64  thf(fact_9304_sum__power__shift,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_power_shift
% 0.29/0.64  thf(fact_9305_sum__power__shift,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64          = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_power_shift
% 0.29/0.64  thf(fact_9306_summable__partial__sum__bound,axiom,
% 0.29/0.64      ! [F: nat > complex,E2: real] :
% 0.29/0.64        ( ( summable_complex @ F )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.64         => ~ ! [N8: nat] :
% 0.29/0.64                ~ ! [M2: nat] :
% 0.29/0.64                    ( ( ord_less_eq_nat @ N8 @ M2 )
% 0.29/0.64                   => ! [N6: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % summable_partial_sum_bound
% 0.29/0.64  thf(fact_9307_summable__partial__sum__bound,axiom,
% 0.29/0.64      ! [F: nat > real,E2: real] :
% 0.29/0.64        ( ( summable_real @ F )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.29/0.64         => ~ ! [N8: nat] :
% 0.29/0.64                ~ ! [M2: nat] :
% 0.29/0.64                    ( ( ord_less_eq_nat @ N8 @ M2 )
% 0.29/0.64                   => ! [N6: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % summable_partial_sum_bound
% 0.29/0.64  thf(fact_9308_sum__gp__multiplied,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.29/0.64          = ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_multiplied
% 0.29/0.64  thf(fact_9309_sum__gp__multiplied,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: complex] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.29/0.64          = ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_multiplied
% 0.29/0.64  thf(fact_9310_sum__gp__multiplied,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.29/0.64          = ( minus_minus_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_multiplied
% 0.29/0.64  thf(fact_9311_sum__gp__multiplied,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 0.29/0.64          = ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_multiplied
% 0.29/0.64  thf(fact_9312_sum_Oin__pairs,axiom,
% 0.29/0.64      ! [G: nat > rat,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.64        = ( groups2906978787729119204at_rat
% 0.29/0.64          @ ^ [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 ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.in_pairs
% 0.29/0.64  thf(fact_9313_sum_Oin__pairs,axiom,
% 0.29/0.64      ! [G: nat > int,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.64        = ( groups3539618377306564664at_int
% 0.29/0.64          @ ^ [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 ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.in_pairs
% 0.29/0.64  thf(fact_9314_sum_Oin__pairs,axiom,
% 0.29/0.64      ! [G: nat > nat,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.64        = ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [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 ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.in_pairs
% 0.29/0.64  thf(fact_9315_sum_Oin__pairs,axiom,
% 0.29/0.64      ! [G: nat > real,M: nat,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.29/0.64        = ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [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 ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum.in_pairs
% 0.29/0.64  thf(fact_9316_polyfun__eq__const,axiom,
% 0.29/0.64      ! [C: nat > complex,N2: nat,K: complex] :
% 0.29/0.64        ( ( ! [X: complex] :
% 0.29/0.64              ( ( groups2073611262835488442omplex
% 0.29/0.64                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 0.29/0.64                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64              = K ) )
% 0.29/0.64        = ( ( ( C @ zero_zero_nat )
% 0.29/0.64            = K )
% 0.29/0.64          & ! [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 0.29/0.64             => ( ( C @ X )
% 0.29/0.64                = zero_zero_complex ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_eq_const
% 0.29/0.64  thf(fact_9317_polyfun__eq__const,axiom,
% 0.29/0.64      ! [C: nat > real,N2: nat,K: real] :
% 0.29/0.64        ( ( ! [X: real] :
% 0.29/0.64              ( ( groups6591440286371151544t_real
% 0.29/0.64                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 0.29/0.64                @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64              = K ) )
% 0.29/0.64        = ( ( ( C @ zero_zero_nat )
% 0.29/0.64            = K )
% 0.29/0.64          & ! [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 0.29/0.64             => ( ( C @ X )
% 0.29/0.64                = zero_zero_real ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_eq_const
% 0.29/0.64  thf(fact_9318_gbinomial__sum__up__index,axiom,
% 0.29/0.64      ! [K: nat,N2: nat] :
% 0.29/0.64        ( ( groups2073611262835488442omplex
% 0.29/0.64          @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gbinomial_sum_up_index
% 0.29/0.64  thf(fact_9319_gbinomial__sum__up__index,axiom,
% 0.29/0.64      ! [K: nat,N2: nat] :
% 0.29/0.64        ( ( groups2906978787729119204at_rat
% 0.29/0.64          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gbinomial_sum_up_index
% 0.29/0.64  thf(fact_9320_gbinomial__sum__up__index,axiom,
% 0.29/0.64      ! [K: nat,N2: nat] :
% 0.29/0.64        ( ( groups6591440286371151544t_real
% 0.29/0.64          @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gbinomial_sum_up_index
% 0.29/0.64  thf(fact_9321_gauss__sum__nat,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [X: nat] : X
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum_nat
% 0.29/0.64  thf(fact_9322_double__arith__series,axiom,
% 0.29/0.64      ! [A: rat,D: rat,N2: nat] :
% 0.29/0.64        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups2906978787729119204at_rat
% 0.29/0.64            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9323_double__arith__series,axiom,
% 0.29/0.64      ! [A: extended_enat,D: extended_enat,N2: nat] :
% 0.29/0.64        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups7108830773950497114d_enat
% 0.29/0.64            @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9324_double__arith__series,axiom,
% 0.29/0.64      ! [A: complex,D: complex,N2: nat] :
% 0.29/0.64        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups2073611262835488442omplex
% 0.29/0.64            @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9325_double__arith__series,axiom,
% 0.29/0.64      ! [A: int,D: int,N2: nat] :
% 0.29/0.64        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups3539618377306564664at_int
% 0.29/0.64            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9326_double__arith__series,axiom,
% 0.29/0.64      ! [A: nat,D: nat,N2: nat] :
% 0.29/0.64        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups3542108847815614940at_nat
% 0.29/0.64            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9327_double__arith__series,axiom,
% 0.29/0.64      ! [A: real,D: real,N2: nat] :
% 0.29/0.64        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.29/0.64          @ ( groups6591440286371151544t_real
% 0.29/0.64            @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_arith_series
% 0.29/0.64  thf(fact_9328_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9329_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9330_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9331_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9332_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9333_double__gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum
% 0.29/0.64  thf(fact_9334_arith__series__nat,axiom,
% 0.29/0.64      ! [A: nat,D: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arith_series_nat
% 0.29/0.64  thf(fact_9335_Sum__Icc__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [X: nat] : X
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Sum_Icc_nat
% 0.29/0.64  thf(fact_9336_arith__series,axiom,
% 0.29/0.64      ! [A: code_integer,D: code_integer,N2: nat] :
% 0.29/0.64        ( ( groups7501900531339628137nteger
% 0.29/0.64          @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arith_series
% 0.29/0.64  thf(fact_9337_arith__series,axiom,
% 0.29/0.64      ! [A: int,D: int,N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int
% 0.29/0.64          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arith_series
% 0.29/0.64  thf(fact_9338_arith__series,axiom,
% 0.29/0.64      ! [A: nat,D: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arith_series
% 0.29/0.64  thf(fact_9339_gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum
% 0.29/0.64  thf(fact_9340_gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum
% 0.29/0.64  thf(fact_9341_gauss__sum,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gauss_sum
% 0.29/0.64  thf(fact_9342_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9343_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9344_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9345_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9346_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9347_double__gauss__sum__from__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 0.29/0.64        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % double_gauss_sum_from_Suc_0
% 0.29/0.64  thf(fact_9348_sum__gp__offset,axiom,
% 0.29/0.64      ! [X4: rat,M: nat,N2: nat] :
% 0.29/0.64        ( ( ( X4 = one_one_rat )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 0.29/0.64        & ( ( X4 != one_one_rat )
% 0.29/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X4 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_offset
% 0.29/0.64  thf(fact_9349_sum__gp__offset,axiom,
% 0.29/0.64      ! [X4: complex,M: nat,N2: nat] :
% 0.29/0.64        ( ( ( X4 = one_one_complex )
% 0.29/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 0.29/0.64        & ( ( X4 != one_one_complex )
% 0.29/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_offset
% 0.29/0.64  thf(fact_9350_sum__gp__offset,axiom,
% 0.29/0.64      ! [X4: real,M: nat,N2: nat] :
% 0.29/0.64        ( ( ( X4 = one_one_real )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 0.29/0.64        & ( ( X4 != one_one_real )
% 0.29/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 0.29/0.64            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_gp_offset
% 0.29/0.64  thf(fact_9351_polyfun__diff,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_rat
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 0.29/0.64            @ ( groups2906978787729119204at_rat
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( times_times_rat
% 0.29/0.64                  @ ( groups2906978787729119204at_rat
% 0.29/0.64                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 0.29/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64                  @ ( power_power_rat @ X4 @ J3 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff
% 0.29/0.64  thf(fact_9352_polyfun__diff,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_complex
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 0.29/0.64            @ ( groups2073611262835488442omplex
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( times_times_complex
% 0.29/0.64                  @ ( groups2073611262835488442omplex
% 0.29/0.64                    @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 0.29/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64                  @ ( power_power_complex @ X4 @ J3 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff
% 0.29/0.64  thf(fact_9353_polyfun__diff,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_int
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 0.29/0.64            @ ( groups3539618377306564664at_int
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( times_times_int
% 0.29/0.64                  @ ( groups3539618377306564664at_int
% 0.29/0.64                    @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 0.29/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64                  @ ( power_power_int @ X4 @ J3 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff
% 0.29/0.64  thf(fact_9354_polyfun__diff,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 0.29/0.64       => ( ( minus_minus_real
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 0.29/0.64              @ ( set_ord_atMost_nat @ N2 ) ) )
% 0.29/0.64          = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 0.29/0.64            @ ( groups6591440286371151544t_real
% 0.29/0.64              @ ^ [J3: nat] :
% 0.29/0.64                  ( times_times_real
% 0.29/0.64                  @ ( groups6591440286371151544t_real
% 0.29/0.64                    @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 0.29/0.64                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 0.29/0.64                  @ ( power_power_real @ X4 @ J3 ) )
% 0.29/0.64              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % polyfun_diff
% 0.29/0.64  thf(fact_9355_pochhammer__times__pochhammer__half,axiom,
% 0.29/0.64      ! [Z: rat,N2: nat] :
% 0.29/0.64        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( groups73079841787564623at_rat
% 0.29/0.64          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pochhammer_times_pochhammer_half
% 0.29/0.64  thf(fact_9356_pochhammer__times__pochhammer__half,axiom,
% 0.29/0.64      ! [Z: complex,N2: nat] :
% 0.29/0.64        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( groups6464643781859351333omplex
% 0.29/0.64          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pochhammer_times_pochhammer_half
% 0.29/0.64  thf(fact_9357_pochhammer__times__pochhammer__half,axiom,
% 0.29/0.64      ! [Z: real,N2: nat] :
% 0.29/0.64        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( groups129246275422532515t_real
% 0.29/0.64          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pochhammer_times_pochhammer_half
% 0.29/0.64  thf(fact_9358_vebt__buildup_Opelims,axiom,
% 0.29/0.64      ! [X4: nat,Y: vEBT_VEBT] :
% 0.29/0.64        ( ( ( vEBT_vebt_buildup @ X4 )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X4 )
% 0.29/0.64         => ( ( ( X4 = zero_zero_nat )
% 0.29/0.64             => ( ( Y
% 0.29/0.64                  = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.64               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.29/0.64           => ( ( ( X4
% 0.29/0.64                  = ( suc @ zero_zero_nat ) )
% 0.29/0.64               => ( ( Y
% 0.29/0.64                    = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.64                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.29/0.64             => ~ ! [Va2: nat] :
% 0.29/0.64                    ( ( X4
% 0.29/0.64                      = ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.64                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.64                         => ( Y
% 0.29/0.64                            = ( 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 ) ) ) ) ) ) )
% 0.29/0.64                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.64                         => ( Y
% 0.29/0.64                            = ( 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 ) ) ) ) ) ) ) ) )
% 0.29/0.64                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % vebt_buildup.pelims
% 0.29/0.64  thf(fact_9359_divmod__algorithm__code_I6_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc4245557441103728435nt_int
% 0.29/0.64          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 0.29/0.64          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(6)
% 0.29/0.64  thf(fact_9360_divmod__algorithm__code_I6_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc2626176000494625587at_nat
% 0.29/0.64          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 0.29/0.64          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(6)
% 0.29/0.64  thf(fact_9361_divmod__algorithm__code_I6_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc6916734918728496179nteger
% 0.29/0.64          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 0.29/0.64          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(6)
% 0.29/0.64  thf(fact_9362_arctan__def,axiom,
% 0.29/0.64      ( arctan
% 0.29/0.64      = ( ^ [Y5: real] :
% 0.29/0.64            ( the_real
% 0.29/0.64            @ ^ [X: real] :
% 0.29/0.64                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.29/0.64                & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.64                & ( ( tan_real @ X )
% 0.29/0.64                  = Y5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arctan_def
% 0.29/0.64  thf(fact_9363_prod_Oneutral__const,axiom,
% 0.29/0.64      ! [A2: set_nat] :
% 0.29/0.64        ( ( groups708209901874060359at_nat
% 0.29/0.64          @ ^ [Uu3: nat] : one_one_nat
% 0.29/0.64          @ A2 )
% 0.29/0.64        = one_one_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral_const
% 0.29/0.64  thf(fact_9364_prod_Oneutral__const,axiom,
% 0.29/0.64      ! [A2: set_nat] :
% 0.29/0.64        ( ( groups705719431365010083at_int
% 0.29/0.64          @ ^ [Uu3: nat] : one_one_int
% 0.29/0.64          @ A2 )
% 0.29/0.64        = one_one_int ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral_const
% 0.29/0.64  thf(fact_9365_prod_Oneutral__const,axiom,
% 0.29/0.64      ! [A2: set_int] :
% 0.29/0.64        ( ( groups1705073143266064639nt_int
% 0.29/0.64          @ ^ [Uu3: int] : one_one_int
% 0.29/0.64          @ A2 )
% 0.29/0.64        = one_one_int ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral_const
% 0.29/0.64  thf(fact_9366_prod_OlessThan__Suc,axiom,
% 0.29/0.64      ! [G: nat > complex,N2: nat] :
% 0.29/0.64        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.lessThan_Suc
% 0.29/0.64  thf(fact_9367_prod_OlessThan__Suc,axiom,
% 0.29/0.64      ! [G: nat > real,N2: nat] :
% 0.29/0.64        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.lessThan_Suc
% 0.29/0.64  thf(fact_9368_prod_OlessThan__Suc,axiom,
% 0.29/0.64      ! [G: nat > nat,N2: nat] :
% 0.29/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.lessThan_Suc
% 0.29/0.64  thf(fact_9369_prod_OlessThan__Suc,axiom,
% 0.29/0.64      ! [G: nat > int,N2: nat] :
% 0.29/0.64        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.lessThan_Suc
% 0.29/0.64  thf(fact_9370_prod_OatMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > complex,N2: nat] :
% 0.29/0.64        ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.atMost_Suc
% 0.29/0.64  thf(fact_9371_prod_OatMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > real,N2: nat] :
% 0.29/0.64        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.atMost_Suc
% 0.29/0.64  thf(fact_9372_prod_OatMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > nat,N2: nat] :
% 0.29/0.64        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.atMost_Suc
% 0.29/0.64  thf(fact_9373_prod_OatMost__Suc,axiom,
% 0.29/0.64      ! [G: nat > int,N2: nat] :
% 0.29/0.64        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 0.29/0.64        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.atMost_Suc
% 0.29/0.64  thf(fact_9374_prod_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > rat] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = one_one_rat ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.cl_ivl_Suc
% 0.29/0.64  thf(fact_9375_prod_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > complex] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = one_one_complex ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.cl_ivl_Suc
% 0.29/0.64  thf(fact_9376_prod_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > real] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = one_one_real ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.cl_ivl_Suc
% 0.29/0.64  thf(fact_9377_prod_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > nat] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = one_one_nat ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.cl_ivl_Suc
% 0.29/0.64  thf(fact_9378_prod_Ocl__ivl__Suc,axiom,
% 0.29/0.64      ! [N2: nat,M: nat,G: nat > int] :
% 0.29/0.64        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = one_one_int ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 0.29/0.64            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.cl_ivl_Suc
% 0.29/0.64  thf(fact_9379_divmod__algorithm__code_I5_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc4245557441103728435nt_int
% 0.29/0.64          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 0.29/0.64          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(5)
% 0.29/0.64  thf(fact_9380_divmod__algorithm__code_I5_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc2626176000494625587at_nat
% 0.29/0.64          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 0.29/0.64          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(5)
% 0.29/0.64  thf(fact_9381_divmod__algorithm__code_I5_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.64        = ( produc6916734918728496179nteger
% 0.29/0.64          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 0.29/0.64          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_algorithm_code(5)
% 0.29/0.64  thf(fact_9382_mod__prod__eq,axiom,
% 0.29/0.64      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.29/0.64        ( ( modulo_modulo_nat
% 0.29/0.64          @ ( groups708209901874060359at_nat
% 0.29/0.64            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 0.29/0.64            @ A2 )
% 0.29/0.64          @ A )
% 0.29/0.64        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 0.29/0.64  
% 0.29/0.64  % mod_prod_eq
% 0.29/0.64  thf(fact_9383_mod__prod__eq,axiom,
% 0.29/0.64      ! [F: nat > int,A: int,A2: set_nat] :
% 0.29/0.64        ( ( modulo_modulo_int
% 0.29/0.64          @ ( groups705719431365010083at_int
% 0.29/0.64            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.29/0.64            @ A2 )
% 0.29/0.64          @ A )
% 0.29/0.64        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 0.29/0.64  
% 0.29/0.64  % mod_prod_eq
% 0.29/0.64  thf(fact_9384_mod__prod__eq,axiom,
% 0.29/0.64      ! [F: int > int,A: int,A2: set_int] :
% 0.29/0.64        ( ( modulo_modulo_int
% 0.29/0.64          @ ( groups1705073143266064639nt_int
% 0.29/0.64            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 0.29/0.64            @ A2 )
% 0.29/0.64          @ A )
% 0.29/0.64        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 0.29/0.64  
% 0.29/0.64  % mod_prod_eq
% 0.29/0.64  thf(fact_9385_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: real > complex,A2: set_real] :
% 0.29/0.64        ( ( ( groups713298508707869441omplex @ G @ A2 )
% 0.29/0.64         != one_one_complex )
% 0.29/0.64       => ~ ! [A5: real] :
% 0.29/0.64              ( ( member_real @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9386_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: nat > complex,A2: set_nat] :
% 0.29/0.64        ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 0.29/0.64         != one_one_complex )
% 0.29/0.64       => ~ ! [A5: nat] :
% 0.29/0.64              ( ( member_nat @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9387_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: complex > complex,A2: set_complex] :
% 0.29/0.64        ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 0.29/0.64         != one_one_complex )
% 0.29/0.64       => ~ ! [A5: complex] :
% 0.29/0.64              ( ( member_complex @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9388_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: int > complex,A2: set_int] :
% 0.29/0.64        ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 0.29/0.64         != one_one_complex )
% 0.29/0.64       => ~ ! [A5: int] :
% 0.29/0.64              ( ( member_int @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_complex ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9389_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: real > real,A2: set_real] :
% 0.29/0.64        ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 0.29/0.64         != one_one_real )
% 0.29/0.64       => ~ ! [A5: real] :
% 0.29/0.64              ( ( member_real @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9390_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: nat > real,A2: set_nat] :
% 0.29/0.64        ( ( ( groups129246275422532515t_real @ G @ A2 )
% 0.29/0.64         != one_one_real )
% 0.29/0.64       => ~ ! [A5: nat] :
% 0.29/0.64              ( ( member_nat @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9391_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: complex > real,A2: set_complex] :
% 0.29/0.64        ( ( ( groups766887009212190081x_real @ G @ A2 )
% 0.29/0.64         != one_one_real )
% 0.29/0.64       => ~ ! [A5: complex] :
% 0.29/0.64              ( ( member_complex @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9392_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: int > real,A2: set_int] :
% 0.29/0.64        ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 0.29/0.64         != one_one_real )
% 0.29/0.64       => ~ ! [A5: int] :
% 0.29/0.64              ( ( member_int @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9393_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: real > rat,A2: set_real] :
% 0.29/0.64        ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 0.29/0.64         != one_one_rat )
% 0.29/0.64       => ~ ! [A5: real] :
% 0.29/0.64              ( ( member_real @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_rat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9394_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.29/0.64      ! [G: nat > rat,A2: set_nat] :
% 0.29/0.64        ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 0.29/0.64         != one_one_rat )
% 0.29/0.64       => ~ ! [A5: nat] :
% 0.29/0.64              ( ( member_nat @ A5 @ A2 )
% 0.29/0.64             => ( ( G @ A5 )
% 0.29/0.64                = one_one_rat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.not_neutral_contains_not_neutral
% 0.29/0.64  thf(fact_9395_prod_Oneutral,axiom,
% 0.29/0.64      ! [A2: set_nat,G: nat > nat] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ( G @ X5 )
% 0.29/0.64              = one_one_nat ) )
% 0.29/0.64       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 0.29/0.64          = one_one_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral
% 0.29/0.64  thf(fact_9396_prod_Oneutral,axiom,
% 0.29/0.64      ! [A2: set_nat,G: nat > int] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ( G @ X5 )
% 0.29/0.64              = one_one_int ) )
% 0.29/0.64       => ( ( groups705719431365010083at_int @ G @ A2 )
% 0.29/0.64          = one_one_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral
% 0.29/0.64  thf(fact_9397_prod_Oneutral,axiom,
% 0.29/0.64      ! [A2: set_int,G: int > int] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ( G @ X5 )
% 0.29/0.64              = one_one_int ) )
% 0.29/0.64       => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 0.29/0.64          = one_one_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod.neutral
% 0.29/0.64  thf(fact_9398_prod__power__distrib,axiom,
% 0.29/0.64      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 0.29/0.64        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
% 0.29/0.64        = ( groups708209901874060359at_nat
% 0.29/0.64          @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N2 )
% 0.29/0.64          @ A2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_power_distrib
% 0.29/0.64  thf(fact_9399_prod__power__distrib,axiom,
% 0.29/0.64      ! [F: nat > int,A2: set_nat,N2: nat] :
% 0.29/0.64        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N2 )
% 0.29/0.64        = ( groups705719431365010083at_int
% 0.29/0.64          @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N2 )
% 0.29/0.64          @ A2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_power_distrib
% 0.29/0.64  thf(fact_9400_prod__power__distrib,axiom,
% 0.29/0.64      ! [F: int > int,A2: set_int,N2: nat] :
% 0.29/0.64        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N2 )
% 0.29/0.64        = ( groups1705073143266064639nt_int
% 0.29/0.64          @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N2 )
% 0.29/0.64          @ A2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_power_distrib
% 0.29/0.64  thf(fact_9401_prod__nonneg,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > nat] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_nonneg
% 0.29/0.64  thf(fact_9402_prod__nonneg,axiom,
% 0.29/0.64      ! [A2: set_nat,F: nat > int] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_nonneg
% 0.29/0.64  thf(fact_9403_prod__nonneg,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > int] :
% 0.29/0.64        ( ! [X5: int] :
% 0.29/0.64            ( ( member_int @ X5 @ A2 )
% 0.29/0.64           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 0.29/0.64       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_nonneg
% 0.29/0.64  thf(fact_9404_prod__mono,axiom,
% 0.29/0.64      ! [A2: set_int,F: int > int,G: int > int] :
% 0.29/0.64        ( ! [I4: int] :
% 0.29/0.64            ( ( member_int @ I4 @ A2 )
% 0.29/0.64           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 0.29/0.64              & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 0.29/0.64       => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ A2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_mono
% 0.29/0.64  thf(fact_9405_ln__neg__is__const,axiom,
% 0.29/0.64      ! [X4: real] :
% 0.29/0.64        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 0.29/0.64       => ( ( ln_ln_real @ X4 )
% 0.29/0.64          = ( the_real
% 0.29/0.64            @ ^ [X: real] : $false ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % ln_neg_is_const
% 0.29/0.64  thf(fact_9406_periodic__finite__ex,axiom,
% 0.29/0.64      ! [D: int,P: int > $o] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D )
% 0.29/0.64       => ( ! [X5: int,K2: int] :
% 0.29/0.64              ( ( P @ X5 )
% 0.29/0.64              = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.29/0.64         => ( ( ? [X3: int] : ( P @ X3 ) )
% 0.29/0.64            = ( ? [X: int] :
% 0.29/0.64                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.29/0.64                  & ( P @ X ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % periodic_finite_ex
% 0.29/0.64  thf(fact_9407_bset_I3_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,B3: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( X2 = T2 )
% 0.29/0.64               => ( ( minus_minus_int @ X2 @ D4 )
% 0.29/0.64                  = T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(3)
% 0.29/0.64  thf(fact_9408_bset_I4_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,B3: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ T2 @ B3 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( X2 != T2 )
% 0.29/0.64               => ( ( minus_minus_int @ X2 @ D4 )
% 0.29/0.64                 != T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(4)
% 0.29/0.64  thf(fact_9409_bset_I5_J,axiom,
% 0.29/0.64      ! [D4: int,B3: set_int,T2: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ! [X2: int] :
% 0.29/0.64            ( ! [Xa2: int] :
% 0.29/0.64                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64               => ! [Xb2: int] :
% 0.29/0.64                    ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                   => ( X2
% 0.29/0.64                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64           => ( ( ord_less_int @ X2 @ T2 )
% 0.29/0.64             => ( ord_less_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(5)
% 0.29/0.64  thf(fact_9410_bset_I7_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,B3: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ T2 @ B3 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( ord_less_int @ T2 @ X2 )
% 0.29/0.64               => ( ord_less_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(7)
% 0.29/0.64  thf(fact_9411_aset_I3_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,A2: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( X2 = T2 )
% 0.29/0.64               => ( ( plus_plus_int @ X2 @ D4 )
% 0.29/0.64                  = T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(3)
% 0.29/0.64  thf(fact_9412_aset_I4_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,A2: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ T2 @ A2 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( X2 != T2 )
% 0.29/0.64               => ( ( plus_plus_int @ X2 @ D4 )
% 0.29/0.64                 != T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(4)
% 0.29/0.64  thf(fact_9413_aset_I5_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,A2: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ T2 @ A2 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( ord_less_int @ X2 @ T2 )
% 0.29/0.64               => ( ord_less_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(5)
% 0.29/0.64  thf(fact_9414_aset_I7_J,axiom,
% 0.29/0.64      ! [D4: int,A2: set_int,T2: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ! [X2: int] :
% 0.29/0.64            ( ! [Xa2: int] :
% 0.29/0.64                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64               => ! [Xb2: int] :
% 0.29/0.64                    ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                   => ( X2
% 0.29/0.64                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64           => ( ( ord_less_int @ T2 @ X2 )
% 0.29/0.64             => ( ord_less_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(7)
% 0.29/0.64  thf(fact_9415_fact__eq__fact__times,axiom,
% 0.29/0.64      ! [N2: nat,M: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.64       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.29/0.64          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 0.29/0.64            @ ( groups708209901874060359at_nat
% 0.29/0.64              @ ^ [X: nat] : X
% 0.29/0.64              @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % fact_eq_fact_times
% 0.29/0.64  thf(fact_9416_bset_I6_J,axiom,
% 0.29/0.64      ! [D4: int,B3: set_int,T2: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ! [X2: int] :
% 0.29/0.64            ( ! [Xa2: int] :
% 0.29/0.64                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64               => ! [Xb2: int] :
% 0.29/0.64                    ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                   => ( X2
% 0.29/0.64                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64           => ( ( ord_less_eq_int @ X2 @ T2 )
% 0.29/0.64             => ( ord_less_eq_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(6)
% 0.29/0.64  thf(fact_9417_bset_I8_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,B3: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ B3 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( ord_less_eq_int @ T2 @ X2 )
% 0.29/0.64               => ( ord_less_eq_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bset(8)
% 0.29/0.64  thf(fact_9418_aset_I6_J,axiom,
% 0.29/0.64      ! [D4: int,T2: int,A2: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 0.29/0.64         => ! [X2: int] :
% 0.29/0.64              ( ! [Xa2: int] :
% 0.29/0.64                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                 => ! [Xb2: int] :
% 0.29/0.64                      ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                     => ( X2
% 0.29/0.64                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64             => ( ( ord_less_eq_int @ X2 @ T2 )
% 0.29/0.64               => ( ord_less_eq_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(6)
% 0.29/0.64  thf(fact_9419_aset_I8_J,axiom,
% 0.29/0.64      ! [D4: int,A2: set_int,T2: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ! [X2: int] :
% 0.29/0.64            ( ! [Xa2: int] :
% 0.29/0.64                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64               => ! [Xb2: int] :
% 0.29/0.64                    ( ( member_int @ Xb2 @ A2 )
% 0.29/0.64                   => ( X2
% 0.29/0.64                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.29/0.64           => ( ( ord_less_eq_int @ T2 @ X2 )
% 0.29/0.64             => ( ord_less_eq_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % aset(8)
% 0.29/0.64  thf(fact_9420_cppi,axiom,
% 0.29/0.64      ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ? [Z3: int] :
% 0.29/0.64            ! [X5: int] :
% 0.29/0.64              ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.64             => ( ( P @ X5 )
% 0.29/0.64                = ( P6 @ X5 ) ) )
% 0.29/0.64         => ( ! [X5: int] :
% 0.29/0.64                ( ! [Xa3: int] :
% 0.29/0.64                    ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                   => ! [Xb3: int] :
% 0.29/0.64                        ( ( member_int @ Xb3 @ A2 )
% 0.29/0.64                       => ( X5
% 0.29/0.64                         != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.29/0.64               => ( ( P @ X5 )
% 0.29/0.64                 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 0.29/0.64           => ( ! [X5: int,K2: int] :
% 0.29/0.64                  ( ( P6 @ X5 )
% 0.29/0.64                  = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.29/0.64             => ( ( ? [X3: int] : ( P @ X3 ) )
% 0.29/0.64                = ( ? [X: int] :
% 0.29/0.64                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                      & ( P6 @ X ) )
% 0.29/0.64                  | ? [X: int] :
% 0.29/0.64                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                      & ? [Y5: int] :
% 0.29/0.64                          ( ( member_int @ Y5 @ A2 )
% 0.29/0.64                          & ( P @ ( minus_minus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % cppi
% 0.29/0.64  thf(fact_9421_cpmi,axiom,
% 0.29/0.64      ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.29/0.64       => ( ? [Z3: int] :
% 0.29/0.64            ! [X5: int] :
% 0.29/0.64              ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.64             => ( ( P @ X5 )
% 0.29/0.64                = ( P6 @ X5 ) ) )
% 0.29/0.64         => ( ! [X5: int] :
% 0.29/0.64                ( ! [Xa3: int] :
% 0.29/0.64                    ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                   => ! [Xb3: int] :
% 0.29/0.64                        ( ( member_int @ Xb3 @ B3 )
% 0.29/0.64                       => ( X5
% 0.29/0.64                         != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.29/0.64               => ( ( P @ X5 )
% 0.29/0.64                 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 0.29/0.64           => ( ! [X5: int,K2: int] :
% 0.29/0.64                  ( ( P6 @ X5 )
% 0.29/0.64                  = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.29/0.64             => ( ( ? [X3: int] : ( P @ X3 ) )
% 0.29/0.64                = ( ? [X: int] :
% 0.29/0.64                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                      & ( P6 @ X ) )
% 0.29/0.64                  | ? [X: int] :
% 0.29/0.64                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.29/0.64                      & ? [Y5: int] :
% 0.29/0.64                          ( ( member_int @ Y5 @ B3 )
% 0.29/0.64                          & ( P @ ( plus_plus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % cpmi
% 0.29/0.64  thf(fact_9422_arccos__def,axiom,
% 0.29/0.64      ( arccos
% 0.29/0.64      = ( ^ [Y5: real] :
% 0.29/0.64            ( the_real
% 0.29/0.64            @ ^ [X: real] :
% 0.29/0.64                ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.64                & ( ord_less_eq_real @ X @ pi )
% 0.29/0.64                & ( ( cos_real @ X )
% 0.29/0.64                  = Y5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arccos_def
% 0.29/0.64  thf(fact_9423_fact__div__fact,axiom,
% 0.29/0.64      ! [N2: nat,M: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.64       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 0.29/0.64          = ( groups708209901874060359at_nat
% 0.29/0.64            @ ^ [X: nat] : X
% 0.29/0.64            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % fact_div_fact
% 0.29/0.64  thf(fact_9424_divmod__step__nat__def,axiom,
% 0.29/0.64      ( unique5026877609467782581ep_nat
% 0.29/0.64      = ( ^ [L2: num] :
% 0.29/0.64            ( produc2626176000494625587at_nat
% 0.29/0.64            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_step_nat_def
% 0.29/0.64  thf(fact_9425_divmod__step__int__def,axiom,
% 0.29/0.64      ( unique5024387138958732305ep_int
% 0.29/0.64      = ( ^ [L2: num] :
% 0.29/0.64            ( produc4245557441103728435nt_int
% 0.29/0.64            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_step_int_def
% 0.29/0.64  thf(fact_9426_pi__half,axiom,
% 0.29/0.64      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.64      = ( the_real
% 0.29/0.64        @ ^ [X: real] :
% 0.29/0.64            ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.64            & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.64            & ( ( cos_real @ X )
% 0.29/0.64              = zero_zero_real ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pi_half
% 0.29/0.64  thf(fact_9427_pi__def,axiom,
% 0.29/0.64      ( pi
% 0.29/0.64      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.29/0.64        @ ( the_real
% 0.29/0.64          @ ^ [X: real] :
% 0.29/0.64              ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.64              & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.64              & ( ( cos_real @ X )
% 0.29/0.64                = zero_zero_real ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pi_def
% 0.29/0.64  thf(fact_9428_Sum__Icc__int,axiom,
% 0.29/0.64      ! [M: int,N2: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ M @ N2 )
% 0.29/0.64       => ( ( groups4538972089207619220nt_int
% 0.29/0.64            @ ^ [X: int] : X
% 0.29/0.64            @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 0.29/0.64          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Sum_Icc_int
% 0.29/0.64  thf(fact_9429_arcsin__def,axiom,
% 0.29/0.64      ( arcsin
% 0.29/0.64      = ( ^ [Y5: real] :
% 0.29/0.64            ( the_real
% 0.29/0.64            @ ^ [X: real] :
% 0.29/0.64                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.29/0.64                & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.64                & ( ( sin_real @ X )
% 0.29/0.64                  = Y5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % arcsin_def
% 0.29/0.64  thf(fact_9430_divmod__nat__if,axiom,
% 0.29/0.64      ( divmod_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] :
% 0.29/0.64            ( if_Pro6206227464963214023at_nat
% 0.29/0.64            @ ( ( N = zero_zero_nat )
% 0.29/0.64              | ( ord_less_nat @ M6 @ N ) )
% 0.29/0.64            @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 0.29/0.64            @ ( produc2626176000494625587at_nat
% 0.29/0.64              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.29/0.64              @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_nat_if
% 0.29/0.64  thf(fact_9431_complex__mult__cnj,axiom,
% 0.29/0.64      ! [Z: complex] :
% 0.29/0.64        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 0.29/0.64        = ( 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 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_mult_cnj
% 0.29/0.64  thf(fact_9432_prod__int__eq,axiom,
% 0.29/0.64      ! [I2: nat,J: nat] :
% 0.29/0.64        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 0.29/0.64        = ( groups1705073143266064639nt_int
% 0.29/0.64          @ ^ [X: int] : X
% 0.29/0.64          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_int_eq
% 0.29/0.64  thf(fact_9433_prod__int__plus__eq,axiom,
% 0.29/0.64      ! [I2: nat,J: nat] :
% 0.29/0.64        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 0.29/0.64        = ( groups1705073143266064639nt_int
% 0.29/0.64          @ ^ [X: int] : X
% 0.29/0.64          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_int_plus_eq
% 0.29/0.64  thf(fact_9434_Re__complex__div__gt__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Re_complex_div_gt_0
% 0.29/0.64  thf(fact_9435_Re__complex__div__lt__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.29/0.64        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Re_complex_div_lt_0
% 0.29/0.64  thf(fact_9436_Re__complex__div__ge__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Re_complex_div_ge_0
% 0.29/0.64  thf(fact_9437_Re__complex__div__le__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.29/0.64        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Re_complex_div_le_0
% 0.29/0.64  thf(fact_9438_Im__complex__div__gt__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Im_complex_div_gt_0
% 0.29/0.64  thf(fact_9439_Im__complex__div__lt__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.29/0.64        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Im_complex_div_lt_0
% 0.29/0.64  thf(fact_9440_Im__complex__div__ge__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Im_complex_div_ge_0
% 0.29/0.64  thf(fact_9441_Im__complex__div__le__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.29/0.64        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Im_complex_div_le_0
% 0.29/0.64  thf(fact_9442_complex__mod__mult__cnj,axiom,
% 0.29/0.64      ! [Z: complex] :
% 0.29/0.64        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.29/0.64        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_mod_mult_cnj
% 0.29/0.64  thf(fact_9443_complex__div__gt__0,axiom,
% 0.29/0.64      ! [A: complex,B: complex] :
% 0.29/0.64        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 0.29/0.64        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.29/0.64          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_div_gt_0
% 0.29/0.64  thf(fact_9444_complex__norm__square,axiom,
% 0.29/0.64      ! [Z: complex] :
% 0.29/0.64        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.29/0.64        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_norm_square
% 0.29/0.64  thf(fact_9445_divmod__nat__def,axiom,
% 0.29/0.64      ( divmod_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N ) @ ( modulo_modulo_nat @ M6 @ N ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_nat_def
% 0.29/0.64  thf(fact_9446_complex__add__cnj,axiom,
% 0.29/0.64      ! [Z: complex] :
% 0.29/0.64        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 0.29/0.64        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_add_cnj
% 0.29/0.64  thf(fact_9447_complex__diff__cnj,axiom,
% 0.29/0.64      ! [Z: complex] :
% 0.29/0.64        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 0.29/0.64        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_diff_cnj
% 0.29/0.64  thf(fact_9448_complex__div__cnj,axiom,
% 0.29/0.64      ( divide1717551699836669952omplex
% 0.29/0.64      = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % complex_div_cnj
% 0.29/0.64  thf(fact_9449_cnj__add__mult__eq__Re,axiom,
% 0.29/0.64      ! [Z: complex,W: complex] :
% 0.29/0.64        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 0.29/0.64        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % cnj_add_mult_eq_Re
% 0.29/0.64  thf(fact_9450_set__encode__def,axiom,
% 0.29/0.64      ( nat_set_encode
% 0.29/0.64      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % set_encode_def
% 0.29/0.64  thf(fact_9451_VEBT_Osize_I3_J,axiom,
% 0.29/0.64      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.29/0.64        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.29/0.64        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % VEBT.size(3)
% 0.29/0.64  thf(fact_9452_VEBT_Osize__gen_I1_J,axiom,
% 0.29/0.64      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.29/0.64        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.29/0.64        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % VEBT.size_gen(1)
% 0.29/0.64  thf(fact_9453_Sum__Ico__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [X: nat] : X
% 0.29/0.64          @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Sum_Ico_nat
% 0.29/0.64  thf(fact_9454_ex__nat__less__eq,axiom,
% 0.29/0.64      ! [N2: nat,P: nat > $o] :
% 0.29/0.64        ( ( ? [M6: nat] :
% 0.29/0.64              ( ( ord_less_nat @ M6 @ N2 )
% 0.29/0.64              & ( P @ M6 ) ) )
% 0.29/0.64        = ( ? [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64              & ( P @ X ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % ex_nat_less_eq
% 0.29/0.64  thf(fact_9455_all__nat__less__eq,axiom,
% 0.29/0.64      ! [N2: nat,P: nat > $o] :
% 0.29/0.64        ( ( ! [M6: nat] :
% 0.29/0.64              ( ( ord_less_nat @ M6 @ N2 )
% 0.29/0.64             => ( P @ M6 ) ) )
% 0.29/0.64        = ( ! [X: nat] :
% 0.29/0.64              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64             => ( P @ X ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % all_nat_less_eq
% 0.29/0.64  thf(fact_9456_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.29/0.64      ! [L: nat,U: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.29/0.64        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThanSuc_atLeastAtMost
% 0.29/0.64  thf(fact_9457_lessThan__atLeast0,axiom,
% 0.29/0.64      ( set_ord_lessThan_nat
% 0.29/0.64      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lessThan_atLeast0
% 0.29/0.64  thf(fact_9458_prod__Suc__fact,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_Suc_fact
% 0.29/0.64  thf(fact_9459_prod__Suc__Suc__fact,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 0.29/0.64        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_Suc_Suc_fact
% 0.29/0.64  thf(fact_9460_VEBT_Osize__gen_I2_J,axiom,
% 0.29/0.64      ! [X21: $o,X222: $o] :
% 0.29/0.64        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.29/0.64        = zero_zero_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % VEBT.size_gen(2)
% 0.29/0.64  thf(fact_9461_sum__power2,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.29/0.64        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sum_power2
% 0.29/0.64  thf(fact_9462_Chebyshev__sum__upper__nat,axiom,
% 0.29/0.64      ! [N2: nat,A: nat > nat,B: nat > nat] :
% 0.29/0.64        ( ! [I4: nat,J2: nat] :
% 0.29/0.64            ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.29/0.64           => ( ( ord_less_nat @ J2 @ N2 )
% 0.29/0.64             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 0.29/0.64       => ( ! [I4: nat,J2: nat] :
% 0.29/0.64              ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.29/0.64             => ( ( ord_less_nat @ J2 @ N2 )
% 0.29/0.64               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 0.29/0.64         => ( ord_less_eq_nat
% 0.29/0.64            @ ( times_times_nat @ N2
% 0.29/0.64              @ ( groups3542108847815614940at_nat
% 0.29/0.64                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 0.29/0.64                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 0.29/0.64            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Chebyshev_sum_upper_nat
% 0.29/0.64  thf(fact_9463_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.29/0.64      ! [L: int,U: int] :
% 0.29/0.64        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.29/0.64        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.29/0.64  thf(fact_9464_int__ge__less__than2__def,axiom,
% 0.29/0.64      ( int_ge_less_than2
% 0.29/0.64      = ( ^ [D5: int] :
% 0.29/0.64            ( collec213857154873943460nt_int
% 0.29/0.64            @ ( produc4947309494688390418_int_o
% 0.29/0.64              @ ^ [Z7: int,Z5: int] :
% 0.29/0.64                  ( ( ord_less_eq_int @ D5 @ Z5 )
% 0.29/0.64                  & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % int_ge_less_than2_def
% 0.29/0.64  thf(fact_9465_int__ge__less__than__def,axiom,
% 0.29/0.64      ( int_ge_less_than
% 0.29/0.64      = ( ^ [D5: int] :
% 0.29/0.64            ( collec213857154873943460nt_int
% 0.29/0.64            @ ( produc4947309494688390418_int_o
% 0.29/0.64              @ ^ [Z7: int,Z5: int] :
% 0.29/0.64                  ( ( ord_less_eq_int @ D5 @ Z7 )
% 0.29/0.64                  & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % int_ge_less_than_def
% 0.29/0.64  thf(fact_9466_upto_Opinduct,axiom,
% 0.29/0.64      ! [A0: int,A12: int,P: int > int > $o] :
% 0.29/0.64        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.29/0.64       => ( ! [I4: int,J2: int] :
% 0.29/0.64              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 0.29/0.64             => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 0.29/0.64                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 0.29/0.64               => ( P @ I4 @ J2 ) ) )
% 0.29/0.64         => ( P @ A0 @ A12 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % upto.pinduct
% 0.29/0.64  thf(fact_9467_divmod__step__integer__def,axiom,
% 0.29/0.64      ( unique4921790084139445826nteger
% 0.29/0.64      = ( ^ [L2: num] :
% 0.29/0.64            ( produc6916734918728496179nteger
% 0.29/0.64            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_step_integer_def
% 0.29/0.64  thf(fact_9468_or__int__rec,axiom,
% 0.29/0.64      ( bit_se1409905431419307370or_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] :
% 0.29/0.64            ( plus_plus_int
% 0.29/0.64            @ ( zero_n2684676970156552555ol_int
% 0.29/0.64              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.29/0.64                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.29/0.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_int_rec
% 0.29/0.64  thf(fact_9469_or__nonnegative__int__iff,axiom,
% 0.29/0.64      ! [K: int,L: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 0.29/0.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.29/0.64          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nonnegative_int_iff
% 0.29/0.64  thf(fact_9470_or__negative__int__iff,axiom,
% 0.29/0.64      ! [K: int,L: int] :
% 0.29/0.64        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 0.29/0.64        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.29/0.64          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_negative_int_iff
% 0.29/0.64  thf(fact_9471_or__minus__numerals_I6_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(6)
% 0.29/0.64  thf(fact_9472_or__minus__numerals_I2_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(2)
% 0.29/0.64  thf(fact_9473_or__minus__minus__numerals,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_minus_numerals
% 0.29/0.64  thf(fact_9474_and__minus__minus__numerals,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_minus_minus_numerals
% 0.29/0.64  thf(fact_9475_divmod__integer_H__def,axiom,
% 0.29/0.64      ( unique3479559517661332726nteger
% 0.29/0.64      = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_integer'_def
% 0.29/0.64  thf(fact_9476_bit__or__int__iff,axiom,
% 0.29/0.64      ! [K: int,L: int,N2: nat] :
% 0.29/0.64        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N2 )
% 0.29/0.64        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 0.29/0.64          | ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bit_or_int_iff
% 0.29/0.64  thf(fact_9477_sgn__integer__code,axiom,
% 0.29/0.64      ( sgn_sgn_Code_integer
% 0.29/0.64      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sgn_integer_code
% 0.29/0.64  thf(fact_9478_less__eq__integer__code_I1_J,axiom,
% 0.29/0.64      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_integer_code(1)
% 0.29/0.64  thf(fact_9479_OR__lower,axiom,
% 0.29/0.64      ! [X4: int,Y: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.64       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.64         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % OR_lower
% 0.29/0.64  thf(fact_9480_or__greater__eq,axiom,
% 0.29/0.64      ! [L: int,K: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.29/0.64       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_greater_eq
% 0.29/0.64  thf(fact_9481_plus__and__or,axiom,
% 0.29/0.64      ! [X4: int,Y: int] :
% 0.29/0.64        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se1409905431419307370or_int @ X4 @ Y ) )
% 0.29/0.64        = ( plus_plus_int @ X4 @ Y ) ) ).
% 0.29/0.64  
% 0.29/0.64  % plus_and_or
% 0.29/0.64  thf(fact_9482_nat_Odisc__eq__case_I1_J,axiom,
% 0.29/0.64      ! [Nat: nat] :
% 0.29/0.64        ( ( Nat = zero_zero_nat )
% 0.29/0.64        = ( case_nat_o @ $true
% 0.29/0.64          @ ^ [Uu3: nat] : $false
% 0.29/0.64          @ Nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat.disc_eq_case(1)
% 0.29/0.64  thf(fact_9483_nat_Odisc__eq__case_I2_J,axiom,
% 0.29/0.64      ! [Nat: nat] :
% 0.29/0.64        ( ( Nat != zero_zero_nat )
% 0.29/0.64        = ( case_nat_o @ $false
% 0.29/0.64          @ ^ [Uu3: nat] : $true
% 0.29/0.64          @ Nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat.disc_eq_case(2)
% 0.29/0.64  thf(fact_9484_or__int__def,axiom,
% 0.29/0.64      ( bit_se1409905431419307370or_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_int_def
% 0.29/0.64  thf(fact_9485_or__not__numerals_I1_J,axiom,
% 0.29/0.64      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.64      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(1)
% 0.29/0.64  thf(fact_9486_xor__int__def,axiom,
% 0.29/0.64      ( bit_se6526347334894502574or_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % xor_int_def
% 0.29/0.64  thf(fact_9487_concat__bit__def,axiom,
% 0.29/0.64      ( bit_concat_bit
% 0.29/0.64      = ( ^ [N: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % concat_bit_def
% 0.29/0.64  thf(fact_9488_set__bit__int__def,axiom,
% 0.29/0.64      ( bit_se7879613467334960850it_int
% 0.29/0.64      = ( ^ [N: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % set_bit_int_def
% 0.29/0.64  thf(fact_9489_one__natural_Orsp,axiom,
% 0.29/0.64      one_one_nat = one_one_nat ).
% 0.29/0.64  
% 0.29/0.64  % one_natural.rsp
% 0.29/0.64  thf(fact_9490_less__eq__nat_Osimps_I2_J,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.29/0.64        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_nat.simps(2)
% 0.29/0.64  thf(fact_9491_or__not__numerals_I4_J,axiom,
% 0.29/0.64      ! [M: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(4)
% 0.29/0.64  thf(fact_9492_or__not__numerals_I2_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(2)
% 0.29/0.64  thf(fact_9493_diff__Suc,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64        = ( case_nat_nat @ zero_zero_nat
% 0.29/0.64          @ ^ [K3: nat] : K3
% 0.29/0.64          @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % diff_Suc
% 0.29/0.64  thf(fact_9494_or__not__numerals_I3_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(3)
% 0.29/0.64  thf(fact_9495_or__not__numerals_I7_J,axiom,
% 0.29/0.64      ! [M: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(7)
% 0.29/0.64  thf(fact_9496_or__not__numerals_I6_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(6)
% 0.29/0.64  thf(fact_9497_OR__upper,axiom,
% 0.29/0.64      ! [X4: int,N2: nat,Y: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.64       => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.64         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 0.29/0.64           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % OR_upper
% 0.29/0.64  thf(fact_9498_or__not__numerals_I5_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.64        = ( 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 @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(5)
% 0.29/0.64  thf(fact_9499_or__not__numerals_I9_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.64        = ( 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 @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(9)
% 0.29/0.64  thf(fact_9500_or__not__numerals_I8_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.64        = ( 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 @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_numerals(8)
% 0.29/0.64  thf(fact_9501_integer__of__int__code,axiom,
% 0.29/0.64      ( code_integer_of_int
% 0.29/0.64      = ( ^ [K3: int] :
% 0.29/0.64            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.29/0.64            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.29/0.64              @ ( if_Code_integer
% 0.29/0.64                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.29/0.64                  = zero_zero_int )
% 0.29/0.64                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.64                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % integer_of_int_code
% 0.29/0.64  thf(fact_9502_or__minus__numerals_I1_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(1)
% 0.29/0.64  thf(fact_9503_or__minus__numerals_I5_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(5)
% 0.29/0.64  thf(fact_9504_or__nat__numerals_I4_J,axiom,
% 0.29/0.64      ! [X4: num] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.64        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_numerals(4)
% 0.29/0.64  thf(fact_9505_or__nat__numerals_I2_J,axiom,
% 0.29/0.64      ! [Y: num] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.29/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_numerals(2)
% 0.29/0.64  thf(fact_9506_or__nat__numerals_I3_J,axiom,
% 0.29/0.64      ! [X4: num] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.64        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_numerals(3)
% 0.29/0.64  thf(fact_9507_or__nat__numerals_I1_J,axiom,
% 0.29/0.64      ! [Y: num] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.29/0.64        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_numerals(1)
% 0.29/0.64  thf(fact_9508_or__minus__numerals_I8_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(8)
% 0.29/0.64  thf(fact_9509_or__minus__numerals_I4_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(4)
% 0.29/0.64  thf(fact_9510_or__minus__numerals_I3_J,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(3)
% 0.29/0.64  thf(fact_9511_or__minus__numerals_I7_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_minus_numerals(7)
% 0.29/0.64  thf(fact_9512_modulo__integer_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: int,X4: int] :
% 0.29/0.64        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 0.29/0.64        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % modulo_integer.abs_eq
% 0.29/0.64  thf(fact_9513_abs__integer__code,axiom,
% 0.29/0.64      ( abs_abs_Code_integer
% 0.29/0.64      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % abs_integer_code
% 0.29/0.64  thf(fact_9514_less__integer__code_I1_J,axiom,
% 0.29/0.64      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.29/0.64  
% 0.29/0.64  % less_integer_code(1)
% 0.29/0.64  thf(fact_9515_less__integer_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: int,X4: int] :
% 0.29/0.64        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 0.29/0.64        = ( ord_less_int @ Xa @ X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_integer.abs_eq
% 0.29/0.64  thf(fact_9516_or__not__num__neg_Osimps_I1_J,axiom,
% 0.29/0.64      ( ( bit_or_not_num_neg @ one @ one )
% 0.29/0.64      = one ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(1)
% 0.29/0.64  thf(fact_9517_less__eq__integer_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: int,X4: int] :
% 0.29/0.64        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 0.29/0.64        = ( ord_less_eq_int @ Xa @ X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_integer.abs_eq
% 0.29/0.64  thf(fact_9518_set__bit__nat__def,axiom,
% 0.29/0.64      ( bit_se7882103937844011126it_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] : ( bit_se1412395901928357646or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % set_bit_nat_def
% 0.29/0.64  thf(fact_9519_or__not__num__neg_Osimps_I4_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 0.29/0.64        = ( bit0 @ one ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(4)
% 0.29/0.64  thf(fact_9520_or__not__num__neg_Osimps_I6_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 0.29/0.64        = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(6)
% 0.29/0.64  thf(fact_9521_or__not__num__neg_Osimps_I3_J,axiom,
% 0.29/0.64      ! [M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 0.29/0.64        = ( bit1 @ M ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(3)
% 0.29/0.64  thf(fact_9522_or__not__num__neg_Osimps_I7_J,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 0.29/0.64        = one ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(7)
% 0.29/0.64  thf(fact_9523_or__not__num__neg_Osimps_I5_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 0.29/0.64        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(5)
% 0.29/0.64  thf(fact_9524_or__not__num__neg_Osimps_I9_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 0.29/0.64        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(9)
% 0.29/0.64  thf(fact_9525_or__nat__def,axiom,
% 0.29/0.64      ( bit_se1412395901928357646or_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_def
% 0.29/0.64  thf(fact_9526_or__not__num__neg_Osimps_I2_J,axiom,
% 0.29/0.64      ! [M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 0.29/0.64        = ( bit1 @ M ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(2)
% 0.29/0.64  thf(fact_9527_or__not__num__neg_Osimps_I8_J,axiom,
% 0.29/0.64      ! [N2: num,M: num] :
% 0.29/0.64        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 0.29/0.64        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.simps(8)
% 0.29/0.64  thf(fact_9528_or__not__num__neg_Oelims,axiom,
% 0.29/0.64      ! [X4: num,Xa: num,Y: num] :
% 0.29/0.64        ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( ( X4 = one )
% 0.29/0.64           => ( ( Xa = one )
% 0.29/0.64             => ( Y != one ) ) )
% 0.29/0.64         => ( ( ( X4 = one )
% 0.29/0.64             => ! [M5: num] :
% 0.29/0.64                  ( ( Xa
% 0.29/0.64                    = ( bit0 @ M5 ) )
% 0.29/0.64                 => ( Y
% 0.29/0.64                   != ( bit1 @ M5 ) ) ) )
% 0.29/0.64           => ( ( ( X4 = one )
% 0.29/0.64               => ! [M5: num] :
% 0.29/0.64                    ( ( Xa
% 0.29/0.64                      = ( bit1 @ M5 ) )
% 0.29/0.64                   => ( Y
% 0.29/0.64                     != ( bit1 @ M5 ) ) ) )
% 0.29/0.64             => ( ( ? [N3: num] :
% 0.29/0.64                      ( X4
% 0.29/0.64                      = ( bit0 @ N3 ) )
% 0.29/0.64                 => ( ( Xa = one )
% 0.29/0.64                   => ( Y
% 0.29/0.64                     != ( bit0 @ one ) ) ) )
% 0.29/0.64               => ( ! [N3: num] :
% 0.29/0.64                      ( ( X4
% 0.29/0.64                        = ( bit0 @ N3 ) )
% 0.29/0.64                     => ! [M5: num] :
% 0.29/0.64                          ( ( Xa
% 0.29/0.64                            = ( bit0 @ M5 ) )
% 0.29/0.64                         => ( Y
% 0.29/0.64                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 0.29/0.64                 => ( ! [N3: num] :
% 0.29/0.64                        ( ( X4
% 0.29/0.64                          = ( bit0 @ N3 ) )
% 0.29/0.64                       => ! [M5: num] :
% 0.29/0.64                            ( ( Xa
% 0.29/0.64                              = ( bit1 @ M5 ) )
% 0.29/0.64                           => ( Y
% 0.29/0.64                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 0.29/0.64                   => ( ( ? [N3: num] :
% 0.29/0.64                            ( X4
% 0.29/0.64                            = ( bit1 @ N3 ) )
% 0.29/0.64                       => ( ( Xa = one )
% 0.29/0.64                         => ( Y != one ) ) )
% 0.29/0.64                     => ( ! [N3: num] :
% 0.29/0.64                            ( ( X4
% 0.29/0.64                              = ( bit1 @ N3 ) )
% 0.29/0.64                           => ! [M5: num] :
% 0.29/0.64                                ( ( Xa
% 0.29/0.64                                  = ( bit0 @ M5 ) )
% 0.29/0.64                               => ( Y
% 0.29/0.64                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 0.29/0.64                       => ~ ! [N3: num] :
% 0.29/0.64                              ( ( X4
% 0.29/0.64                                = ( bit1 @ N3 ) )
% 0.29/0.64                             => ! [M5: num] :
% 0.29/0.64                                  ( ( Xa
% 0.29/0.64                                    = ( bit1 @ M5 ) )
% 0.29/0.64                                 => ( Y
% 0.29/0.64                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.elims
% 0.29/0.64  thf(fact_9529_numeral__or__not__num__eq,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % numeral_or_not_num_eq
% 0.29/0.64  thf(fact_9530_int__numeral__not__or__num__neg,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % int_numeral_not_or_num_neg
% 0.29/0.64  thf(fact_9531_int__numeral__or__not__num__neg,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % int_numeral_or_not_num_neg
% 0.29/0.64  thf(fact_9532_floor__real__def,axiom,
% 0.29/0.64      ( archim6058952711729229775r_real
% 0.29/0.64      = ( ^ [X: real] :
% 0.29/0.64            ( the_int
% 0.29/0.64            @ ^ [Z5: int] :
% 0.29/0.64                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 0.29/0.64                & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % floor_real_def
% 0.29/0.64  thf(fact_9533_or__Suc__0__eq,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.64        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_Suc_0_eq
% 0.29/0.64  thf(fact_9534_Suc__0__or__eq,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.64        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Suc_0_or_eq
% 0.29/0.64  thf(fact_9535_or__nat__rec,axiom,
% 0.29/0.64      ( bit_se1412395901928357646or_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] :
% 0.29/0.64            ( plus_plus_nat
% 0.29/0.64            @ ( zero_n2687167440665602831ol_nat
% 0.29/0.64              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.29/0.64                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.64            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_rec
% 0.29/0.64  thf(fact_9536_or__not__num__neg_Opelims,axiom,
% 0.29/0.64      ! [X4: num,Xa: num,Y: num] :
% 0.29/0.64        ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 0.29/0.64         => ( ( ( X4 = one )
% 0.29/0.64             => ( ( Xa = one )
% 0.29/0.64               => ( ( Y = one )
% 0.29/0.64                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.29/0.64           => ( ( ( X4 = one )
% 0.29/0.64               => ! [M5: num] :
% 0.29/0.64                    ( ( Xa
% 0.29/0.64                      = ( bit0 @ M5 ) )
% 0.29/0.64                   => ( ( Y
% 0.29/0.64                        = ( bit1 @ M5 ) )
% 0.29/0.64                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 0.29/0.64             => ( ( ( X4 = one )
% 0.29/0.64                 => ! [M5: num] :
% 0.29/0.64                      ( ( Xa
% 0.29/0.64                        = ( bit1 @ M5 ) )
% 0.29/0.64                     => ( ( Y
% 0.29/0.64                          = ( bit1 @ M5 ) )
% 0.29/0.64                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 0.29/0.64               => ( ! [N3: num] :
% 0.29/0.64                      ( ( X4
% 0.29/0.64                        = ( bit0 @ N3 ) )
% 0.29/0.64                     => ( ( Xa = one )
% 0.29/0.64                       => ( ( Y
% 0.29/0.64                            = ( bit0 @ one ) )
% 0.29/0.64                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 0.29/0.64                 => ( ! [N3: num] :
% 0.29/0.64                        ( ( X4
% 0.29/0.64                          = ( bit0 @ N3 ) )
% 0.29/0.64                       => ! [M5: num] :
% 0.29/0.64                            ( ( Xa
% 0.29/0.64                              = ( bit0 @ M5 ) )
% 0.29/0.64                           => ( ( Y
% 0.29/0.64                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 0.29/0.64                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 0.29/0.64                   => ( ! [N3: num] :
% 0.29/0.64                          ( ( X4
% 0.29/0.64                            = ( bit0 @ N3 ) )
% 0.29/0.64                         => ! [M5: num] :
% 0.29/0.64                              ( ( Xa
% 0.29/0.64                                = ( bit1 @ M5 ) )
% 0.29/0.64                             => ( ( Y
% 0.29/0.64                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 0.29/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 0.29/0.64                     => ( ! [N3: num] :
% 0.29/0.64                            ( ( X4
% 0.29/0.64                              = ( bit1 @ N3 ) )
% 0.29/0.64                           => ( ( Xa = one )
% 0.29/0.64                             => ( ( Y = one )
% 0.29/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 0.29/0.64                       => ( ! [N3: num] :
% 0.29/0.64                              ( ( X4
% 0.29/0.64                                = ( bit1 @ N3 ) )
% 0.29/0.64                             => ! [M5: num] :
% 0.29/0.64                                  ( ( Xa
% 0.29/0.64                                    = ( bit0 @ M5 ) )
% 0.29/0.64                                 => ( ( Y
% 0.29/0.64                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 0.29/0.64                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 0.29/0.64                         => ~ ! [N3: num] :
% 0.29/0.64                                ( ( X4
% 0.29/0.64                                  = ( bit1 @ N3 ) )
% 0.29/0.64                               => ! [M5: num] :
% 0.29/0.64                                    ( ( Xa
% 0.29/0.64                                      = ( bit1 @ M5 ) )
% 0.29/0.64                                   => ( ( Y
% 0.29/0.64                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 0.29/0.64                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_not_num_neg.pelims
% 0.29/0.64  thf(fact_9537_or__int__unfold,axiom,
% 0.29/0.64      ( bit_se1409905431419307370or_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] :
% 0.29/0.64            ( if_int
% 0.29/0.64            @ ( ( K3
% 0.29/0.64                = ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.64              | ( L2
% 0.29/0.64                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.29/0.64            @ ( uminus_uminus_int @ one_one_int )
% 0.29/0.64            @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_int_unfold
% 0.29/0.64  thf(fact_9538_max__enat__simps_I2_J,axiom,
% 0.29/0.64      ! [Q3: extended_enat] :
% 0.29/0.64        ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 0.29/0.64        = Q3 ) ).
% 0.29/0.64  
% 0.29/0.64  % max_enat_simps(2)
% 0.29/0.64  thf(fact_9539_max__enat__simps_I3_J,axiom,
% 0.29/0.64      ! [Q3: extended_enat] :
% 0.29/0.64        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 0.29/0.64        = Q3 ) ).
% 0.29/0.64  
% 0.29/0.64  % max_enat_simps(3)
% 0.29/0.64  thf(fact_9540_max__Suc__Suc,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/0.64        = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_Suc_Suc
% 0.29/0.64  thf(fact_9541_max__0R,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 0.29/0.64        = N2 ) ).
% 0.29/0.64  
% 0.29/0.64  % max_0R
% 0.29/0.64  thf(fact_9542_max__0L,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 0.29/0.64        = N2 ) ).
% 0.29/0.64  
% 0.29/0.64  % max_0L
% 0.29/0.64  thf(fact_9543_max__nat_Oright__neutral,axiom,
% 0.29/0.64      ! [A: nat] :
% 0.29/0.64        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.29/0.64        = A ) ).
% 0.29/0.64  
% 0.29/0.64  % max_nat.right_neutral
% 0.29/0.64  thf(fact_9544_max__nat_Oneutr__eq__iff,axiom,
% 0.29/0.64      ! [A: nat,B: nat] :
% 0.29/0.64        ( ( zero_zero_nat
% 0.29/0.64          = ( ord_max_nat @ A @ B ) )
% 0.29/0.64        = ( ( A = zero_zero_nat )
% 0.29/0.64          & ( B = zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_nat.neutr_eq_iff
% 0.29/0.64  thf(fact_9545_max__nat_Oleft__neutral,axiom,
% 0.29/0.64      ! [A: nat] :
% 0.29/0.64        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.29/0.64        = A ) ).
% 0.29/0.64  
% 0.29/0.64  % max_nat.left_neutral
% 0.29/0.64  thf(fact_9546_max__nat_Oeq__neutr__iff,axiom,
% 0.29/0.64      ! [A: nat,B: nat] :
% 0.29/0.64        ( ( ( ord_max_nat @ A @ B )
% 0.29/0.64          = zero_zero_nat )
% 0.29/0.64        = ( ( A = zero_zero_nat )
% 0.29/0.64          & ( B = zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_nat.eq_neutr_iff
% 0.29/0.64  thf(fact_9547_max__Suc__numeral,axiom,
% 0.29/0.64      ! [N2: nat,K: num] :
% 0.29/0.64        ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64        = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_Suc_numeral
% 0.29/0.64  thf(fact_9548_max__numeral__Suc,axiom,
% 0.29/0.64      ! [K: num,N2: nat] :
% 0.29/0.64        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.29/0.64        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_numeral_Suc
% 0.29/0.64  thf(fact_9549_nat__add__max__left,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.64        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 0.29/0.64        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_add_max_left
% 0.29/0.64  thf(fact_9550_nat__add__max__right,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.64        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 0.29/0.64        = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_add_max_right
% 0.29/0.64  thf(fact_9551_nat__mult__max__right,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.64        ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 0.29/0.64        = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_mult_max_right
% 0.29/0.64  thf(fact_9552_nat__mult__max__left,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.64        ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 0.29/0.64        = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_mult_max_left
% 0.29/0.64  thf(fact_9553_nat__minus__add__max,axiom,
% 0.29/0.64      ! [N2: nat,M: nat] :
% 0.29/0.64        ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 0.29/0.64        = ( ord_max_nat @ N2 @ M ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_minus_add_max
% 0.29/0.64  thf(fact_9554_max__Suc2,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64        = ( case_nat_nat @ ( suc @ N2 )
% 0.29/0.64          @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N2 ) )
% 0.29/0.64          @ M ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_Suc2
% 0.29/0.64  thf(fact_9555_max__Suc1,axiom,
% 0.29/0.64      ! [N2: nat,M: nat] :
% 0.29/0.64        ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 0.29/0.64        = ( case_nat_nat @ ( suc @ N2 )
% 0.29/0.64          @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N2 @ M3 ) )
% 0.29/0.64          @ M ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_Suc1
% 0.29/0.64  thf(fact_9556_or__nat__unfold,axiom,
% 0.29/0.64      ( bit_se1412395901928357646or_nat
% 0.29/0.64      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % or_nat_unfold
% 0.29/0.64  thf(fact_9557_floor__rat__def,axiom,
% 0.29/0.64      ( archim3151403230148437115or_rat
% 0.29/0.64      = ( ^ [X: rat] :
% 0.29/0.64            ( the_int
% 0.29/0.64            @ ^ [Z5: int] :
% 0.29/0.64                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 0.29/0.64                & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % floor_rat_def
% 0.29/0.64  thf(fact_9558_bit__cut__integer__def,axiom,
% 0.29/0.64      ( code_bit_cut_integer
% 0.29/0.64      = ( ^ [K3: code_integer] :
% 0.29/0.64            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.29/0.64            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bit_cut_integer_def
% 0.29/0.64  thf(fact_9559_divmod__integer__def,axiom,
% 0.29/0.64      ( code_divmod_integer
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L2 ) @ ( modulo364778990260209775nteger @ K3 @ L2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_integer_def
% 0.29/0.64  thf(fact_9560_sgn__rat__def,axiom,
% 0.29/0.64      ( sgn_sgn_rat
% 0.29/0.64      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sgn_rat_def
% 0.29/0.64  thf(fact_9561_obtain__pos__sum,axiom,
% 0.29/0.64      ! [R3: rat] :
% 0.29/0.64        ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 0.29/0.64       => ~ ! [S3: rat] :
% 0.29/0.64              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 0.29/0.64             => ! [T3: rat] :
% 0.29/0.64                  ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 0.29/0.64                 => ( R3
% 0.29/0.64                   != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % obtain_pos_sum
% 0.29/0.64  thf(fact_9562_less__eq__rat__def,axiom,
% 0.29/0.64      ( ord_less_eq_rat
% 0.29/0.64      = ( ^ [X: rat,Y5: rat] :
% 0.29/0.64            ( ( ord_less_rat @ X @ Y5 )
% 0.29/0.64            | ( X = Y5 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_rat_def
% 0.29/0.64  thf(fact_9563_abs__rat__def,axiom,
% 0.29/0.64      ( abs_abs_rat
% 0.29/0.64      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % abs_rat_def
% 0.29/0.64  thf(fact_9564_pred__def,axiom,
% 0.29/0.64      ( pred
% 0.29/0.64      = ( case_nat_nat @ zero_zero_nat
% 0.29/0.64        @ ^ [X24: nat] : X24 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pred_def
% 0.29/0.64  thf(fact_9565_bit__cut__integer__code,axiom,
% 0.29/0.64      ( code_bit_cut_integer
% 0.29/0.64      = ( ^ [K3: code_integer] :
% 0.29/0.64            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.29/0.64            @ ( produc9125791028180074456eger_o
% 0.29/0.64              @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 0.29/0.64              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bit_cut_integer_code
% 0.29/0.64  thf(fact_9566_normalize__negative,axiom,
% 0.29/0.64      ! [Q3: int,P2: int] :
% 0.29/0.64        ( ( ord_less_int @ Q3 @ zero_zero_int )
% 0.29/0.64       => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 0.29/0.64          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % normalize_negative
% 0.29/0.64  thf(fact_9567_divmod__abs__def,axiom,
% 0.29/0.64      ( code_divmod_abs
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_abs_def
% 0.29/0.64  thf(fact_9568_prod__decode__aux_Oelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.29/0.64        ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 0.29/0.64          & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_decode_aux.elims
% 0.29/0.64  thf(fact_9569_normalize__denom__pos,axiom,
% 0.29/0.64      ! [R3: product_prod_int_int,P2: int,Q3: int] :
% 0.29/0.64        ( ( ( normalize @ R3 )
% 0.29/0.64          = ( product_Pair_int_int @ P2 @ Q3 ) )
% 0.29/0.64       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % normalize_denom_pos
% 0.29/0.64  thf(fact_9570_prod__decode__aux_Osimps,axiom,
% 0.29/0.64      ( nat_prod_decode_aux
% 0.29/0.64      = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_decode_aux.simps
% 0.29/0.64  thf(fact_9571_prod__decode__aux_Opelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.29/0.64        ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 0.29/0.64         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 0.29/0.64                & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) )
% 0.29/0.64             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % prod_decode_aux.pelims
% 0.29/0.64  thf(fact_9572_divmod__integer__code,axiom,
% 0.29/0.64      ( code_divmod_integer
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] :
% 0.29/0.64            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.29/0.64            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.29/0.64              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 0.29/0.64                @ ( produc6916734918728496179nteger
% 0.29/0.64                  @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 0.29/0.64                  @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 0.29/0.64              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.29/0.64                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.29/0.64                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 0.29/0.64                    @ ( produc6916734918728496179nteger
% 0.29/0.64                      @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 0.29/0.64                      @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % divmod_integer_code
% 0.29/0.64  thf(fact_9573_Suc__0__div__numeral,axiom,
% 0.29/0.64      ! [K: num] :
% 0.29/0.64        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Suc_0_div_numeral
% 0.29/0.64  thf(fact_9574_finite__atLeastAtMost,axiom,
% 0.29/0.64      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atLeastAtMost
% 0.29/0.64  thf(fact_9575_finite__atLeastLessThan,axiom,
% 0.29/0.64      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atLeastLessThan
% 0.29/0.64  thf(fact_9576_finite__lessThan,axiom,
% 0.29/0.64      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_lessThan
% 0.29/0.64  thf(fact_9577_finite__atMost,axiom,
% 0.29/0.64      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atMost
% 0.29/0.64  thf(fact_9578_fst__divmod__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 0.29/0.64        = ( divide_divide_nat @ M @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % fst_divmod_nat
% 0.29/0.64  thf(fact_9579_finite__nat__set__iff__bounded__le,axiom,
% 0.29/0.64      ( finite_finite_nat
% 0.29/0.64      = ( ^ [N9: set_nat] :
% 0.29/0.64          ? [M6: nat] :
% 0.29/0.64          ! [X: nat] :
% 0.29/0.64            ( ( member_nat @ X @ N9 )
% 0.29/0.64           => ( ord_less_eq_nat @ X @ M6 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nat_set_iff_bounded_le
% 0.29/0.64  thf(fact_9580_finite__less__ub,axiom,
% 0.29/0.64      ! [F: nat > nat,U: nat] :
% 0.29/0.64        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 0.29/0.64       => ( finite_finite_nat
% 0.29/0.64          @ ( collect_nat
% 0.29/0.64            @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_less_ub
% 0.29/0.64  thf(fact_9581_finite__M__bounded__by__nat,axiom,
% 0.29/0.64      ! [P: nat > $o,I2: nat] :
% 0.29/0.64        ( finite_finite_nat
% 0.29/0.64        @ ( collect_nat
% 0.29/0.64          @ ^ [K3: nat] :
% 0.29/0.64              ( ( P @ K3 )
% 0.29/0.64              & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_M_bounded_by_nat
% 0.29/0.64  thf(fact_9582_bounded__nat__set__is__finite,axiom,
% 0.29/0.64      ! [N4: set_nat,N2: nat] :
% 0.29/0.64        ( ! [X5: nat] :
% 0.29/0.64            ( ( member_nat @ X5 @ N4 )
% 0.29/0.64           => ( ord_less_nat @ X5 @ N2 ) )
% 0.29/0.64       => ( finite_finite_nat @ N4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bounded_nat_set_is_finite
% 0.29/0.64  thf(fact_9583_finite__nat__set__iff__bounded,axiom,
% 0.29/0.64      ( finite_finite_nat
% 0.29/0.64      = ( ^ [N9: set_nat] :
% 0.29/0.64          ? [M6: nat] :
% 0.29/0.64          ! [X: nat] :
% 0.29/0.64            ( ( member_nat @ X @ N9 )
% 0.29/0.64           => ( ord_less_nat @ X @ M6 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nat_set_iff_bounded
% 0.29/0.64  thf(fact_9584_finite__divisors__nat,axiom,
% 0.29/0.64      ! [M: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.64       => ( finite_finite_nat
% 0.29/0.64          @ ( collect_nat
% 0.29/0.64            @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_divisors_nat
% 0.29/0.64  thf(fact_9585_subset__eq__atLeast0__atMost__finite,axiom,
% 0.29/0.64      ! [N4: set_nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64       => ( finite_finite_nat @ N4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % subset_eq_atLeast0_atMost_finite
% 0.29/0.64  thf(fact_9586_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.29/0.64      ! [N4: set_nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64       => ( finite_finite_nat @ N4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % subset_eq_atLeast0_lessThan_finite
% 0.29/0.64  thf(fact_9587_even__set__encode__iff,axiom,
% 0.29/0.64      ! [A2: set_nat] :
% 0.29/0.64        ( ( finite_finite_nat @ A2 )
% 0.29/0.64       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 0.29/0.64          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % even_set_encode_iff
% 0.29/0.64  thf(fact_9588_finite__Collect__le__nat,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( finite_finite_nat
% 0.29/0.64        @ ( collect_nat
% 0.29/0.64          @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_Collect_le_nat
% 0.29/0.64  thf(fact_9589_finite__Collect__less__nat,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( finite_finite_nat
% 0.29/0.64        @ ( collect_nat
% 0.29/0.64          @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_Collect_less_nat
% 0.29/0.64  thf(fact_9590_finite__atLeastAtMost__int,axiom,
% 0.29/0.64      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atLeastAtMost_int
% 0.29/0.64  thf(fact_9591_finite__atLeastLessThan__int,axiom,
% 0.29/0.64      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atLeastLessThan_int
% 0.29/0.64  thf(fact_9592_finite__interval__int1,axiom,
% 0.29/0.64      ! [A: int,B: int] :
% 0.29/0.64        ( finite_finite_int
% 0.29/0.64        @ ( collect_int
% 0.29/0.64          @ ^ [I3: int] :
% 0.29/0.64              ( ( ord_less_eq_int @ A @ I3 )
% 0.29/0.64              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_interval_int1
% 0.29/0.64  thf(fact_9593_finite__interval__int4,axiom,
% 0.29/0.64      ! [A: int,B: int] :
% 0.29/0.64        ( finite_finite_int
% 0.29/0.64        @ ( collect_int
% 0.29/0.64          @ ^ [I3: int] :
% 0.29/0.64              ( ( ord_less_int @ A @ I3 )
% 0.29/0.64              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_interval_int4
% 0.29/0.64  thf(fact_9594_finite__interval__int2,axiom,
% 0.29/0.64      ! [A: int,B: int] :
% 0.29/0.64        ( finite_finite_int
% 0.29/0.64        @ ( collect_int
% 0.29/0.64          @ ^ [I3: int] :
% 0.29/0.64              ( ( ord_less_eq_int @ A @ I3 )
% 0.29/0.64              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_interval_int2
% 0.29/0.64  thf(fact_9595_finite__interval__int3,axiom,
% 0.29/0.64      ! [A: int,B: int] :
% 0.29/0.64        ( finite_finite_int
% 0.29/0.64        @ ( collect_int
% 0.29/0.64          @ ^ [I3: int] :
% 0.29/0.64              ( ( ord_less_int @ A @ I3 )
% 0.29/0.64              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_interval_int3
% 0.29/0.64  thf(fact_9596_finite__nth__roots,axiom,
% 0.29/0.64      ! [N2: nat,C: complex] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( finite3207457112153483333omplex
% 0.29/0.64          @ ( collect_complex
% 0.29/0.64            @ ^ [Z5: complex] :
% 0.29/0.64                ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                = C ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nth_roots
% 0.29/0.64  thf(fact_9597_finite__atLeastZeroLessThan__int,axiom,
% 0.29/0.64      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_atLeastZeroLessThan_int
% 0.29/0.64  thf(fact_9598_finite__nat__iff__bounded__le,axiom,
% 0.29/0.64      ( finite_finite_nat
% 0.29/0.64      = ( ^ [S5: set_nat] :
% 0.29/0.64          ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nat_iff_bounded_le
% 0.29/0.64  thf(fact_9599_finite__nat__iff__bounded,axiom,
% 0.29/0.64      ( finite_finite_nat
% 0.29/0.64      = ( ^ [S5: set_nat] :
% 0.29/0.64          ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nat_iff_bounded
% 0.29/0.64  thf(fact_9600_finite__nat__bounded,axiom,
% 0.29/0.64      ! [S2: set_nat] :
% 0.29/0.64        ( ( finite_finite_nat @ S2 )
% 0.29/0.64       => ? [K2: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_nat_bounded
% 0.29/0.64  thf(fact_9601_infinite__int__iff__unbounded__le,axiom,
% 0.29/0.64      ! [S2: set_int] :
% 0.29/0.64        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.29/0.64        = ( ! [M6: int] :
% 0.29/0.64            ? [N: int] :
% 0.29/0.64              ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N ) )
% 0.29/0.64              & ( member_int @ N @ S2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % infinite_int_iff_unbounded_le
% 0.29/0.64  thf(fact_9602_infinite__int__iff__unbounded,axiom,
% 0.29/0.64      ! [S2: set_int] :
% 0.29/0.64        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.29/0.64        = ( ! [M6: int] :
% 0.29/0.64            ? [N: int] :
% 0.29/0.64              ( ( ord_less_int @ M6 @ ( abs_abs_int @ N ) )
% 0.29/0.64              & ( member_int @ N @ S2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % infinite_int_iff_unbounded
% 0.29/0.64  thf(fact_9603_unbounded__k__infinite,axiom,
% 0.29/0.64      ! [K: nat,S2: set_nat] :
% 0.29/0.64        ( ! [M5: nat] :
% 0.29/0.64            ( ( ord_less_nat @ K @ M5 )
% 0.29/0.64           => ? [N6: nat] :
% 0.29/0.64                ( ( ord_less_nat @ M5 @ N6 )
% 0.29/0.64                & ( member_nat @ N6 @ S2 ) ) )
% 0.29/0.64       => ~ ( finite_finite_nat @ S2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % unbounded_k_infinite
% 0.29/0.64  thf(fact_9604_infinite__nat__iff__unbounded,axiom,
% 0.29/0.64      ! [S2: set_nat] :
% 0.29/0.64        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.29/0.64        = ( ! [M6: nat] :
% 0.29/0.64            ? [N: nat] :
% 0.29/0.64              ( ( ord_less_nat @ M6 @ N )
% 0.29/0.64              & ( member_nat @ N @ S2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % infinite_nat_iff_unbounded
% 0.29/0.64  thf(fact_9605_infinite__nat__iff__unbounded__le,axiom,
% 0.29/0.64      ! [S2: set_nat] :
% 0.29/0.64        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.29/0.64        = ( ! [M6: nat] :
% 0.29/0.64            ? [N: nat] :
% 0.29/0.64              ( ( ord_less_eq_nat @ M6 @ N )
% 0.29/0.64              & ( member_nat @ N @ S2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % infinite_nat_iff_unbounded_le
% 0.29/0.64  thf(fact_9606_bij__betw__nth__root__unity,axiom,
% 0.29/0.64      ! [C: complex,N2: nat] :
% 0.29/0.64        ( ( C != zero_zero_complex )
% 0.29/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 0.29/0.64            @ ( collect_complex
% 0.29/0.64              @ ^ [Z5: complex] :
% 0.29/0.64                  ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                  = one_one_complex ) )
% 0.29/0.64            @ ( collect_complex
% 0.29/0.64              @ ^ [Z5: complex] :
% 0.29/0.64                  ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                  = C ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bij_betw_nth_root_unity
% 0.29/0.64  thf(fact_9607_real__root__Suc__0,axiom,
% 0.29/0.64      ! [X4: real] :
% 0.29/0.64        ( ( root @ ( suc @ zero_zero_nat ) @ X4 )
% 0.29/0.64        = X4 ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_Suc_0
% 0.29/0.64  thf(fact_9608_real__root__eq__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ( root @ N2 @ X4 )
% 0.29/0.64            = ( root @ N2 @ Y ) )
% 0.29/0.64          = ( X4 = Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_eq_iff
% 0.29/0.64  thf(fact_9609_real__root__eq__0__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ( root @ N2 @ X4 )
% 0.29/0.64            = zero_zero_real )
% 0.29/0.64          = ( X4 = zero_zero_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_eq_0_iff
% 0.29/0.64  thf(fact_9610_real__root__less__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_real @ X4 @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_less_iff
% 0.29/0.64  thf(fact_9611_real__root__le__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_le_iff
% 0.29/0.64  thf(fact_9612_real__root__one,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( root @ N2 @ one_one_real )
% 0.29/0.64          = one_one_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_one
% 0.29/0.64  thf(fact_9613_real__root__eq__1__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ( root @ N2 @ X4 )
% 0.29/0.64            = one_one_real )
% 0.29/0.64          = ( X4 = one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_eq_1_iff
% 0.29/0.64  thf(fact_9614_real__root__gt__0__iff,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_gt_0_iff
% 0.29/0.64  thf(fact_9615_real__root__lt__0__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 0.29/0.64          = ( ord_less_real @ X4 @ zero_zero_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_lt_0_iff
% 0.29/0.64  thf(fact_9616_real__root__ge__0__iff,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_ge_0_iff
% 0.29/0.64  thf(fact_9617_real__root__le__0__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 0.29/0.64          = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_le_0_iff
% 0.29/0.64  thf(fact_9618_real__root__gt__1__iff,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_gt_1_iff
% 0.29/0.64  thf(fact_9619_real__root__lt__1__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 0.29/0.64          = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_lt_1_iff
% 0.29/0.64  thf(fact_9620_real__root__ge__1__iff,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 0.29/0.64          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_ge_1_iff
% 0.29/0.64  thf(fact_9621_real__root__le__1__iff,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 0.29/0.64          = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_le_1_iff
% 0.29/0.64  thf(fact_9622_real__root__pow__pos2,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 0.29/0.64            = X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_pow_pos2
% 0.29/0.64  thf(fact_9623_real__root__pos__pos__le,axiom,
% 0.29/0.64      ! [X4: real,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.64       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_pos_pos_le
% 0.29/0.64  thf(fact_9624_real__root__less__mono,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ X4 @ Y )
% 0.29/0.64         => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_less_mono
% 0.29/0.64  thf(fact_9625_real__root__le__mono,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ X4 @ Y )
% 0.29/0.64         => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_le_mono
% 0.29/0.64  thf(fact_9626_real__root__power,axiom,
% 0.29/0.64      ! [N2: nat,X4: real,K: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( root @ N2 @ ( power_power_real @ X4 @ K ) )
% 0.29/0.64          = ( power_power_real @ ( root @ N2 @ X4 ) @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_power
% 0.29/0.64  thf(fact_9627_real__root__abs,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( root @ N2 @ ( abs_abs_real @ X4 ) )
% 0.29/0.64          = ( abs_abs_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_abs
% 0.29/0.64  thf(fact_9628_sgn__root,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( sgn_sgn_real @ ( root @ N2 @ X4 ) )
% 0.29/0.64          = ( sgn_sgn_real @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sgn_root
% 0.29/0.64  thf(fact_9629_real__root__gt__zero,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_gt_zero
% 0.29/0.64  thf(fact_9630_real__root__strict__decreasing,axiom,
% 0.29/0.64      ! [N2: nat,N4: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.64         => ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.64           => ( ord_less_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_strict_decreasing
% 0.29/0.64  thf(fact_9631_sqrt__def,axiom,
% 0.29/0.64      ( sqrt
% 0.29/0.64      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sqrt_def
% 0.29/0.64  thf(fact_9632_root__abs__power,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 0.29/0.64          = ( abs_abs_real @ Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % root_abs_power
% 0.29/0.64  thf(fact_9633_real__root__pos__pos,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_pos_pos
% 0.29/0.64  thf(fact_9634_real__root__strict__increasing,axiom,
% 0.29/0.64      ! [N2: nat,N4: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_nat @ N2 @ N4 )
% 0.29/0.64         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64           => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.64             => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_strict_increasing
% 0.29/0.64  thf(fact_9635_real__root__decreasing,axiom,
% 0.29/0.64      ! [N2: nat,N4: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.64         => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 0.29/0.64           => ( ord_less_eq_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_decreasing
% 0.29/0.64  thf(fact_9636_real__root__pow__pos,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 0.29/0.64            = X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_pow_pos
% 0.29/0.64  thf(fact_9637_real__root__pos__unique,axiom,
% 0.29/0.64      ! [N2: nat,Y: real,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.29/0.64         => ( ( ( power_power_real @ Y @ N2 )
% 0.29/0.64              = X4 )
% 0.29/0.64           => ( ( root @ N2 @ X4 )
% 0.29/0.64              = Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_pos_unique
% 0.29/0.64  thf(fact_9638_real__root__power__cancel,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.64            = X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_power_cancel
% 0.29/0.64  thf(fact_9639_odd__real__root__power__cancel,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.64       => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 0.29/0.64          = X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % odd_real_root_power_cancel
% 0.29/0.64  thf(fact_9640_odd__real__root__unique,axiom,
% 0.29/0.64      ! [N2: nat,Y: real,X4: real] :
% 0.29/0.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.64       => ( ( ( power_power_real @ Y @ N2 )
% 0.29/0.64            = X4 )
% 0.29/0.64         => ( ( root @ N2 @ X4 )
% 0.29/0.64            = Y ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % odd_real_root_unique
% 0.29/0.64  thf(fact_9641_odd__real__root__pow,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.64       => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 0.29/0.64          = X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % odd_real_root_pow
% 0.29/0.64  thf(fact_9642_real__root__increasing,axiom,
% 0.29/0.64      ! [N2: nat,N4: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.29/0.64         => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.64           => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.64             => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % real_root_increasing
% 0.29/0.64  thf(fact_9643_root__sgn__power,axiom,
% 0.29/0.64      ! [N2: nat,Y: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 0.29/0.64          = Y ) ) ).
% 0.29/0.64  
% 0.29/0.64  % root_sgn_power
% 0.29/0.64  thf(fact_9644_sgn__power__root,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X4 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X4 ) ) @ N2 ) )
% 0.29/0.64          = X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sgn_power_root
% 0.29/0.64  thf(fact_9645_ln__root,axiom,
% 0.29/0.64      ! [N2: nat,B: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.64         => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 0.29/0.64            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % ln_root
% 0.29/0.64  thf(fact_9646_log__root,axiom,
% 0.29/0.64      ! [N2: nat,A: real,B: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.29/0.64         => ( ( log @ B @ ( root @ N2 @ A ) )
% 0.29/0.64            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % log_root
% 0.29/0.64  thf(fact_9647_log__base__root,axiom,
% 0.29/0.64      ! [N2: nat,B: real,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.29/0.64         => ( ( log @ ( root @ N2 @ B ) @ X4 )
% 0.29/0.64            = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % log_base_root
% 0.29/0.64  thf(fact_9648_split__root,axiom,
% 0.29/0.64      ! [P: real > $o,N2: nat,X4: real] :
% 0.29/0.64        ( ( P @ ( root @ N2 @ X4 ) )
% 0.29/0.64        = ( ( ( N2 = zero_zero_nat )
% 0.29/0.64           => ( P @ zero_zero_real ) )
% 0.29/0.64          & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64           => ! [Y5: real] :
% 0.29/0.64                ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 0.29/0.64                  = X4 )
% 0.29/0.64               => ( P @ Y5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % split_root
% 0.29/0.64  thf(fact_9649_root__powr__inverse,axiom,
% 0.29/0.64      ! [N2: nat,X4: real] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.64         => ( ( root @ N2 @ X4 )
% 0.29/0.64            = ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % root_powr_inverse
% 0.29/0.64  thf(fact_9650_set__encode__insert,axiom,
% 0.29/0.64      ! [A2: set_nat,N2: nat] :
% 0.29/0.64        ( ( finite_finite_nat @ A2 )
% 0.29/0.64       => ( ~ ( member_nat @ N2 @ A2 )
% 0.29/0.64         => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 0.29/0.64            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % set_encode_insert
% 0.29/0.64  thf(fact_9651_Suc__0__mod__numeral,axiom,
% 0.29/0.64      ! [K: num] :
% 0.29/0.64        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Suc_0_mod_numeral
% 0.29/0.64  thf(fact_9652_card__lessThan,axiom,
% 0.29/0.64      ! [U: nat] :
% 0.29/0.64        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.29/0.64        = U ) ).
% 0.29/0.64  
% 0.29/0.64  % card_lessThan
% 0.29/0.64  thf(fact_9653_card__Collect__less__nat,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( finite_card_nat
% 0.29/0.64          @ ( collect_nat
% 0.29/0.64            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N2 ) ) )
% 0.29/0.64        = N2 ) ).
% 0.29/0.64  
% 0.29/0.64  % card_Collect_less_nat
% 0.29/0.64  thf(fact_9654_card__atMost,axiom,
% 0.29/0.64      ! [U: nat] :
% 0.29/0.64        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.29/0.64        = ( suc @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atMost
% 0.29/0.64  thf(fact_9655_card__atLeastLessThan,axiom,
% 0.29/0.64      ! [L: nat,U: nat] :
% 0.29/0.64        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.29/0.64        = ( minus_minus_nat @ U @ L ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atLeastLessThan
% 0.29/0.64  thf(fact_9656_card__Collect__le__nat,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( finite_card_nat
% 0.29/0.64          @ ( collect_nat
% 0.29/0.64            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N2 ) ) )
% 0.29/0.64        = ( suc @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_Collect_le_nat
% 0.29/0.64  thf(fact_9657_card__atLeastAtMost,axiom,
% 0.29/0.64      ! [L: nat,U: nat] :
% 0.29/0.64        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.29/0.64        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atLeastAtMost
% 0.29/0.64  thf(fact_9658_card__atLeastLessThan__int,axiom,
% 0.29/0.64      ! [L: int,U: int] :
% 0.29/0.64        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.29/0.64        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atLeastLessThan_int
% 0.29/0.64  thf(fact_9659_snd__divmod__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 0.29/0.64        = ( modulo_modulo_nat @ M @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % snd_divmod_nat
% 0.29/0.64  thf(fact_9660_card__atLeastAtMost__int,axiom,
% 0.29/0.64      ! [L: int,U: int] :
% 0.29/0.64        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.29/0.64        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atLeastAtMost_int
% 0.29/0.64  thf(fact_9661_lessThan__Suc,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.29/0.64        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lessThan_Suc
% 0.29/0.64  thf(fact_9662_atMost__Suc,axiom,
% 0.29/0.64      ! [K: nat] :
% 0.29/0.64        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.29/0.64        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atMost_Suc
% 0.29/0.64  thf(fact_9663_atLeast0__atMost__Suc,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.29/0.64        = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeast0_atMost_Suc
% 0.29/0.64  thf(fact_9664_atLeast0__lessThan__Suc,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.29/0.64        = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeast0_lessThan_Suc
% 0.29/0.64  thf(fact_9665_Icc__eq__insert__lb__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 0.29/0.64          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Icc_eq_insert_lb_nat
% 0.29/0.64  thf(fact_9666_atLeastAtMostSuc__conv,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64          = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMostSuc_conv
% 0.29/0.64  thf(fact_9667_atLeastAtMost__insertL,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 0.29/0.64          = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMost_insertL
% 0.29/0.64  thf(fact_9668_lessThan__nat__numeral,axiom,
% 0.29/0.64      ! [K: num] :
% 0.29/0.64        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lessThan_nat_numeral
% 0.29/0.64  thf(fact_9669_card__less,axiom,
% 0.29/0.64      ! [M7: set_nat,I2: nat] :
% 0.29/0.64        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.29/0.64       => ( ( finite_card_nat
% 0.29/0.64            @ ( collect_nat
% 0.29/0.64              @ ^ [K3: nat] :
% 0.29/0.64                  ( ( member_nat @ K3 @ M7 )
% 0.29/0.64                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 0.29/0.64         != zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_less
% 0.29/0.64  thf(fact_9670_card__less__Suc,axiom,
% 0.29/0.64      ! [M7: set_nat,I2: nat] :
% 0.29/0.64        ( ( member_nat @ zero_zero_nat @ M7 )
% 0.29/0.64       => ( ( suc
% 0.29/0.64            @ ( finite_card_nat
% 0.29/0.64              @ ( collect_nat
% 0.29/0.64                @ ^ [K3: nat] :
% 0.29/0.64                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.29/0.64                    & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 0.29/0.64          = ( finite_card_nat
% 0.29/0.64            @ ( collect_nat
% 0.29/0.64              @ ^ [K3: nat] :
% 0.29/0.64                  ( ( member_nat @ K3 @ M7 )
% 0.29/0.64                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_less_Suc
% 0.29/0.64  thf(fact_9671_card__less__Suc2,axiom,
% 0.29/0.64      ! [M7: set_nat,I2: nat] :
% 0.29/0.64        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.29/0.64       => ( ( finite_card_nat
% 0.29/0.64            @ ( collect_nat
% 0.29/0.64              @ ^ [K3: nat] :
% 0.29/0.64                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.29/0.64                  & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 0.29/0.64          = ( finite_card_nat
% 0.29/0.64            @ ( collect_nat
% 0.29/0.64              @ ^ [K3: nat] :
% 0.29/0.64                  ( ( member_nat @ K3 @ M7 )
% 0.29/0.64                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_less_Suc2
% 0.29/0.64  thf(fact_9672_atMost__nat__numeral,axiom,
% 0.29/0.64      ! [K: num] :
% 0.29/0.64        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atMost_nat_numeral
% 0.29/0.64  thf(fact_9673_card__atLeastZeroLessThan__int,axiom,
% 0.29/0.64      ! [U: int] :
% 0.29/0.64        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.29/0.64        = ( nat2 @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_atLeastZeroLessThan_int
% 0.29/0.64  thf(fact_9674_subset__card__intvl__is__intvl,axiom,
% 0.29/0.64      ! [A2: set_nat,K: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 0.29/0.64       => ( A2
% 0.29/0.64          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % subset_card_intvl_is_intvl
% 0.29/0.64  thf(fact_9675_subset__eq__atLeast0__lessThan__card,axiom,
% 0.29/0.64      ! [N4: set_nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 0.29/0.64       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % subset_eq_atLeast0_lessThan_card
% 0.29/0.64  thf(fact_9676_card__sum__le__nat__sum,axiom,
% 0.29/0.64      ! [S2: set_nat] :
% 0.29/0.64        ( ord_less_eq_nat
% 0.29/0.64        @ ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [X: nat] : X
% 0.29/0.64          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.29/0.64        @ ( groups3542108847815614940at_nat
% 0.29/0.64          @ ^ [X: nat] : X
% 0.29/0.64          @ S2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_sum_le_nat_sum
% 0.29/0.64  thf(fact_9677_card__nth__roots,axiom,
% 0.29/0.64      ! [C: complex,N2: nat] :
% 0.29/0.64        ( ( C != zero_zero_complex )
% 0.29/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ( ( finite_card_complex
% 0.29/0.64              @ ( collect_complex
% 0.29/0.64                @ ^ [Z5: complex] :
% 0.29/0.64                    ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                    = C ) ) )
% 0.29/0.64            = N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_nth_roots
% 0.29/0.64  thf(fact_9678_card__roots__unity__eq,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( finite_card_complex
% 0.29/0.64            @ ( collect_complex
% 0.29/0.64              @ ^ [Z5: complex] :
% 0.29/0.64                  ( ( power_power_complex @ Z5 @ N2 )
% 0.29/0.64                  = one_one_complex ) ) )
% 0.29/0.64          = N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_roots_unity_eq
% 0.29/0.64  thf(fact_9679_set__decode__plus__power__2,axiom,
% 0.29/0.64      ! [N2: nat,Z: nat] :
% 0.29/0.64        ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 0.29/0.64       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 0.29/0.64          = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % set_decode_plus_power_2
% 0.29/0.64  thf(fact_9680_snd__divmod__integer,axiom,
% 0.29/0.64      ! [K: code_integer,L: code_integer] :
% 0.29/0.64        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 0.29/0.64        = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 0.29/0.64  
% 0.29/0.64  % snd_divmod_integer
% 0.29/0.64  thf(fact_9681_snd__divmod__abs,axiom,
% 0.29/0.64      ! [K: code_integer,L: code_integer] :
% 0.29/0.64        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 0.29/0.64        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % snd_divmod_abs
% 0.29/0.64  thf(fact_9682_atLeastAtMostPlus1__int__conv,axiom,
% 0.29/0.64      ! [M: int,N2: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.29/0.64       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 0.29/0.64          = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastAtMostPlus1_int_conv
% 0.29/0.64  thf(fact_9683_minus__one__mod__numeral,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.64        = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % minus_one_mod_numeral
% 0.29/0.64  thf(fact_9684_one__mod__minus__numeral,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % one_mod_minus_numeral
% 0.29/0.64  thf(fact_9685_minus__numeral__mod__numeral,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.64        = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % minus_numeral_mod_numeral
% 0.29/0.64  thf(fact_9686_numeral__mod__minus__numeral,axiom,
% 0.29/0.64      ! [M: num,N2: num] :
% 0.29/0.64        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % numeral_mod_minus_numeral
% 0.29/0.64  thf(fact_9687_Divides_Oadjust__mod__def,axiom,
% 0.29/0.64      ( adjust_mod
% 0.29/0.64      = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Divides.adjust_mod_def
% 0.29/0.64  thf(fact_9688_and__int_Oelims,axiom,
% 0.29/0.64      ! [X4: int,Xa: int,Y: int] :
% 0.29/0.64        ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( uminus_uminus_int
% 0.29/0.64                @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.29/0.64          & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( plus_plus_int
% 0.29/0.64                @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.29/0.64                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_int.elims
% 0.29/0.64  thf(fact_9689_and__int_Osimps,axiom,
% 0.29/0.64      ( bit_se725231765392027082nd_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] :
% 0.29/0.64            ( if_int
% 0.29/0.64            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64            @ ( uminus_uminus_int
% 0.29/0.64              @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.29/0.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.29/0.64            @ ( plus_plus_int
% 0.29/0.64              @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.29/0.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.29/0.64              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_int.simps
% 0.29/0.64  thf(fact_9690_bezw_Oelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 0.29/0.64        ( ( ( bezw @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( ( Xa = zero_zero_nat )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.29/0.64          & ( ( Xa != zero_zero_nat )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezw.elims
% 0.29/0.64  thf(fact_9691_simp__from__to,axiom,
% 0.29/0.64      ( set_or1266510415728281911st_int
% 0.29/0.64      = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % simp_from_to
% 0.29/0.64  thf(fact_9692_bezw__non__0,axiom,
% 0.29/0.64      ! [Y: nat,X4: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.29/0.64       => ( ( bezw @ X4 @ Y )
% 0.29/0.64          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezw_non_0
% 0.29/0.64  thf(fact_9693_bezw_Osimps,axiom,
% 0.29/0.64      ( bezw
% 0.29/0.64      = ( ^ [X: nat,Y5: nat] : ( if_Pro3027730157355071871nt_int @ ( Y5 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y5 ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezw.simps
% 0.29/0.64  thf(fact_9694_bezw_Opelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 0.29/0.64        ( ( ( bezw @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 0.29/0.64         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.29/0.64                & ( ( Xa != zero_zero_nat )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) )
% 0.29/0.64             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezw.pelims
% 0.29/0.64  thf(fact_9695_and__int_Opsimps,axiom,
% 0.29/0.64      ! [K: int,L: int] :
% 0.29/0.64        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.29/0.64       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.29/0.64              = ( uminus_uminus_int
% 0.29/0.64                @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.29/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.29/0.64          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.29/0.64              = ( plus_plus_int
% 0.29/0.64                @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.29/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.29/0.64                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_int.psimps
% 0.29/0.64  thf(fact_9696_and__int_Opelims,axiom,
% 0.29/0.64      ! [X4: int,Xa: int,Y: int] :
% 0.29/0.64        ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 0.29/0.64         => ~ ( ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( uminus_uminus_int
% 0.29/0.64                      @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.64                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.29/0.64                & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( plus_plus_int
% 0.29/0.64                      @ ( zero_n2684676970156552555ol_int
% 0.29/0.64                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 0.29/0.64                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.29/0.64                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.29/0.64             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_int.pelims
% 0.29/0.64  thf(fact_9697_lessThan__0,axiom,
% 0.29/0.64      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.29/0.64      = bot_bot_set_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % lessThan_0
% 0.29/0.64  thf(fact_9698_atLeastLessThan__singleton,axiom,
% 0.29/0.64      ! [M: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.29/0.64        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThan_singleton
% 0.29/0.64  thf(fact_9699_atMost__0,axiom,
% 0.29/0.64      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.29/0.64      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atMost_0
% 0.29/0.64  thf(fact_9700_bot__enat__def,axiom,
% 0.29/0.64      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 0.29/0.64  
% 0.29/0.64  % bot_enat_def
% 0.29/0.64  thf(fact_9701_bot__nat__def,axiom,
% 0.29/0.64      bot_bot_nat = zero_zero_nat ).
% 0.29/0.64  
% 0.29/0.64  % bot_nat_def
% 0.29/0.64  thf(fact_9702_atLeastLessThan0,axiom,
% 0.29/0.64      ! [M: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.29/0.64        = bot_bot_set_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThan0
% 0.29/0.64  thf(fact_9703_lessThan__empty__iff,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ( set_ord_lessThan_nat @ N2 )
% 0.29/0.64          = bot_bot_set_nat )
% 0.29/0.64        = ( N2 = zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % lessThan_empty_iff
% 0.29/0.64  thf(fact_9704_atLeastLessThanSuc,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64            = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 0.29/0.64            = bot_bot_set_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThanSuc
% 0.29/0.64  thf(fact_9705_atLeast1__lessThan__eq__remove0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.64        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeast1_lessThan_eq_remove0
% 0.29/0.64  thf(fact_9706_atLeast1__atMost__eq__remove0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 0.29/0.64        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeast1_atMost_eq_remove0
% 0.29/0.64  thf(fact_9707_atLeastLessThan__nat__numeral,axiom,
% 0.29/0.64      ! [M: nat,K: num] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.29/0.64         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.29/0.64         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.29/0.64            = bot_bot_set_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastLessThan_nat_numeral
% 0.29/0.64  thf(fact_9708_and__int_Opinduct,axiom,
% 0.29/0.64      ! [A0: int,A12: int,P: int > int > $o] :
% 0.29/0.64        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.29/0.64       => ( ! [K2: int,L4: int] :
% 0.29/0.64              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 0.29/0.64             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.29/0.64                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.29/0.64                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.29/0.64               => ( P @ K2 @ L4 ) ) )
% 0.29/0.64         => ( P @ A0 @ A12 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % and_int.pinduct
% 0.29/0.64  thf(fact_9709_normalize__def,axiom,
% 0.29/0.64      ( normalize
% 0.29/0.64      = ( ^ [P5: product_prod_int_int] :
% 0.29/0.64            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 0.29/0.64            @ ( if_Pro3027730157355071871nt_int
% 0.29/0.64              @ ( ( product_snd_int_int @ P5 )
% 0.29/0.64                = zero_zero_int )
% 0.29/0.64              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.29/0.64              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % normalize_def
% 0.29/0.64  thf(fact_9710_gcd__pos__int,axiom,
% 0.29/0.64      ! [M: int,N2: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 0.29/0.64        = ( ( M != zero_zero_int )
% 0.29/0.64          | ( N2 != zero_zero_int ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_pos_int
% 0.29/0.64  thf(fact_9711_gcd__red__int,axiom,
% 0.29/0.64      ( gcd_gcd_int
% 0.29/0.64      = ( ^ [X: int,Y5: int] : ( gcd_gcd_int @ Y5 @ ( modulo_modulo_int @ X @ Y5 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_red_int
% 0.29/0.64  thf(fact_9712_gcd__ge__0__int,axiom,
% 0.29/0.64      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X4 @ Y ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_ge_0_int
% 0.29/0.64  thf(fact_9713_gcd__le1__int,axiom,
% 0.29/0.64      ! [A: int,B: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.64       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_le1_int
% 0.29/0.64  thf(fact_9714_gcd__le2__int,axiom,
% 0.29/0.64      ! [B: int,A: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.64       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_le2_int
% 0.29/0.64  thf(fact_9715_gcd__cases__int,axiom,
% 0.29/0.64      ! [X4: int,Y: int,P: int > $o] :
% 0.29/0.64        ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.64         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.64           => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) )
% 0.29/0.64       => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.29/0.64           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.29/0.64             => ( P @ ( gcd_gcd_int @ X4 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.29/0.64         => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 0.29/0.64             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.29/0.64               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ Y ) ) ) )
% 0.29/0.64           => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 0.29/0.64               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.29/0.64                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.29/0.64             => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_cases_int
% 0.29/0.64  thf(fact_9716_gcd__unique__int,axiom,
% 0.29/0.64      ! [D: int,A: int,B: int] :
% 0.29/0.64        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.29/0.64          & ( dvd_dvd_int @ D @ A )
% 0.29/0.64          & ( dvd_dvd_int @ D @ B )
% 0.29/0.64          & ! [E3: int] :
% 0.29/0.64              ( ( ( dvd_dvd_int @ E3 @ A )
% 0.29/0.64                & ( dvd_dvd_int @ E3 @ B ) )
% 0.29/0.64             => ( dvd_dvd_int @ E3 @ D ) ) )
% 0.29/0.64        = ( D
% 0.29/0.64          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_unique_int
% 0.29/0.64  thf(fact_9717_gcd__non__0__int,axiom,
% 0.29/0.64      ! [Y: int,X4: int] :
% 0.29/0.64        ( ( ord_less_int @ zero_zero_int @ Y )
% 0.29/0.64       => ( ( gcd_gcd_int @ X4 @ Y )
% 0.29/0.64          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X4 @ Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_non_0_int
% 0.29/0.64  thf(fact_9718_gcd__code__int,axiom,
% 0.29/0.64      ( gcd_gcd_int
% 0.29/0.64      = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_code_int
% 0.29/0.64  thf(fact_9719_gcd__1__nat,axiom,
% 0.29/0.64      ! [M: nat] :
% 0.29/0.64        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 0.29/0.64        = one_one_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_1_nat
% 0.29/0.64  thf(fact_9720_gcd__Suc__0,axiom,
% 0.29/0.64      ! [M: nat] :
% 0.29/0.64        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.29/0.64        = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_Suc_0
% 0.29/0.64  thf(fact_9721_gcd__pos__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 0.29/0.64        = ( ( M != zero_zero_nat )
% 0.29/0.64          | ( N2 != zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_pos_nat
% 0.29/0.64  thf(fact_9722_gcd__red__nat,axiom,
% 0.29/0.64      ( gcd_gcd_nat
% 0.29/0.64      = ( ^ [X: nat,Y5: nat] : ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_red_nat
% 0.29/0.64  thf(fact_9723_gcd__le1__nat,axiom,
% 0.29/0.64      ! [A: nat,B: nat] :
% 0.29/0.64        ( ( A != zero_zero_nat )
% 0.29/0.64       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_le1_nat
% 0.29/0.64  thf(fact_9724_gcd__le2__nat,axiom,
% 0.29/0.64      ! [B: nat,A: nat] :
% 0.29/0.64        ( ( B != zero_zero_nat )
% 0.29/0.64       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_le2_nat
% 0.29/0.64  thf(fact_9725_gcd__diff1__nat,axiom,
% 0.29/0.64      ! [N2: nat,M: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/0.64       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 0.29/0.64          = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_diff1_nat
% 0.29/0.64  thf(fact_9726_gcd__diff2__nat,axiom,
% 0.29/0.64      ! [M: nat,N2: nat] :
% 0.29/0.64        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.64       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 0.29/0.64          = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_diff2_nat
% 0.29/0.64  thf(fact_9727_gcd__non__0__nat,axiom,
% 0.29/0.64      ! [Y: nat,X4: nat] :
% 0.29/0.64        ( ( Y != zero_zero_nat )
% 0.29/0.64       => ( ( gcd_gcd_nat @ X4 @ Y )
% 0.29/0.64          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_non_0_nat
% 0.29/0.64  thf(fact_9728_gcd__nat_Osimps,axiom,
% 0.29/0.64      ( gcd_gcd_nat
% 0.29/0.64      = ( ^ [X: nat,Y5: nat] : ( if_nat @ ( Y5 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_nat.simps
% 0.29/0.64  thf(fact_9729_gcd__nat_Oelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: nat] :
% 0.29/0.64        ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( ( Xa = zero_zero_nat )
% 0.29/0.64           => ( Y = X4 ) )
% 0.29/0.64          & ( ( Xa != zero_zero_nat )
% 0.29/0.64           => ( Y
% 0.29/0.64              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_nat.elims
% 0.29/0.64  thf(fact_9730_bezout__nat,axiom,
% 0.29/0.64      ! [A: nat,B: nat] :
% 0.29/0.64        ( ( A != zero_zero_nat )
% 0.29/0.64       => ? [X5: nat,Y3: nat] :
% 0.29/0.64            ( ( times_times_nat @ A @ X5 )
% 0.29/0.64            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezout_nat
% 0.29/0.64  thf(fact_9731_bezout__gcd__nat_H,axiom,
% 0.29/0.64      ! [B: nat,A: nat] :
% 0.29/0.64      ? [X5: nat,Y3: nat] :
% 0.29/0.64        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 0.29/0.64          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.29/0.64            = ( gcd_gcd_nat @ A @ B ) ) )
% 0.29/0.64        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 0.29/0.64          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.29/0.64            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % bezout_gcd_nat'
% 0.29/0.64  thf(fact_9732_gcd__code__integer,axiom,
% 0.29/0.64      ( gcd_gcd_Code_integer
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_code_integer
% 0.29/0.64  thf(fact_9733_nat__descend__induct,axiom,
% 0.29/0.64      ! [N2: nat,P: nat > $o,M: nat] :
% 0.29/0.64        ( ! [K2: nat] :
% 0.29/0.64            ( ( ord_less_nat @ N2 @ K2 )
% 0.29/0.64           => ( P @ K2 ) )
% 0.29/0.64       => ( ! [K2: nat] :
% 0.29/0.64              ( ( ord_less_eq_nat @ K2 @ N2 )
% 0.29/0.64             => ( ! [I: nat] :
% 0.29/0.64                    ( ( ord_less_nat @ K2 @ I )
% 0.29/0.64                   => ( P @ I ) )
% 0.29/0.64               => ( P @ K2 ) ) )
% 0.29/0.64         => ( P @ M ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_descend_induct
% 0.29/0.64  thf(fact_9734_gcd__nat_Opelims,axiom,
% 0.29/0.64      ! [X4: nat,Xa: nat,Y: nat] :
% 0.29/0.64        ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 0.29/0.64          = Y )
% 0.29/0.64       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 0.29/0.64         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.29/0.64                 => ( Y = X4 ) )
% 0.29/0.64                & ( ( Xa != zero_zero_nat )
% 0.29/0.64                 => ( Y
% 0.29/0.64                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) )
% 0.29/0.64             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % gcd_nat.pelims
% 0.29/0.64  thf(fact_9735_drop__bit__numeral__minus__bit1,axiom,
% 0.29/0.64      ! [L: num,K: num] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.64        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_numeral_minus_bit1
% 0.29/0.64  thf(fact_9736_finite__enumerate,axiom,
% 0.29/0.64      ! [S2: set_nat] :
% 0.29/0.64        ( ( finite_finite_nat @ S2 )
% 0.29/0.64       => ? [R2: nat > nat] :
% 0.29/0.64            ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 0.29/0.64            & ! [N6: nat] :
% 0.29/0.64                ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 0.29/0.64               => ( member_nat @ ( R2 @ N6 ) @ S2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_enumerate
% 0.29/0.64  thf(fact_9737_drop__bit__nonnegative__int__iff,axiom,
% 0.29/0.64      ! [N2: nat,K: int] :
% 0.29/0.64        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 0.29/0.64        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_nonnegative_int_iff
% 0.29/0.64  thf(fact_9738_drop__bit__negative__int__iff,axiom,
% 0.29/0.64      ! [N2: nat,K: int] :
% 0.29/0.64        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 0.29/0.64        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_negative_int_iff
% 0.29/0.64  thf(fact_9739_drop__bit__minus__one,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.64        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_minus_one
% 0.29/0.64  thf(fact_9740_drop__bit__Suc__minus__bit0,axiom,
% 0.29/0.64      ! [N2: nat,K: num] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.64        = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_Suc_minus_bit0
% 0.29/0.64  thf(fact_9741_drop__bit__numeral__minus__bit0,axiom,
% 0.29/0.64      ! [L: num,K: num] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.29/0.64        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_numeral_minus_bit0
% 0.29/0.64  thf(fact_9742_drop__bit__Suc__minus__bit1,axiom,
% 0.29/0.64      ! [N2: nat,K: num] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.29/0.64        = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_Suc_minus_bit1
% 0.29/0.64  thf(fact_9743_drop__bit__push__bit__int,axiom,
% 0.29/0.64      ! [M: nat,N2: nat,K: int] :
% 0.29/0.64        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 0.29/0.64        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_push_bit_int
% 0.29/0.64  thf(fact_9744_drop__bit__int__def,axiom,
% 0.29/0.64      ( bit_se8568078237143864401it_int
% 0.29/0.64      = ( ^ [N: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_int_def
% 0.29/0.64  thf(fact_9745_drop__bit__of__Suc__0,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/0.64        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_of_Suc_0
% 0.29/0.64  thf(fact_9746_drop__bit__nat__eq,axiom,
% 0.29/0.64      ! [N2: nat,K: int] :
% 0.29/0.64        ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 0.29/0.64        = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_nat_eq
% 0.29/0.64  thf(fact_9747_drop__bit__nat__def,axiom,
% 0.29/0.64      ( bit_se8570568707652914677it_nat
% 0.29/0.64      = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % drop_bit_nat_def
% 0.29/0.64  thf(fact_9748_card__greaterThanLessThan__int,axiom,
% 0.29/0.64      ! [L: int,U: int] :
% 0.29/0.64        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.29/0.64        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_greaterThanLessThan_int
% 0.29/0.64  thf(fact_9749_finite__greaterThanLessThan__int,axiom,
% 0.29/0.64      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_greaterThanLessThan_int
% 0.29/0.64  thf(fact_9750_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.29/0.64      ! [L: int,U: int] :
% 0.29/0.64        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.29/0.64        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.29/0.64  thf(fact_9751_xor__minus__numerals_I1_J,axiom,
% 0.29/0.64      ! [N2: num,K: int] :
% 0.29/0.64        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % xor_minus_numerals(1)
% 0.29/0.64  thf(fact_9752_xor__minus__numerals_I2_J,axiom,
% 0.29/0.64      ! [K: int,N2: num] :
% 0.29/0.64        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % xor_minus_numerals(2)
% 0.29/0.64  thf(fact_9753_finite__greaterThanLessThan,axiom,
% 0.29/0.64      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % finite_greaterThanLessThan
% 0.29/0.64  thf(fact_9754_card__greaterThanLessThan,axiom,
% 0.29/0.64      ! [L: nat,U: nat] :
% 0.29/0.64        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.29/0.64        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % card_greaterThanLessThan
% 0.29/0.64  thf(fact_9755_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.29/0.64      ! [L: nat,U: nat] :
% 0.29/0.64        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.29/0.64        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.29/0.64  
% 0.29/0.64  % atLeastSucLessThan_greaterThanLessThan
% 0.29/0.64  thf(fact_9756_tanh__real__bounds,axiom,
% 0.29/0.64      ! [X4: real] : ( member_real @ ( tanh_real @ X4 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 0.29/0.64  
% 0.29/0.64  % tanh_real_bounds
% 0.29/0.64  thf(fact_9757_sub__BitM__One__eq,axiom,
% 0.29/0.64      ! [N2: num] :
% 0.29/0.64        ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 0.29/0.64        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % sub_BitM_One_eq
% 0.29/0.64  thf(fact_9758_Suc__funpow,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( compow_nat_nat @ N2 @ suc )
% 0.29/0.64        = ( plus_plus_nat @ N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % Suc_funpow
% 0.29/0.64  thf(fact_9759_nat__of__integer__non__positive,axiom,
% 0.29/0.64      ! [K: code_integer] :
% 0.29/0.64        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.29/0.64       => ( ( code_nat_of_integer @ K )
% 0.29/0.64          = zero_zero_nat ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_of_integer_non_positive
% 0.29/0.64  thf(fact_9760_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.29/0.64      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.29/0.64      @ ^ [X: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X )
% 0.29/0.64      @ ^ [X: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X ) ) ).
% 0.29/0.64  
% 0.29/0.64  % max_nat.semilattice_neutr_order_axioms
% 0.29/0.64  thf(fact_9761_nat__of__integer__code__post_I3_J,axiom,
% 0.29/0.64      ! [K: num] :
% 0.29/0.64        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.29/0.64        = ( numeral_numeral_nat @ K ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_of_integer_code_post(3)
% 0.29/0.64  thf(fact_9762_nat__of__integer__code__post_I2_J,axiom,
% 0.29/0.64      ( ( code_nat_of_integer @ one_one_Code_integer )
% 0.29/0.64      = one_one_nat ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_of_integer_code_post(2)
% 0.29/0.64  thf(fact_9763_nat__of__integer__code,axiom,
% 0.29/0.64      ( code_nat_of_integer
% 0.29/0.64      = ( ^ [K3: code_integer] :
% 0.29/0.64            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.29/0.64            @ ( produc1555791787009142072er_nat
% 0.29/0.64              @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 0.29/0.64              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % nat_of_integer_code
% 0.29/0.64  thf(fact_9764_int__of__integer__code,axiom,
% 0.29/0.64      ( code_int_of_integer
% 0.29/0.64      = ( ^ [K3: code_integer] :
% 0.29/0.64            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 0.29/0.64            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.29/0.64              @ ( produc1553301316500091796er_int
% 0.29/0.64                @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 0.29/0.64                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % int_of_integer_code
% 0.29/0.64  thf(fact_9765_modulo__integer_Orep__eq,axiom,
% 0.29/0.64      ! [X4: code_integer,Xa: code_integer] :
% 0.29/0.64        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X4 @ Xa ) )
% 0.29/0.64        = ( modulo_modulo_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % modulo_integer.rep_eq
% 0.29/0.64  thf(fact_9766_integer__less__iff,axiom,
% 0.29/0.64      ( ord_le6747313008572928689nteger
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % integer_less_iff
% 0.29/0.64  thf(fact_9767_less__integer_Orep__eq,axiom,
% 0.29/0.64      ( ord_le6747313008572928689nteger
% 0.29/0.64      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_integer.rep_eq
% 0.29/0.64  thf(fact_9768_less__eq__integer_Orep__eq,axiom,
% 0.29/0.64      ( ord_le3102999989581377725nteger
% 0.29/0.64      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_integer.rep_eq
% 0.29/0.64  thf(fact_9769_integer__less__eq__iff,axiom,
% 0.29/0.64      ( ord_le3102999989581377725nteger
% 0.29/0.64      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % integer_less_eq_iff
% 0.29/0.64  thf(fact_9770_times__int_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 0.29/0.64        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 0.29/0.64        = ( abs_Integ
% 0.29/0.64          @ ( produc27273713700761075at_nat
% 0.29/0.64            @ ^ [X: nat,Y5: nat] :
% 0.29/0.64                ( produc2626176000494625587at_nat
% 0.29/0.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 0.29/0.64            @ Xa
% 0.29/0.64            @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % times_int.abs_eq
% 0.29/0.64  thf(fact_9771_one__int__def,axiom,
% 0.29/0.64      ( one_one_int
% 0.29/0.64      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % one_int_def
% 0.29/0.64  thf(fact_9772_less__int_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 0.29/0.64        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 0.29/0.64        = ( produc8739625826339149834_nat_o
% 0.29/0.64          @ ^ [X: nat,Y5: nat] :
% 0.29/0.64              ( produc6081775807080527818_nat_o
% 0.29/0.64              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 0.29/0.64          @ Xa
% 0.29/0.64          @ X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_int.abs_eq
% 0.29/0.64  thf(fact_9773_less__eq__int_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 0.29/0.64        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 0.29/0.64        = ( produc8739625826339149834_nat_o
% 0.29/0.64          @ ^ [X: nat,Y5: nat] :
% 0.29/0.64              ( produc6081775807080527818_nat_o
% 0.29/0.64              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 0.29/0.64          @ Xa
% 0.29/0.64          @ X4 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % less_eq_int.abs_eq
% 0.29/0.64  thf(fact_9774_plus__int_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 0.29/0.64        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 0.29/0.64        = ( abs_Integ
% 0.29/0.64          @ ( produc27273713700761075at_nat
% 0.29/0.64            @ ^ [X: nat,Y5: nat] :
% 0.29/0.64                ( produc2626176000494625587at_nat
% 0.29/0.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 0.29/0.64            @ Xa
% 0.29/0.64            @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % plus_int.abs_eq
% 0.29/0.64  thf(fact_9775_minus__int_Oabs__eq,axiom,
% 0.29/0.64      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 0.29/0.64        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 0.29/0.64        = ( abs_Integ
% 0.29/0.64          @ ( produc27273713700761075at_nat
% 0.29/0.64            @ ^ [X: nat,Y5: nat] :
% 0.29/0.64                ( produc2626176000494625587at_nat
% 0.29/0.64                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 0.29/0.64            @ Xa
% 0.29/0.64            @ X4 ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % minus_int.abs_eq
% 0.29/0.64  thf(fact_9776_num__of__nat_Osimps_I2_J,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ( ( num_of_nat @ ( suc @ N2 ) )
% 0.29/0.64            = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 0.29/0.64        & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64         => ( ( num_of_nat @ ( suc @ N2 ) )
% 0.29/0.64            = one ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % num_of_nat.simps(2)
% 0.29/0.64  thf(fact_9777_pred__nat__def,axiom,
% 0.29/0.64      ( pred_nat
% 0.29/0.64      = ( collec3392354462482085612at_nat
% 0.29/0.64        @ ( produc6081775807080527818_nat_o
% 0.29/0.64          @ ^ [M6: nat,N: nat] :
% 0.29/0.64              ( N
% 0.29/0.64              = ( suc @ M6 ) ) ) ) ) ).
% 0.29/0.64  
% 0.29/0.64  % pred_nat_def
% 0.29/0.64  thf(fact_9778_num__of__nat__numeral__eq,axiom,
% 0.29/0.64      ! [Q3: num] :
% 0.29/0.64        ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 0.29/0.64        = Q3 ) ).
% 0.29/0.64  
% 0.29/0.64  % num_of_nat_numeral_eq
% 0.29/0.64  thf(fact_9779_num__of__nat_Osimps_I1_J,axiom,
% 0.29/0.64      ( ( num_of_nat @ zero_zero_nat )
% 0.29/0.64      = one ) ).
% 0.29/0.64  
% 0.29/0.64  % num_of_nat.simps(1)
% 0.29/0.64  thf(fact_9780_numeral__num__of__nat,axiom,
% 0.29/0.64      ! [N2: nat] :
% 0.29/0.64        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.64       => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 0.29/0.64          = N2 ) ) ).
% 0.29/0.64  
% 0.29/0.64  % numeral_num_of_nat
% 0.29/0.64  thf(fact_9781_num__of__nat__One,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 0.29/0.65       => ( ( num_of_nat @ N2 )
% 0.29/0.65          = one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % num_of_nat_One
% 0.29/0.65  thf(fact_9782_num__of__nat__double,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 0.29/0.65          = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % num_of_nat_double
% 0.29/0.65  thf(fact_9783_num__of__nat__plus__distrib,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 0.29/0.65            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % num_of_nat_plus_distrib
% 0.29/0.65  thf(fact_9784_less__eq__int_Orep__eq,axiom,
% 0.29/0.65      ( ord_less_eq_int
% 0.29/0.65      = ( ^ [X: int,Xa4: int] :
% 0.29/0.65            ( produc8739625826339149834_nat_o
% 0.29/0.65            @ ^ [Y5: nat,Z5: nat] :
% 0.29/0.65                ( produc6081775807080527818_nat_o
% 0.29/0.65                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 0.29/0.65            @ ( rep_Integ @ X )
% 0.29/0.65            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % less_eq_int.rep_eq
% 0.29/0.65  thf(fact_9785_less__int_Orep__eq,axiom,
% 0.29/0.65      ( ord_less_int
% 0.29/0.65      = ( ^ [X: int,Xa4: int] :
% 0.29/0.65            ( produc8739625826339149834_nat_o
% 0.29/0.65            @ ^ [Y5: nat,Z5: nat] :
% 0.29/0.65                ( produc6081775807080527818_nat_o
% 0.29/0.65                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 0.29/0.65            @ ( rep_Integ @ X )
% 0.29/0.65            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % less_int.rep_eq
% 0.29/0.65  thf(fact_9786_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.65        ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( X4
% 0.29/0.65                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65           => ( Xa = one_one_nat ) )
% 0.29/0.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65               => ( ( Deg2 = Xa )
% 0.29/0.65                  & ! [X5: vEBT_VEBT] :
% 0.29/0.65                      ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                     => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                  & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                  & ( case_o184042715313410164at_nat
% 0.29/0.65                    @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                      & ! [X: vEBT_VEBT] :
% 0.29/0.65                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                         => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                    @ ( produc6081775807080527818_nat_o
% 0.29/0.65                      @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                          ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                          & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                          & ! [I3: nat] :
% 0.29/0.65                              ( ( 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 ) ) ) ) ) )
% 0.29/0.65                             => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                          & ( ( Mi2 = Ma2 )
% 0.29/0.65                           => ! [X: vEBT_VEBT] :
% 0.29/0.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                          & ( ( Mi2 != Ma2 )
% 0.29/0.65                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                              & ! [X: nat] :
% 0.29/0.65                                  ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                   => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                      & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                    @ Mima ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.elims(3)
% 0.29/0.65  thf(fact_9787_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.65        ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( X4
% 0.29/0.65                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65           => ( Xa != one_one_nat ) )
% 0.29/0.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65               => ~ ( ( Deg2 = Xa )
% 0.29/0.65                    & ! [X2: vEBT_VEBT] :
% 0.29/0.65                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                       => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                    & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                    & ( case_o184042715313410164at_nat
% 0.29/0.65                      @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                        & ! [X: vEBT_VEBT] :
% 0.29/0.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                           => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                      @ ( produc6081775807080527818_nat_o
% 0.29/0.65                        @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                            ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                            & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                            & ! [I3: nat] :
% 0.29/0.65                                ( ( 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 ) ) ) ) ) )
% 0.29/0.65                               => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                  = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                            & ( ( Mi2 = Ma2 )
% 0.29/0.65                             => ! [X: vEBT_VEBT] :
% 0.29/0.65                                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                                 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                            & ( ( Mi2 != Ma2 )
% 0.29/0.65                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                                & ! [X: nat] :
% 0.29/0.65                                    ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                     => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                        & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                      @ Mima ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.elims(2)
% 0.29/0.65  thf(fact_9788_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.65        ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( X4
% 0.29/0.65                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65           => ( Y
% 0.29/0.65              = ( Xa != one_one_nat ) ) )
% 0.29/0.65         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65               => ( Y
% 0.29/0.65                  = ( ~ ( ( Deg2 = Xa )
% 0.29/0.65                        & ! [X: vEBT_VEBT] :
% 0.29/0.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                        & ( case_o184042715313410164at_nat
% 0.29/0.65                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                            & ! [X: vEBT_VEBT] :
% 0.29/0.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                          @ ( produc6081775807080527818_nat_o
% 0.29/0.65                            @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                & ! [I3: nat] :
% 0.29/0.65                                    ( ( 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 ) ) ) ) ) )
% 0.29/0.65                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                                & ( ( Mi2 = Ma2 )
% 0.29/0.65                                 => ! [X: vEBT_VEBT] :
% 0.29/0.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                                & ( ( Mi2 != Ma2 )
% 0.29/0.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                                    & ! [X: nat] :
% 0.29/0.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                         => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                          @ Mima ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.elims(1)
% 0.29/0.65  thf(fact_9789_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.29/0.65      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 0.29/0.65        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 0.29/0.65        = ( ( Deg = Deg4 )
% 0.29/0.65          & ! [X: vEBT_VEBT] :
% 0.29/0.65              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.29/0.65             => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.29/0.65            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65          & ( case_o184042715313410164at_nat
% 0.29/0.65            @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X3 )
% 0.29/0.65              & ! [X: vEBT_VEBT] :
% 0.29/0.65                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.29/0.65                 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65            @ ( produc6081775807080527818_nat_o
% 0.29/0.65              @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                  ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                  & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.65                  & ! [I3: nat] :
% 0.29/0.65                      ( ( 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 ) ) ) ) ) )
% 0.29/0.65                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X3 ) )
% 0.29/0.65                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.29/0.65                  & ( ( Mi2 = Ma2 )
% 0.29/0.65                   => ! [X: vEBT_VEBT] :
% 0.29/0.65                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.29/0.65                       => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                  & ( ( Mi2 != Ma2 )
% 0.29/0.65                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma2 )
% 0.29/0.65                      & ! [X: nat] :
% 0.29/0.65                          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.29/0.65                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 0.29/0.65                           => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65            @ Mima2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.simps(2)
% 0.29/0.65  thf(fact_9790_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 0.29/0.65        ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.65         => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65               => ( ( Y
% 0.29/0.65                    = ( Xa = one_one_nat ) )
% 0.29/0.65                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 0.29/0.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                  ( ( X4
% 0.29/0.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65                 => ( ( Y
% 0.29/0.65                      = ( ( Deg2 = Xa )
% 0.29/0.65                        & ! [X: vEBT_VEBT] :
% 0.29/0.65                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                        & ( case_o184042715313410164at_nat
% 0.29/0.65                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                            & ! [X: vEBT_VEBT] :
% 0.29/0.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                          @ ( produc6081775807080527818_nat_o
% 0.29/0.65                            @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                & ! [I3: nat] :
% 0.29/0.65                                    ( ( 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 ) ) ) ) ) )
% 0.29/0.65                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                                & ( ( Mi2 = Ma2 )
% 0.29/0.65                                 => ! [X: vEBT_VEBT] :
% 0.29/0.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                                & ( ( Mi2 != Ma2 )
% 0.29/0.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                                    & ! [X: nat] :
% 0.29/0.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                         => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                          @ Mima ) ) )
% 0.29/0.65                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.pelims(1)
% 0.29/0.65  thf(fact_9791_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.65        ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.65         => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 0.29/0.65                 => ( Xa != one_one_nat ) ) )
% 0.29/0.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                  ( ( X4
% 0.29/0.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 0.29/0.65                   => ~ ( ( Deg2 = Xa )
% 0.29/0.65                        & ! [X2: vEBT_VEBT] :
% 0.29/0.65                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                        & ( case_o184042715313410164at_nat
% 0.29/0.65                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                            & ! [X: vEBT_VEBT] :
% 0.29/0.65                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                          @ ( produc6081775807080527818_nat_o
% 0.29/0.65                            @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                & ! [I3: nat] :
% 0.29/0.65                                    ( ( 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 ) ) ) ) ) )
% 0.29/0.65                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                                & ( ( Mi2 = Ma2 )
% 0.29/0.65                                 => ! [X: vEBT_VEBT] :
% 0.29/0.65                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                                & ( ( Mi2 != Ma2 )
% 0.29/0.65                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                                    & ! [X: nat] :
% 0.29/0.65                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                         => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                          @ Mima ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.pelims(2)
% 0.29/0.65  thf(fact_9792_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.29/0.65      ! [X4: vEBT_VEBT,Xa: nat] :
% 0.29/0.65        ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 0.29/0.65       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 0.29/0.65         => ( ! [Uu2: $o,Uv2: $o] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.29/0.65               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 0.29/0.65                 => ( Xa = one_one_nat ) ) )
% 0.29/0.65           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 0.29/0.65                  ( ( X4
% 0.29/0.65                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 0.29/0.65                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 0.29/0.65                   => ( ( Deg2 = Xa )
% 0.29/0.65                      & ! [X5: vEBT_VEBT] :
% 0.29/0.65                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                         => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                      & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.29/0.65                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65                      & ( case_o184042715313410164at_nat
% 0.29/0.65                        @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 0.29/0.65                          & ! [X: vEBT_VEBT] :
% 0.29/0.65                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                             => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                        @ ( produc6081775807080527818_nat_o
% 0.29/0.65                          @ ^ [Mi2: nat,Ma2: nat] :
% 0.29/0.65                              ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.29/0.65                              & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                              & ! [I3: nat] :
% 0.29/0.65                                  ( ( 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 ) ) ) ) ) )
% 0.29/0.65                                 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 0.29/0.65                                    = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.29/0.65                              & ( ( Mi2 = Ma2 )
% 0.29/0.65                               => ! [X: vEBT_VEBT] :
% 0.29/0.65                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.29/0.65                                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 0.29/0.65                              & ( ( Mi2 != Ma2 )
% 0.29/0.65                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 0.29/0.65                                  & ! [X: nat] :
% 0.29/0.65                                      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.29/0.65                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 0.29/0.65                                       => ( ( ord_less_nat @ Mi2 @ X )
% 0.29/0.65                                          & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 0.29/0.65                        @ Mima ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % VEBT_internal.valid'.pelims(3)
% 0.29/0.65  thf(fact_9793_Sup__int__def,axiom,
% 0.29/0.65      ( complete_Sup_Sup_int
% 0.29/0.65      = ( ^ [X3: set_int] :
% 0.29/0.65            ( the_int
% 0.29/0.65            @ ^ [X: int] :
% 0.29/0.65                ( ( member_int @ X @ X3 )
% 0.29/0.65                & ! [Y5: int] :
% 0.29/0.65                    ( ( member_int @ Y5 @ X3 )
% 0.29/0.65                   => ( ord_less_eq_int @ Y5 @ X ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Sup_int_def
% 0.29/0.65  thf(fact_9794_take__bit__numeral__minus__numeral__int,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int
% 0.29/0.65          @ ^ [Q5: 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 @ Q5 ) ) )
% 0.29/0.65          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_numeral_minus_numeral_int
% 0.29/0.65  thf(fact_9795_and__minus__numerals_I7_J,axiom,
% 0.29/0.65      ! [N2: num,M: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_minus_numerals(7)
% 0.29/0.65  thf(fact_9796_take__bit__num__simps_I1_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.29/0.65        = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(1)
% 0.29/0.65  thf(fact_9797_take__bit__num__simps_I2_J,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 0.29/0.65        = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(2)
% 0.29/0.65  thf(fact_9798_take__bit__num__simps_I5_J,axiom,
% 0.29/0.65      ! [R3: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ one )
% 0.29/0.65        = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(5)
% 0.29/0.65  thf(fact_9799_take__bit__num__simps_I3_J,axiom,
% 0.29/0.65      ! [N2: nat,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 0.29/0.65        = ( case_o6005452278849405969um_num @ none_num
% 0.29/0.65          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.29/0.65          @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(3)
% 0.29/0.65  thf(fact_9800_take__bit__num__simps_I4_J,axiom,
% 0.29/0.65      ! [N2: nat,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 0.29/0.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(4)
% 0.29/0.65  thf(fact_9801_take__bit__num__simps_I6_J,axiom,
% 0.29/0.65      ! [R3: num,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 0.29/0.65        = ( case_o6005452278849405969um_num @ none_num
% 0.29/0.65          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.29/0.65          @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(6)
% 0.29/0.65  thf(fact_9802_take__bit__num__simps_I7_J,axiom,
% 0.29/0.65      ! [R3: num,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 0.29/0.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_simps(7)
% 0.29/0.65  thf(fact_9803_and__minus__numerals_I8_J,axiom,
% 0.29/0.65      ! [N2: num,M: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_minus_numerals(8)
% 0.29/0.65  thf(fact_9804_and__minus__numerals_I4_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_minus_numerals(4)
% 0.29/0.65  thf(fact_9805_and__minus__numerals_I3_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_minus_numerals(3)
% 0.29/0.65  thf(fact_9806_and__not__num_Osimps_I1_J,axiom,
% 0.29/0.65      ( ( bit_and_not_num @ one @ one )
% 0.29/0.65      = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(1)
% 0.29/0.65  thf(fact_9807_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 0.29/0.65      ! [N2: nat,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 0.29/0.65        = ( case_nat_option_num @ none_num
% 0.29/0.65          @ ^ [N: nat] :
% 0.29/0.65              ( case_o6005452278849405969um_num @ none_num
% 0.29/0.65              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.29/0.65              @ ( bit_take_bit_num @ N @ M ) )
% 0.29/0.65          @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Code_Abstract_Nat.take_bit_num_code(2)
% 0.29/0.65  thf(fact_9808_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( bit_take_bit_num @ N2 @ one )
% 0.29/0.65        = ( case_nat_option_num @ none_num
% 0.29/0.65          @ ^ [N: nat] : ( some_num @ one )
% 0.29/0.65          @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Code_Abstract_Nat.take_bit_num_code(1)
% 0.29/0.65  thf(fact_9809_and__not__num_Osimps_I2_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(2)
% 0.29/0.65  thf(fact_9810_and__not__num_Osimps_I4_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 0.29/0.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(4)
% 0.29/0.65  thf(fact_9811_GreatestI__ex__nat,axiom,
% 0.29/0.65      ! [P: nat > $o,B: nat] :
% 0.29/0.65        ( ? [X_1: nat] : ( P @ X_1 )
% 0.29/0.65       => ( ! [Y3: nat] :
% 0.29/0.65              ( ( P @ Y3 )
% 0.29/0.65             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.65         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % GreatestI_ex_nat
% 0.29/0.65  thf(fact_9812_Greatest__le__nat,axiom,
% 0.29/0.65      ! [P: nat > $o,K: nat,B: nat] :
% 0.29/0.65        ( ( P @ K )
% 0.29/0.65       => ( ! [Y3: nat] :
% 0.29/0.65              ( ( P @ Y3 )
% 0.29/0.65             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.65         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Greatest_le_nat
% 0.29/0.65  thf(fact_9813_GreatestI__nat,axiom,
% 0.29/0.65      ! [P: nat > $o,K: nat,B: nat] :
% 0.29/0.65        ( ( P @ K )
% 0.29/0.65       => ( ! [Y3: nat] :
% 0.29/0.65              ( ( P @ Y3 )
% 0.29/0.65             => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.65         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % GreatestI_nat
% 0.29/0.65  thf(fact_9814_and__not__num_Osimps_I3_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 0.29/0.65        = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(3)
% 0.29/0.65  thf(fact_9815_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 0.29/0.65      ! [N2: nat,M: num] :
% 0.29/0.65        ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 0.29/0.65        = ( case_nat_option_num @ none_num
% 0.29/0.65          @ ^ [N: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) )
% 0.29/0.65          @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Code_Abstract_Nat.take_bit_num_code(3)
% 0.29/0.65  thf(fact_9816_and__not__num_Osimps_I7_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 0.29/0.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(7)
% 0.29/0.65  thf(fact_9817_and__not__num__eq__Some__iff,axiom,
% 0.29/0.65      ! [M: num,N2: num,Q3: num] :
% 0.29/0.65        ( ( ( bit_and_not_num @ M @ N2 )
% 0.29/0.65          = ( some_num @ Q3 ) )
% 0.29/0.65        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65          = ( numeral_numeral_int @ Q3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num_eq_Some_iff
% 0.29/0.65  thf(fact_9818_and__not__num_Osimps_I8_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65          @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(8)
% 0.29/0.65  thf(fact_9819_and__not__num__eq__None__iff,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( bit_and_not_num @ M @ N2 )
% 0.29/0.65          = none_num )
% 0.29/0.65        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65          = zero_zero_int ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num_eq_None_iff
% 0.29/0.65  thf(fact_9820_int__numeral__not__and__num,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % int_numeral_not_and_num
% 0.29/0.65  thf(fact_9821_int__numeral__and__not__num,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % int_numeral_and_not_num
% 0.29/0.65  thf(fact_9822_take__bit__num__def,axiom,
% 0.29/0.65      ( bit_take_bit_num
% 0.29/0.65      = ( ^ [N: nat,M6: num] :
% 0.29/0.65            ( if_option_num
% 0.29/0.65            @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) )
% 0.29/0.65              = zero_zero_nat )
% 0.29/0.65            @ none_num
% 0.29/0.65            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_num_def
% 0.29/0.65  thf(fact_9823_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.29/0.65      ! [N2: nat,J: nat,I2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 0.29/0.65       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 0.29/0.65          = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nth_sorted_list_of_set_greaterThanLessThan
% 0.29/0.65  thf(fact_9824_and__not__num_Oelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_and_not_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ( X4 = one )
% 0.29/0.65           => ( ( Xa = one )
% 0.29/0.65             => ( Y != none_num ) ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ( ? [N3: num] :
% 0.29/0.65                    ( Xa
% 0.29/0.65                    = ( bit0 @ N3 ) )
% 0.29/0.65               => ( Y
% 0.29/0.65                 != ( some_num @ one ) ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ( ? [N3: num] :
% 0.29/0.65                      ( Xa
% 0.29/0.65                      = ( bit1 @ N3 ) )
% 0.29/0.65                 => ( Y != none_num ) ) )
% 0.29/0.65             => ( ! [M5: num] :
% 0.29/0.65                    ( ( X4
% 0.29/0.65                      = ( bit0 @ M5 ) )
% 0.29/0.65                   => ( ( Xa = one )
% 0.29/0.65                     => ( Y
% 0.29/0.65                       != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ! [N3: num] :
% 0.29/0.65                          ( ( Xa
% 0.29/0.65                            = ( bit0 @ N3 ) )
% 0.29/0.65                         => ( Y
% 0.29/0.65                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit1 @ N3 ) )
% 0.29/0.65                           => ( Y
% 0.29/0.65                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                   => ( ! [M5: num] :
% 0.29/0.65                          ( ( X4
% 0.29/0.65                            = ( bit1 @ M5 ) )
% 0.29/0.65                         => ( ( Xa = one )
% 0.29/0.65                           => ( Y
% 0.29/0.65                             != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ! [N3: num] :
% 0.29/0.65                                ( ( Xa
% 0.29/0.65                                  = ( bit0 @ N3 ) )
% 0.29/0.65                               => ( Y
% 0.29/0.65                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65                                    @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                       => ~ ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit1 @ N3 ) )
% 0.29/0.65                                 => ( Y
% 0.29/0.65                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.elims
% 0.29/0.65  thf(fact_9825_Bit__Operations_Otake__bit__num__code,axiom,
% 0.29/0.65      ( bit_take_bit_num
% 0.29/0.65      = ( ^ [N: nat,M6: num] :
% 0.29/0.65            ( produc478579273971653890on_num
% 0.29/0.65            @ ^ [A3: nat,X: num] :
% 0.29/0.65                ( case_nat_option_num @ none_num
% 0.29/0.65                @ ^ [O: nat] :
% 0.29/0.65                    ( case_num_option_num @ ( some_num @ one )
% 0.29/0.65                    @ ^ [P5: num] :
% 0.29/0.65                        ( case_o6005452278849405969um_num @ none_num
% 0.29/0.65                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.29/0.65                        @ ( bit_take_bit_num @ O @ P5 ) )
% 0.29/0.65                    @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 0.29/0.65                    @ X )
% 0.29/0.65                @ A3 )
% 0.29/0.65            @ ( product_Pair_nat_num @ N @ M6 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Bit_Operations.take_bit_num_code
% 0.29/0.65  thf(fact_9826_and__not__num_Osimps_I5_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(5)
% 0.29/0.65  thf(fact_9827_and__not__num_Osimps_I9_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(9)
% 0.29/0.65  thf(fact_9828_and__not__num_Osimps_I6_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.simps(6)
% 0.29/0.65  thf(fact_9829_and__not__num_Opelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_and_not_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ( ( Xa = one )
% 0.29/0.65               => ( ( Y = none_num )
% 0.29/0.65                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ! [N3: num] :
% 0.29/0.65                    ( ( Xa
% 0.29/0.65                      = ( bit0 @ N3 ) )
% 0.29/0.65                   => ( ( Y
% 0.29/0.65                        = ( some_num @ one ) )
% 0.29/0.65                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65             => ( ( ( X4 = one )
% 0.29/0.65                 => ! [N3: num] :
% 0.29/0.65                      ( ( Xa
% 0.29/0.65                        = ( bit1 @ N3 ) )
% 0.29/0.65                     => ( ( Y = none_num )
% 0.29/0.65                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ( ( Xa = one )
% 0.29/0.65                       => ( ( Y
% 0.29/0.65                            = ( some_num @ ( bit0 @ M5 ) ) )
% 0.29/0.65                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit0 @ N3 ) )
% 0.29/0.65                           => ( ( Y
% 0.29/0.65                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 0.29/0.65                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                   => ( ! [M5: num] :
% 0.29/0.65                          ( ( X4
% 0.29/0.65                            = ( bit0 @ M5 ) )
% 0.29/0.65                         => ! [N3: num] :
% 0.29/0.65                              ( ( Xa
% 0.29/0.65                                = ( bit1 @ N3 ) )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ( ( Xa = one )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( some_num @ ( bit0 @ M5 ) ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                       => ( ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit0 @ N3 ) )
% 0.29/0.65                                 => ( ( Y
% 0.29/0.65                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65                                        @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 0.29/0.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                         => ~ ! [M5: num] :
% 0.29/0.65                                ( ( X4
% 0.29/0.65                                  = ( bit1 @ M5 ) )
% 0.29/0.65                               => ! [N3: num] :
% 0.29/0.65                                    ( ( Xa
% 0.29/0.65                                      = ( bit1 @ N3 ) )
% 0.29/0.65                                   => ( ( Y
% 0.29/0.65                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 0.29/0.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_not_num.pelims
% 0.29/0.65  thf(fact_9830_and__num_Oelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ( X4 = one )
% 0.29/0.65           => ( ( Xa = one )
% 0.29/0.65             => ( Y
% 0.29/0.65               != ( some_num @ one ) ) ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ( ? [N3: num] :
% 0.29/0.65                    ( Xa
% 0.29/0.65                    = ( bit0 @ N3 ) )
% 0.29/0.65               => ( Y != none_num ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ( ? [N3: num] :
% 0.29/0.65                      ( Xa
% 0.29/0.65                      = ( bit1 @ N3 ) )
% 0.29/0.65                 => ( Y
% 0.29/0.65                   != ( some_num @ one ) ) ) )
% 0.29/0.65             => ( ( ? [M5: num] :
% 0.29/0.65                      ( X4
% 0.29/0.65                      = ( bit0 @ M5 ) )
% 0.29/0.65                 => ( ( Xa = one )
% 0.29/0.65                   => ( Y != none_num ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ! [N3: num] :
% 0.29/0.65                          ( ( Xa
% 0.29/0.65                            = ( bit0 @ N3 ) )
% 0.29/0.65                         => ( Y
% 0.29/0.65                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit1 @ N3 ) )
% 0.29/0.65                           => ( Y
% 0.29/0.65                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                   => ( ( ? [M5: num] :
% 0.29/0.65                            ( X4
% 0.29/0.65                            = ( bit1 @ M5 ) )
% 0.29/0.65                       => ( ( Xa = one )
% 0.29/0.65                         => ( Y
% 0.29/0.65                           != ( some_num @ one ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ! [N3: num] :
% 0.29/0.65                                ( ( Xa
% 0.29/0.65                                  = ( bit0 @ N3 ) )
% 0.29/0.65                               => ( Y
% 0.29/0.65                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                       => ~ ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit1 @ N3 ) )
% 0.29/0.65                                 => ( Y
% 0.29/0.65                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65                                      @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.elims
% 0.29/0.65  thf(fact_9831_xor__num_Oelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ( X4 = one )
% 0.29/0.65           => ( ( Xa = one )
% 0.29/0.65             => ( Y != none_num ) ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ! [N3: num] :
% 0.29/0.65                  ( ( Xa
% 0.29/0.65                    = ( bit0 @ N3 ) )
% 0.29/0.65                 => ( Y
% 0.29/0.65                   != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ! [N3: num] :
% 0.29/0.65                    ( ( Xa
% 0.29/0.65                      = ( bit1 @ N3 ) )
% 0.29/0.65                   => ( Y
% 0.29/0.65                     != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 0.29/0.65             => ( ! [M5: num] :
% 0.29/0.65                    ( ( X4
% 0.29/0.65                      = ( bit0 @ M5 ) )
% 0.29/0.65                   => ( ( Xa = one )
% 0.29/0.65                     => ( Y
% 0.29/0.65                       != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ! [N3: num] :
% 0.29/0.65                          ( ( Xa
% 0.29/0.65                            = ( bit0 @ N3 ) )
% 0.29/0.65                         => ( Y
% 0.29/0.65                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit1 @ N3 ) )
% 0.29/0.65                           => ( Y
% 0.29/0.65                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 0.29/0.65                   => ( ! [M5: num] :
% 0.29/0.65                          ( ( X4
% 0.29/0.65                            = ( bit1 @ M5 ) )
% 0.29/0.65                         => ( ( Xa = one )
% 0.29/0.65                           => ( Y
% 0.29/0.65                             != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ! [N3: num] :
% 0.29/0.65                                ( ( Xa
% 0.29/0.65                                  = ( bit0 @ N3 ) )
% 0.29/0.65                               => ( Y
% 0.29/0.65                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 0.29/0.65                       => ~ ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit1 @ N3 ) )
% 0.29/0.65                                 => ( Y
% 0.29/0.65                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.elims
% 0.29/0.65  thf(fact_9832_and__num_Osimps_I1_J,axiom,
% 0.29/0.65      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 0.29/0.65      = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(1)
% 0.29/0.65  thf(fact_9833_xor__num_Osimps_I1_J,axiom,
% 0.29/0.65      ( ( bit_un2480387367778600638or_num @ one @ one )
% 0.29/0.65      = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(1)
% 0.29/0.65  thf(fact_9834_and__num_Osimps_I5_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(5)
% 0.29/0.65  thf(fact_9835_xor__num_Osimps_I5_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(5)
% 0.29/0.65  thf(fact_9836_and__num_Osimps_I7_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 0.29/0.65        = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(7)
% 0.29/0.65  thf(fact_9837_and__num_Osimps_I3_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( some_num @ one ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(3)
% 0.29/0.65  thf(fact_9838_and__num_Osimps_I4_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 0.29/0.65        = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(4)
% 0.29/0.65  thf(fact_9839_and__num_Osimps_I2_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 0.29/0.65        = none_num ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(2)
% 0.29/0.65  thf(fact_9840_xor__num_Osimps_I9_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(9)
% 0.29/0.65  thf(fact_9841_and__num_Osimps_I6_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(6)
% 0.29/0.65  thf(fact_9842_and__num_Osimps_I8_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(8)
% 0.29/0.65  thf(fact_9843_xor__num_Osimps_I7_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 0.29/0.65        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(7)
% 0.29/0.65  thf(fact_9844_xor__num_Osimps_I4_J,axiom,
% 0.29/0.65      ! [M: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 0.29/0.65        = ( some_num @ ( bit1 @ M ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(4)
% 0.29/0.65  thf(fact_9845_xor__num_Osimps_I3_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(3)
% 0.29/0.65  thf(fact_9846_xor__num_Osimps_I2_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(2)
% 0.29/0.65  thf(fact_9847_and__num_Osimps_I9_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65          @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.simps(9)
% 0.29/0.65  thf(fact_9848_xor__num_Osimps_I8_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(8)
% 0.29/0.65  thf(fact_9849_xor__num_Osimps_I6_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.simps(6)
% 0.29/0.65  thf(fact_9850_and__num_Opelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ( ( Xa = one )
% 0.29/0.65               => ( ( Y
% 0.29/0.65                    = ( some_num @ one ) )
% 0.29/0.65                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ! [N3: num] :
% 0.29/0.65                    ( ( Xa
% 0.29/0.65                      = ( bit0 @ N3 ) )
% 0.29/0.65                   => ( ( Y = none_num )
% 0.29/0.65                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65             => ( ( ( X4 = one )
% 0.29/0.65                 => ! [N3: num] :
% 0.29/0.65                      ( ( Xa
% 0.29/0.65                        = ( bit1 @ N3 ) )
% 0.29/0.65                     => ( ( Y
% 0.29/0.65                          = ( some_num @ one ) )
% 0.29/0.65                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ( ( Xa = one )
% 0.29/0.65                       => ( ( Y = none_num )
% 0.29/0.65                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit0 @ N3 ) )
% 0.29/0.65                           => ( ( Y
% 0.29/0.65                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 0.29/0.65                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                   => ( ! [M5: num] :
% 0.29/0.65                          ( ( X4
% 0.29/0.65                            = ( bit0 @ M5 ) )
% 0.29/0.65                         => ! [N3: num] :
% 0.29/0.65                              ( ( Xa
% 0.29/0.65                                = ( bit1 @ N3 ) )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ( ( Xa = one )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( some_num @ one ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                       => ( ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit0 @ N3 ) )
% 0.29/0.65                                 => ( ( Y
% 0.29/0.65                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 0.29/0.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                         => ~ ! [M5: num] :
% 0.29/0.65                                ( ( X4
% 0.29/0.65                                  = ( bit1 @ M5 ) )
% 0.29/0.65                               => ! [N3: num] :
% 0.29/0.65                                    ( ( Xa
% 0.29/0.65                                      = ( bit1 @ N3 ) )
% 0.29/0.65                                   => ( ( Y
% 0.29/0.65                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.29/0.65                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 0.29/0.65                                          @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 0.29/0.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % and_num.pelims
% 0.29/0.65  thf(fact_9851_xor__num_Opelims,axiom,
% 0.29/0.65      ! [X4: num,Xa: num,Y: option_num] :
% 0.29/0.65        ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 0.29/0.65         => ( ( ( X4 = one )
% 0.29/0.65             => ( ( Xa = one )
% 0.29/0.65               => ( ( Y = none_num )
% 0.29/0.65                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.29/0.65           => ( ( ( X4 = one )
% 0.29/0.65               => ! [N3: num] :
% 0.29/0.65                    ( ( Xa
% 0.29/0.65                      = ( bit0 @ N3 ) )
% 0.29/0.65                   => ( ( Y
% 0.29/0.65                        = ( some_num @ ( bit1 @ N3 ) ) )
% 0.29/0.65                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65             => ( ( ( X4 = one )
% 0.29/0.65                 => ! [N3: num] :
% 0.29/0.65                      ( ( Xa
% 0.29/0.65                        = ( bit1 @ N3 ) )
% 0.29/0.65                     => ( ( Y
% 0.29/0.65                          = ( some_num @ ( bit0 @ N3 ) ) )
% 0.29/0.65                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65               => ( ! [M5: num] :
% 0.29/0.65                      ( ( X4
% 0.29/0.65                        = ( bit0 @ M5 ) )
% 0.29/0.65                     => ( ( Xa = one )
% 0.29/0.65                       => ( ( Y
% 0.29/0.65                            = ( some_num @ ( bit1 @ M5 ) ) )
% 0.29/0.65                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                 => ( ! [M5: num] :
% 0.29/0.65                        ( ( X4
% 0.29/0.65                          = ( bit0 @ M5 ) )
% 0.29/0.65                       => ! [N3: num] :
% 0.29/0.65                            ( ( Xa
% 0.29/0.65                              = ( bit0 @ N3 ) )
% 0.29/0.65                           => ( ( Y
% 0.29/0.65                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 0.29/0.65                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                   => ( ! [M5: num] :
% 0.29/0.65                          ( ( X4
% 0.29/0.65                            = ( bit0 @ M5 ) )
% 0.29/0.65                         => ! [N3: num] :
% 0.29/0.65                              ( ( Xa
% 0.29/0.65                                = ( bit1 @ N3 ) )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.29/0.65                     => ( ! [M5: num] :
% 0.29/0.65                            ( ( X4
% 0.29/0.65                              = ( bit1 @ M5 ) )
% 0.29/0.65                           => ( ( Xa = one )
% 0.29/0.65                             => ( ( Y
% 0.29/0.65                                  = ( some_num @ ( bit0 @ M5 ) ) )
% 0.29/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 0.29/0.65                       => ( ! [M5: num] :
% 0.29/0.65                              ( ( X4
% 0.29/0.65                                = ( bit1 @ M5 ) )
% 0.29/0.65                             => ! [N3: num] :
% 0.29/0.65                                  ( ( Xa
% 0.29/0.65                                    = ( bit0 @ N3 ) )
% 0.29/0.65                                 => ( ( Y
% 0.29/0.65                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 0.29/0.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.29/0.65                         => ~ ! [M5: num] :
% 0.29/0.65                                ( ( X4
% 0.29/0.65                                  = ( bit1 @ M5 ) )
% 0.29/0.65                               => ! [N3: num] :
% 0.29/0.65                                    ( ( Xa
% 0.29/0.65                                      = ( bit1 @ N3 ) )
% 0.29/0.65                                   => ( ( Y
% 0.29/0.65                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 0.29/0.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % xor_num.pelims
% 0.29/0.65  thf(fact_9852_xor__num__dict,axiom,
% 0.29/0.65      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 0.29/0.65  
% 0.29/0.65  % xor_num_dict
% 0.29/0.65  thf(fact_9853_and__num__rel__dict,axiom,
% 0.29/0.65      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 0.29/0.65  
% 0.29/0.65  % and_num_rel_dict
% 0.29/0.65  thf(fact_9854_xor__num__rel__dict,axiom,
% 0.29/0.65      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 0.29/0.65  
% 0.29/0.65  % xor_num_rel_dict
% 0.29/0.65  thf(fact_9855_and__num__dict,axiom,
% 0.29/0.65      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 0.29/0.65  
% 0.29/0.65  % and_num_dict
% 0.29/0.65  thf(fact_9856_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.29/0.65      ! [N2: nat,J: nat,I2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 0.29/0.65       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 0.29/0.65          = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nth_sorted_list_of_set_greaterThanAtMost
% 0.29/0.65  thf(fact_9857_pow_Osimps_I3_J,axiom,
% 0.29/0.65      ! [X4: num,Y: num] :
% 0.29/0.65        ( ( pow @ X4 @ ( bit1 @ Y ) )
% 0.29/0.65        = ( times_times_num @ ( sqr @ ( pow @ X4 @ Y ) ) @ X4 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % pow.simps(3)
% 0.29/0.65  thf(fact_9858_finite__greaterThanAtMost,axiom,
% 0.29/0.65      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.29/0.65  
% 0.29/0.65  % finite_greaterThanAtMost
% 0.29/0.65  thf(fact_9859_card__greaterThanAtMost,axiom,
% 0.29/0.65      ! [L: nat,U: nat] :
% 0.29/0.65        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 0.29/0.65        = ( minus_minus_nat @ U @ L ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_greaterThanAtMost
% 0.29/0.65  thf(fact_9860_sqr_Osimps_I2_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( sqr @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sqr.simps(2)
% 0.29/0.65  thf(fact_9861_sqr_Osimps_I1_J,axiom,
% 0.29/0.65      ( ( sqr @ one )
% 0.29/0.65      = one ) ).
% 0.29/0.65  
% 0.29/0.65  % sqr.simps(1)
% 0.29/0.65  thf(fact_9862_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.29/0.65      ! [L: nat,U: nat] :
% 0.29/0.65        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.29/0.65        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastSucAtMost_greaterThanAtMost
% 0.29/0.65  thf(fact_9863_sqr__conv__mult,axiom,
% 0.29/0.65      ( sqr
% 0.29/0.65      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sqr_conv_mult
% 0.29/0.65  thf(fact_9864_pow_Osimps_I2_J,axiom,
% 0.29/0.65      ! [X4: num,Y: num] :
% 0.29/0.65        ( ( pow @ X4 @ ( bit0 @ Y ) )
% 0.29/0.65        = ( sqr @ ( pow @ X4 @ Y ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % pow.simps(2)
% 0.29/0.65  thf(fact_9865_sqr_Osimps_I3_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( sqr @ ( bit1 @ N2 ) )
% 0.29/0.65        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sqr.simps(3)
% 0.29/0.65  thf(fact_9866_integer__of__num__triv_I2_J,axiom,
% 0.29/0.65      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.29/0.65      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % integer_of_num_triv(2)
% 0.29/0.65  thf(fact_9867_finite__greaterThanAtMost__int,axiom,
% 0.29/0.65      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.29/0.65  
% 0.29/0.65  % finite_greaterThanAtMost_int
% 0.29/0.65  thf(fact_9868_card__greaterThanAtMost__int,axiom,
% 0.29/0.65      ! [L: int,U: int] :
% 0.29/0.65        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.29/0.65        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_greaterThanAtMost_int
% 0.29/0.65  thf(fact_9869_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.29/0.65      ! [L: int,U: int] :
% 0.29/0.65        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.29/0.65        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.29/0.65  thf(fact_9870_integer__of__num__triv_I1_J,axiom,
% 0.29/0.65      ( ( code_integer_of_num @ one )
% 0.29/0.65      = one_one_Code_integer ) ).
% 0.29/0.65  
% 0.29/0.65  % integer_of_num_triv(1)
% 0.29/0.65  thf(fact_9871_integer__of__num_I2_J,axiom,
% 0.29/0.65      ! [N2: num] :
% 0.29/0.65        ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 0.29/0.65        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % integer_of_num(2)
% 0.29/0.65  thf(fact_9872_Rats__eq__int__div__nat,axiom,
% 0.29/0.65      ( field_5140801741446780682s_real
% 0.29/0.65      = ( collect_real
% 0.29/0.65        @ ^ [Uu3: real] :
% 0.29/0.65          ? [I3: int,N: nat] :
% 0.29/0.65            ( ( Uu3
% 0.29/0.65              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.29/0.65            & ( N != zero_zero_nat ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_eq_int_div_nat
% 0.29/0.65  thf(fact_9873_image__minus__const__atLeastLessThan__nat,axiom,
% 0.29/0.65      ! [C: nat,Y: nat,X4: nat] :
% 0.29/0.65        ( ( ( ord_less_nat @ C @ Y )
% 0.29/0.65         => ( ( image_nat_nat
% 0.29/0.65              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.29/0.65              @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 0.29/0.65            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X4 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_nat @ C @ Y )
% 0.29/0.65         => ( ( ( ord_less_nat @ X4 @ Y )
% 0.29/0.65             => ( ( image_nat_nat
% 0.29/0.65                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.29/0.65                  @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 0.29/0.65                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.29/0.65            & ( ~ ( ord_less_nat @ X4 @ Y )
% 0.29/0.65             => ( ( image_nat_nat
% 0.29/0.65                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.29/0.65                  @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 0.29/0.65                = bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_minus_const_atLeastLessThan_nat
% 0.29/0.65  thf(fact_9874_bij__betw__Suc,axiom,
% 0.29/0.65      ! [M7: set_nat,N4: set_nat] :
% 0.29/0.65        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 0.29/0.65        = ( ( image_nat_nat @ suc @ M7 )
% 0.29/0.65          = N4 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % bij_betw_Suc
% 0.29/0.65  thf(fact_9875_Rats__abs__iff,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( member_real @ ( abs_abs_real @ X4 ) @ field_5140801741446780682s_real )
% 0.29/0.65        = ( member_real @ X4 @ field_5140801741446780682s_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_abs_iff
% 0.29/0.65  thf(fact_9876_image__Suc__atLeastAtMost,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 0.29/0.65        = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_Suc_atLeastAtMost
% 0.29/0.65  thf(fact_9877_image__Suc__atLeastLessThan,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 0.29/0.65        = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_Suc_atLeastLessThan
% 0.29/0.65  thf(fact_9878_Rats__dense__in__real,axiom,
% 0.29/0.65      ! [X4: real,Y: real] :
% 0.29/0.65        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.65       => ? [X5: real] :
% 0.29/0.65            ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 0.29/0.65            & ( ord_less_real @ X4 @ X5 )
% 0.29/0.65            & ( ord_less_real @ X5 @ Y ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_dense_in_real
% 0.29/0.65  thf(fact_9879_Rats__no__bot__less,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65      ? [X5: real] :
% 0.29/0.65        ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 0.29/0.65        & ( ord_less_real @ X5 @ X4 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_no_bot_less
% 0.29/0.65  thf(fact_9880_Rats__no__top__le,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65      ? [X5: real] :
% 0.29/0.65        ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 0.29/0.65        & ( ord_less_eq_real @ X4 @ X5 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_no_top_le
% 0.29/0.65  thf(fact_9881_zero__notin__Suc__image,axiom,
% 0.29/0.65      ! [A2: set_nat] :
% 0.29/0.65        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % zero_notin_Suc_image
% 0.29/0.65  thf(fact_9882_image__Suc__lessThan,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65        = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_Suc_lessThan
% 0.29/0.65  thf(fact_9883_image__Suc__atMost,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 0.29/0.65        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_Suc_atMost
% 0.29/0.65  thf(fact_9884_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.29/0.65        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast0_atMost_Suc_eq_insert_0
% 0.29/0.65  thf(fact_9885_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 0.29/0.65        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast0_lessThan_Suc_eq_insert_0
% 0.29/0.65  thf(fact_9886_lessThan__Suc__eq__insert__0,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 0.29/0.65        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % lessThan_Suc_eq_insert_0
% 0.29/0.65  thf(fact_9887_atMost__Suc__eq__insert__0,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 0.29/0.65        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atMost_Suc_eq_insert_0
% 0.29/0.65  thf(fact_9888_Rats__eq__int__div__int,axiom,
% 0.29/0.65      ( field_5140801741446780682s_real
% 0.29/0.65      = ( collect_real
% 0.29/0.65        @ ^ [Uu3: real] :
% 0.29/0.65          ? [I3: int,J3: int] :
% 0.29/0.65            ( ( Uu3
% 0.29/0.65              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 0.29/0.65            & ( J3 != zero_zero_int ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rats_eq_int_div_int
% 0.29/0.65  thf(fact_9889_Inf__real__def,axiom,
% 0.29/0.65      ( comple4887499456419720421f_real
% 0.29/0.65      = ( ^ [X3: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X3 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Inf_real_def
% 0.29/0.65  thf(fact_9890_finite__int__iff__bounded__le,axiom,
% 0.29/0.65      ( finite_finite_int
% 0.29/0.65      = ( ^ [S5: set_int] :
% 0.29/0.65          ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % finite_int_iff_bounded_le
% 0.29/0.65  thf(fact_9891_finite__int__iff__bounded,axiom,
% 0.29/0.65      ( finite_finite_int
% 0.29/0.65      = ( ^ [S5: set_int] :
% 0.29/0.65          ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % finite_int_iff_bounded
% 0.29/0.65  thf(fact_9892_image__int__atLeastAtMost,axiom,
% 0.29/0.65      ! [A: nat,B: nat] :
% 0.29/0.65        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.29/0.65        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_int_atLeastAtMost
% 0.29/0.65  thf(fact_9893_image__int__atLeastLessThan,axiom,
% 0.29/0.65      ! [A: nat,B: nat] :
% 0.29/0.65        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.29/0.65        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_int_atLeastLessThan
% 0.29/0.65  thf(fact_9894_image__add__int__atLeastLessThan,axiom,
% 0.29/0.65      ! [L: int,U: int] :
% 0.29/0.65        ( ( image_int_int
% 0.29/0.65          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 0.29/0.65          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.29/0.65        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_add_int_atLeastLessThan
% 0.29/0.65  thf(fact_9895_image__atLeastZeroLessThan__int,axiom,
% 0.29/0.65      ! [U: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.29/0.65       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.29/0.65          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % image_atLeastZeroLessThan_int
% 0.29/0.65  thf(fact_9896_suminf__eq__SUP__real,axiom,
% 0.29/0.65      ! [X8: nat > real] :
% 0.29/0.65        ( ( summable_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 0.29/0.65         => ( ( suminf_real @ X8 )
% 0.29/0.65            = ( comple1385675409528146559p_real
% 0.29/0.65              @ ( image_nat_real
% 0.29/0.65                @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 0.29/0.65                @ top_top_set_nat ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % suminf_eq_SUP_real
% 0.29/0.65  thf(fact_9897_UN__atMost__UNIV,axiom,
% 0.29/0.65      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.29/0.65      = top_top_set_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % UN_atMost_UNIV
% 0.29/0.65  thf(fact_9898_UN__lessThan__UNIV,axiom,
% 0.29/0.65      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.29/0.65      = top_top_set_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % UN_lessThan_UNIV
% 0.29/0.65  thf(fact_9899_range__mod,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( image_nat_nat
% 0.29/0.65            @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 0.29/0.65            @ top_top_set_nat )
% 0.29/0.65          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % range_mod
% 0.29/0.65  thf(fact_9900_UNIV__nat__eq,axiom,
% 0.29/0.65      ( top_top_set_nat
% 0.29/0.65      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % UNIV_nat_eq
% 0.29/0.65  thf(fact_9901_card__UNIV__unit,axiom,
% 0.29/0.65      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.29/0.65      = one_one_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % card_UNIV_unit
% 0.29/0.65  thf(fact_9902_card__UNIV__bool,axiom,
% 0.29/0.65      ( ( finite_card_o @ top_top_set_o )
% 0.29/0.65      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_UNIV_bool
% 0.29/0.65  thf(fact_9903_root__def,axiom,
% 0.29/0.65      ( root
% 0.29/0.65      = ( ^ [N: nat,X: real] :
% 0.29/0.65            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 0.29/0.65            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.29/0.65              @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 0.29/0.65              @ X ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % root_def
% 0.29/0.65  thf(fact_9904_card__UNIV__char,axiom,
% 0.29/0.65      ( ( finite_card_char @ top_top_set_char )
% 0.29/0.65      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_UNIV_char
% 0.29/0.65  thf(fact_9905_DERIV__even__real__root,axiom,
% 0.29/0.65      ! [N2: nat,X4: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65         => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.65           => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_even_real_root
% 0.29/0.65  thf(fact_9906_MVT2,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,F4: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65         => ? [Z2: real] :
% 0.29/0.65              ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65              & ( ord_less_real @ Z2 @ B )
% 0.29/0.65              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.29/0.65                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % MVT2
% 0.29/0.65  thf(fact_9907_DERIV__nonneg__imp__nondecreasing,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 0.29/0.65         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_nonneg_imp_nondecreasing
% 0.29/0.65  thf(fact_9908_DERIV__nonpos__imp__nonincreasing,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 0.29/0.65         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_nonpos_imp_nonincreasing
% 0.29/0.65  thf(fact_9909_DERIV__neg__imp__decreasing,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 0.29/0.65         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_neg_imp_decreasing
% 0.29/0.65  thf(fact_9910_DERIV__pos__imp__increasing,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 0.29/0.65         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pos_imp_increasing
% 0.29/0.65  thf(fact_9911_deriv__nonneg__imp__mono,axiom,
% 0.29/0.65      ! [A: real,B: real,G: real > real,G2: real > real] :
% 0.29/0.65        ( ! [X5: real] :
% 0.29/0.65            ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.29/0.65           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.29/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 0.29/0.65         => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.65           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % deriv_nonneg_imp_mono
% 0.29/0.65  thf(fact_9912_DERIV__isconst3,axiom,
% 0.29/0.65      ! [A: real,B: real,X4: real,Y: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65           => ( ! [X5: real] :
% 0.29/0.65                  ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 0.29/0.65             => ( ( F @ X4 )
% 0.29/0.65                = ( F @ Y ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_isconst3
% 0.29/0.65  thf(fact_9913_DERIV__local__const,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,D: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.29/0.65         => ( ! [Y3: real] :
% 0.29/0.65                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 0.29/0.65               => ( ( F @ X4 )
% 0.29/0.65                  = ( F @ Y3 ) ) )
% 0.29/0.65           => ( L = zero_zero_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_local_const
% 0.29/0.65  thf(fact_9914_DERIV__neg__dec__left,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                   => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_neg_dec_left
% 0.29/0.65  thf(fact_9915_DERIV__pos__inc__left,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pos_inc_left
% 0.29/0.65  thf(fact_9916_DERIV__neg__dec__right,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_neg_dec_right
% 0.29/0.65  thf(fact_9917_DERIV__pos__inc__right,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                   => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pos_inc_right
% 0.29/0.65  thf(fact_9918_DERIV__ln,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_ln
% 0.29/0.65  thf(fact_9919_has__real__derivative__neg__dec__right,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 0.29/0.65       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 0.29/0.65                   => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % has_real_derivative_neg_dec_right
% 0.29/0.65  thf(fact_9920_has__real__derivative__pos__inc__right,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 0.29/0.65                   => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                     => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % has_real_derivative_pos_inc_right
% 0.29/0.65  thf(fact_9921_has__real__derivative__pos__inc__left,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 0.29/0.65                   => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % has_real_derivative_pos_inc_left
% 0.29/0.65  thf(fact_9922_has__real__derivative__neg__dec__left,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 0.29/0.65       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.29/0.65         => ? [D3: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.29/0.65              & ! [H4: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.29/0.65                 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 0.29/0.65                   => ( ( ord_less_real @ H4 @ D3 )
% 0.29/0.65                     => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % has_real_derivative_neg_dec_left
% 0.29/0.65  thf(fact_9923_DERIV__const__average,axiom,
% 0.29/0.65      ! [A: real,B: real,V: real > real,K: real] :
% 0.29/0.65        ( ( A != B )
% 0.29/0.65       => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.29/0.65            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_const_average
% 0.29/0.65  thf(fact_9924_DERIV__local__max,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,D: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.29/0.65         => ( ! [Y3: real] :
% 0.29/0.65                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 0.29/0.65               => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 0.29/0.65           => ( L = zero_zero_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_local_max
% 0.29/0.65  thf(fact_9925_DERIV__local__min,axiom,
% 0.29/0.65      ! [F: real > real,L: real,X4: real,D: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.29/0.65         => ( ! [Y3: real] :
% 0.29/0.65                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 0.29/0.65               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.29/0.65           => ( L = zero_zero_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_local_min
% 0.29/0.65  thf(fact_9926_DERIV__ln__divide,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_ln_divide
% 0.29/0.65  thf(fact_9927_DERIV__fun__pow,axiom,
% 0.29/0.65      ! [G: real > real,M: real,X4: real,N2: nat] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( has_fi5821293074295781190e_real
% 0.29/0.65          @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N2 )
% 0.29/0.65          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X4 ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 0.29/0.65          @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_fun_pow
% 0.29/0.65  thf(fact_9928_DERIV__pow,axiom,
% 0.29/0.65      ! [N2: nat,X4: real,S: set_real] :
% 0.29/0.65        ( has_fi5821293074295781190e_real
% 0.29/0.65        @ ^ [X: real] : ( power_power_real @ X @ N2 )
% 0.29/0.65        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 0.29/0.65        @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pow
% 0.29/0.65  thf(fact_9929_has__real__derivative__powr,axiom,
% 0.29/0.65      ! [Z: real,R3: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.29/0.65       => ( has_fi5821293074295781190e_real
% 0.29/0.65          @ ^ [Z5: real] : ( powr_real @ Z5 @ R3 )
% 0.29/0.65          @ ( times_times_real @ R3 @ ( powr_real @ Z @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 0.29/0.65          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % has_real_derivative_powr
% 0.29/0.65  thf(fact_9930_DERIV__log,axiom,
% 0.29/0.65      ! [X4: real,B: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X4 ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_log
% 0.29/0.65  thf(fact_9931_DERIV__fun__powr,axiom,
% 0.29/0.65      ! [G: real > real,M: real,X4: real,R3: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 0.29/0.65         => ( has_fi5821293074295781190e_real
% 0.29/0.65            @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R3 )
% 0.29/0.65            @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G @ X4 ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.29/0.65            @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_fun_powr
% 0.29/0.65  thf(fact_9932_DERIV__powr,axiom,
% 0.29/0.65      ! [G: real > real,M: real,X4: real,F: real > real,R3: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 0.29/0.65         => ( ( has_fi5821293074295781190e_real @ F @ R3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 0.29/0.65           => ( has_fi5821293074295781190e_real
% 0.29/0.65              @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 0.29/0.65              @ ( times_times_real @ ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G @ X4 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X4 ) ) @ ( G @ X4 ) ) ) )
% 0.29/0.65              @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_powr
% 0.29/0.65  thf(fact_9933_DERIV__real__sqrt,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_real_sqrt
% 0.29/0.65  thf(fact_9934_DERIV__series_H,axiom,
% 0.29/0.65      ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.29/0.65        ( ! [N3: nat] :
% 0.29/0.65            ( has_fi5821293074295781190e_real
% 0.29/0.65            @ ^ [X: real] : ( F @ X @ N3 )
% 0.29/0.65            @ ( F4 @ X0 @ N3 )
% 0.29/0.65            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65             => ( summable_real @ ( F @ X5 ) ) )
% 0.29/0.65         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65           => ( ( summable_real @ ( F4 @ X0 ) )
% 0.29/0.65             => ( ( summable_real @ L5 )
% 0.29/0.65               => ( ! [N3: nat,X5: real,Y3: real] :
% 0.29/0.65                      ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65                     => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y3 ) ) ) ) ) )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real
% 0.29/0.65                    @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 0.29/0.65                    @ ( suminf_real @ ( F4 @ X0 ) )
% 0.29/0.65                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_series'
% 0.29/0.65  thf(fact_9935_DERIV__arctan,axiom,
% 0.29/0.65      ! [X4: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_arctan
% 0.29/0.65  thf(fact_9936_DERIV__real__sqrt__generic,axiom,
% 0.29/0.65      ! [X4: real,D4: real] :
% 0.29/0.65        ( ( X4 != zero_zero_real )
% 0.29/0.65       => ( ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65           => ( D4
% 0.29/0.65              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65         => ( ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.65             => ( D4
% 0.29/0.65                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.29/0.65           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_real_sqrt_generic
% 0.29/0.65  thf(fact_9937_arsinh__real__has__field__derivative,axiom,
% 0.29/0.65      ! [X4: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % arsinh_real_has_field_derivative
% 0.29/0.65  thf(fact_9938_arcosh__real__has__field__derivative,axiom,
% 0.29/0.65      ! [X4: real,A2: set_real] :
% 0.29/0.65        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % arcosh_real_has_field_derivative
% 0.29/0.65  thf(fact_9939_artanh__real__has__field__derivative,axiom,
% 0.29/0.65      ! [X4: real,A2: set_real] :
% 0.29/0.65        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.65       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % artanh_real_has_field_derivative
% 0.29/0.65  thf(fact_9940_DERIV__power__series_H,axiom,
% 0.29/0.65      ! [R: real,F: nat > real,X0: real] :
% 0.29/0.65        ( ! [X5: real] :
% 0.29/0.65            ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 0.29/0.65           => ( summable_real
% 0.29/0.65              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X5 @ N ) ) ) )
% 0.29/0.65       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 0.29/0.65         => ( ( ord_less_real @ zero_zero_real @ R )
% 0.29/0.65           => ( has_fi5821293074295781190e_real
% 0.29/0.65              @ ^ [X: real] :
% 0.29/0.65                  ( suminf_real
% 0.29/0.65                  @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ ( suc @ N ) ) ) )
% 0.29/0.65              @ ( suminf_real
% 0.29/0.65                @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 0.29/0.65              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_power_series'
% 0.29/0.65  thf(fact_9941_DERIV__real__root,axiom,
% 0.29/0.65      ! [N2: nat,X4: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_real_root
% 0.29/0.65  thf(fact_9942_DERIV__arccos,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_arccos
% 0.29/0.65  thf(fact_9943_DERIV__arcsin,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_arcsin
% 0.29/0.65  thf(fact_9944_Maclaurin__all__le__objl,axiom,
% 0.29/0.65      ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 0.29/0.65        ( ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65            = F )
% 0.29/0.65          & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 0.29/0.65       => ? [T3: real] :
% 0.29/0.65            ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.65            & ( ( F @ X4 )
% 0.29/0.65              = ( plus_plus_real
% 0.29/0.65                @ ( groups6591440286371151544t_real
% 0.29/0.65                  @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.65                  @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_all_le_objl
% 0.29/0.65  thf(fact_9945_Maclaurin__all__le,axiom,
% 0.29/0.65      ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 0.29/0.65        ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65          = F )
% 0.29/0.65       => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65         => ? [T3: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.65              & ( ( F @ X4 )
% 0.29/0.65                = ( plus_plus_real
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_all_le
% 0.29/0.65  thf(fact_9946_DERIV__odd__real__root,axiom,
% 0.29/0.65      ! [N2: nat,X4: real] :
% 0.29/0.65        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65       => ( ( X4 != zero_zero_real )
% 0.29/0.65         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_odd_real_root
% 0.29/0.65  thf(fact_9947_Maclaurin__minus,axiom,
% 0.29/0.65      ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ H @ zero_zero_real )
% 0.29/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65         => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65              = F )
% 0.29/0.65           => ( ! [M5: nat,T3: real] :
% 0.29/0.65                  ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                    & ( ord_less_eq_real @ H @ T3 )
% 0.29/0.65                    & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65             => ? [T3: real] :
% 0.29/0.65                  ( ( ord_less_real @ H @ T3 )
% 0.29/0.65                  & ( ord_less_real @ T3 @ zero_zero_real )
% 0.29/0.65                  & ( ( F @ H )
% 0.29/0.65                    = ( plus_plus_real
% 0.29/0.65                      @ ( groups6591440286371151544t_real
% 0.29/0.65                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.29/0.65                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_minus
% 0.29/0.65  thf(fact_9948_Maclaurin2,axiom,
% 0.29/0.65      ! [H: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ H )
% 0.29/0.65       => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65            = F )
% 0.29/0.65         => ( ! [M5: nat,T3: real] :
% 0.29/0.65                ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                  & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.65                  & ( ord_less_eq_real @ T3 @ H ) )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65           => ? [T3: real] :
% 0.29/0.65                ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.29/0.65                & ( ord_less_eq_real @ T3 @ H )
% 0.29/0.65                & ( ( F @ H )
% 0.29/0.65                  = ( plus_plus_real
% 0.29/0.65                    @ ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin2
% 0.29/0.65  thf(fact_9949_Maclaurin,axiom,
% 0.29/0.65      ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ H )
% 0.29/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65         => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65              = F )
% 0.29/0.65           => ( ! [M5: nat,T3: real] :
% 0.29/0.65                  ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                    & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.65                    & ( ord_less_eq_real @ T3 @ H ) )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65             => ? [T3: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ T3 )
% 0.29/0.65                  & ( ord_less_real @ T3 @ H )
% 0.29/0.65                  & ( ( F @ H )
% 0.29/0.65                    = ( plus_plus_real
% 0.29/0.65                      @ ( groups6591440286371151544t_real
% 0.29/0.65                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.29/0.65                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin
% 0.29/0.65  thf(fact_9950_Maclaurin__all__lt,axiom,
% 0.29/0.65      ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 0.29/0.65        ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65          = F )
% 0.29/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65         => ( ( X4 != zero_zero_real )
% 0.29/0.65           => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65             => ? [T3: real] :
% 0.29/0.65                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 0.29/0.65                  & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.65                  & ( ( F @ X4 )
% 0.29/0.65                    = ( plus_plus_real
% 0.29/0.65                      @ ( groups6591440286371151544t_real
% 0.29/0.65                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.65                        @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_all_lt
% 0.29/0.65  thf(fact_9951_Maclaurin__bi__le,axiom,
% 0.29/0.65      ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 0.29/0.65        ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65          = F )
% 0.29/0.65       => ( ! [M5: nat,T3: real] :
% 0.29/0.65              ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) ) )
% 0.29/0.65             => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65         => ? [T3: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 0.29/0.65              & ( ( F @ X4 )
% 0.29/0.65                = ( plus_plus_real
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_bi_le
% 0.29/0.65  thf(fact_9952_Taylor__down,axiom,
% 0.29/0.65      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65            = F )
% 0.29/0.65         => ( ! [M5: nat,T3: real] :
% 0.29/0.65                ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                  & ( ord_less_eq_real @ A @ T3 )
% 0.29/0.65                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65           => ( ( ord_less_real @ A @ C )
% 0.29/0.65             => ( ( ord_less_eq_real @ C @ B )
% 0.29/0.65               => ? [T3: real] :
% 0.29/0.65                    ( ( ord_less_real @ A @ T3 )
% 0.29/0.65                    & ( ord_less_real @ T3 @ C )
% 0.29/0.65                    & ( ( F @ A )
% 0.29/0.65                      = ( plus_plus_real
% 0.29/0.65                        @ ( groups6591440286371151544t_real
% 0.29/0.65                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 0.29/0.65                          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Taylor_down
% 0.29/0.65  thf(fact_9953_Taylor__up,axiom,
% 0.29/0.65      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65            = F )
% 0.29/0.65         => ( ! [M5: nat,T3: real] :
% 0.29/0.65                ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                  & ( ord_less_eq_real @ A @ T3 )
% 0.29/0.65                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65           => ( ( ord_less_eq_real @ A @ C )
% 0.29/0.65             => ( ( ord_less_real @ C @ B )
% 0.29/0.65               => ? [T3: real] :
% 0.29/0.65                    ( ( ord_less_real @ C @ T3 )
% 0.29/0.65                    & ( ord_less_real @ T3 @ B )
% 0.29/0.65                    & ( ( F @ B )
% 0.29/0.65                      = ( plus_plus_real
% 0.29/0.65                        @ ( groups6591440286371151544t_real
% 0.29/0.65                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 0.29/0.65                          @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Taylor_up
% 0.29/0.65  thf(fact_9954_Taylor,axiom,
% 0.29/0.65      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X4: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( ( Diff @ zero_zero_nat )
% 0.29/0.65            = F )
% 0.29/0.65         => ( ! [M5: nat,T3: real] :
% 0.29/0.65                ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65                  & ( ord_less_eq_real @ A @ T3 )
% 0.29/0.65                  & ( ord_less_eq_real @ T3 @ B ) )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65           => ( ( ord_less_eq_real @ A @ C )
% 0.29/0.65             => ( ( ord_less_eq_real @ C @ B )
% 0.29/0.65               => ( ( ord_less_eq_real @ A @ X4 )
% 0.29/0.65                 => ( ( ord_less_eq_real @ X4 @ B )
% 0.29/0.65                   => ( ( X4 != C )
% 0.29/0.65                     => ? [T3: real] :
% 0.29/0.65                          ( ( ( ord_less_real @ X4 @ C )
% 0.29/0.65                           => ( ( ord_less_real @ X4 @ T3 )
% 0.29/0.65                              & ( ord_less_real @ T3 @ C ) ) )
% 0.29/0.65                          & ( ~ ( ord_less_real @ X4 @ C )
% 0.29/0.65                           => ( ( ord_less_real @ C @ T3 )
% 0.29/0.65                              & ( ord_less_real @ T3 @ X4 ) ) )
% 0.29/0.65                          & ( ( F @ X4 )
% 0.29/0.65                            = ( plus_plus_real
% 0.29/0.65                              @ ( groups6591440286371151544t_real
% 0.29/0.65                                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ M6 ) )
% 0.29/0.65                                @ ( set_ord_lessThan_nat @ N2 ) )
% 0.29/0.65                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Taylor
% 0.29/0.65  thf(fact_9955_Maclaurin__lemma2,axiom,
% 0.29/0.65      ! [N2: nat,H: real,Diff: nat > real > real,K: nat,B3: real] :
% 0.29/0.65        ( ! [M5: nat,T3: real] :
% 0.29/0.65            ( ( ( ord_less_nat @ M5 @ N2 )
% 0.29/0.65              & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 0.29/0.65              & ( ord_less_eq_real @ T3 @ H ) )
% 0.29/0.65           => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 0.29/0.65       => ( ( N2
% 0.29/0.65            = ( suc @ K ) )
% 0.29/0.65         => ! [M2: nat,T4: real] :
% 0.29/0.65              ( ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.65                & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 0.29/0.65                & ( ord_less_eq_real @ T4 @ H ) )
% 0.29/0.65             => ( has_fi5821293074295781190e_real
% 0.29/0.65                @ ^ [U2: real] :
% 0.29/0.65                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 0.29/0.65                    @ ( plus_plus_real
% 0.29/0.65                      @ ( groups6591440286371151544t_real
% 0.29/0.65                        @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 0.29/0.65                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 0.29/0.65                      @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 0.29/0.65                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 0.29/0.65                  @ ( plus_plus_real
% 0.29/0.65                    @ ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T4 @ P5 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 0.29/0.65                    @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 0.29/0.65                @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Maclaurin_lemma2
% 0.29/0.65  thf(fact_9956_DERIV__arctan__series,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.65       => ( has_fi5821293074295781190e_real
% 0.29/0.65          @ ^ [X9: real] :
% 0.29/0.65              ( suminf_real
% 0.29/0.65              @ ^ [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 @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.29/0.65          @ ( suminf_real
% 0.29/0.65            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.29/0.65          @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_arctan_series
% 0.29/0.65  thf(fact_9957_DERIV__real__root__generic,axiom,
% 0.29/0.65      ! [N2: nat,X4: real,D4: real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( X4 != zero_zero_real )
% 0.29/0.65         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65             => ( ( ord_less_real @ zero_zero_real @ X4 )
% 0.29/0.65               => ( D4
% 0.29/0.65                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.29/0.65           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65               => ( ( ord_less_real @ X4 @ zero_zero_real )
% 0.29/0.65                 => ( D4
% 0.29/0.65                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.29/0.65             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65                 => ( D4
% 0.29/0.65                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.29/0.65               => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_real_root_generic
% 0.29/0.65  thf(fact_9958_UNIV__char__of__nat,axiom,
% 0.29/0.65      ( top_top_set_char
% 0.29/0.65      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % UNIV_char_of_nat
% 0.29/0.65  thf(fact_9959_nat__of__char__less__256,axiom,
% 0.29/0.65      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nat_of_char_less_256
% 0.29/0.65  thf(fact_9960_range__nat__of__char,axiom,
% 0.29/0.65      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.29/0.65      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % range_nat_of_char
% 0.29/0.65  thf(fact_9961_integer__of__char__code,axiom,
% 0.29/0.65      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 0.29/0.65        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 0.29/0.65        = ( 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 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % integer_of_char_code
% 0.29/0.65  thf(fact_9962_String_Ochar__of__ascii__of,axiom,
% 0.29/0.65      ! [C: char] :
% 0.29/0.65        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 0.29/0.65        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % String.char_of_ascii_of
% 0.29/0.65  thf(fact_9963_sorted__list__of__set__lessThan__Suc,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 0.29/0.65        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_list_of_set_lessThan_Suc
% 0.29/0.65  thf(fact_9964_sorted__list__of__set__atMost__Suc,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 0.29/0.65        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_list_of_set_atMost_Suc
% 0.29/0.65  thf(fact_9965_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 0.29/0.65       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 0.29/0.65          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_list_of_set_greaterThanAtMost
% 0.29/0.65  thf(fact_9966_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 0.29/0.65       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 0.29/0.65          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_list_of_set_greaterThanLessThan
% 0.29/0.65  thf(fact_9967_upto__aux__rec,axiom,
% 0.29/0.65      ( upto_aux
% 0.29/0.65      = ( ^ [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 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_aux_rec
% 0.29/0.65  thf(fact_9968_upto_Opelims,axiom,
% 0.29/0.65      ! [X4: int,Xa: int,Y: list_int] :
% 0.29/0.65        ( ( ( upto @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 0.29/0.65         => ~ ( ( ( ( ord_less_eq_int @ X4 @ Xa )
% 0.29/0.65                 => ( Y
% 0.29/0.65                    = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 0.29/0.65                & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 0.29/0.65                 => ( Y = nil_int ) ) )
% 0.29/0.65             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto.pelims
% 0.29/0.65  thf(fact_9969_upto__Nil,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( ( upto @ I2 @ J )
% 0.29/0.65          = nil_int )
% 0.29/0.65        = ( ord_less_int @ J @ I2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_Nil
% 0.29/0.65  thf(fact_9970_upto__Nil2,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( nil_int
% 0.29/0.65          = ( upto @ I2 @ J ) )
% 0.29/0.65        = ( ord_less_int @ J @ I2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_Nil2
% 0.29/0.65  thf(fact_9971_upto__empty,axiom,
% 0.29/0.65      ! [J: int,I2: int] :
% 0.29/0.65        ( ( ord_less_int @ J @ I2 )
% 0.29/0.65       => ( ( upto @ I2 @ J )
% 0.29/0.65          = nil_int ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_empty
% 0.29/0.65  thf(fact_9972_upto__single,axiom,
% 0.29/0.65      ! [I2: int] :
% 0.29/0.65        ( ( upto @ I2 @ I2 )
% 0.29/0.65        = ( cons_int @ I2 @ nil_int ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_single
% 0.29/0.65  thf(fact_9973_nth__upto,axiom,
% 0.29/0.65      ! [I2: int,K: nat,J: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.29/0.65       => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 0.29/0.65          = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nth_upto
% 0.29/0.65  thf(fact_9974_length__upto,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 0.29/0.65        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % length_upto
% 0.29/0.65  thf(fact_9975_upto__rec__numeral_I1_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65            = nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec_numeral(1)
% 0.29/0.65  thf(fact_9976_upto__rec__numeral_I2_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65            = nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec_numeral(2)
% 0.29/0.65  thf(fact_9977_upto__rec__numeral_I3_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65            = ( 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 @ N2 ) ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 0.29/0.65            = nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec_numeral(3)
% 0.29/0.65  thf(fact_9978_upto__rec__numeral_I4_J,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65            = ( 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 @ N2 ) ) ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 0.29/0.65            = nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec_numeral(4)
% 0.29/0.65  thf(fact_9979_upto__aux__def,axiom,
% 0.29/0.65      ( upto_aux
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( append_int @ ( upto @ I3 @ J3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_aux_def
% 0.29/0.65  thf(fact_9980_sup__enat__def,axiom,
% 0.29/0.65      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 0.29/0.65  
% 0.29/0.65  % sup_enat_def
% 0.29/0.65  thf(fact_9981_sup__nat__def,axiom,
% 0.29/0.65      sup_sup_nat = ord_max_nat ).
% 0.29/0.65  
% 0.29/0.65  % sup_nat_def
% 0.29/0.65  thf(fact_9982_upto__code,axiom,
% 0.29/0.65      ( upto
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( upto_aux @ I3 @ J3 @ nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_code
% 0.29/0.65  thf(fact_9983_atLeastAtMost__upto,axiom,
% 0.29/0.65      ( set_or1266510415728281911st_int
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastAtMost_upto
% 0.29/0.65  thf(fact_9984_distinct__upto,axiom,
% 0.29/0.65      ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 0.29/0.65  
% 0.29/0.65  % distinct_upto
% 0.29/0.65  thf(fact_9985_atLeastLessThan__add__Un,axiom,
% 0.29/0.65      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.65       => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.65          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastLessThan_add_Un
% 0.29/0.65  thf(fact_9986_upto__split2,axiom,
% 0.29/0.65      ! [I2: int,J: int,K: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.29/0.65         => ( ( upto @ I2 @ K )
% 0.29/0.65            = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_split2
% 0.29/0.65  thf(fact_9987_upto__split1,axiom,
% 0.29/0.65      ! [I2: int,J: int,K: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.29/0.65         => ( ( upto @ I2 @ K )
% 0.29/0.65            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_split1
% 0.29/0.65  thf(fact_9988_atLeastLessThan__upto,axiom,
% 0.29/0.65      ( set_or4662586982721622107an_int
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastLessThan_upto
% 0.29/0.65  thf(fact_9989_greaterThanAtMost__upto,axiom,
% 0.29/0.65      ( set_or6656581121297822940st_int
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThanAtMost_upto
% 0.29/0.65  thf(fact_9990_upto_Osimps,axiom,
% 0.29/0.65      ( upto
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto.simps
% 0.29/0.65  thf(fact_9991_upto_Oelims,axiom,
% 0.29/0.65      ! [X4: int,Xa: int,Y: list_int] :
% 0.29/0.65        ( ( ( upto @ X4 @ Xa )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ( ord_less_eq_int @ X4 @ Xa )
% 0.29/0.65           => ( Y
% 0.29/0.65              = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 0.29/0.65          & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 0.29/0.65           => ( Y = nil_int ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto.elims
% 0.29/0.65  thf(fact_9992_upto__rec1,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65       => ( ( upto @ I2 @ J )
% 0.29/0.65          = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec1
% 0.29/0.65  thf(fact_9993_upto__rec2,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65       => ( ( upto @ I2 @ J )
% 0.29/0.65          = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_rec2
% 0.29/0.65  thf(fact_9994_greaterThanLessThan__upto,axiom,
% 0.29/0.65      ( set_or5832277885323065728an_int
% 0.29/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThanLessThan_upto
% 0.29/0.65  thf(fact_9995_upto__split3,axiom,
% 0.29/0.65      ! [I2: int,J: int,K: int] :
% 0.29/0.65        ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.29/0.65         => ( ( upto @ I2 @ K )
% 0.29/0.65            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto_split3
% 0.29/0.65  thf(fact_9996_upto_Opsimps,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 0.29/0.65       => ( ( ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65           => ( ( upto @ I2 @ J )
% 0.29/0.65              = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 0.29/0.65          & ( ~ ( ord_less_eq_int @ I2 @ J )
% 0.29/0.65           => ( ( upto @ I2 @ J )
% 0.29/0.65              = nil_int ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upto.psimps
% 0.29/0.65  thf(fact_9997_LIM__fun__gt__zero,axiom,
% 0.29/0.65      ! [F: real > real,L: real,C: real] :
% 0.29/0.65        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ zero_zero_real @ L )
% 0.29/0.65         => ? [R2: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.29/0.65              & ! [X2: real] :
% 0.29/0.65                  ( ( ( X2 != C )
% 0.29/0.65                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 0.29/0.65                 => ( ord_less_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIM_fun_gt_zero
% 0.29/0.65  thf(fact_9998_LIM__fun__not__zero,axiom,
% 0.29/0.65      ! [F: real > real,L: real,C: real] :
% 0.29/0.65        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.29/0.65       => ( ( L != zero_zero_real )
% 0.29/0.65         => ? [R2: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.29/0.65              & ! [X2: real] :
% 0.29/0.65                  ( ( ( X2 != C )
% 0.29/0.65                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 0.29/0.65                 => ( ( F @ X2 )
% 0.29/0.65                   != zero_zero_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIM_fun_not_zero
% 0.29/0.65  thf(fact_9999_LIM__fun__less__zero,axiom,
% 0.29/0.65      ! [F: real > real,L: real,C: real] :
% 0.29/0.65        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.29/0.65       => ( ( ord_less_real @ L @ zero_zero_real )
% 0.29/0.65         => ? [R2: real] :
% 0.29/0.65              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.29/0.65              & ! [X2: real] :
% 0.29/0.65                  ( ( ( X2 != C )
% 0.29/0.65                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 0.29/0.65                 => ( ord_less_real @ ( F @ X2 ) @ zero_zero_real ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIM_fun_less_zero
% 0.29/0.65  thf(fact_10000_LIM__cos__div__sin,axiom,
% 0.29/0.65      ( filterlim_real_real
% 0.29/0.65      @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 0.29/0.65      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIM_cos_div_sin
% 0.29/0.65  thf(fact_10001_summable__Leibniz_I3_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ( topolo6980174941875973593q_real @ A )
% 0.29/0.65         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.29/0.65           => ! [N6: nat] :
% 0.29/0.65                ( member_real
% 0.29/0.65                @ ( suminf_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.29/0.65                @ ( set_or1222579329274155063t_real
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz(3)
% 0.29/0.65  thf(fact_10002_summable__Leibniz_I2_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ( topolo6980174941875973593q_real @ A )
% 0.29/0.65         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.29/0.65           => ! [N6: nat] :
% 0.29/0.65                ( member_real
% 0.29/0.65                @ ( suminf_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.29/0.65                @ ( set_or1222579329274155063t_real
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.29/0.65                  @ ( groups6591440286371151544t_real
% 0.29/0.65                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz(2)
% 0.29/0.65  thf(fact_10003_filterlim__Suc,axiom,
% 0.29/0.65      filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 0.29/0.65  
% 0.29/0.65  % filterlim_Suc
% 0.29/0.65  thf(fact_10004_mult__nat__left__at__top,axiom,
% 0.29/0.65      ! [C: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.65       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % mult_nat_left_at_top
% 0.29/0.65  thf(fact_10005_mult__nat__right__at__top,axiom,
% 0.29/0.65      ! [C: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.65       => ( filterlim_nat_nat
% 0.29/0.65          @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 0.29/0.65          @ at_top_nat
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % mult_nat_right_at_top
% 0.29/0.65  thf(fact_10006_monoseq__convergent,axiom,
% 0.29/0.65      ! [X8: nat > real,B3: real] :
% 0.29/0.65        ( ( topolo6980174941875973593q_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 0.29/0.65         => ~ ! [L6: real] :
% 0.29/0.65                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % monoseq_convergent
% 0.29/0.65  thf(fact_10007_LIMSEQ__root,axiom,
% 0.29/0.65      ( filterlim_nat_real
% 0.29/0.65      @ ^ [N: nat] : ( root @ N @ ( semiri5074537144036343181t_real @ N ) )
% 0.29/0.65      @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.29/0.65      @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_root
% 0.29/0.65  thf(fact_10008_nested__sequence__unique,axiom,
% 0.29/0.65      ! [F: nat > real,G: nat > real] :
% 0.29/0.65        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.29/0.65           => ( ( filterlim_nat_real
% 0.29/0.65                @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 0.29/0.65                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65                @ at_top_nat )
% 0.29/0.65             => ? [L4: real] :
% 0.29/0.65                  ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L4 )
% 0.29/0.65                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 0.29/0.65                  & ! [N6: nat] : ( ord_less_eq_real @ L4 @ ( G @ N6 ) )
% 0.29/0.65                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nested_sequence_unique
% 0.29/0.65  thf(fact_10009_LIMSEQ__inverse__zero,axiom,
% 0.29/0.65      ! [X8: nat > real] :
% 0.29/0.65        ( ! [R2: real] :
% 0.29/0.65          ? [N7: nat] :
% 0.29/0.65          ! [N3: nat] :
% 0.29/0.65            ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.29/0.65           => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 0.29/0.65       => ( filterlim_nat_real
% 0.29/0.65          @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_zero
% 0.29/0.65  thf(fact_10010_lim__inverse__n_H,axiom,
% 0.29/0.65      ( filterlim_nat_real
% 0.29/0.65      @ ^ [N: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.29/0.65      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65      @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % lim_inverse_n'
% 0.29/0.65  thf(fact_10011_LIMSEQ__root__const,axiom,
% 0.29/0.65      ! [C: real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ C )
% 0.29/0.65       => ( filterlim_nat_real
% 0.29/0.65          @ ^ [N: nat] : ( root @ N @ C )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_root_const
% 0.29/0.65  thf(fact_10012_LIMSEQ__inverse__real__of__nat,axiom,
% 0.29/0.65      ( filterlim_nat_real
% 0.29/0.65      @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.29/0.65      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65      @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_real_of_nat
% 0.29/0.65  thf(fact_10013_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.29/0.65      ! [R3: real] :
% 0.29/0.65        ( filterlim_nat_real
% 0.29/0.65        @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ R3 )
% 0.29/0.65        @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_real_of_nat_add
% 0.29/0.65  thf(fact_10014_increasing__LIMSEQ,axiom,
% 0.29/0.65      ! [F: nat > real,L: real] :
% 0.29/0.65        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 0.29/0.65         => ( ! [E: real] :
% 0.29/0.65                ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.65               => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 0.29/0.65           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % increasing_LIMSEQ
% 0.29/0.65  thf(fact_10015_LIMSEQ__realpow__zero,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( filterlim_nat_real @ ( power_power_real @ X4 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_realpow_zero
% 0.29/0.65  thf(fact_10016_LIMSEQ__divide__realpow__zero,axiom,
% 0.29/0.65      ! [X4: real,A: real] :
% 0.29/0.65        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.65       => ( filterlim_nat_real
% 0.29/0.65          @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X4 @ N ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_divide_realpow_zero
% 0.29/0.65  thf(fact_10017_LIMSEQ__abs__realpow__zero2,axiom,
% 0.29/0.65      ! [C: real] :
% 0.29/0.65        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.29/0.65       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_abs_realpow_zero2
% 0.29/0.65  thf(fact_10018_LIMSEQ__abs__realpow__zero,axiom,
% 0.29/0.65      ! [C: real] :
% 0.29/0.65        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.29/0.65       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_abs_realpow_zero
% 0.29/0.65  thf(fact_10019_LIMSEQ__inverse__realpow__zero,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.65       => ( filterlim_nat_real
% 0.29/0.65          @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X4 @ N ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_realpow_zero
% 0.29/0.65  thf(fact_10020_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.29/0.65      ! [R3: real] :
% 0.29/0.65        ( filterlim_nat_real
% 0.29/0.65        @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ R3 )
% 0.29/0.65        @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_real_of_nat_add_minus
% 0.29/0.65  thf(fact_10021_tendsto__exp__limit__sequentially,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( filterlim_nat_real
% 0.29/0.65        @ ^ [N: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 0.29/0.65        @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_exp_limit_sequentially
% 0.29/0.65  thf(fact_10022_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.29/0.65      ! [R3: real] :
% 0.29/0.65        ( filterlim_nat_real
% 0.29/0.65        @ ^ [N: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ R3 )
% 0.29/0.65        @ at_top_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.29/0.65  thf(fact_10023_summable__Leibniz_I1_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ( topolo6980174941875973593q_real @ A )
% 0.29/0.65         => ( summable_real
% 0.29/0.65            @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz(1)
% 0.29/0.65  thf(fact_10024_summable,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65           => ( summable_real
% 0.29/0.65              @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable
% 0.29/0.65  thf(fact_10025_cos__diff__limit__1,axiom,
% 0.29/0.65      ! [Theta: nat > real,Theta2: real] :
% 0.29/0.65        ( ( filterlim_nat_real
% 0.29/0.65          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.29/0.65          @ at_top_nat )
% 0.29/0.65       => ~ ! [K2: nat > int] :
% 0.29/0.65              ~ ( filterlim_nat_real
% 0.29/0.65                @ ^ [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 ) ) )
% 0.29/0.65                @ ( topolo2815343760600316023s_real @ Theta2 )
% 0.29/0.65                @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % cos_diff_limit_1
% 0.29/0.65  thf(fact_10026_cos__limit__1,axiom,
% 0.29/0.65      ! [Theta: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real
% 0.29/0.65          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.29/0.65          @ at_top_nat )
% 0.29/0.65       => ? [K2: nat > int] :
% 0.29/0.65            ( filterlim_nat_real
% 0.29/0.65            @ ^ [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 ) ) )
% 0.29/0.65            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65            @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % cos_limit_1
% 0.29/0.65  thf(fact_10027_summable__Leibniz_I4_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ( topolo6980174941875973593q_real @ A )
% 0.29/0.65         => ( filterlim_nat_real
% 0.29/0.65            @ ^ [N: nat] :
% 0.29/0.65                ( groups6591440286371151544t_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.65            @ ( topolo2815343760600316023s_real
% 0.29/0.65              @ ( suminf_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.29/0.65            @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz(4)
% 0.29/0.65  thf(fact_10028_zeroseq__arctan__series,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 0.29/0.65       => ( filterlim_nat_real
% 0.29/0.65          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.29/0.65          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % zeroseq_arctan_series
% 0.29/0.65  thf(fact_10029_summable__Leibniz_H_I2_J,axiom,
% 0.29/0.65      ! [A: nat > real,N2: nat] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65           => ( ord_less_eq_real
% 0.29/0.65              @ ( groups6591440286371151544t_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.29/0.65              @ ( suminf_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz'(2)
% 0.29/0.65  thf(fact_10030_summable__Leibniz_H_I3_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65           => ( filterlim_nat_real
% 0.29/0.65              @ ^ [N: nat] :
% 0.29/0.65                  ( groups6591440286371151544t_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.65              @ ( topolo2815343760600316023s_real
% 0.29/0.65                @ ( suminf_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.29/0.65              @ at_top_nat ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz'(3)
% 0.29/0.65  thf(fact_10031_sums__alternating__upper__lower,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65           => ? [L4: real] :
% 0.29/0.65                ( ! [N6: nat] :
% 0.29/0.65                    ( ord_less_eq_real
% 0.29/0.65                    @ ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.29/0.65                    @ L4 )
% 0.29/0.65                & ( filterlim_nat_real
% 0.29/0.65                  @ ^ [N: nat] :
% 0.29/0.65                      ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.29/0.65                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.29/0.65                  @ at_top_nat )
% 0.29/0.65                & ! [N6: nat] :
% 0.29/0.65                    ( ord_less_eq_real @ L4
% 0.29/0.65                    @ ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 0.29/0.65                & ( filterlim_nat_real
% 0.29/0.65                  @ ^ [N: nat] :
% 0.29/0.65                      ( groups6591440286371151544t_real
% 0.29/0.65                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.29/0.65                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.29/0.65                  @ at_top_nat ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sums_alternating_upper_lower
% 0.29/0.65  thf(fact_10032_summable__Leibniz_I5_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ( topolo6980174941875973593q_real @ A )
% 0.29/0.65         => ( filterlim_nat_real
% 0.29/0.65            @ ^ [N: nat] :
% 0.29/0.65                ( groups6591440286371151544t_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.29/0.65            @ ( topolo2815343760600316023s_real
% 0.29/0.65              @ ( suminf_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.29/0.65            @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz(5)
% 0.29/0.65  thf(fact_10033_summable__Leibniz_H_I5_J,axiom,
% 0.29/0.65      ! [A: nat > real] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65           => ( filterlim_nat_real
% 0.29/0.65              @ ^ [N: nat] :
% 0.29/0.65                  ( groups6591440286371151544t_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 0.29/0.65              @ ( topolo2815343760600316023s_real
% 0.29/0.65                @ ( suminf_real
% 0.29/0.65                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.29/0.65              @ at_top_nat ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz'(5)
% 0.29/0.65  thf(fact_10034_summable__Leibniz_H_I4_J,axiom,
% 0.29/0.65      ! [A: nat > real,N2: nat] :
% 0.29/0.65        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.29/0.65       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.29/0.65         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.29/0.65           => ( ord_less_eq_real
% 0.29/0.65              @ ( suminf_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.29/0.65              @ ( groups6591440286371151544t_real
% 0.29/0.65                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.29/0.65                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_Leibniz'(4)
% 0.29/0.65  thf(fact_10035_eventually__sequentially__Suc,axiom,
% 0.29/0.65      ! [P: nat > $o] :
% 0.29/0.65        ( ( eventually_nat
% 0.29/0.65          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 0.29/0.65          @ at_top_nat )
% 0.29/0.65        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_sequentially_Suc
% 0.29/0.65  thf(fact_10036_eventually__sequentially__seg,axiom,
% 0.29/0.65      ! [P: nat > $o,K: nat] :
% 0.29/0.65        ( ( eventually_nat
% 0.29/0.65          @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 0.29/0.65          @ at_top_nat )
% 0.29/0.65        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_sequentially_seg
% 0.29/0.65  thf(fact_10037_le__sequentially,axiom,
% 0.29/0.65      ! [F5: filter_nat] :
% 0.29/0.65        ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 0.29/0.65        = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F5 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % le_sequentially
% 0.29/0.65  thf(fact_10038_eventually__sequentially,axiom,
% 0.29/0.65      ! [P: nat > $o] :
% 0.29/0.65        ( ( eventually_nat @ P @ at_top_nat )
% 0.29/0.65        = ( ? [N9: nat] :
% 0.29/0.65            ! [N: nat] :
% 0.29/0.65              ( ( ord_less_eq_nat @ N9 @ N )
% 0.29/0.65             => ( P @ N ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_sequentially
% 0.29/0.65  thf(fact_10039_eventually__sequentiallyI,axiom,
% 0.29/0.65      ! [C: nat,P: nat > $o] :
% 0.29/0.65        ( ! [X5: nat] :
% 0.29/0.65            ( ( ord_less_eq_nat @ C @ X5 )
% 0.29/0.65           => ( P @ X5 ) )
% 0.29/0.65       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_sequentiallyI
% 0.29/0.65  thf(fact_10040_sequentially__offset,axiom,
% 0.29/0.65      ! [P: nat > $o,K: nat] :
% 0.29/0.65        ( ( eventually_nat @ P @ at_top_nat )
% 0.29/0.65       => ( eventually_nat
% 0.29/0.65          @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 0.29/0.65          @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sequentially_offset
% 0.29/0.65  thf(fact_10041_eventually__at__left__real,axiom,
% 0.29/0.65      ! [B: real,A: real] :
% 0.29/0.65        ( ( ord_less_real @ B @ A )
% 0.29/0.65       => ( eventually_real
% 0.29/0.65          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 0.29/0.65          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_at_left_real
% 0.29/0.65  thf(fact_10042_tanh__real__at__top,axiom,
% 0.29/0.65      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 0.29/0.65  
% 0.29/0.65  % tanh_real_at_top
% 0.29/0.65  thf(fact_10043_artanh__real__at__left__1,axiom,
% 0.29/0.65      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % artanh_real_at_left_1
% 0.29/0.65  thf(fact_10044_tendsto__power__div__exp__0,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( filterlim_real_real
% 0.29/0.65        @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.29/0.65        @ at_top_real ) ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_power_div_exp_0
% 0.29/0.65  thf(fact_10045_tendsto__exp__limit__at__top,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( filterlim_real_real
% 0.29/0.65        @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ Y5 ) ) @ Y5 )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 0.29/0.65        @ at_top_real ) ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_exp_limit_at_top
% 0.29/0.65  thf(fact_10046_filterlim__tan__at__left,axiom,
% 0.29/0.65      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 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % filterlim_tan_at_left
% 0.29/0.65  thf(fact_10047_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.29/0.65      ! [B: real,F: real > real,Flim: real] :
% 0.29/0.65        ( ! [X5: real] :
% 0.29/0.65            ( ( ord_less_eq_real @ B @ X5 )
% 0.29/0.65           => ? [Y4: real] :
% 0.29/0.65                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 0.29/0.65       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.29/0.65         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_neg_imp_decreasing_at_top
% 0.29/0.65  thf(fact_10048_tendsto__arctan__at__top,axiom,
% 0.29/0.65      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_arctan_at_top
% 0.29/0.65  thf(fact_10049_at__top__le__at__infinity,axiom,
% 0.29/0.65      ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 0.29/0.65  
% 0.29/0.65  % at_top_le_at_infinity
% 0.29/0.65  thf(fact_10050_Bseq__eq__bounded,axiom,
% 0.29/0.65      ! [F: nat > real,A: real,B: real] :
% 0.29/0.65        ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.29/0.65       => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Bseq_eq_bounded
% 0.29/0.65  thf(fact_10051_Bseq__realpow,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.29/0.65       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 0.29/0.65         => ( bfun_nat_real @ ( power_power_real @ X4 ) @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Bseq_realpow
% 0.29/0.65  thf(fact_10052_filterlim__pow__at__bot__even,axiom,
% 0.29/0.65      ! [N2: nat,F: real > real,F5: filter_real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 0.29/0.65         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65           => ( filterlim_real_real
% 0.29/0.65              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 0.29/0.65              @ at_top_real
% 0.29/0.65              @ F5 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % filterlim_pow_at_bot_even
% 0.29/0.65  thf(fact_10053_at__bot__le__at__infinity,axiom,
% 0.29/0.65      ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 0.29/0.65  
% 0.29/0.65  % at_bot_le_at_infinity
% 0.29/0.65  thf(fact_10054_tanh__real__at__bot,axiom,
% 0.29/0.65      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 0.29/0.65  
% 0.29/0.65  % tanh_real_at_bot
% 0.29/0.65  thf(fact_10055_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.29/0.65      ! [B: real,F: real > real,Flim: real] :
% 0.29/0.65        ( ! [X5: real] :
% 0.29/0.65            ( ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65           => ? [Y4: real] :
% 0.29/0.65                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 0.29/0.65       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.29/0.65         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pos_imp_increasing_at_bot
% 0.29/0.65  thf(fact_10056_filterlim__pow__at__bot__odd,axiom,
% 0.29/0.65      ! [N2: nat,F: real > real,F5: filter_real] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 0.29/0.65         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.29/0.65           => ( filterlim_real_real
% 0.29/0.65              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 0.29/0.65              @ at_bot_real
% 0.29/0.65              @ F5 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % filterlim_pow_at_bot_odd
% 0.29/0.65  thf(fact_10057_tendsto__arctan__at__bot,axiom,
% 0.29/0.65      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_arctan_at_bot
% 0.29/0.65  thf(fact_10058_tendsto__exp__limit__at__right,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( filterlim_real_real
% 0.29/0.65        @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X4 @ Y5 ) ) @ ( divide_divide_real @ one_one_real @ Y5 ) )
% 0.29/0.65        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 0.29/0.65        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_exp_limit_at_right
% 0.29/0.65  thf(fact_10059_filterlim__tan__at__right,axiom,
% 0.29/0.65      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 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % filterlim_tan_at_right
% 0.29/0.65  thf(fact_10060_eventually__at__right__real,axiom,
% 0.29/0.65      ! [A: real,B: real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( eventually_real
% 0.29/0.65          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.29/0.65          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % eventually_at_right_real
% 0.29/0.65  thf(fact_10061_tendsto__arcosh__at__left__1,axiom,
% 0.29/0.65      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % tendsto_arcosh_at_left_1
% 0.29/0.65  thf(fact_10062_artanh__real__at__right__1,axiom,
% 0.29/0.65      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 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % artanh_real_at_right_1
% 0.29/0.65  thf(fact_10063_atLeast__0,axiom,
% 0.29/0.65      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.29/0.65      = top_top_set_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast_0
% 0.29/0.65  thf(fact_10064_atLeast__Suc__greaterThan,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.29/0.65        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast_Suc_greaterThan
% 0.29/0.65  thf(fact_10065_decseq__bounded,axiom,
% 0.29/0.65      ! [X8: nat > real,B3: real] :
% 0.29/0.65        ( ( order_9091379641038594480t_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 0.29/0.65         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % decseq_bounded
% 0.29/0.65  thf(fact_10066_INT__greaterThan__UNIV,axiom,
% 0.29/0.65      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.29/0.65      = bot_bot_set_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % INT_greaterThan_UNIV
% 0.29/0.65  thf(fact_10067_greaterThan__0,axiom,
% 0.29/0.65      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.29/0.65      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThan_0
% 0.29/0.65  thf(fact_10068_greaterThan__Suc,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.29/0.65        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThan_Suc
% 0.29/0.65  thf(fact_10069_decseq__convergent,axiom,
% 0.29/0.65      ! [X8: nat > real,B3: real] :
% 0.29/0.65        ( ( order_9091379641038594480t_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 0.29/0.65         => ~ ! [L6: real] :
% 0.29/0.65                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.29/0.65               => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % decseq_convergent
% 0.29/0.65  thf(fact_10070_UN__atLeast__UNIV,axiom,
% 0.29/0.65      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.29/0.65      = top_top_set_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % UN_atLeast_UNIV
% 0.29/0.65  thf(fact_10071_atLeast__Suc,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.29/0.65        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast_Suc
% 0.29/0.65  thf(fact_10072_isCont__Lb__Ub,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65                & ( ord_less_eq_real @ X5 @ B ) )
% 0.29/0.65             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 0.29/0.65         => ? [L6: real,M9: real] :
% 0.29/0.65              ( ! [X2: real] :
% 0.29/0.65                  ( ( ( ord_less_eq_real @ A @ X2 )
% 0.29/0.65                    & ( ord_less_eq_real @ X2 @ B ) )
% 0.29/0.65                 => ( ( ord_less_eq_real @ L6 @ ( F @ X2 ) )
% 0.29/0.65                    & ( ord_less_eq_real @ ( F @ X2 ) @ M9 ) ) )
% 0.29/0.65              & ! [Y4: real] :
% 0.29/0.65                  ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 0.29/0.65                    & ( ord_less_eq_real @ Y4 @ M9 ) )
% 0.29/0.65                 => ? [X5: real] :
% 0.29/0.65                      ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65                      & ( ord_less_eq_real @ X5 @ B )
% 0.29/0.65                      & ( ( F @ X5 )
% 0.29/0.65                        = Y4 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_Lb_Ub
% 0.29/0.65  thf(fact_10073_less__eq,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.29/0.65        = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % less_eq
% 0.29/0.65  thf(fact_10074_isCont__inverse__function2,axiom,
% 0.29/0.65      ! [A: real,X4: real,B: real,G: real > real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ B )
% 0.29/0.65         => ( ! [Z2: real] :
% 0.29/0.65                ( ( ord_less_eq_real @ A @ Z2 )
% 0.29/0.65               => ( ( ord_less_eq_real @ Z2 @ B )
% 0.29/0.65                 => ( ( G @ ( F @ Z2 ) )
% 0.29/0.65                    = Z2 ) ) )
% 0.29/0.65           => ( ! [Z2: real] :
% 0.29/0.65                  ( ( ord_less_eq_real @ A @ Z2 )
% 0.29/0.65                 => ( ( ord_less_eq_real @ Z2 @ B )
% 0.29/0.65                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 0.29/0.65             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_inverse_function2
% 0.29/0.65  thf(fact_10075_isCont__arcosh,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ one_one_real @ X4 )
% 0.29/0.65       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcosh_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_arcosh
% 0.29/0.65  thf(fact_10076_DERIV__inverse__function,axiom,
% 0.29/0.65      ! [F: real > real,D4: real,G: real > real,X4: real,A: real,B: real] :
% 0.29/0.65        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X4 ) @ top_top_set_real ) )
% 0.29/0.65       => ( ( D4 != zero_zero_real )
% 0.29/0.65         => ( ( ord_less_real @ A @ X4 )
% 0.29/0.65           => ( ( ord_less_real @ X4 @ B )
% 0.29/0.65             => ( ! [Y3: real] :
% 0.29/0.65                    ( ( ord_less_real @ A @ Y3 )
% 0.29/0.65                   => ( ( ord_less_real @ Y3 @ B )
% 0.29/0.65                     => ( ( F @ ( G @ Y3 ) )
% 0.29/0.65                        = Y3 ) ) )
% 0.29/0.65               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_inverse_function
% 0.29/0.65  thf(fact_10077_isCont__arccos,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arccos ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_arccos
% 0.29/0.65  thf(fact_10078_isCont__arcsin,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcsin ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_arcsin
% 0.29/0.65  thf(fact_10079_LIM__less__bound,axiom,
% 0.29/0.65      ! [B: real,X4: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ B @ X4 )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X4 ) )
% 0.29/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 0.29/0.65         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F )
% 0.29/0.65           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % LIM_less_bound
% 0.29/0.65  thf(fact_10080_isCont__artanh,axiom,
% 0.29/0.65      ! [X4: real] :
% 0.29/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 0.29/0.65       => ( ( ord_less_real @ X4 @ one_one_real )
% 0.29/0.65         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_artanh
% 0.29/0.65  thf(fact_10081_isCont__inverse__function,axiom,
% 0.29/0.65      ! [D: real,X4: real,G: real > real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ zero_zero_real @ D )
% 0.29/0.65       => ( ! [Z2: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 0.29/0.65             => ( ( G @ ( F @ Z2 ) )
% 0.29/0.65                = Z2 ) )
% 0.29/0.65         => ( ! [Z2: real] :
% 0.29/0.65                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 0.29/0.65               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 0.29/0.65           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % isCont_inverse_function
% 0.29/0.65  thf(fact_10082_GMVT_H,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [Z2: real] :
% 0.29/0.65              ( ( ord_less_eq_real @ A @ Z2 )
% 0.29/0.65             => ( ( ord_less_eq_real @ Z2 @ B )
% 0.29/0.65               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 0.29/0.65         => ( ! [Z2: real] :
% 0.29/0.65                ( ( ord_less_eq_real @ A @ Z2 )
% 0.29/0.65               => ( ( ord_less_eq_real @ Z2 @ B )
% 0.29/0.65                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 0.29/0.65           => ( ! [Z2: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65                 => ( ( ord_less_real @ Z2 @ B )
% 0.29/0.65                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 0.29/0.65             => ( ! [Z2: real] :
% 0.29/0.65                    ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65                   => ( ( ord_less_real @ Z2 @ B )
% 0.29/0.65                     => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 0.29/0.65               => ? [C3: real] :
% 0.29/0.65                    ( ( ord_less_real @ A @ C3 )
% 0.29/0.65                    & ( ord_less_real @ C3 @ B )
% 0.29/0.65                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 0.29/0.65                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % GMVT'
% 0.29/0.65  thf(fact_10083_GMVT,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,G: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65                & ( ord_less_eq_real @ X5 @ B ) )
% 0.29/0.65             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 0.29/0.65         => ( ! [X5: real] :
% 0.29/0.65                ( ( ( ord_less_real @ A @ X5 )
% 0.29/0.65                  & ( ord_less_real @ X5 @ B ) )
% 0.29/0.65               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 0.29/0.65           => ( ! [X5: real] :
% 0.29/0.65                  ( ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.65                    & ( ord_less_eq_real @ X5 @ B ) )
% 0.29/0.65                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 0.29/0.65             => ( ! [X5: real] :
% 0.29/0.65                    ( ( ( ord_less_real @ A @ X5 )
% 0.29/0.65                      & ( ord_less_real @ X5 @ B ) )
% 0.29/0.65                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 0.29/0.65               => ? [G_c: real,F_c: real,C3: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 0.29/0.65                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_real @ A @ C3 )
% 0.29/0.65                    & ( ord_less_real @ C3 @ B )
% 0.29/0.65                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 0.29/0.65                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % GMVT
% 0.29/0.65  thf(fact_10084_MVT,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65         => ( ! [X5: real] :
% 0.29/0.65                ( ( ord_less_real @ A @ X5 )
% 0.29/0.65               => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65           => ? [L4: real,Z2: real] :
% 0.29/0.65                ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65                & ( ord_less_real @ Z2 @ B )
% 0.29/0.65                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 0.29/0.65                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.29/0.65                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % MVT
% 0.29/0.65  thf(fact_10085_continuous__on__arcosh_H,axiom,
% 0.29/0.65      ! [A2: set_real,F: real > real] :
% 0.29/0.65        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( member_real @ X5 @ A2 )
% 0.29/0.65             => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 0.29/0.65         => ( topolo5044208981011980120l_real @ A2
% 0.29/0.65            @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_arcosh'
% 0.29/0.65  thf(fact_10086_continuous__image__closed__interval,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.29/0.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65         => ? [C3: real,D3: real] :
% 0.29/0.65              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.29/0.65                = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 0.29/0.65              & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % continuous_image_closed_interval
% 0.29/0.65  thf(fact_10087_continuous__on__arcosh,axiom,
% 0.29/0.65      ! [A2: set_real] :
% 0.29/0.65        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 0.29/0.65       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_arcosh
% 0.29/0.65  thf(fact_10088_continuous__on__arccos_H,axiom,
% 0.29/0.65      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_arccos'
% 0.29/0.65  thf(fact_10089_continuous__on__arcsin_H,axiom,
% 0.29/0.65      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_arcsin'
% 0.29/0.65  thf(fact_10090_continuous__on__artanh_H,axiom,
% 0.29/0.65      ! [A2: set_real,F: real > real] :
% 0.29/0.65        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( member_real @ X5 @ A2 )
% 0.29/0.65             => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 0.29/0.65         => ( topolo5044208981011980120l_real @ A2
% 0.29/0.65            @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_artanh'
% 0.29/0.65  thf(fact_10091_Rolle__deriv,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( ( F @ A )
% 0.29/0.65            = ( F @ B ) )
% 0.29/0.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65           => ( ! [X5: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ X5 )
% 0.29/0.65                 => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                   => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65             => ? [Z2: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65                  & ( ord_less_real @ Z2 @ B )
% 0.29/0.65                  & ( ( F4 @ Z2 )
% 0.29/0.65                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rolle_deriv
% 0.29/0.65  thf(fact_10092_mvt,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65         => ( ! [X5: real] :
% 0.29/0.65                ( ( ord_less_real @ A @ X5 )
% 0.29/0.65               => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65           => ~ ! [Xi: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ Xi )
% 0.29/0.65                 => ( ( ord_less_real @ Xi @ B )
% 0.29/0.65                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.29/0.65                     != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % mvt
% 0.29/0.65  thf(fact_10093_DERIV__pos__imp__increasing__open,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 0.29/0.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_pos_imp_increasing_open
% 0.29/0.65  thf(fact_10094_DERIV__neg__imp__decreasing__open,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ! [X5: real] :
% 0.29/0.65              ( ( ord_less_real @ A @ X5 )
% 0.29/0.65             => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65               => ? [Y4: real] :
% 0.29/0.65                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 0.29/0.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_neg_imp_decreasing_open
% 0.29/0.65  thf(fact_10095_DERIV__isconst__end,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65         => ( ! [X5: real] :
% 0.29/0.65                ( ( ord_less_real @ A @ X5 )
% 0.29/0.65               => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65           => ( ( F @ B )
% 0.29/0.65              = ( F @ A ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_isconst_end
% 0.29/0.65  thf(fact_10096_continuous__on__artanh,axiom,
% 0.29/0.65      ! [A2: set_real] :
% 0.29/0.65        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 0.29/0.65       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % continuous_on_artanh
% 0.29/0.65  thf(fact_10097_DERIV__isconst2,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real,X4: real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65         => ( ! [X5: real] :
% 0.29/0.65                ( ( ord_less_real @ A @ X5 )
% 0.29/0.65               => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65           => ( ( ord_less_eq_real @ A @ X4 )
% 0.29/0.65             => ( ( ord_less_eq_real @ X4 @ B )
% 0.29/0.65               => ( ( F @ X4 )
% 0.29/0.65                  = ( F @ A ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DERIV_isconst2
% 0.29/0.65  thf(fact_10098_Rolle,axiom,
% 0.29/0.65      ! [A: real,B: real,F: real > real] :
% 0.29/0.65        ( ( ord_less_real @ A @ B )
% 0.29/0.65       => ( ( ( F @ A )
% 0.29/0.65            = ( F @ B ) )
% 0.29/0.65         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.29/0.65           => ( ! [X5: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ X5 )
% 0.29/0.65                 => ( ( ord_less_real @ X5 @ B )
% 0.29/0.65                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 0.29/0.65             => ? [Z2: real] :
% 0.29/0.65                  ( ( ord_less_real @ A @ Z2 )
% 0.29/0.65                  & ( ord_less_real @ Z2 @ B )
% 0.29/0.65                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rolle
% 0.29/0.65  thf(fact_10099_mono__Suc,axiom,
% 0.29/0.65      order_mono_nat_nat @ suc ).
% 0.29/0.65  
% 0.29/0.65  % mono_Suc
% 0.29/0.65  thf(fact_10100_mono__times__nat,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % mono_times_nat
% 0.29/0.65  thf(fact_10101_incseq__bounded,axiom,
% 0.29/0.65      ! [X8: nat > real,B3: real] :
% 0.29/0.65        ( ( order_mono_nat_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 0.29/0.65         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % incseq_bounded
% 0.29/0.65  thf(fact_10102_incseq__convergent,axiom,
% 0.29/0.65      ! [X8: nat > real,B3: real] :
% 0.29/0.65        ( ( order_mono_nat_real @ X8 )
% 0.29/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 0.29/0.65         => ~ ! [L6: real] :
% 0.29/0.65                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.29/0.65               => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % incseq_convergent
% 0.29/0.65  thf(fact_10103_mono__ge2__power__minus__self,axiom,
% 0.29/0.65      ! [K: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.29/0.65       => ( order_mono_nat_nat
% 0.29/0.65          @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % mono_ge2_power_minus_self
% 0.29/0.65  thf(fact_10104_nonneg__incseq__Bseq__subseq__iff,axiom,
% 0.29/0.65      ! [F: nat > real,G: nat > nat] :
% 0.29/0.65        ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 0.29/0.65       => ( ( order_mono_nat_real @ F )
% 0.29/0.65         => ( ( order_5726023648592871131at_nat @ G )
% 0.29/0.65           => ( ( bfun_nat_real
% 0.29/0.65                @ ^ [X: nat] : ( F @ ( G @ X ) )
% 0.29/0.65                @ at_top_nat )
% 0.29/0.65              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nonneg_incseq_Bseq_subseq_iff
% 0.29/0.65  thf(fact_10105_strict__mono__imp__increasing,axiom,
% 0.29/0.65      ! [F: nat > nat,N2: nat] :
% 0.29/0.65        ( ( order_5726023648592871131at_nat @ F )
% 0.29/0.65       => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % strict_mono_imp_increasing
% 0.29/0.65  thf(fact_10106_inj__sgn__power,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( inj_on_real_real
% 0.29/0.65          @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 0.29/0.65          @ top_top_set_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % inj_sgn_power
% 0.29/0.65  thf(fact_10107_log__inj,axiom,
% 0.29/0.65      ! [B: real] :
% 0.29/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.29/0.65       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % log_inj
% 0.29/0.65  thf(fact_10108_pos__deriv__imp__strict__mono,axiom,
% 0.29/0.65      ! [F: real > real,F4: real > real] :
% 0.29/0.65        ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 0.29/0.65       => ( ! [X5: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X5 ) )
% 0.29/0.65         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % pos_deriv_imp_strict_mono
% 0.29/0.65  thf(fact_10109_inj__on__diff__nat,axiom,
% 0.29/0.65      ! [N4: set_nat,K: nat] :
% 0.29/0.65        ( ! [N3: nat] :
% 0.29/0.65            ( ( member_nat @ N3 @ N4 )
% 0.29/0.65           => ( ord_less_eq_nat @ K @ N3 ) )
% 0.29/0.65       => ( inj_on_nat_nat
% 0.29/0.65          @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 0.29/0.65          @ N4 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % inj_on_diff_nat
% 0.29/0.65  thf(fact_10110_inj__Suc,axiom,
% 0.29/0.65      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 0.29/0.65  
% 0.29/0.65  % inj_Suc
% 0.29/0.65  thf(fact_10111_inj__on__char__of__nat,axiom,
% 0.29/0.65      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % inj_on_char_of_nat
% 0.29/0.65  thf(fact_10112_suminf__reindex,axiom,
% 0.29/0.65      ! [F: nat > real,G: nat > nat] :
% 0.29/0.65        ( ( summable_real @ F )
% 0.29/0.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.29/0.65         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 0.29/0.65           => ( ! [X5: nat] :
% 0.29/0.65                  ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.29/0.65                 => ( ( F @ X5 )
% 0.29/0.65                    = zero_zero_real ) )
% 0.29/0.65             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 0.29/0.65                = ( suminf_real @ F ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % suminf_reindex
% 0.29/0.65  thf(fact_10113_summable__reindex,axiom,
% 0.29/0.65      ! [F: nat > real,G: nat > nat] :
% 0.29/0.65        ( ( summable_real @ F )
% 0.29/0.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.29/0.65         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 0.29/0.65           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % summable_reindex
% 0.29/0.65  thf(fact_10114_suminf__reindex__mono,axiom,
% 0.29/0.65      ! [F: nat > real,G: nat > nat] :
% 0.29/0.65        ( ( summable_real @ F )
% 0.29/0.65       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.29/0.65         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 0.29/0.65           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % suminf_reindex_mono
% 0.29/0.65  thf(fact_10115_card_Ocomp__fun__commute__on,axiom,
% 0.29/0.65      ( ( comp_nat_nat_nat @ suc @ suc )
% 0.29/0.65      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card.comp_fun_commute_on
% 0.29/0.65  thf(fact_10116_pred__nat__trancl__eq__le,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.29/0.65        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % pred_nat_trancl_eq_le
% 0.29/0.65  thf(fact_10117_uniformity__real__def,axiom,
% 0.29/0.65      ( topolo1511823702728130853y_real
% 0.29/0.65      = ( comple2936214249959783750l_real
% 0.29/0.65        @ ( image_2178119161166701260l_real
% 0.29/0.65          @ ^ [E3: real] :
% 0.29/0.65              ( princi6114159922880469582l_real
% 0.29/0.65              @ ( collec3799799289383736868l_real
% 0.29/0.65                @ ( produc5414030515140494994real_o
% 0.29/0.65                  @ ^ [X: real,Y5: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y5 ) @ E3 ) ) ) )
% 0.29/0.65          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % uniformity_real_def
% 0.29/0.65  thf(fact_10118_uniformity__complex__def,axiom,
% 0.29/0.65      ( topolo896644834953643431omplex
% 0.29/0.65      = ( comple8358262395181532106omplex
% 0.29/0.65        @ ( image_5971271580939081552omplex
% 0.29/0.65          @ ^ [E3: real] :
% 0.29/0.65              ( princi3496590319149328850omplex
% 0.29/0.65              @ ( collec8663557070575231912omplex
% 0.29/0.65                @ ( produc6771430404735790350plex_o
% 0.29/0.65                  @ ^ [X: complex,Y5: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y5 ) @ E3 ) ) ) )
% 0.29/0.65          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % uniformity_complex_def
% 0.29/0.65  thf(fact_10119_rat__floor__lemma,axiom,
% 0.29/0.65      ! [A: int,B: int] :
% 0.29/0.65        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.29/0.65        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % rat_floor_lemma
% 0.29/0.65  thf(fact_10120_less__rat,axiom,
% 0.29/0.65      ! [B: int,D: int,A: int,C: int] :
% 0.29/0.65        ( ( B != zero_zero_int )
% 0.29/0.65       => ( ( D != zero_zero_int )
% 0.29/0.65         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.29/0.65            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % less_rat
% 0.29/0.65  thf(fact_10121_le__rat,axiom,
% 0.29/0.65      ! [B: int,D: int,A: int,C: int] :
% 0.29/0.65        ( ( B != zero_zero_int )
% 0.29/0.65       => ( ( D != zero_zero_int )
% 0.29/0.65         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.29/0.65            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % le_rat
% 0.29/0.65  thf(fact_10122_Rat__induct__pos,axiom,
% 0.29/0.65      ! [P: rat > $o,Q3: rat] :
% 0.29/0.65        ( ! [A5: int,B5: int] :
% 0.29/0.65            ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.29/0.65           => ( P @ ( fract @ A5 @ B5 ) ) )
% 0.29/0.65       => ( P @ Q3 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rat_induct_pos
% 0.29/0.65  thf(fact_10123_Fract__less__zero__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.29/0.65          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Fract_less_zero_iff
% 0.29/0.65  thf(fact_10124_zero__less__Fract__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.29/0.65          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % zero_less_Fract_iff
% 0.29/0.65  thf(fact_10125_Fract__less__one__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.29/0.65          = ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Fract_less_one_iff
% 0.29/0.65  thf(fact_10126_one__less__Fract__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.29/0.65          = ( ord_less_int @ B @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % one_less_Fract_iff
% 0.29/0.65  thf(fact_10127_Fract__le__zero__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.29/0.65          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Fract_le_zero_iff
% 0.29/0.65  thf(fact_10128_zero__le__Fract__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.29/0.65          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % zero_le_Fract_iff
% 0.29/0.65  thf(fact_10129_Fract__le__one__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.29/0.65          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Fract_le_one_iff
% 0.29/0.65  thf(fact_10130_one__le__Fract__iff,axiom,
% 0.29/0.65      ! [B: int,A: int] :
% 0.29/0.65        ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.65       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.29/0.65          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % one_le_Fract_iff
% 0.29/0.65  thf(fact_10131_positive__rat,axiom,
% 0.29/0.65      ! [A: int,B: int] :
% 0.29/0.65        ( ( positive @ ( fract @ A @ B ) )
% 0.29/0.65        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % positive_rat
% 0.29/0.65  thf(fact_10132_less__rat__def,axiom,
% 0.29/0.65      ( ord_less_rat
% 0.29/0.65      = ( ^ [X: rat,Y5: rat] : ( positive @ ( minus_minus_rat @ Y5 @ X ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % less_rat_def
% 0.29/0.65  thf(fact_10133_Rat_Opositive_Orep__eq,axiom,
% 0.29/0.65      ( positive
% 0.29/0.65      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rat.positive.rep_eq
% 0.29/0.65  thf(fact_10134_min__Suc__Suc,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/0.65        = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_Suc_Suc
% 0.29/0.65  thf(fact_10135_min__0R,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 0.29/0.65        = zero_zero_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % min_0R
% 0.29/0.65  thf(fact_10136_min__0L,axiom,
% 0.29/0.65      ! [N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 0.29/0.65        = zero_zero_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % min_0L
% 0.29/0.65  thf(fact_10137_min__Suc__numeral,axiom,
% 0.29/0.65      ! [N2: nat,K: num] :
% 0.29/0.65        ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 0.29/0.65        = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_Suc_numeral
% 0.29/0.65  thf(fact_10138_min__numeral__Suc,axiom,
% 0.29/0.65      ! [K: num,N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 0.29/0.65        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_numeral_Suc
% 0.29/0.65  thf(fact_10139_inf__nat__def,axiom,
% 0.29/0.65      inf_inf_nat = ord_min_nat ).
% 0.29/0.65  
% 0.29/0.65  % inf_nat_def
% 0.29/0.65  thf(fact_10140_nat__mult__min__left,axiom,
% 0.29/0.65      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.65        ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q3 )
% 0.29/0.65        = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nat_mult_min_left
% 0.29/0.65  thf(fact_10141_nat__mult__min__right,axiom,
% 0.29/0.65      ! [M: nat,N2: nat,Q3: nat] :
% 0.29/0.65        ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q3 ) )
% 0.29/0.65        = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nat_mult_min_right
% 0.29/0.65  thf(fact_10142_min__diff,axiom,
% 0.29/0.65      ! [M: nat,I2: nat,N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 0.29/0.65        = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_diff
% 0.29/0.65  thf(fact_10143_concat__bit__assoc__sym,axiom,
% 0.29/0.65      ! [M: nat,N2: nat,K: int,L: int,R3: int] :
% 0.29/0.65        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 )
% 0.29/0.65        = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N2 ) @ L @ R3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % concat_bit_assoc_sym
% 0.29/0.65  thf(fact_10144_take__bit__concat__bit__eq,axiom,
% 0.29/0.65      ! [M: nat,N2: nat,K: int,L: int] :
% 0.29/0.65        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N2 @ K @ L ) )
% 0.29/0.65        = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ L ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_bit_concat_bit_eq
% 0.29/0.65  thf(fact_10145_min__Suc1,axiom,
% 0.29/0.65      ! [N2: nat,M: nat] :
% 0.29/0.65        ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 0.29/0.65        = ( case_nat_nat @ zero_zero_nat
% 0.29/0.65          @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N2 @ M3 ) )
% 0.29/0.65          @ M ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_Suc1
% 0.29/0.65  thf(fact_10146_min__Suc2,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 0.29/0.65        = ( case_nat_nat @ zero_zero_nat
% 0.29/0.65          @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N2 ) )
% 0.29/0.65          @ M ) ) ).
% 0.29/0.65  
% 0.29/0.65  % min_Suc2
% 0.29/0.65  thf(fact_10147_min__enat__simps_I2_J,axiom,
% 0.29/0.65      ! [Q3: extended_enat] :
% 0.29/0.65        ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 0.29/0.65        = zero_z5237406670263579293d_enat ) ).
% 0.29/0.65  
% 0.29/0.65  % min_enat_simps(2)
% 0.29/0.65  thf(fact_10148_min__enat__simps_I3_J,axiom,
% 0.29/0.65      ! [Q3: extended_enat] :
% 0.29/0.65        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 0.29/0.65        = zero_z5237406670263579293d_enat ) ).
% 0.29/0.65  
% 0.29/0.65  % min_enat_simps(3)
% 0.29/0.65  thf(fact_10149_inf__enat__def,axiom,
% 0.29/0.65      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 0.29/0.65  
% 0.29/0.65  % inf_enat_def
% 0.29/0.65  thf(fact_10150_num__of__integer__code,axiom,
% 0.29/0.65      ( code_num_of_integer
% 0.29/0.65      = ( ^ [K3: code_integer] :
% 0.29/0.65            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 0.29/0.65            @ ( produc7336495610019696514er_num
% 0.29/0.65              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 0.29/0.65              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % num_of_integer_code
% 0.29/0.65  thf(fact_10151_card__le__Suc__Max,axiom,
% 0.29/0.65      ! [S2: set_nat] :
% 0.29/0.65        ( ( finite_finite_nat @ S2 )
% 0.29/0.65       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_le_Suc_Max
% 0.29/0.65  thf(fact_10152_divide__nat__def,axiom,
% 0.29/0.65      ( divide_divide_nat
% 0.29/0.65      = ( ^ [M6: nat,N: nat] :
% 0.29/0.65            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 0.29/0.65            @ ( lattic8265883725875713057ax_nat
% 0.29/0.65              @ ( collect_nat
% 0.29/0.65                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M6 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % divide_nat_def
% 0.29/0.65  thf(fact_10153_gcd__is__Max__divisors__nat,axiom,
% 0.29/0.65      ! [N2: nat,M: nat] :
% 0.29/0.65        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.65       => ( ( gcd_gcd_nat @ M @ N2 )
% 0.29/0.65          = ( lattic8265883725875713057ax_nat
% 0.29/0.65            @ ( collect_nat
% 0.29/0.65              @ ^ [D5: nat] :
% 0.29/0.65                  ( ( dvd_dvd_nat @ D5 @ M )
% 0.29/0.65                  & ( dvd_dvd_nat @ D5 @ N2 ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % gcd_is_Max_divisors_nat
% 0.29/0.65  thf(fact_10154_upt__rec__numeral,axiom,
% 0.29/0.65      ! [M: num,N2: num] :
% 0.29/0.65        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.65         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.65            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.65         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 0.29/0.65            = nil_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_rec_numeral
% 0.29/0.65  thf(fact_10155_remdups__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 0.29/0.65        = ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % remdups_upt
% 0.29/0.65  thf(fact_10156_tl__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( tl_nat @ ( upt @ M @ N2 ) )
% 0.29/0.65        = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % tl_upt
% 0.29/0.65  thf(fact_10157_hd__upt,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.65       => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 0.29/0.65          = I2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % hd_upt
% 0.29/0.65  thf(fact_10158_drop__upt,axiom,
% 0.29/0.65      ! [M: nat,I2: nat,J: nat] :
% 0.29/0.65        ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 0.29/0.65        = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 0.29/0.65  
% 0.29/0.65  % drop_upt
% 0.29/0.65  thf(fact_10159_length__upt,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 0.29/0.65        = ( minus_minus_nat @ J @ I2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % length_upt
% 0.29/0.65  thf(fact_10160_take__upt,axiom,
% 0.29/0.65      ! [I2: nat,M: nat,N2: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 0.29/0.65       => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 0.29/0.65          = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % take_upt
% 0.29/0.65  thf(fact_10161_upt__conv__Nil,axiom,
% 0.29/0.65      ! [J: nat,I2: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ J @ I2 )
% 0.29/0.65       => ( ( upt @ I2 @ J )
% 0.29/0.65          = nil_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_conv_Nil
% 0.29/0.65  thf(fact_10162_sorted__list__of__set__range,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 0.29/0.65        = ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_list_of_set_range
% 0.29/0.65  thf(fact_10163_upt__eq__Nil__conv,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ( upt @ I2 @ J )
% 0.29/0.65          = nil_nat )
% 0.29/0.65        = ( ( J = zero_zero_nat )
% 0.29/0.65          | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_eq_Nil_conv
% 0.29/0.65  thf(fact_10164_nth__upt,axiom,
% 0.29/0.65      ! [I2: nat,K: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 0.29/0.65       => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 0.29/0.65          = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % nth_upt
% 0.29/0.65  thf(fact_10165_greaterThanLessThan__upt,axiom,
% 0.29/0.65      ( set_or5834768355832116004an_nat
% 0.29/0.65      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M6 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThanLessThan_upt
% 0.29/0.65  thf(fact_10166_atLeastLessThan__upt,axiom,
% 0.29/0.65      ( set_or4665077453230672383an_nat
% 0.29/0.65      = ( ^ [I3: nat,J3: nat] : ( set_nat2 @ ( upt @ I3 @ J3 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastLessThan_upt
% 0.29/0.65  thf(fact_10167_atLeastAtMost__upt,axiom,
% 0.29/0.65      ( set_or1269000886237332187st_nat
% 0.29/0.65      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M6 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeastAtMost_upt
% 0.29/0.65  thf(fact_10168_greaterThanAtMost__upt,axiom,
% 0.29/0.65      ( set_or6659071591806873216st_nat
% 0.29/0.65      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M6 ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % greaterThanAtMost_upt
% 0.29/0.65  thf(fact_10169_atLeast__upt,axiom,
% 0.29/0.65      ( set_ord_lessThan_nat
% 0.29/0.65      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atLeast_upt
% 0.29/0.65  thf(fact_10170_upt__conv__Cons__Cons,axiom,
% 0.29/0.65      ! [M: nat,N2: nat,Ns: list_nat,Q3: nat] :
% 0.29/0.65        ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 0.29/0.65          = ( upt @ M @ Q3 ) )
% 0.29/0.65        = ( ( cons_nat @ N2 @ Ns )
% 0.29/0.65          = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_conv_Cons_Cons
% 0.29/0.65  thf(fact_10171_distinct__upt,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 0.29/0.65  
% 0.29/0.65  % distinct_upt
% 0.29/0.65  thf(fact_10172_upt__0,axiom,
% 0.29/0.65      ! [I2: nat] :
% 0.29/0.65        ( ( upt @ I2 @ zero_zero_nat )
% 0.29/0.65        = nil_nat ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_0
% 0.29/0.65  thf(fact_10173_atMost__upto,axiom,
% 0.29/0.65      ( set_ord_atMost_nat
% 0.29/0.65      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % atMost_upto
% 0.29/0.65  thf(fact_10174_upt__conv__Cons,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_nat @ I2 @ J )
% 0.29/0.65       => ( ( upt @ I2 @ J )
% 0.29/0.65          = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_conv_Cons
% 0.29/0.65  thf(fact_10175_upt__add__eq__append,axiom,
% 0.29/0.65      ! [I2: nat,J: nat,K: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.65       => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.65          = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_add_eq_append
% 0.29/0.65  thf(fact_10176_upt__eq__Cons__conv,axiom,
% 0.29/0.65      ! [I2: nat,J: nat,X4: nat,Xs: list_nat] :
% 0.29/0.65        ( ( ( upt @ I2 @ J )
% 0.29/0.65          = ( cons_nat @ X4 @ Xs ) )
% 0.29/0.65        = ( ( ord_less_nat @ I2 @ J )
% 0.29/0.65          & ( I2 = X4 )
% 0.29/0.65          & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 0.29/0.65            = Xs ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_eq_Cons_conv
% 0.29/0.65  thf(fact_10177_upt__rec,axiom,
% 0.29/0.65      ( upt
% 0.29/0.65      = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_rec
% 0.29/0.65  thf(fact_10178_upt__Suc,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.65         => ( ( upt @ I2 @ ( suc @ J ) )
% 0.29/0.65            = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.29/0.65        & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.65         => ( ( upt @ I2 @ ( suc @ J ) )
% 0.29/0.65            = nil_nat ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_Suc
% 0.29/0.65  thf(fact_10179_upt__Suc__append,axiom,
% 0.29/0.65      ! [I2: nat,J: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ I2 @ J )
% 0.29/0.65       => ( ( upt @ I2 @ ( suc @ J ) )
% 0.29/0.65          = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % upt_Suc_append
% 0.29/0.65  thf(fact_10180_sum__list__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.65       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 0.29/0.65          = ( groups3542108847815614940at_nat
% 0.29/0.65            @ ^ [X: nat] : X
% 0.29/0.65            @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sum_list_upt
% 0.29/0.65  thf(fact_10181_map__Suc__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 0.29/0.65        = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % map_Suc_upt
% 0.29/0.65  thf(fact_10182_map__add__upt,axiom,
% 0.29/0.65      ! [N2: nat,M: nat] :
% 0.29/0.65        ( ( map_nat_nat
% 0.29/0.65          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 0.29/0.65          @ ( upt @ zero_zero_nat @ M ) )
% 0.29/0.65        = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % map_add_upt
% 0.29/0.65  thf(fact_10183_map__decr__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( map_nat_nat
% 0.29/0.65          @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.29/0.65          @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 0.29/0.65        = ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % map_decr_upt
% 0.29/0.65  thf(fact_10184_Divides_Oadjust__div__def,axiom,
% 0.29/0.65      ( adjust_div
% 0.29/0.65      = ( produc8211389475949308722nt_int
% 0.29/0.65        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Divides.adjust_div_def
% 0.29/0.65  thf(fact_10185_card__length__sum__list__rec,axiom,
% 0.29/0.65      ! [M: nat,N4: nat] :
% 0.29/0.65        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.29/0.65       => ( ( finite_card_list_nat
% 0.29/0.65            @ ( collect_list_nat
% 0.29/0.65              @ ^ [L2: list_nat] :
% 0.29/0.65                  ( ( ( size_size_list_nat @ L2 )
% 0.29/0.65                    = M )
% 0.29/0.65                  & ( ( groups4561878855575611511st_nat @ L2 )
% 0.29/0.65                    = N4 ) ) ) )
% 0.29/0.65          = ( plus_plus_nat
% 0.29/0.65            @ ( finite_card_list_nat
% 0.29/0.65              @ ( collect_list_nat
% 0.29/0.65                @ ^ [L2: list_nat] :
% 0.29/0.65                    ( ( ( size_size_list_nat @ L2 )
% 0.29/0.65                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.29/0.65                    & ( ( groups4561878855575611511st_nat @ L2 )
% 0.29/0.65                      = N4 ) ) ) )
% 0.29/0.65            @ ( finite_card_list_nat
% 0.29/0.65              @ ( collect_list_nat
% 0.29/0.65                @ ^ [L2: list_nat] :
% 0.29/0.65                    ( ( ( size_size_list_nat @ L2 )
% 0.29/0.65                      = M )
% 0.29/0.65                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.29/0.65                      = N4 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_length_sum_list_rec
% 0.29/0.65  thf(fact_10186_card__length__sum__list,axiom,
% 0.29/0.65      ! [M: nat,N4: nat] :
% 0.29/0.65        ( ( finite_card_list_nat
% 0.29/0.65          @ ( collect_list_nat
% 0.29/0.65            @ ^ [L2: list_nat] :
% 0.29/0.65                ( ( ( size_size_list_nat @ L2 )
% 0.29/0.65                  = M )
% 0.29/0.65                & ( ( groups4561878855575611511st_nat @ L2 )
% 0.29/0.65                  = N4 ) ) ) )
% 0.29/0.65        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % card_length_sum_list
% 0.29/0.65  thf(fact_10187_sorted__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_upt
% 0.29/0.65  thf(fact_10188_sorted__wrt__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_wrt_upt
% 0.29/0.65  thf(fact_10189_sorted__wrt__less__idx,axiom,
% 0.29/0.65      ! [Ns: list_nat,I2: nat] :
% 0.29/0.65        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.29/0.65       => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 0.29/0.65         => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_wrt_less_idx
% 0.29/0.65  thf(fact_10190_sorted__wrt__upto,axiom,
% 0.29/0.65      ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_wrt_upto
% 0.29/0.65  thf(fact_10191_sorted__upto,axiom,
% 0.29/0.65      ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sorted_upto
% 0.29/0.65  thf(fact_10192_pairs__le__eq__Sigma,axiom,
% 0.29/0.65      ! [M: nat] :
% 0.29/0.65        ( ( collec3392354462482085612at_nat
% 0.29/0.65          @ ( produc6081775807080527818_nat_o
% 0.29/0.65            @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 0.29/0.65        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 0.29/0.65          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % pairs_le_eq_Sigma
% 0.29/0.65  thf(fact_10193_prod__encode__prod__decode__aux,axiom,
% 0.29/0.65      ! [K: nat,M: nat] :
% 0.29/0.65        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 0.29/0.65        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 0.29/0.65  
% 0.29/0.65  % prod_encode_prod_decode_aux
% 0.29/0.65  thf(fact_10194_le__prod__encode__1,axiom,
% 0.29/0.65      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % le_prod_encode_1
% 0.29/0.65  thf(fact_10195_le__prod__encode__2,axiom,
% 0.29/0.65      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % le_prod_encode_2
% 0.29/0.65  thf(fact_10196_prod__encode__def,axiom,
% 0.29/0.65      ( nat_prod_encode
% 0.29/0.65      = ( produc6842872674320459806at_nat
% 0.29/0.65        @ ^ [M6: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N ) ) @ M6 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % prod_encode_def
% 0.29/0.65  thf(fact_10197_list__encode_Oelims,axiom,
% 0.29/0.65      ! [X4: list_nat,Y: nat] :
% 0.29/0.65        ( ( ( nat_list_encode @ X4 )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( ( X4 = nil_nat )
% 0.29/0.65           => ( Y != zero_zero_nat ) )
% 0.29/0.65         => ~ ! [X5: nat,Xs2: list_nat] :
% 0.29/0.65                ( ( X4
% 0.29/0.65                  = ( cons_nat @ X5 @ Xs2 ) )
% 0.29/0.65               => ( Y
% 0.29/0.65                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % list_encode.elims
% 0.29/0.65  thf(fact_10198_list__encode_Osimps_I2_J,axiom,
% 0.29/0.65      ! [X4: nat,Xs: list_nat] :
% 0.29/0.65        ( ( nat_list_encode @ ( cons_nat @ X4 @ Xs ) )
% 0.29/0.65        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % list_encode.simps(2)
% 0.29/0.65  thf(fact_10199_list__encode_Opelims,axiom,
% 0.29/0.65      ! [X4: list_nat,Y: nat] :
% 0.29/0.65        ( ( ( nat_list_encode @ X4 )
% 0.29/0.65          = Y )
% 0.29/0.65       => ( ( accp_list_nat @ nat_list_encode_rel @ X4 )
% 0.29/0.65         => ( ( ( X4 = nil_nat )
% 0.29/0.65             => ( ( Y = zero_zero_nat )
% 0.29/0.65               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.29/0.65           => ~ ! [X5: nat,Xs2: list_nat] :
% 0.29/0.65                  ( ( X4
% 0.29/0.65                    = ( cons_nat @ X5 @ Xs2 ) )
% 0.29/0.65                 => ( ( Y
% 0.29/0.65                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 0.29/0.65                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % list_encode.pelims
% 0.29/0.65  thf(fact_10200_Gcd__int__greater__eq__0,axiom,
% 0.29/0.65      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Gcd_int_greater_eq_0
% 0.29/0.65  thf(fact_10201_Gcd__nat__eq__one,axiom,
% 0.29/0.65      ! [N4: set_nat] :
% 0.29/0.65        ( ( member_nat @ one_one_nat @ N4 )
% 0.29/0.65       => ( ( gcd_Gcd_nat @ N4 )
% 0.29/0.65          = one_one_nat ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Gcd_nat_eq_one
% 0.29/0.65  thf(fact_10202_sort__upt,axiom,
% 0.29/0.65      ! [M: nat,N2: nat] :
% 0.29/0.65        ( ( linord738340561235409698at_nat
% 0.29/0.65          @ ^ [X: nat] : X
% 0.29/0.65          @ ( upt @ M @ N2 ) )
% 0.29/0.65        = ( upt @ M @ N2 ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sort_upt
% 0.29/0.65  thf(fact_10203_sort__upto,axiom,
% 0.29/0.65      ! [I2: int,J: int] :
% 0.29/0.65        ( ( linord1735203802627413978nt_int
% 0.29/0.65          @ ^ [X: int] : X
% 0.29/0.65          @ ( upto @ I2 @ J ) )
% 0.29/0.65        = ( upto @ I2 @ J ) ) ).
% 0.29/0.65  
% 0.29/0.65  % sort_upto
% 0.29/0.65  thf(fact_10204_of__nat__eq__id,axiom,
% 0.29/0.65      semiri1316708129612266289at_nat = id_nat ).
% 0.29/0.65  
% 0.29/0.65  % of_nat_eq_id
% 0.29/0.65  thf(fact_10205_Rat_Opositive__def,axiom,
% 0.29/0.65      ( positive
% 0.29/0.65      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 0.29/0.65        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % Rat.positive_def
% 0.29/0.65  thf(fact_10206_rcis__inverse,axiom,
% 0.29/0.65      ! [R3: real,A: real] :
% 0.29/0.65        ( ( invers8013647133539491842omplex @ ( rcis @ R3 @ A ) )
% 0.29/0.65        = ( rcis @ ( divide_divide_real @ one_one_real @ R3 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % rcis_inverse
% 0.29/0.65  thf(fact_10207_cis__rcis__eq,axiom,
% 0.29/0.65      ( cis
% 0.29/0.65      = ( rcis @ one_one_real ) ) ).
% 0.29/0.65  
% 0.29/0.65  % cis_rcis_eq
% 0.29/0.65  thf(fact_10208_DeMoivre2,axiom,
% 0.29/0.65      ! [R3: real,A: real,N2: nat] :
% 0.29/0.65        ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N2 )
% 0.29/0.65        = ( rcis @ ( power_power_real @ R3 @ N2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % DeMoivre2
% 0.29/0.65  thf(fact_10209_of__rat__dense,axiom,
% 0.29/0.65      ! [X4: real,Y: real] :
% 0.29/0.65        ( ( ord_less_real @ X4 @ Y )
% 0.29/0.65       => ? [Q2: rat] :
% 0.29/0.65            ( ( ord_less_real @ X4 @ ( field_7254667332652039916t_real @ Q2 ) )
% 0.29/0.65            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q2 ) @ Y ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  % of_rat_dense
% 0.29/0.65  
% 0.29/0.65  % Helper facts (38)
% 0.29/0.65  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.29/0.65      ! [X4: int,Y: int] :
% 0.29/0.65        ( ( if_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.29/0.65      ! [X4: int,Y: int] :
% 0.29/0.65        ( ( if_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.29/0.65      ! [X4: nat,Y: nat] :
% 0.29/0.65        ( ( if_nat @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.29/0.65      ! [X4: nat,Y: nat] :
% 0.29/0.65        ( ( if_nat @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.29/0.65      ! [X4: num,Y: num] :
% 0.29/0.65        ( ( if_num @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.29/0.65      ! [X4: num,Y: num] :
% 0.29/0.65        ( ( if_num @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.29/0.65      ! [X4: rat,Y: rat] :
% 0.29/0.65        ( ( if_rat @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.29/0.65      ! [X4: rat,Y: rat] :
% 0.29/0.65        ( ( if_rat @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.65      ! [X4: real,Y: real] :
% 0.29/0.65        ( ( if_real @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.65      ! [X4: real,Y: real] :
% 0.29/0.65        ( ( if_real @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 0.29/0.65      ! [P: real > $o] :
% 0.29/0.65        ( ( P @ ( fChoice_real @ P ) )
% 0.29/0.65        = ( ? [X3: real] : ( P @ X3 ) ) ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.29/0.65      ! [X4: complex,Y: complex] :
% 0.29/0.65        ( ( if_complex @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.29/0.65      ! [X4: complex,Y: complex] :
% 0.29/0.65        ( ( if_complex @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.29/0.65      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.65        ( ( if_Code_integer @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.29/0.65      ! [X4: code_integer,Y: code_integer] :
% 0.29/0.65        ( ( if_Code_integer @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: set_int,Y: set_int] :
% 0.29/0.65        ( ( if_set_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: set_int,Y: set_int] :
% 0.29/0.65        ( ( if_set_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: list_int,Y: list_int] :
% 0.29/0.65        ( ( if_list_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: list_int,Y: list_int] :
% 0.29/0.65        ( ( if_list_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.29/0.65      ! [X4: list_nat,Y: list_nat] :
% 0.29/0.65        ( ( if_list_nat @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.29/0.65      ! [X4: list_nat,Y: list_nat] :
% 0.29/0.65        ( ( if_list_nat @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: int > int,Y: int > int] :
% 0.29/0.65        ( ( if_int_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: int > int,Y: int > int] :
% 0.29/0.65        ( ( if_int_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.29/0.65      ! [X4: option_num,Y: option_num] :
% 0.29/0.65        ( ( if_option_num @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.29/0.65      ! [X4: option_num,Y: option_num] :
% 0.29/0.65        ( ( if_option_num @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 0.29/0.65        ( ( if_Pro3027730157355071871nt_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.29/0.65      ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 0.29/0.65        ( ( if_Pro3027730157355071871nt_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.29/0.65      ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.29/0.65        ( ( if_Pro6206227464963214023at_nat @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.29/0.65      ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.29/0.65        ( ( if_Pro6206227464963214023at_nat @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 0.29/0.65      ! [X4: nat > int > int,Y: nat > int > int] :
% 0.29/0.65        ( ( if_nat_int_int @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 0.29/0.65      ! [X4: nat > int > int,Y: nat > int > int] :
% 0.29/0.65        ( ( if_nat_int_int @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 0.29/0.65      ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 0.29/0.65        ( ( if_nat_nat_nat @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 0.29/0.65      ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 0.29/0.65        ( ( if_nat_nat_nat @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.29/0.65      ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.29/0.65        ( ( if_Pro5737122678794959658eger_o @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.29/0.65      ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.29/0.65        ( ( if_Pro5737122678794959658eger_o @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.29/0.65      ! [P: $o] :
% 0.29/0.65        ( ( P = $true )
% 0.29/0.65        | ( P = $false ) ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.29/0.65      ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.29/0.65        ( ( if_Pro6119634080678213985nteger @ $false @ X4 @ Y )
% 0.29/0.65        = Y ) ).
% 0.29/0.65  
% 0.29/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.29/0.65      ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.29/0.65        ( ( if_Pro6119634080678213985nteger @ $true @ X4 @ Y )
% 0.29/0.65        = X4 ) ).
% 0.29/0.65  
% 0.29/0.65  % Conjectures (1)
% 0.29/0.65  thf(conj_0,conjecture,
% 0.29/0.65      vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ).
% 0.29/0.65  
% 0.29/0.65  %------------------------------------------------------------------------------
% 0.29/0.65  ------------------------
% 8.04/3.06  ---- Embedded in THF ---
% 8.04/3.07  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 8.04/3.07  %%% Generated on Thu Feb 26 07:37:17 EST 2026
% 8.04/3.07  %%% using '$$dhol' embedding, version 1.3.0.
% 8.04/3.07  %%% Logic specification used:
% 8.04/3.07  %%% thf(spec, logic, $$dhol).
% 8.04/3.07  
% 8.04/3.07  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2DTF7681.p
% See solution above
% 8.04/3.10  ------------------------
% 11.00/6.11  ---- Cleaned THF ---
% 11.00/6.11  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,
% 11.00/6.11      produc3368934014287244435at_num: $tType ).
% 11.00/6.11  
% 11.00/6.11  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,
% 11.00/6.11      produc4471711990508489141at_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 11.00/6.11      set_fi4554929511873752355omplex: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      list_P7413028617227757229T_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 11.00/6.11      produc2963631642982155120at_num: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      produc7248412053542808358at_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 11.00/6.11      set_fi7789364187291644575l_real: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 11.00/6.11      filter6041513312241820739omplex: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      list_P7037539587688870467BT_nat: $tType ).
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% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 11.00/6.11      list_P4547456442757143711BT_int: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      list_P5647936690300460905T_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      produc8243902056947475879T_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 11.00/6.11      set_Pr5085853215250843933omplex: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 11.00/6.11      produc8923325533196201883nteger: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 11.00/6.11      list_P3126845725202233233VEBT_o: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      list_P7495141550334521929T_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
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% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
% 11.00/6.11      list_P8526636022914148096eger_o: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      option4927543243414619207at_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 11.00/6.11      set_Pr6218003697084177305l_real: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J,type,
% 11.00/6.11      list_P3744719386663036955um_num: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      list_P6011104703257516679at_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 11.00/6.11      produc9072475918466114483BT_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 11.00/6.11      produc4894624898956917775BT_int: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      set_Pr1261947904930325089at_nat: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 11.00/6.11      set_Pr958786334691620121nt_int: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 11.00/6.11      produc4411394909380815293omplex: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      list_list_VEBT_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 11.00/6.11      list_P7333126701944960589_nat_o: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      list_P6285523579766656935_o_nat: $tType ).
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% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 11.00/6.11      list_P3795440434834930179_o_int: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Set__Oset_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
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% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 11.00/6.11      produc334124729049499915VEBT_o: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      produc2504756804600209347T_VEBT: $tType ).
% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
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% 11.00/6.11  
% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
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% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
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% 11.00/6.11  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 11.00/6.11  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
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% 11.00/6.11  thf(ty_n_t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
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% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 11.00/6.11  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
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% 11.00/6.11  thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
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% 11.00/6.11  thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
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% 11.00/6.11  thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
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% 11.00/6.11      nat2: int > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      ring_11222124179247155820nteger: set_Code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 11.00/6.11      ring_1_Ints_complex: set_complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 11.00/6.11      ring_1_Ints_int: set_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 11.00/6.11      ring_1_Ints_rat: set_rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 11.00/6.11      ring_1_Ints_real: set_real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      ring_18347121197199848620nteger: int > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 11.00/6.11      ring_17405671764205052669omplex: int > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 11.00/6.11      ring_1_of_int_int: int > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 11.00/6.11      ring_1_of_int_rat: int > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 11.00/6.11      ring_1_of_int_real: int > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 11.00/6.11      inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 11.00/6.11      inf_inf_nat: nat > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 11.00/6.11      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 11.00/6.11      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 11.00/6.11      sup_sup_nat: nat > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 11.00/6.11      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 11.00/6.11      lattic8265883725875713057ax_nat: set_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 11.00/6.11      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 11.00/6.11      at_infinity_real: filter_real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 11.00/6.11      append_int: list_int > list_int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 11.00/6.11      append_nat: list_nat > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oconcat_001_Eo,type,
% 11.00/6.11      concat_o: list_list_o > list_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 11.00/6.11      concat_int: list_list_int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 11.00/6.11      concat_nat: list_list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 11.00/6.11      distinct_int: list_int > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 11.00/6.11      distinct_nat: list_nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 11.00/6.11      drop_nat: nat > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 11.00/6.11      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.00/6.11      linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 11.00/6.11      linord2614967742042102400et_nat: set_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 11.00/6.11      cons_int: int > list_int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 11.00/6.11      cons_nat: nat > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 11.00/6.11      nil_int: list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 11.00/6.11      nil_nat: list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 11.00/6.11      hd_nat: list_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.00/6.11      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 11.00/6.11      set_o2: list_o > set_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 11.00/6.11      set_complex2: list_complex > set_complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 11.00/6.11      set_int2: list_int > set_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 11.00/6.11      set_list_o2: list_list_o > set_list_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 11.00/6.11      set_list_int2: list_list_int > set_list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 11.00/6.11      set_list_nat2: list_list_nat > set_list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 11.00/6.11      set_nat2: list_nat > set_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.00/6.11      set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 11.00/6.11      set_real2: list_real > set_real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 11.00/6.11      tl_nat: list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001_Eo,type,
% 11.00/6.11      nth_o: list_o > nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      nth_Code_integer: list_Code_integer > nat > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 11.00/6.11      nth_complex: list_complex > nat > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 11.00/6.11      nth_int: list_int > nat > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 11.00/6.11      nth_list_nat: list_list_nat > nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 11.00/6.11      nth_nat: list_nat > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 11.00/6.11      nth_num: list_num > nat > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 11.00/6.11      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 11.00/6.11      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 11.00/6.11      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 11.00/6.11      nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.00/6.11      nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 11.00/6.11      nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 11.00/6.11      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 11.00/6.11      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 11.00/6.11      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 11.00/6.11      nth_real: list_real > nat > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 11.00/6.11      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 11.00/6.11      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 11.00/6.11      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 11.00/6.11      produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 11.00/6.11      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 11.00/6.11      product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 11.00/6.11      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 11.00/6.11      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 11.00/6.11      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 11.00/6.11      remdups_nat: list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001_Eo,type,
% 11.00/6.11      replicate_o: nat > $o > list_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 11.00/6.11      replicate_complex: nat > complex > list_complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 11.00/6.11      replicate_int: nat > int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 11.00/6.11      replicate_nat: nat > nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.00/6.11      replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 11.00/6.11      replicate_real: nat > real > list_real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 11.00/6.11      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 11.00/6.11      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osubseqs_001_Eo,type,
% 11.00/6.11      subseqs_o: list_o > list_list_o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 11.00/6.11      subseqs_int: list_int > list_list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 11.00/6.11      subseqs_nat: list_nat > list_list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 11.00/6.11      take_nat: nat > list_nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oupt,type,
% 11.00/6.11      upt: nat > nat > list_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oupto,type,
% 11.00/6.11      upto: int > int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oupto__aux,type,
% 11.00/6.11      upto_aux: int > int > list_int > list_int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_List_Oupto__rel,type,
% 11.00/6.11      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_OSuc,type,
% 11.00/6.11      suc: nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.00/6.11      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 11.00/6.11      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 11.00/6.11      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 11.00/6.11      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Onat_Opred,type,
% 11.00/6.11      pred: nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      semiri4939895301339042750nteger: nat > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 11.00/6.11      semiri8010041392384452111omplex: nat > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 11.00/6.11      semiri4216267220026989637d_enat: nat > extended_enat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 11.00/6.11      semiri1314217659103216013at_int: nat > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 11.00/6.11      semiri1316708129612266289at_nat: nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 11.00/6.11      semiri681578069525770553at_rat: nat > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 11.00/6.11      semiri5074537144036343181t_real: nat > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 11.00/6.11      semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 11.00/6.11      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 11.00/6.11      semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 11.00/6.11      semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 11.00/6.11      semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 11.00/6.11      size_size_list_o: list_o > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 11.00/6.11      size_s3445333598471063425nteger: list_Code_integer > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 11.00/6.11      size_s3451745648224563538omplex: list_complex > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 11.00/6.11      size_size_list_int: list_int > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 11.00/6.11      size_s2710708370519433104list_o: list_list_o > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 11.00/6.11      size_s533118279054570080st_int: list_list_int > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 11.00/6.11      size_s3023201423986296836st_nat: list_list_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 11.00/6.11      size_size_list_nat: list_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 11.00/6.11      size_size_list_num: list_num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 11.00/6.11      size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 11.00/6.11      size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 11.00/6.11      size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 11.00/6.11      size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 11.00/6.11      size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 11.00/6.11      size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  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,
% 11.00/6.11      size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 11.00/6.11      size_size_list_real: list_real > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 11.00/6.11      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 11.00/6.11      size_size_num: num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 11.00/6.11      size_size_option_num: option_num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.00/6.11      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 11.00/6.11      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 11.00/6.11      nat_list_encode: list_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 11.00/6.11      nat_list_encode_rel: list_nat > list_nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 11.00/6.11      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 11.00/6.11      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 11.00/6.11      nat_prod_encode: product_prod_nat_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 11.00/6.11      nat_set_decode: nat > set_nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 11.00/6.11      nat_set_encode: set_nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Nat__Bijection_Otriangle,type,
% 11.00/6.11      nat_triangle: nat > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_NthRoot_Oroot,type,
% 11.00/6.11      root: nat > real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_NthRoot_Osqrt,type,
% 11.00/6.11      sqrt: real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_OBitM,type,
% 11.00/6.11      bitM: num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oinc,type,
% 11.00/6.11      inc: num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 11.00/6.11      neg_nu7009210354673126013omplex: complex > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 11.00/6.11      neg_numeral_dbl_int: int > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 11.00/6.11      neg_numeral_dbl_rat: rat > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 11.00/6.11      neg_numeral_dbl_real: real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 11.00/6.11      neg_nu6511756317524482435omplex: complex > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 11.00/6.11      neg_nu3811975205180677377ec_int: int > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 11.00/6.11      neg_nu3179335615603231917ec_rat: rat > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 11.00/6.11      neg_nu6075765906172075777c_real: real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 11.00/6.11      neg_nu8557863876264182079omplex: complex > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 11.00/6.11      neg_nu5851722552734809277nc_int: int > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 11.00/6.11      neg_nu5219082963157363817nc_rat: rat > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 11.00/6.11      neg_nu8295874005876285629c_real: real > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 11.00/6.11      neg_numeral_sub_int: num > num > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum_OBit0,type,
% 11.00/6.11      bit0: num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum_OBit1,type,
% 11.00/6.11      bit1: num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum_OOne,type,
% 11.00/6.11      one: num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 11.00/6.11      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum_Osize__num,type,
% 11.00/6.11      size_num: num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onum__of__nat,type,
% 11.00/6.11      num_of_nat: nat > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 11.00/6.11      numera6620942414471956472nteger: num > code_integer ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 11.00/6.11      numera6690914467698888265omplex: num > complex ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 11.00/6.11      numera1916890842035813515d_enat: num > extended_enat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 11.00/6.11      numeral_numeral_int: num > int ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 11.00/6.11      numeral_numeral_nat: num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 11.00/6.11      numeral_numeral_rat: num > rat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 11.00/6.11      numeral_numeral_real: num > real ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Opow,type,
% 11.00/6.11      pow: num > num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Opred__numeral,type,
% 11.00/6.11      pred_numeral: num > nat ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Num_Osqr,type,
% 11.00/6.11      sqr: num > num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 11.00/6.11      none_num: option_num ).
% 11.00/6.11  
% 11.00/6.11  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.00/6.11      none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 11.00/6.11  
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% 11.11/6.11      product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 11.11/6.11      produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 11.11/6.11      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 11.11/6.11      product_Pair_int_int: int > int > product_prod_int_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 11.11/6.11      product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.11/6.11      produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 11.11/6.11      produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 11.11/6.11      product_Pair_num_num: num > num > product_prod_num_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 11.11/6.11      produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 11.11/6.11      produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 11.11/6.11      produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 11.11/6.11      produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 11.11/6.11      produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 11.11/6.11      produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 11.11/6.11      produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 11.11/6.11      produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 11.11/6.11      produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 11.11/6.11      produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 11.11/6.11      produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 11.11/6.11      produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 11.11/6.11      produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 11.11/6.11      produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 11.11/6.11      produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 11.11/6.11      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.11/6.11      produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 11.11/6.11      produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 11.11/6.11      produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 11.11/6.11      product_fst_int_int: product_prod_int_int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      product_fst_nat_nat: product_prod_nat_nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 11.11/6.11      product_snd_int_int: product_prod_int_int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_OFract,type,
% 11.11/6.11      fract: int > int > rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_ORep__Rat,type,
% 11.11/6.11      rep_Rat: rat > product_prod_int_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 11.11/6.11      field_5140801741446780682s_real: set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 11.11/6.11      field_7254667332652039916t_real: rat > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_Onormalize,type,
% 11.11/6.11      normalize: product_prod_int_int > product_prod_int_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rat_Opositive,type,
% 11.11/6.11      positive: rat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 11.11/6.11      real_V2521375963428798218omplex: set_complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_OReals_001t__Real__Oreal,type,
% 11.11/6.11      real_V470468836141973256s_real: set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 11.11/6.11      real_V3694042436643373181omplex: complex > complex > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 11.11/6.11      real_V975177566351809787t_real: real > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 11.11/6.11      real_V1022390504157884413omplex: complex > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 11.11/6.11      real_V7735802525324610683m_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 11.11/6.11      real_V4546457046886955230omplex: real > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 11.11/6.11      real_V1803761363581548252l_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 11.11/6.11      real_V2046097035970521341omplex: real > complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 11.11/6.11      real_V1485227260804924795R_real: real > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 11.11/6.11      divide1717551699836669952omplex: complex > complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 11.11/6.11      divide_divide_int: int > int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 11.11/6.11      divide_divide_nat: nat > nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 11.11/6.11      divide_divide_rat: rat > rat > rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 11.11/6.11      divide_divide_real: real > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 11.11/6.11      dvd_dvd_complex: complex > complex > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 11.11/6.11      dvd_dvd_int: int > int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 11.11/6.11      dvd_dvd_nat: nat > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 11.11/6.11      dvd_dvd_rat: rat > rat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 11.11/6.11      dvd_dvd_real: real > real > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 11.11/6.11      modulo_modulo_int: int > int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 11.11/6.11      modulo_modulo_nat: nat > nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      zero_n356916108424825756nteger: $o > code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 11.11/6.11      zero_n1201886186963655149omplex: $o > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 11.11/6.11      zero_n2684676970156552555ol_int: $o > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 11.11/6.11      zero_n2687167440665602831ol_nat: $o > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 11.11/6.11      zero_n2052037380579107095ol_rat: $o > rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 11.11/6.11      zero_n3304061248610475627l_real: $o > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 11.11/6.11      suminf_complex: ( nat > complex ) > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 11.11/6.11      suminf_int: ( nat > int ) > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 11.11/6.11      suminf_nat: ( nat > nat ) > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 11.11/6.11      suminf_real: ( nat > real ) > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 11.11/6.11      summable_complex: ( nat > complex ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 11.11/6.11      summable_int: ( nat > int ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 11.11/6.11      summable_nat: ( nat > nat ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 11.11/6.11      summable_real: ( nat > real ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 11.11/6.11      sums_complex: ( nat > complex ) > complex > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 11.11/6.11      sums_int: ( nat > int ) > int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 11.11/6.11      sums_nat: ( nat > nat ) > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 11.11/6.11      sums_real: ( nat > real ) > real > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001_Eo,type,
% 11.11/6.11      collect_o: ( $o > $o ) > set_o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 11.11/6.11      collect_complex: ( complex > $o ) > set_complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 11.11/6.11      collect_int: ( int > $o ) > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 11.11/6.11      collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 11.11/6.11      collect_nat: ( nat > $o ) > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 11.11/6.11      collect_num: ( num > $o ) > set_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 11.11/6.11      collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 11.11/6.11      collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.11/6.11      collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 11.11/6.11      collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 11.11/6.11      collect_rat: ( rat > $o ) > set_rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 11.11/6.11      collect_real: ( real > $o ) > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 11.11/6.11      collect_set_int: ( set_int > $o ) > set_set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_OCollect_001t__VEBT____Definitions__OVEBT,type,
% 11.11/6.11      collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 11.11/6.11      image_int_int: ( int > int ) > set_int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 11.11/6.11      image_nat_int: ( nat > int ) > set_nat > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 11.11/6.11      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 11.11/6.11      image_nat_real: ( nat > real ) > set_nat > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 11.11/6.11      image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 11.11/6.11      image_nat_char: ( nat > char ) > set_nat > set_char ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 11.11/6.11      image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 11.11/6.11      image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 11.11/6.11      image_real_real: ( real > real ) > set_real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 11.11/6.11      image_char_nat: ( char > nat ) > set_char > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 11.11/6.11      insert_int: int > set_int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 11.11/6.11      insert_nat: nat > set_nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 11.11/6.11      set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 11.11/6.11      set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 11.11/6.11      set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 11.11/6.11      set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 11.11/6.11      set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 11.11/6.11      set_or1266510415728281911st_int: int > int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 11.11/6.11      set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 11.11/6.11      set_or7049704709247886629st_num: num > num > set_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 11.11/6.11      set_or633870826150836451st_rat: rat > rat > set_rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 11.11/6.11      set_or1222579329274155063t_real: real > real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 11.11/6.11      set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 11.11/6.11      set_or4662586982721622107an_int: int > int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 11.11/6.11      set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 11.11/6.11      set_ord_atLeast_nat: nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 11.11/6.11      set_ord_atLeast_real: real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 11.11/6.11      set_ord_atMost_int: int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 11.11/6.11      set_ord_atMost_nat: nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 11.11/6.11      set_ord_atMost_num: num > set_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 11.11/6.11      set_ord_atMost_rat: rat > set_rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 11.11/6.11      set_ord_atMost_real: real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
% 11.11/6.11      set_or58775011639299419et_int: set_int > set_set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 11.11/6.11      set_or6656581121297822940st_int: int > int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 11.11/6.11      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 11.11/6.11      set_or5832277885323065728an_int: int > int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 11.11/6.11      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 11.11/6.11      set_or1633881224788618240n_real: real > real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 11.11/6.11      set_or1210151606488870762an_nat: nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 11.11/6.11      set_or5849166863359141190n_real: real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 11.11/6.11      set_ord_lessThan_int: int > set_int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 11.11/6.11      set_ord_lessThan_nat: nat > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 11.11/6.11      set_ord_lessThan_num: num > set_num ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 11.11/6.11      set_ord_lessThan_rat: rat > set_rat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 11.11/6.11      set_or5984915006950818249n_real: real > set_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_String_Oascii__of,type,
% 11.11/6.11      ascii_of: char > char ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_String_Ochar_OChar,type,
% 11.11/6.11      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 11.11/6.11      comm_s629917340098488124ar_nat: char > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_String_Ointeger__of__char,type,
% 11.11/6.11      integer_of_char: char > code_integer ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 11.11/6.11      unique3096191561947761185of_nat: nat > char ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 11.11/6.11      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 11.11/6.11      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 11.11/6.11      topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 11.11/6.11      topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 11.11/6.11      topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 11.11/6.11      topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 11.11/6.11      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 11.11/6.11      topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 11.11/6.11      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 11.11/6.11      topolo2815343760600316023s_real: real > filter_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 11.11/6.11      topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 11.11/6.11      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 11.11/6.11      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 11.11/6.11      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oarccos,type,
% 11.11/6.11      arccos: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 11.11/6.11      arcosh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oarcsin,type,
% 11.11/6.11      arcsin: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oarctan,type,
% 11.11/6.11      arctan: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 11.11/6.11      arsinh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 11.11/6.11      artanh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 11.11/6.11      cos_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 11.11/6.11      cos_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocos__coeff,type,
% 11.11/6.11      cos_coeff: nat > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 11.11/6.11      cosh_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 11.11/6.11      cosh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 11.11/6.11      cot_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 11.11/6.11      cot_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 11.11/6.11      diffs_complex: ( nat > complex ) > nat > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 11.11/6.11      diffs_int: ( nat > int ) > nat > int ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 11.11/6.11      diffs_real: ( nat > real ) > nat > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 11.11/6.11      exp_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 11.11/6.11      exp_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 11.11/6.11      ln_ln_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Olog,type,
% 11.11/6.11      log: real > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Opi,type,
% 11.11/6.11      pi: real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 11.11/6.11      powr_real: real > real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 11.11/6.11      sin_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 11.11/6.11      sin_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Osin__coeff,type,
% 11.11/6.11      sin_coeff: nat > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 11.11/6.11      sinh_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 11.11/6.11      sinh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 11.11/6.11      tan_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 11.11/6.11      tan_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 11.11/6.11      tanh_complex: complex > complex ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 11.11/6.11      tanh_real: real > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 11.11/6.11      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 11.11/6.11      transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 11.11/6.11      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 11.11/6.11      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 11.11/6.11      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 11.11/6.11      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 11.11/6.11      vEBT_VEBT_high: nat > nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 11.11/6.11      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 11.11/6.11      vEBT_VEBT_low: nat > nat > nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 11.11/6.11      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 11.11/6.11      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 11.11/6.11      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 11.11/6.11      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 11.11/6.11      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 11.11/6.11      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 11.11/6.11      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 11.11/6.11      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 11.11/6.11      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 11.11/6.11      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 11.11/6.11      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 11.11/6.11      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 11.11/6.11      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.11/6.11      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 11.11/6.11      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 11.11/6.11      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_Wellfounded_Opred__nat,type,
% 11.11/6.11      pred_nat: set_Pr1261947904930325089at_nat ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 11.11/6.11      fChoice_real: ( real > $o ) > real ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001_Eo,type,
% 11.11/6.11      member_o: $o > set_o > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 11.11/6.11      member_Code_integer: code_integer > set_Code_integer > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 11.11/6.11      member_complex: complex > set_complex > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__Int__Oint,type,
% 11.11/6.11      member_int: int > set_int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 11.11/6.11      member_list_o: list_o > set_list_o > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 11.11/6.11      member_list_int: list_int > set_list_int > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 11.11/6.11      member_list_nat: list_nat > set_list_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 11.11/6.11      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__Nat__Onat,type,
% 11.11/6.11      member_nat: nat > set_nat > $o ).
% 11.11/6.11  
% 11.11/6.11  thf(sy_c_member_001t__Num__Onum,type,
% 11.11/6.12      member_num: num > set_num > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 11.11/6.12      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_c_member_001t__Rat__Orat,type,
% 11.11/6.12      member_rat: rat > set_rat > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_c_member_001t__Real__Oreal,type,
% 11.11/6.12      member_real: real > set_real > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 11.11/6.12      member_set_int: set_int > set_set_int > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 11.11/6.12      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_deg,type,
% 11.11/6.12      deg: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_info,type,
% 11.11/6.12      info: option4927543243414619207at_nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_m____,type,
% 11.11/6.12      m: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_ma____,type,
% 11.11/6.12      ma: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_mi____,type,
% 11.11/6.12      mi: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_n,type,
% 11.11/6.12      n: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_na____,type,
% 11.11/6.12      na: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_summary,type,
% 11.11/6.12      summary: vEBT_VEBT ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_treeList,type,
% 11.11/6.12      treeList: list_VEBT_VEBT ).
% 11.11/6.12  
% 11.11/6.12  thf(sy_v_x,type,
% 11.11/6.12      x: nat ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_0_both__member__options__def,axiom,
% 11.11/6.12      ( vEBT_V8194947554948674370ptions
% 11.11/6.12      = ( ^ [T: vEBT_VEBT,X: nat] :
% 11.11/6.12            ( ( vEBT_V5719532721284313246member @ T @ X )
% 11.11/6.12            | ( vEBT_VEBT_membermima @ T @ X ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_1__092_060open_0621_A_060_Adeg_092_060close_062,axiom,
% 11.11/6.12      ord_less_nat @ one_one_nat @ deg ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_2_VEBT_Oinject_I1_J,axiom,
% 11.11/6.12      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 11.11/6.12        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 11.11/6.12          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 11.11/6.12        = ( ( X11 = Y11 )
% 11.11/6.12          & ( X12 = Y12 )
% 11.11/6.12          & ( X13 = Y13 )
% 11.11/6.12          & ( X14 = Y14 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_3__C5_Ohyps_C_I3_J,axiom,
% 11.11/6.12      ( ( summary
% 11.11/6.12        = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 11.11/6.12     => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_4__C5_Ohyps_C_I2_J,axiom,
% 11.11/6.12      vEBT_invar_vebt @ summary @ m ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_5_assms_I1_J,axiom,
% 11.11/6.12      vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ n ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_6_assms_I2_J,axiom,
% 11.11/6.12      ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 11.11/6.12      ( ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) )
% 11.11/6.12     => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 11.11/6.12      ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
% 11.11/6.12     => ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_9__092_060open_062high_Ax_A_Ideg_Adiv_A2_J_A_060_A2_A_094_Am_092_060close_062,axiom,
% 11.11/6.12      ord_less_nat @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
% 11.11/6.12      ( ( vEBT_VEBT_membermima @ ( 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 ) ) ) ) )
% 11.11/6.12      | ( vEBT_V5719532721284313246member @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_11_assms_I3_J,axiom,
% 11.11/6.12      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 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_12__C5_Ohyps_C_I1_J,axiom,
% 11.11/6.12      ! [X2: vEBT_VEBT] :
% 11.11/6.12        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 11.11/6.12       => ( ( vEBT_invar_vebt @ X2 @ na )
% 11.11/6.12          & ( ( X2
% 11.11/6.12              = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 11.11/6.12           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_13__C5_Ohyps_C_I7_J,axiom,
% 11.11/6.12      ! [I: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 11.11/6.12       => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X3 ) )
% 11.11/6.12          = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_14__C5_Ohyps_C_I6_J,axiom,
% 11.11/6.12      ( deg
% 11.11/6.12      = ( plus_plus_nat @ na @ m ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_15__C5_Ohyps_C_I10_J,axiom,
% 11.11/6.12      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_16_high__def,axiom,
% 11.11/6.12      ( vEBT_VEBT_high
% 11.11/6.12      = ( ^ [X: nat,N: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_17_high__bound__aux,axiom,
% 11.11/6.12      ! [Ma: nat,N2: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 11.11/6.12       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_18__C5_Ohyps_C_I8_J,axiom,
% 11.11/6.12      ( ( mi = ma )
% 11.11/6.12     => ! [X2: vEBT_VEBT] :
% 11.11/6.12          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 11.11/6.12         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_19__C5_Ohyps_C_I5_J,axiom,
% 11.11/6.12      ( m
% 11.11/6.12      = ( suc @ na ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_20__C5_Ohyps_C_I4_J,axiom,
% 11.11/6.12      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 11.11/6.12      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_21_in__children__def,axiom,
% 11.11/6.12      ( vEBT_V5917875025757280293ildren
% 11.11/6.12      = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N ) ) @ ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_22_add__self__div__2,axiom,
% 11.11/6.12      ! [M: nat] :
% 11.11/6.12        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12        = M ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_23__C5_Ohyps_C_I11_J,axiom,
% 11.11/6.12      ( ( mi != ma )
% 11.11/6.12     => ! [I: nat] :
% 11.11/6.12          ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 11.11/6.12         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 11.11/6.12                = I )
% 11.11/6.12             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 11.11/6.12            & ! [X2: nat] :
% 11.11/6.12                ( ( ( ( vEBT_VEBT_high @ X2 @ na )
% 11.11/6.12                    = I )
% 11.11/6.12                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
% 11.11/6.12               => ( ( ord_less_nat @ mi @ X2 )
% 11.11/6.12                  & ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_24_one__add__one,axiom,
% 11.11/6.12      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 11.11/6.12      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_25_one__add__one,axiom,
% 11.11/6.12      ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 11.11/6.12      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_26_one__add__one,axiom,
% 11.11/6.12      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 11.11/6.12      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_27_one__add__one,axiom,
% 11.11/6.12      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 11.11/6.12      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_28_one__add__one,axiom,
% 11.11/6.12      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 11.11/6.12      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_29_one__add__one,axiom,
% 11.11/6.12      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 11.11/6.12      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_30_power__strict__increasing__iff,axiom,
% 11.11/6.12      ! [B: real,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.12       => ( ( ord_less_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 11.11/6.12          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_31_power__strict__increasing__iff,axiom,
% 11.11/6.12      ! [B: rat,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ B )
% 11.11/6.12       => ( ( ord_less_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 11.11/6.12          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_32_power__strict__increasing__iff,axiom,
% 11.11/6.12      ! [B: nat,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ B )
% 11.11/6.12       => ( ( ord_less_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 11.11/6.12          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_33_power__strict__increasing__iff,axiom,
% 11.11/6.12      ! [B: int,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ B )
% 11.11/6.12       => ( ( ord_less_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 11.11/6.12          = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_34_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 11.11/6.12        = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_35_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 11.11/6.12        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_36_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 11.11/6.12        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_37_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 11.11/6.12        = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_38_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 11.11/6.12        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_39_numeral__plus__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 11.11/6.12        = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_40_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_41_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_42_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.12        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_43_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_44_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_45_one__plus__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_46_one__less__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ one @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_47_one__less__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ one @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_48_one__less__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ one @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_49_one__less__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ one @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_50_one__less__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ one @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_51_power__inject__exp,axiom,
% 11.11/6.12      ! [A: real,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.12       => ( ( ( power_power_real @ A @ M )
% 11.11/6.12            = ( power_power_real @ A @ N2 ) )
% 11.11/6.12          = ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_52_power__inject__exp,axiom,
% 11.11/6.12      ! [A: rat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.12       => ( ( ( power_power_rat @ A @ M )
% 11.11/6.12            = ( power_power_rat @ A @ N2 ) )
% 11.11/6.12          = ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_53_power__inject__exp,axiom,
% 11.11/6.12      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.12       => ( ( ( power_power_nat @ A @ M )
% 11.11/6.12            = ( power_power_nat @ A @ N2 ) )
% 11.11/6.12          = ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_54_power__inject__exp,axiom,
% 11.11/6.12      ! [A: int,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.12       => ( ( ( power_power_int @ A @ M )
% 11.11/6.12            = ( power_power_int @ A @ N2 ) )
% 11.11/6.12          = ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_55_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_rat @ N2 )
% 11.11/6.12          = one_one_rat )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_56_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numera1916890842035813515d_enat @ N2 )
% 11.11/6.12          = one_on7984719198319812577d_enat )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_57_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numera6690914467698888265omplex @ N2 )
% 11.11/6.12          = one_one_complex )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_58_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_real @ N2 )
% 11.11/6.12          = one_one_real )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_59_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_nat @ N2 )
% 11.11/6.12          = one_one_nat )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_60_numeral__eq__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_int @ N2 )
% 11.11/6.12          = one_one_int )
% 11.11/6.12        = ( N2 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_61_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_one_rat
% 11.11/6.12          = ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_62_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_on7984719198319812577d_enat
% 11.11/6.12          = ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_63_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_one_complex
% 11.11/6.12          = ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_64_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_one_real
% 11.11/6.12          = ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_65_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_one_nat
% 11.11/6.12          = ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_66_one__eq__numeral__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( one_one_int
% 11.11/6.12          = ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( one = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_67_div__exp__eq,axiom,
% 11.11/6.12      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.12        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_68_div__exp__eq,axiom,
% 11.11/6.12      ! [A: int,M: nat,N2: nat] :
% 11.11/6.12        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.12        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_69_div__exp__eq,axiom,
% 11.11/6.12      ! [A: code_integer,M: nat,N2: nat] :
% 11.11/6.12        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.12        = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_70_even__odd__cases,axiom,
% 11.11/6.12      ! [X4: nat] :
% 11.11/6.12        ( ! [N3: nat] :
% 11.11/6.12            ( X4
% 11.11/6.12           != ( plus_plus_nat @ N3 @ N3 ) )
% 11.11/6.12       => ~ ! [N3: nat] :
% 11.11/6.12              ( X4
% 11.11/6.12             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_71__C5_Ohyps_C_I9_J,axiom,
% 11.11/6.12      ord_less_eq_nat @ mi @ ma ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_72_inthall,axiom,
% 11.11/6.12      ! [Xs: list_real,P: real > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: real] :
% 11.11/6.12            ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_73_inthall,axiom,
% 11.11/6.12      ! [Xs: list_complex,P: complex > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: complex] :
% 11.11/6.12            ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_complex @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_74_inthall,axiom,
% 11.11/6.12      ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: product_prod_nat_nat] :
% 11.11/6.12            ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_75_inthall,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: vEBT_VEBT] :
% 11.11/6.12            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_76_inthall,axiom,
% 11.11/6.12      ! [Xs: list_o,P: $o > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: $o] :
% 11.11/6.12            ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_77_inthall,axiom,
% 11.11/6.12      ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: nat] :
% 11.11/6.12            ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_78_inthall,axiom,
% 11.11/6.12      ! [Xs: list_int,P: int > $o,N2: nat] :
% 11.11/6.12        ( ! [X5: int] :
% 11.11/6.12            ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 11.11/6.12           => ( P @ X5 ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_79_numeral__eq__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( numera1916890842035813515d_enat @ M )
% 11.11/6.12          = ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_80_numeral__eq__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( numera6690914467698888265omplex @ M )
% 11.11/6.12          = ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_81_numeral__eq__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_real @ M )
% 11.11/6.12          = ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_82_numeral__eq__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_nat @ M )
% 11.11/6.12          = ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_83_numeral__eq__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( numeral_numeral_int @ M )
% 11.11/6.12          = ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_84_numeral__le__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_85_numeral__le__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_86_numeral__le__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_87_numeral__le__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_88_numeral__le__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_89_bits__div__by__1,axiom,
% 11.11/6.12      ! [A: nat] :
% 11.11/6.12        ( ( divide_divide_nat @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_90_bits__div__by__1,axiom,
% 11.11/6.12      ! [A: int] :
% 11.11/6.12        ( ( divide_divide_int @ A @ one_one_int )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_91_bits__div__by__1,axiom,
% 11.11/6.12      ! [A: code_integer] :
% 11.11/6.12        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_92_power__one,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( power_power_rat @ one_one_rat @ N2 )
% 11.11/6.12        = one_one_rat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_93_power__one,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( power_power_nat @ one_one_nat @ N2 )
% 11.11/6.12        = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_94_power__one,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( power_power_real @ one_one_real @ N2 )
% 11.11/6.12        = one_one_real ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_95_power__one,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( power_power_int @ one_one_int @ N2 )
% 11.11/6.12        = one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_96_power__one,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( power_power_complex @ one_one_complex @ N2 )
% 11.11/6.12        = one_one_complex ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_97_power__one__right,axiom,
% 11.11/6.12      ! [A: nat] :
% 11.11/6.12        ( ( power_power_nat @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_98_power__one__right,axiom,
% 11.11/6.12      ! [A: real] :
% 11.11/6.12        ( ( power_power_real @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_99_power__one__right,axiom,
% 11.11/6.12      ! [A: int] :
% 11.11/6.12        ( ( power_power_int @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_100_power__one__right,axiom,
% 11.11/6.12      ! [A: complex] :
% 11.11/6.12        ( ( power_power_complex @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_101_set__n__deg__not__0,axiom,
% 11.11/6.12      ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 11.11/6.12        ( ! [X5: vEBT_VEBT] :
% 11.11/6.12            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.12           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 11.11/6.12       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.12            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.12         => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_102_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 11.11/6.12        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_103_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: extended_enat] :
% 11.11/6.12        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 11.11/6.12        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_104_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: complex] :
% 11.11/6.12        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 11.11/6.12        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_105_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: real] :
% 11.11/6.12        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 11.11/6.12        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_106_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 11.11/6.12        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_107_add__numeral__left,axiom,
% 11.11/6.12      ! [V: num,W: num,Z: int] :
% 11.11/6.12        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 11.11/6.12        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_108_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 11.11/6.12        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_109_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: complex,P: complex > $o] :
% 11.11/6.12        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_110_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: real,P: real > $o] :
% 11.11/6.12        ( ( member_real @ A @ ( collect_real @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_111_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: list_nat,P: list_nat > $o] :
% 11.11/6.12        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_112_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: nat,P: nat > $o] :
% 11.11/6.12        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_113_mem__Collect__eq,axiom,
% 11.11/6.12      ! [A: int,P: int > $o] :
% 11.11/6.12        ( ( member_int @ A @ ( collect_int @ P ) )
% 11.11/6.12        = ( P @ A ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_114_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_Pr1261947904930325089at_nat] :
% 11.11/6.12        ( ( collec3392354462482085612at_nat
% 11.11/6.12          @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_115_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_complex] :
% 11.11/6.12        ( ( collect_complex
% 11.11/6.12          @ ^ [X: complex] : ( member_complex @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_116_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_real] :
% 11.11/6.12        ( ( collect_real
% 11.11/6.12          @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_117_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_list_nat] :
% 11.11/6.12        ( ( collect_list_nat
% 11.11/6.12          @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_118_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_nat] :
% 11.11/6.12        ( ( collect_nat
% 11.11/6.12          @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_119_Collect__mem__eq,axiom,
% 11.11/6.12      ! [A2: set_int] :
% 11.11/6.12        ( ( collect_int
% 11.11/6.12          @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 11.11/6.12        = A2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_120_Collect__cong,axiom,
% 11.11/6.12      ! [P: complex > $o,Q: complex > $o] :
% 11.11/6.12        ( ! [X5: complex] :
% 11.11/6.12            ( ( P @ X5 )
% 11.11/6.12            = ( Q @ X5 ) )
% 11.11/6.12       => ( ( collect_complex @ P )
% 11.11/6.12          = ( collect_complex @ Q ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_121_Collect__cong,axiom,
% 11.11/6.12      ! [P: real > $o,Q: real > $o] :
% 11.11/6.12        ( ! [X5: real] :
% 11.11/6.12            ( ( P @ X5 )
% 11.11/6.12            = ( Q @ X5 ) )
% 11.11/6.12       => ( ( collect_real @ P )
% 11.11/6.12          = ( collect_real @ Q ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_122_Collect__cong,axiom,
% 11.11/6.12      ! [P: list_nat > $o,Q: list_nat > $o] :
% 11.11/6.12        ( ! [X5: list_nat] :
% 11.11/6.12            ( ( P @ X5 )
% 11.11/6.12            = ( Q @ X5 ) )
% 11.11/6.12       => ( ( collect_list_nat @ P )
% 11.11/6.12          = ( collect_list_nat @ Q ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_123_Collect__cong,axiom,
% 11.11/6.12      ! [P: nat > $o,Q: nat > $o] :
% 11.11/6.12        ( ! [X5: nat] :
% 11.11/6.12            ( ( P @ X5 )
% 11.11/6.12            = ( Q @ X5 ) )
% 11.11/6.12       => ( ( collect_nat @ P )
% 11.11/6.12          = ( collect_nat @ Q ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_124_Collect__cong,axiom,
% 11.11/6.12      ! [P: int > $o,Q: int > $o] :
% 11.11/6.12        ( ! [X5: int] :
% 11.11/6.12            ( ( P @ X5 )
% 11.11/6.12            = ( Q @ X5 ) )
% 11.11/6.12       => ( ( collect_int @ P )
% 11.11/6.12          = ( collect_int @ Q ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_125_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_126_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_127_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.12        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_128_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_129_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_130_numeral__plus__numeral,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_131_numeral__less__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_132_numeral__less__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_133_numeral__less__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_134_numeral__less__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_135_numeral__less__iff,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_136_numeral__le__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 11.11/6.12        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_137_numeral__le__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 11.11/6.12        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_138_numeral__le__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 11.11/6.12        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_139_numeral__le__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 11.11/6.12        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_140_numeral__le__one__iff,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 11.11/6.12        = ( ord_less_eq_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_141_Suc__numeral,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.12        = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_142_power__increasing__iff,axiom,
% 11.11/6.12      ! [B: real,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.12       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 11.11/6.12          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_143_power__increasing__iff,axiom,
% 11.11/6.12      ! [B: rat,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ B )
% 11.11/6.12       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 11.11/6.12          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_144_power__increasing__iff,axiom,
% 11.11/6.12      ! [B: nat,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ B )
% 11.11/6.12       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 11.11/6.12          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_145_power__increasing__iff,axiom,
% 11.11/6.12      ! [B: int,X4: nat,Y: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ B )
% 11.11/6.12       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 11.11/6.12          = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_146_add__2__eq__Suc_H,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( suc @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_147_add__2__eq__Suc,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.12        = ( suc @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_148_Suc__1,axiom,
% 11.11/6.12      ( ( suc @ one_one_nat )
% 11.11/6.12      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_149_div2__Suc__Suc,axiom,
% 11.11/6.12      ! [M: nat] :
% 11.11/6.12        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_150_Suc__div__le__mono,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_151_add__One__commute,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( plus_plus_num @ one @ N2 )
% 11.11/6.12        = ( plus_plus_num @ N2 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_152_le__numeral__extra_I4_J,axiom,
% 11.11/6.12      ord_less_eq_real @ one_one_real @ one_one_real ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_153_le__numeral__extra_I4_J,axiom,
% 11.11/6.12      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_154_le__numeral__extra_I4_J,axiom,
% 11.11/6.12      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_155_le__numeral__extra_I4_J,axiom,
% 11.11/6.12      ord_less_eq_int @ one_one_int @ one_one_int ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_156_div__le__dividend,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_157_div__le__mono,axiom,
% 11.11/6.12      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_158_power__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: real] :
% 11.11/6.12        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_eq_real @ one_one_real @ A )
% 11.11/6.12         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_159_power__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: rat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 11.11/6.12         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_160_power__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 11.11/6.12         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_161_power__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: int] :
% 11.11/6.12        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_eq_int @ one_one_int @ A )
% 11.11/6.12         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_162_power__le__imp__le__exp,axiom,
% 11.11/6.12      ! [A: real,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.12       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_163_power__le__imp__le__exp,axiom,
% 11.11/6.12      ! [A: rat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.12       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_164_power__le__imp__le__exp,axiom,
% 11.11/6.12      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.12       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_165_power__le__imp__le__exp,axiom,
% 11.11/6.12      ! [A: int,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.12       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_166_Suc__nat__number__of__add,axiom,
% 11.11/6.12      ! [V: num,N2: nat] :
% 11.11/6.12        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 11.11/6.12        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_167_one__le__numeral,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_168_one__le__numeral,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_169_one__le__numeral,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_170_one__le__numeral,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_171_one__le__numeral,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_172_one__le__power,axiom,
% 11.11/6.12      ! [A: real,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_real @ one_one_real @ A )
% 11.11/6.12       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_173_one__le__power,axiom,
% 11.11/6.12      ! [A: rat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 11.11/6.12       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_174_one__le__power,axiom,
% 11.11/6.12      ! [A: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 11.11/6.12       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_175_one__le__power,axiom,
% 11.11/6.12      ! [A: int,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_int @ one_one_int @ A )
% 11.11/6.12       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_176_power__gt1,axiom,
% 11.11/6.12      ! [A: real,N2: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.12       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_177_power__gt1,axiom,
% 11.11/6.12      ! [A: rat,N2: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.12       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_178_power__gt1,axiom,
% 11.11/6.12      ! [A: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.12       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_179_power__gt1,axiom,
% 11.11/6.12      ! [A: int,N2: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.12       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_180_power2__nat__le__imp__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_181_power2__nat__le__eq__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.12        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_182_self__le__ge2__pow,axiom,
% 11.11/6.12      ! [K: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_183_is__num__normalize_I1_J,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_184_is__num__normalize_I1_J,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_185_is__num__normalize_I1_J,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_186_ex__power__ivl2,axiom,
% 11.11/6.12      ! [B: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.12       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 11.11/6.12         => ? [N3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 11.11/6.12              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_187_ex__power__ivl1,axiom,
% 11.11/6.12      ! [B: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.12       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 11.11/6.12         => ? [N3: nat] :
% 11.11/6.12              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 11.11/6.12              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_188_less__numeral__extra_I4_J,axiom,
% 11.11/6.12      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_189_less__numeral__extra_I4_J,axiom,
% 11.11/6.12      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_190_less__numeral__extra_I4_J,axiom,
% 11.11/6.12      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_191_less__numeral__extra_I4_J,axiom,
% 11.11/6.12      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_192_power__divide,axiom,
% 11.11/6.12      ! [A: real,B: real,N2: nat] :
% 11.11/6.12        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 11.11/6.12        = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_193_power__divide,axiom,
% 11.11/6.12      ! [A: complex,B: complex,N2: nat] :
% 11.11/6.12        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 11.11/6.12        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_194_not__numeral__less__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_195_not__numeral__less__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_196_not__numeral__less__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_197_not__numeral__less__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_198_not__numeral__less__one,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_199_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X4 ) )
% 11.11/6.12        = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_200_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X4 ) )
% 11.11/6.12        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_201_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X4 ) )
% 11.11/6.12        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_202_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X4 ) )
% 11.11/6.12        = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_203_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X4 ) )
% 11.11/6.12        = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_204_one__plus__numeral__commute,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X4 ) )
% 11.11/6.12        = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_205_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_206_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_207_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_208_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_209_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_210_numeral__Bit0,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_211_numeral__One,axiom,
% 11.11/6.12      ( ( numeral_numeral_rat @ one )
% 11.11/6.12      = one_one_rat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_212_numeral__One,axiom,
% 11.11/6.12      ( ( numera1916890842035813515d_enat @ one )
% 11.11/6.12      = one_on7984719198319812577d_enat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_213_numeral__One,axiom,
% 11.11/6.12      ( ( numera6690914467698888265omplex @ one )
% 11.11/6.12      = one_one_complex ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_214_numeral__One,axiom,
% 11.11/6.12      ( ( numeral_numeral_real @ one )
% 11.11/6.12      = one_one_real ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_215_numeral__One,axiom,
% 11.11/6.12      ( ( numeral_numeral_nat @ one )
% 11.11/6.12      = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_216_numeral__One,axiom,
% 11.11/6.12      ( ( numeral_numeral_int @ one )
% 11.11/6.12      = one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_217_divide__numeral__1,axiom,
% 11.11/6.12      ! [A: real] :
% 11.11/6.12        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_218_divide__numeral__1,axiom,
% 11.11/6.12      ! [A: complex] :
% 11.11/6.12        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_219_power__one__over,axiom,
% 11.11/6.12      ! [A: rat,N2: nat] :
% 11.11/6.12        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 11.11/6.12        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_220_power__one__over,axiom,
% 11.11/6.12      ! [A: real,N2: nat] :
% 11.11/6.12        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 11.11/6.12        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_221_power__one__over,axiom,
% 11.11/6.12      ! [A: complex,N2: nat] :
% 11.11/6.12        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 11.11/6.12        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_222_numerals_I1_J,axiom,
% 11.11/6.12      ( ( numeral_numeral_nat @ one )
% 11.11/6.12      = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_223_numeral__Bit0__div__2,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_224_numeral__Bit0__div__2,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_225_numeral__Bit0__div__2,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_226_power__strict__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: real] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.12         => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_227_power__strict__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: rat] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.12         => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_228_power__strict__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: nat] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.12         => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_229_power__strict__increasing,axiom,
% 11.11/6.12      ! [N2: nat,N4: nat,A: int] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.12       => ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.12         => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_230_power__less__imp__less__exp,axiom,
% 11.11/6.12      ! [A: real,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.12       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_231_power__less__imp__less__exp,axiom,
% 11.11/6.12      ! [A: rat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.12       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_232_power__less__imp__less__exp,axiom,
% 11.11/6.12      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.12       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_233_power__less__imp__less__exp,axiom,
% 11.11/6.12      ! [A: int,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.12       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_234_one__power2,axiom,
% 11.11/6.12      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_rat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_235_one__power2,axiom,
% 11.11/6.12      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_236_one__power2,axiom,
% 11.11/6.12      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_real ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_237_one__power2,axiom,
% 11.11/6.12      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_238_one__power2,axiom,
% 11.11/6.12      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_complex ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_239_nat__1__add__1,axiom,
% 11.11/6.12      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 11.11/6.12      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_240_less__exp,axiom,
% 11.11/6.12      ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_241_semiring__norm_I76_J,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_242_semiring__norm_I2_J,axiom,
% 11.11/6.12      ( ( plus_plus_num @ one @ one )
% 11.11/6.12      = ( bit0 @ one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_243_field__less__half__sum,axiom,
% 11.11/6.12      ! [X4: rat,Y: rat] :
% 11.11/6.12        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.12       => ( ord_less_rat @ X4 @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_244_field__less__half__sum,axiom,
% 11.11/6.12      ! [X4: real,Y: real] :
% 11.11/6.12        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.12       => ( ord_less_real @ X4 @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_245_semiring__norm_I75_J,axiom,
% 11.11/6.12      ! [M: num] :
% 11.11/6.12        ~ ( ord_less_num @ M @ one ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_246_semiring__norm_I78_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_247_semiring__norm_I6_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_248_nat__add__left__cancel__le,axiom,
% 11.11/6.12      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_249_nat__add__left__cancel__less,axiom,
% 11.11/6.12      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 11.11/6.12        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_250_add__Suc__right,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_251_enat__ord__number_I2_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_252_Suc__le__mono,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 11.11/6.12        = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_253_Suc__less__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 11.11/6.12        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_254_semiring__norm_I87_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ( bit0 @ M )
% 11.11/6.12          = ( bit0 @ N2 ) )
% 11.11/6.12        = ( M = N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_255_nat_Oinject,axiom,
% 11.11/6.12      ! [X22: nat,Y2: nat] :
% 11.11/6.12        ( ( ( suc @ X22 )
% 11.11/6.12          = ( suc @ Y2 ) )
% 11.11/6.12        = ( X22 = Y2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_256_old_Onat_Oinject,axiom,
% 11.11/6.12      ! [Nat: nat,Nat2: nat] :
% 11.11/6.12        ( ( ( suc @ Nat )
% 11.11/6.12          = ( suc @ Nat2 ) )
% 11.11/6.12        = ( Nat = Nat2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_257_semiring__norm_I85_J,axiom,
% 11.11/6.12      ! [M: num] :
% 11.11/6.12        ( ( bit0 @ M )
% 11.11/6.12       != one ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_258_semiring__norm_I83_J,axiom,
% 11.11/6.12      ! [N2: num] :
% 11.11/6.12        ( one
% 11.11/6.12       != ( bit0 @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_259_lessI,axiom,
% 11.11/6.12      ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_260_Suc__mono,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_261_semiring__norm_I71_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_262_semiring__norm_I68_J,axiom,
% 11.11/6.12      ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_263_semiring__norm_I69_J,axiom,
% 11.11/6.12      ! [M: num] :
% 11.11/6.12        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_264_enat__ord__number_I1_J,axiom,
% 11.11/6.12      ! [M: num,N2: num] :
% 11.11/6.12        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_265_enat__less__induct,axiom,
% 11.11/6.12      ! [P: extended_enat > $o,N2: extended_enat] :
% 11.11/6.12        ( ! [N3: extended_enat] :
% 11.11/6.12            ( ! [M2: extended_enat] :
% 11.11/6.12                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 11.11/6.12               => ( P @ M2 ) )
% 11.11/6.12           => ( P @ N3 ) )
% 11.11/6.12       => ( P @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_266_le__num__One__iff,axiom,
% 11.11/6.12      ! [X4: num] :
% 11.11/6.12        ( ( ord_less_eq_num @ X4 @ one )
% 11.11/6.12        = ( X4 = one ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_267_two__realpow__ge__one,axiom,
% 11.11/6.12      ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_268_Suc__inject,axiom,
% 11.11/6.12      ! [X4: nat,Y: nat] :
% 11.11/6.12        ( ( ( suc @ X4 )
% 11.11/6.12          = ( suc @ Y ) )
% 11.11/6.12       => ( X4 = Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_269_n__not__Suc__n,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ( N2
% 11.11/6.12       != ( suc @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_270_nat__neq__iff,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( M != N2 )
% 11.11/6.12        = ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12          | ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_271_less__not__refl,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_272_less__not__refl2,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ M )
% 11.11/6.12       => ( M != N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_273_less__not__refl3,axiom,
% 11.11/6.12      ! [S: nat,T2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ S @ T2 )
% 11.11/6.12       => ( S != T2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_274_less__irrefl__nat,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ~ ( ord_less_nat @ N2 @ N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_275_nat__less__induct,axiom,
% 11.11/6.12      ! [P: nat > $o,N2: nat] :
% 11.11/6.12        ( ! [N3: nat] :
% 11.11/6.12            ( ! [M2: nat] :
% 11.11/6.12                ( ( ord_less_nat @ M2 @ N3 )
% 11.11/6.12               => ( P @ M2 ) )
% 11.11/6.12           => ( P @ N3 ) )
% 11.11/6.12       => ( P @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_276_infinite__descent,axiom,
% 11.11/6.12      ! [P: nat > $o,N2: nat] :
% 11.11/6.12        ( ! [N3: nat] :
% 11.11/6.12            ( ~ ( P @ N3 )
% 11.11/6.12           => ? [M2: nat] :
% 11.11/6.12                ( ( ord_less_nat @ M2 @ N3 )
% 11.11/6.12                & ~ ( P @ M2 ) ) )
% 11.11/6.12       => ( P @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_277_linorder__neqE__nat,axiom,
% 11.11/6.12      ! [X4: nat,Y: nat] :
% 11.11/6.12        ( ( X4 != Y )
% 11.11/6.12       => ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.12         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_278_le__refl,axiom,
% 11.11/6.12      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_279_le__trans,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ( ord_less_eq_nat @ J @ K )
% 11.11/6.12         => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_280_eq__imp__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( M = N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_281_le__antisym,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.12         => ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_282_nat__le__linear,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12        | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_283_Nat_Oex__has__greatest__nat,axiom,
% 11.11/6.12      ! [P: nat > $o,K: nat,B: nat] :
% 11.11/6.12        ( ( P @ K )
% 11.11/6.12       => ( ! [Y3: nat] :
% 11.11/6.12              ( ( P @ Y3 )
% 11.11/6.12             => ( ord_less_eq_nat @ Y3 @ B ) )
% 11.11/6.12         => ? [X5: nat] :
% 11.11/6.12              ( ( P @ X5 )
% 11.11/6.12              & ! [Y4: nat] :
% 11.11/6.12                  ( ( P @ Y4 )
% 11.11/6.12                 => ( ord_less_eq_nat @ Y4 @ X5 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_284_size__neq__size__imp__neq,axiom,
% 11.11/6.12      ! [X4: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 11.11/6.12        ( ( ( size_s6755466524823107622T_VEBT @ X4 )
% 11.11/6.12         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 11.11/6.12       => ( X4 != Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_285_size__neq__size__imp__neq,axiom,
% 11.11/6.12      ! [X4: list_o,Y: list_o] :
% 11.11/6.12        ( ( ( size_size_list_o @ X4 )
% 11.11/6.12         != ( size_size_list_o @ Y ) )
% 11.11/6.12       => ( X4 != Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_286_size__neq__size__imp__neq,axiom,
% 11.11/6.12      ! [X4: list_nat,Y: list_nat] :
% 11.11/6.12        ( ( ( size_size_list_nat @ X4 )
% 11.11/6.12         != ( size_size_list_nat @ Y ) )
% 11.11/6.12       => ( X4 != Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_287_size__neq__size__imp__neq,axiom,
% 11.11/6.12      ! [X4: list_int,Y: list_int] :
% 11.11/6.12        ( ( ( size_size_list_int @ X4 )
% 11.11/6.12         != ( size_size_list_int @ Y ) )
% 11.11/6.12       => ( X4 != Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_288_size__neq__size__imp__neq,axiom,
% 11.11/6.12      ! [X4: num,Y: num] :
% 11.11/6.12        ( ( ( size_size_num @ X4 )
% 11.11/6.12         != ( size_size_num @ Y ) )
% 11.11/6.12       => ( X4 != Y ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_289_Nat_OlessE,axiom,
% 11.11/6.12      ! [I2: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ K )
% 11.11/6.12       => ( ( K
% 11.11/6.12           != ( suc @ I2 ) )
% 11.11/6.12         => ~ ! [J2: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I2 @ J2 )
% 11.11/6.12               => ( K
% 11.11/6.12                 != ( suc @ J2 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_290_Suc__lessD,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_291_Suc__lessE,axiom,
% 11.11/6.12      ! [I2: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 11.11/6.12       => ~ ! [J2: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I2 @ J2 )
% 11.11/6.12             => ( K
% 11.11/6.12               != ( suc @ J2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_292_Suc__lessI,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ( ( suc @ M )
% 11.11/6.12           != N2 )
% 11.11/6.12         => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_293_less__SucE,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12       => ( ~ ( ord_less_nat @ M @ N2 )
% 11.11/6.12         => ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_294_less__SucI,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_295_Ex__less__Suc,axiom,
% 11.11/6.12      ! [N2: nat,P: nat > $o] :
% 11.11/6.12        ( ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 11.11/6.12              & ( P @ I3 ) ) )
% 11.11/6.12        = ( ( P @ N2 )
% 11.11/6.12          | ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ N2 )
% 11.11/6.12              & ( P @ I3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_296_less__Suc__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12        = ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12          | ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_297_not__less__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 11.11/6.12        = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_298_All__less__Suc,axiom,
% 11.11/6.12      ! [N2: nat,P: nat > $o] :
% 11.11/6.12        ( ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 11.11/6.12             => ( P @ I3 ) ) )
% 11.11/6.12        = ( ( P @ N2 )
% 11.11/6.12          & ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ N2 )
% 11.11/6.12             => ( P @ I3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_299_Suc__less__eq2,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.12        = ( ? [M3: nat] :
% 11.11/6.12              ( ( M
% 11.11/6.12                = ( suc @ M3 ) )
% 11.11/6.12              & ( ord_less_nat @ N2 @ M3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_300_less__antisym,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] :
% 11.11/6.12        ( ~ ( ord_less_nat @ N2 @ M )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 11.11/6.12         => ( M = N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_301_Suc__less__SucD,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 11.11/6.12       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_302_less__trans__Suc,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ( ord_less_nat @ J @ K )
% 11.11/6.12         => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_303_less__Suc__induct,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,P: nat > nat > $o] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 11.11/6.12         => ( ! [I4: nat,J2: nat,K2: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I4 @ J2 )
% 11.11/6.12               => ( ( ord_less_nat @ J2 @ K2 )
% 11.11/6.12                 => ( ( P @ I4 @ J2 )
% 11.11/6.12                   => ( ( P @ J2 @ K2 )
% 11.11/6.12                     => ( P @ I4 @ K2 ) ) ) ) )
% 11.11/6.12           => ( P @ I2 @ J ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_304_strict__inc__induct,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,P: nat > $o] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ! [I4: nat] :
% 11.11/6.12              ( ( J
% 11.11/6.12                = ( suc @ I4 ) )
% 11.11/6.12             => ( P @ I4 ) )
% 11.11/6.12         => ( ! [I4: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I4 @ J )
% 11.11/6.12               => ( ( P @ ( suc @ I4 ) )
% 11.11/6.12                 => ( P @ I4 ) ) )
% 11.11/6.12           => ( P @ I2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_305_not__less__less__Suc__eq,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] :
% 11.11/6.12        ( ~ ( ord_less_nat @ N2 @ M )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 11.11/6.12          = ( N2 = M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_306_Suc__leD,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_307_le__SucE,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12       => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12         => ( M
% 11.11/6.12            = ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_308_le__SucI,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_309_Suc__le__D,axiom,
% 11.11/6.12      ! [N2: nat,M4: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M4 )
% 11.11/6.12       => ? [M5: nat] :
% 11.11/6.12            ( M4
% 11.11/6.12            = ( suc @ M5 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_310_le__Suc__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12        = ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12          | ( M
% 11.11/6.12            = ( suc @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_311_Suc__n__not__le__n,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12        ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_312_not__less__eq__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_313_full__nat__induct,axiom,
% 11.11/6.12      ! [P: nat > $o,N2: nat] :
% 11.11/6.12        ( ! [N3: nat] :
% 11.11/6.12            ( ! [M2: nat] :
% 11.11/6.12                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 11.11/6.12               => ( P @ M2 ) )
% 11.11/6.12           => ( P @ N3 ) )
% 11.11/6.12       => ( P @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_314_nat__induct__at__least,axiom,
% 11.11/6.12      ! [M: nat,N2: nat,P: nat > $o] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ( P @ M )
% 11.11/6.12         => ( ! [N3: nat] :
% 11.11/6.12                ( ( ord_less_eq_nat @ M @ N3 )
% 11.11/6.12               => ( ( P @ N3 )
% 11.11/6.12                 => ( P @ ( suc @ N3 ) ) ) )
% 11.11/6.12           => ( P @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_315_transitive__stepwise__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat,R: nat > nat > $o] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 11.11/6.12         => ( ! [X5: nat,Y3: nat,Z2: nat] :
% 11.11/6.12                ( ( R @ X5 @ Y3 )
% 11.11/6.12               => ( ( R @ Y3 @ Z2 )
% 11.11/6.12                 => ( R @ X5 @ Z2 ) ) )
% 11.11/6.12           => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 11.11/6.12             => ( R @ M @ N2 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_316_nat__arith_Osuc1,axiom,
% 11.11/6.12      ! [A2: nat,K: nat,A: nat] :
% 11.11/6.12        ( ( A2
% 11.11/6.12          = ( plus_plus_nat @ K @ A ) )
% 11.11/6.12       => ( ( suc @ A2 )
% 11.11/6.12          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_317_add__Suc,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12        = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_318_add__Suc__shift,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12        = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_319_nat__less__le,axiom,
% 11.11/6.12      ( ord_less_nat
% 11.11/6.12      = ( ^ [M6: nat,N: nat] :
% 11.11/6.12            ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.12            & ( M6 != N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_320_less__imp__le__nat,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_321_le__eq__less__or__eq,axiom,
% 11.11/6.12      ( ord_less_eq_nat
% 11.11/6.12      = ( ^ [M6: nat,N: nat] :
% 11.11/6.12            ( ( ord_less_nat @ M6 @ N )
% 11.11/6.12            | ( M6 = N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_322_less__or__eq__imp__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12          | ( M = N2 ) )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_323_le__neq__implies__less,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ( M != N2 )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_324_less__mono__imp__le__mono,axiom,
% 11.11/6.12      ! [F: nat > nat,I2: nat,J: nat] :
% 11.11/6.12        ( ! [I4: nat,J2: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ J2 )
% 11.11/6.12           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12         => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_325_add__lessD1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 11.11/6.12       => ( ord_less_nat @ I2 @ K ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_326_add__less__mono,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ( ord_less_nat @ K @ L )
% 11.11/6.12         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_327_not__add__less1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat] :
% 11.11/6.12        ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_328_not__add__less2,axiom,
% 11.11/6.12      ! [J: nat,I2: nat] :
% 11.11/6.12        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_329_add__less__mono1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_330_trans__less__add1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_331_trans__less__add2,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_332_less__add__eq__less,axiom,
% 11.11/6.12      ! [K: nat,L: nat,M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ K @ L )
% 11.11/6.12       => ( ( ( plus_plus_nat @ M @ L )
% 11.11/6.12            = ( plus_plus_nat @ K @ N2 ) )
% 11.11/6.12         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_333_add__leE,axiom,
% 11.11/6.12      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 11.11/6.12       => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12           => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_334_le__add1,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_335_le__add2,axiom,
% 11.11/6.12      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_336_add__leD1,axiom,
% 11.11/6.12      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_337_add__leD2,axiom,
% 11.11/6.12      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_338_le__Suc__ex,axiom,
% 11.11/6.12      ! [K: nat,L: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ K @ L )
% 11.11/6.12       => ? [N3: nat] :
% 11.11/6.12            ( L
% 11.11/6.12            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_339_add__le__mono,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ( ord_less_eq_nat @ K @ L )
% 11.11/6.12         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_340_add__le__mono1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_341_trans__le__add1,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_342_trans__le__add2,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,M: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_343_nat__le__iff__add,axiom,
% 11.11/6.12      ( ord_less_eq_nat
% 11.11/6.12      = ( ^ [M6: nat,N: nat] :
% 11.11/6.12          ? [K3: nat] :
% 11.11/6.12            ( N
% 11.11/6.12            = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_344_lift__Suc__mono__less,axiom,
% 11.11/6.12      ! [F: nat > real,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_345_lift__Suc__mono__less,axiom,
% 11.11/6.12      ! [F: nat > rat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_346_lift__Suc__mono__less,axiom,
% 11.11/6.12      ! [F: nat > num,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_347_lift__Suc__mono__less,axiom,
% 11.11/6.12      ! [F: nat > nat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_348_lift__Suc__mono__less,axiom,
% 11.11/6.12      ! [F: nat > int,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_349_lift__Suc__mono__less__iff,axiom,
% 11.11/6.12      ! [F: nat > real,N2: nat,M: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 11.11/6.12          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_350_lift__Suc__mono__less__iff,axiom,
% 11.11/6.12      ! [F: nat > rat,N2: nat,M: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 11.11/6.12          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_351_lift__Suc__mono__less__iff,axiom,
% 11.11/6.12      ! [F: nat > num,N2: nat,M: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 11.11/6.12          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_352_lift__Suc__mono__less__iff,axiom,
% 11.11/6.12      ! [F: nat > nat,N2: nat,M: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 11.11/6.12          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_353_lift__Suc__mono__less__iff,axiom,
% 11.11/6.12      ! [F: nat > int,N2: nat,M: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 11.11/6.12          = ( ord_less_nat @ N2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_354_lift__Suc__mono__le,axiom,
% 11.11/6.12      ! [F: nat > set_int,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_355_lift__Suc__mono__le,axiom,
% 11.11/6.12      ! [F: nat > rat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_356_lift__Suc__mono__le,axiom,
% 11.11/6.12      ! [F: nat > num,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_357_lift__Suc__mono__le,axiom,
% 11.11/6.12      ! [F: nat > nat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_358_lift__Suc__mono__le,axiom,
% 11.11/6.12      ! [F: nat > int,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_359_lift__Suc__antimono__le,axiom,
% 11.11/6.12      ! [F: nat > set_int,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_360_lift__Suc__antimono__le,axiom,
% 11.11/6.12      ! [F: nat > rat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_361_lift__Suc__antimono__le,axiom,
% 11.11/6.12      ! [F: nat > num,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_362_lift__Suc__antimono__le,axiom,
% 11.11/6.12      ! [F: nat > nat,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_363_lift__Suc__antimono__le,axiom,
% 11.11/6.12      ! [F: nat > int,N2: nat,N5: nat] :
% 11.11/6.12        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 11.11/6.12       => ( ( ord_less_eq_nat @ N2 @ N5 )
% 11.11/6.12         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_364_le__imp__less__Suc,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_365_less__eq__Suc__le,axiom,
% 11.11/6.12      ( ord_less_nat
% 11.11/6.12      = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_366_less__Suc__eq__le,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 11.11/6.12        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_367_le__less__Suc__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.12       => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 11.11/6.12          = ( N2 = M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_368_Suc__le__lessD,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_369_inc__induct,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,P: nat > $o] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ( P @ J )
% 11.11/6.12         => ( ! [N3: nat] :
% 11.11/6.12                ( ( ord_less_eq_nat @ I2 @ N3 )
% 11.11/6.12               => ( ( ord_less_nat @ N3 @ J )
% 11.11/6.12                 => ( ( P @ ( suc @ N3 ) )
% 11.11/6.12                   => ( P @ N3 ) ) ) )
% 11.11/6.12           => ( P @ I2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_370_dec__induct,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,P: nat > $o] :
% 11.11/6.12        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12       => ( ( P @ I2 )
% 11.11/6.12         => ( ! [N3: nat] :
% 11.11/6.12                ( ( ord_less_eq_nat @ I2 @ N3 )
% 11.11/6.12               => ( ( ord_less_nat @ N3 @ J )
% 11.11/6.12                 => ( ( P @ N3 )
% 11.11/6.12                   => ( P @ ( suc @ N3 ) ) ) ) )
% 11.11/6.12           => ( P @ J ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_371_Suc__le__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 11.11/6.12        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_372_Suc__leI,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_373_less__natE,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ~ ! [Q2: nat] :
% 11.11/6.12              ( N2
% 11.11/6.12             != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_374_less__add__Suc1,axiom,
% 11.11/6.12      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_375_less__add__Suc2,axiom,
% 11.11/6.12      ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_376_less__iff__Suc__add,axiom,
% 11.11/6.12      ( ord_less_nat
% 11.11/6.12      = ( ^ [M6: nat,N: nat] :
% 11.11/6.12          ? [K3: nat] :
% 11.11/6.12            ( N
% 11.11/6.12            = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_377_less__imp__Suc__add,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ? [K2: nat] :
% 11.11/6.12            ( N2
% 11.11/6.12            = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_378_mono__nat__linear__lb,axiom,
% 11.11/6.12      ! [F: nat > nat,M: nat,K: nat] :
% 11.11/6.12        ( ! [M5: nat,N3: nat] :
% 11.11/6.12            ( ( ord_less_nat @ M5 @ N3 )
% 11.11/6.12           => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_379_Suc__eq__plus1,axiom,
% 11.11/6.12      ( suc
% 11.11/6.12      = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_380_plus__1__eq__Suc,axiom,
% 11.11/6.12      ( ( plus_plus_nat @ one_one_nat )
% 11.11/6.12      = suc ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_381_Suc__eq__plus1__left,axiom,
% 11.11/6.12      ( suc
% 11.11/6.12      = ( plus_plus_nat @ one_one_nat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_382_field__sum__of__halves,axiom,
% 11.11/6.12      ! [X4: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 11.11/6.12        = X4 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_383_field__sum__of__halves,axiom,
% 11.11/6.12      ! [X4: real] :
% 11.11/6.12        ( ( plus_plus_real @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.12        = X4 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_384_div__by__1,axiom,
% 11.11/6.12      ! [A: rat] :
% 11.11/6.12        ( ( divide_divide_rat @ A @ one_one_rat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_385_div__by__1,axiom,
% 11.11/6.12      ! [A: nat] :
% 11.11/6.12        ( ( divide_divide_nat @ A @ one_one_nat )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_386_div__by__1,axiom,
% 11.11/6.12      ! [A: int] :
% 11.11/6.12        ( ( divide_divide_int @ A @ one_one_int )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_387_div__by__1,axiom,
% 11.11/6.12      ! [A: real] :
% 11.11/6.12        ( ( divide_divide_real @ A @ one_one_real )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_388_div__by__1,axiom,
% 11.11/6.12      ! [A: complex] :
% 11.11/6.12        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_389_div__by__1,axiom,
% 11.11/6.12      ! [A: code_integer] :
% 11.11/6.12        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 11.11/6.12        = A ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_390_add__less__cancel__left,axiom,
% 11.11/6.12      ! [C: real,A: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 11.11/6.12        = ( ord_less_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_391_add__less__cancel__left,axiom,
% 11.11/6.12      ! [C: rat,A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 11.11/6.12        = ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_392_add__less__cancel__left,axiom,
% 11.11/6.12      ! [C: nat,A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 11.11/6.12        = ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_393_add__less__cancel__left,axiom,
% 11.11/6.12      ! [C: int,A: int,B: int] :
% 11.11/6.12        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 11.11/6.12        = ( ord_less_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_394_add__less__cancel__right,axiom,
% 11.11/6.12      ! [A: real,C: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.12        = ( ord_less_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_395_add__less__cancel__right,axiom,
% 11.11/6.12      ! [A: rat,C: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.12        = ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_396_add__less__cancel__right,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.12        = ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_397_add__less__cancel__right,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.12        = ( ord_less_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_398_add__le__cancel__left,axiom,
% 11.11/6.12      ! [C: real,A: real,B: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 11.11/6.12        = ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_399_add__le__cancel__left,axiom,
% 11.11/6.12      ! [C: rat,A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 11.11/6.12        = ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_400_add__le__cancel__left,axiom,
% 11.11/6.12      ! [C: nat,A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 11.11/6.12        = ( ord_less_eq_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_401_add__le__cancel__left,axiom,
% 11.11/6.12      ! [C: int,A: int,B: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 11.11/6.12        = ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_402_add__le__cancel__right,axiom,
% 11.11/6.12      ! [A: real,C: real,B: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.12        = ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_403_add__le__cancel__right,axiom,
% 11.11/6.12      ! [A: rat,C: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.12        = ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_404_add__le__cancel__right,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.12        = ( ord_less_eq_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_405_add__le__cancel__right,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.12        = ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_406_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_real] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 11.11/6.12       => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_407_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_complex] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 11.11/6.12       => ( member_complex @ ( nth_complex @ Xs @ N2 ) @ ( set_complex2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_408_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_P6011104703257516679at_nat] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 11.11/6.12       => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_409_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_VEBT_VEBT] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_410_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_o] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12       => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_411_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_nat] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12       => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_412_nth__mem,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_int] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12       => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_413_list__ball__nth,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12       => ( ! [X5: vEBT_VEBT] :
% 11.11/6.12              ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12             => ( P @ X5 ) )
% 11.11/6.12         => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_414_list__ball__nth,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_o,P: $o > $o] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12       => ( ! [X5: $o] :
% 11.11/6.12              ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 11.11/6.12             => ( P @ X5 ) )
% 11.11/6.12         => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_415_list__ball__nth,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12       => ( ! [X5: nat] :
% 11.11/6.12              ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 11.11/6.12             => ( P @ X5 ) )
% 11.11/6.12         => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_416_list__ball__nth,axiom,
% 11.11/6.12      ! [N2: nat,Xs: list_int,P: int > $o] :
% 11.11/6.12        ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12       => ( ! [X5: int] :
% 11.11/6.12              ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 11.11/6.12             => ( P @ X5 ) )
% 11.11/6.12         => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_417_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: real,Xs: list_real] :
% 11.11/6.12        ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 11.11/6.12              & ( ( nth_real @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_418_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: complex,Xs: list_complex] :
% 11.11/6.12        ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 11.11/6.12              & ( ( nth_complex @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_419_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 11.11/6.12        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 11.11/6.12              & ( ( nth_Pr7617993195940197384at_nat @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_420_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 11.11/6.12        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12              & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_421_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: $o,Xs: list_o] :
% 11.11/6.12        ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12              & ( ( nth_o @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_422_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: nat,Xs: list_nat] :
% 11.11/6.12        ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12              & ( ( nth_nat @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_423_in__set__conv__nth,axiom,
% 11.11/6.12      ! [X4: int,Xs: list_int] :
% 11.11/6.12        ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 11.11/6.12        = ( ? [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12              & ( ( nth_int @ Xs @ I3 )
% 11.11/6.12                = X4 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_424_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_real,P: real > $o,X4: real] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_425_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_complex,P: complex > $o,X4: complex] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_426_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X4: product_prod_nat_nat] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_427_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_428_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_o,P: $o > $o,X4: $o] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_429_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_nat,P: nat > $o,X4: nat] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_430_all__nth__imp__all__set,axiom,
% 11.11/6.12      ! [Xs: list_int,P: int > $o,X4: int] :
% 11.11/6.12        ( ! [I4: nat] :
% 11.11/6.12            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12           => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 11.11/6.12       => ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 11.11/6.12         => ( P @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_431_all__set__conv__all__nth,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 11.11/6.12        ( ( ! [X: vEBT_VEBT] :
% 11.11/6.12              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12             => ( P @ X ) ) )
% 11.11/6.12        = ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12             => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_432_all__set__conv__all__nth,axiom,
% 11.11/6.12      ! [Xs: list_o,P: $o > $o] :
% 11.11/6.12        ( ( ! [X: $o] :
% 11.11/6.12              ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 11.11/6.12             => ( P @ X ) ) )
% 11.11/6.12        = ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12             => ( P @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_433_all__set__conv__all__nth,axiom,
% 11.11/6.12      ! [Xs: list_nat,P: nat > $o] :
% 11.11/6.12        ( ( ! [X: nat] :
% 11.11/6.12              ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 11.11/6.12             => ( P @ X ) ) )
% 11.11/6.12        = ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12             => ( P @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_434_all__set__conv__all__nth,axiom,
% 11.11/6.12      ! [Xs: list_int,P: int > $o] :
% 11.11/6.12        ( ( ! [X: int] :
% 11.11/6.12              ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 11.11/6.12             => ( P @ X ) ) )
% 11.11/6.12        = ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12             => ( P @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_435_gt__half__sum,axiom,
% 11.11/6.12      ! [A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_436_gt__half__sum,axiom,
% 11.11/6.12      ! [A: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_437_less__half__sum,axiom,
% 11.11/6.12      ! [A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_438_less__half__sum,axiom,
% 11.11/6.12      ! [A: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_439_add__right__cancel,axiom,
% 11.11/6.12      ! [B: real,A: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ B @ A )
% 11.11/6.12          = ( plus_plus_real @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_440_add__right__cancel,axiom,
% 11.11/6.12      ! [B: rat,A: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ B @ A )
% 11.11/6.12          = ( plus_plus_rat @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_441_add__right__cancel,axiom,
% 11.11/6.12      ! [B: nat,A: nat,C: nat] :
% 11.11/6.12        ( ( ( plus_plus_nat @ B @ A )
% 11.11/6.12          = ( plus_plus_nat @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_442_add__right__cancel,axiom,
% 11.11/6.12      ! [B: int,A: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ B @ A )
% 11.11/6.12          = ( plus_plus_int @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_443_add__left__cancel,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.12          = ( plus_plus_real @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_444_add__left__cancel,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.12          = ( plus_plus_rat @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_445_add__left__cancel,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ( plus_plus_nat @ A @ B )
% 11.11/6.12          = ( plus_plus_nat @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_446_add__left__cancel,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.12          = ( plus_plus_int @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_447_real__arch__pow,axiom,
% 11.11/6.12      ! [X4: real,Y: real] :
% 11.11/6.12        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.12       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X4 @ N3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_448_less__eq__real__def,axiom,
% 11.11/6.12      ( ord_less_eq_real
% 11.11/6.12      = ( ^ [X: real,Y5: real] :
% 11.11/6.12            ( ( ord_less_real @ X @ Y5 )
% 11.11/6.12            | ( X = Y5 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_449_complete__real,axiom,
% 11.11/6.12      ! [S2: set_real] :
% 11.11/6.12        ( ? [X2: real] : ( member_real @ X2 @ S2 )
% 11.11/6.12       => ( ? [Z3: real] :
% 11.11/6.12            ! [X5: real] :
% 11.11/6.12              ( ( member_real @ X5 @ S2 )
% 11.11/6.12             => ( ord_less_eq_real @ X5 @ Z3 ) )
% 11.11/6.12         => ? [Y3: real] :
% 11.11/6.12              ( ! [X2: real] :
% 11.11/6.12                  ( ( member_real @ X2 @ S2 )
% 11.11/6.12                 => ( ord_less_eq_real @ X2 @ Y3 ) )
% 11.11/6.12              & ! [Z3: real] :
% 11.11/6.12                  ( ! [X5: real] :
% 11.11/6.12                      ( ( member_real @ X5 @ S2 )
% 11.11/6.12                     => ( ord_less_eq_real @ X5 @ Z3 ) )
% 11.11/6.12                 => ( ord_less_eq_real @ Y3 @ Z3 ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_450_linorder__neqE__linordered__idom,axiom,
% 11.11/6.12      ! [X4: real,Y: real] :
% 11.11/6.12        ( ( X4 != Y )
% 11.11/6.12       => ( ~ ( ord_less_real @ X4 @ Y )
% 11.11/6.12         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_451_linorder__neqE__linordered__idom,axiom,
% 11.11/6.12      ! [X4: rat,Y: rat] :
% 11.11/6.12        ( ( X4 != Y )
% 11.11/6.12       => ( ~ ( ord_less_rat @ X4 @ Y )
% 11.11/6.12         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_452_linorder__neqE__linordered__idom,axiom,
% 11.11/6.12      ! [X4: int,Y: int] :
% 11.11/6.12        ( ( X4 != Y )
% 11.11/6.12       => ( ~ ( ord_less_int @ X4 @ Y )
% 11.11/6.12         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_453_linordered__field__no__ub,axiom,
% 11.11/6.12      ! [X2: real] :
% 11.11/6.12      ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_454_linordered__field__no__ub,axiom,
% 11.11/6.12      ! [X2: rat] :
% 11.11/6.12      ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_455_linordered__field__no__lb,axiom,
% 11.11/6.12      ! [X2: real] :
% 11.11/6.12      ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_456_linordered__field__no__lb,axiom,
% 11.11/6.12      ! [X2: rat] :
% 11.11/6.12      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_457_one__reorient,axiom,
% 11.11/6.12      ! [X4: complex] :
% 11.11/6.12        ( ( one_one_complex = X4 )
% 11.11/6.12        = ( X4 = one_one_complex ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_458_one__reorient,axiom,
% 11.11/6.12      ! [X4: real] :
% 11.11/6.12        ( ( one_one_real = X4 )
% 11.11/6.12        = ( X4 = one_one_real ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_459_one__reorient,axiom,
% 11.11/6.12      ! [X4: rat] :
% 11.11/6.12        ( ( one_one_rat = X4 )
% 11.11/6.12        = ( X4 = one_one_rat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_460_one__reorient,axiom,
% 11.11/6.12      ! [X4: nat] :
% 11.11/6.12        ( ( one_one_nat = X4 )
% 11.11/6.12        = ( X4 = one_one_nat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_461_one__reorient,axiom,
% 11.11/6.12      ! [X4: int] :
% 11.11/6.12        ( ( one_one_int = X4 )
% 11.11/6.12        = ( X4 = one_one_int ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_462_add__right__imp__eq,axiom,
% 11.11/6.12      ! [B: real,A: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ B @ A )
% 11.11/6.12          = ( plus_plus_real @ C @ A ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_463_add__right__imp__eq,axiom,
% 11.11/6.12      ! [B: rat,A: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ B @ A )
% 11.11/6.12          = ( plus_plus_rat @ C @ A ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_464_add__right__imp__eq,axiom,
% 11.11/6.12      ! [B: nat,A: nat,C: nat] :
% 11.11/6.12        ( ( ( plus_plus_nat @ B @ A )
% 11.11/6.12          = ( plus_plus_nat @ C @ A ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_465_add__right__imp__eq,axiom,
% 11.11/6.12      ! [B: int,A: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ B @ A )
% 11.11/6.12          = ( plus_plus_int @ C @ A ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_466_add__left__imp__eq,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.12          = ( plus_plus_real @ A @ C ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_467_add__left__imp__eq,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.12          = ( plus_plus_rat @ A @ C ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_468_add__left__imp__eq,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ( plus_plus_nat @ A @ B )
% 11.11/6.12          = ( plus_plus_nat @ A @ C ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_469_add__left__imp__eq,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.12          = ( plus_plus_int @ A @ C ) )
% 11.11/6.12       => ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_470_add_Oleft__commute,axiom,
% 11.11/6.12      ! [B: real,A: real,C: real] :
% 11.11/6.12        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 11.11/6.12        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_471_add_Oleft__commute,axiom,
% 11.11/6.12      ! [B: rat,A: rat,C: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 11.11/6.12        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_472_add_Oleft__commute,axiom,
% 11.11/6.12      ! [B: nat,A: nat,C: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 11.11/6.12        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_473_add_Oleft__commute,axiom,
% 11.11/6.12      ! [B: int,A: int,C: int] :
% 11.11/6.12        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 11.11/6.12        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_474_add_Ocommute,axiom,
% 11.11/6.12      ( plus_plus_real
% 11.11/6.12      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_475_add_Ocommute,axiom,
% 11.11/6.12      ( plus_plus_rat
% 11.11/6.12      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_476_add_Ocommute,axiom,
% 11.11/6.12      ( plus_plus_nat
% 11.11/6.12      = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_477_add_Ocommute,axiom,
% 11.11/6.12      ( plus_plus_int
% 11.11/6.12      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_478_add_Oright__cancel,axiom,
% 11.11/6.12      ! [B: real,A: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ B @ A )
% 11.11/6.12          = ( plus_plus_real @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_479_add_Oright__cancel,axiom,
% 11.11/6.12      ! [B: rat,A: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ B @ A )
% 11.11/6.12          = ( plus_plus_rat @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_480_add_Oright__cancel,axiom,
% 11.11/6.12      ! [B: int,A: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ B @ A )
% 11.11/6.12          = ( plus_plus_int @ C @ A ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_481_add_Oleft__cancel,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.12          = ( plus_plus_real @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_482_add_Oleft__cancel,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.12          = ( plus_plus_rat @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_483_add_Oleft__cancel,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.12          = ( plus_plus_int @ A @ C ) )
% 11.11/6.12        = ( B = C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_484_add_Oassoc,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_485_add_Oassoc,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_486_add_Oassoc,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_487_add_Oassoc,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_488_group__cancel_Oadd2,axiom,
% 11.11/6.12      ! [B3: real,K: real,B: real,A: real] :
% 11.11/6.12        ( ( B3
% 11.11/6.12          = ( plus_plus_real @ K @ B ) )
% 11.11/6.12       => ( ( plus_plus_real @ A @ B3 )
% 11.11/6.12          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_489_group__cancel_Oadd2,axiom,
% 11.11/6.12      ! [B3: rat,K: rat,B: rat,A: rat] :
% 11.11/6.12        ( ( B3
% 11.11/6.12          = ( plus_plus_rat @ K @ B ) )
% 11.11/6.12       => ( ( plus_plus_rat @ A @ B3 )
% 11.11/6.12          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_490_group__cancel_Oadd2,axiom,
% 11.11/6.12      ! [B3: nat,K: nat,B: nat,A: nat] :
% 11.11/6.12        ( ( B3
% 11.11/6.12          = ( plus_plus_nat @ K @ B ) )
% 11.11/6.12       => ( ( plus_plus_nat @ A @ B3 )
% 11.11/6.12          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_491_group__cancel_Oadd2,axiom,
% 11.11/6.12      ! [B3: int,K: int,B: int,A: int] :
% 11.11/6.12        ( ( B3
% 11.11/6.12          = ( plus_plus_int @ K @ B ) )
% 11.11/6.12       => ( ( plus_plus_int @ A @ B3 )
% 11.11/6.12          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_492_group__cancel_Oadd1,axiom,
% 11.11/6.12      ! [A2: real,K: real,A: real,B: real] :
% 11.11/6.12        ( ( A2
% 11.11/6.12          = ( plus_plus_real @ K @ A ) )
% 11.11/6.12       => ( ( plus_plus_real @ A2 @ B )
% 11.11/6.12          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_493_group__cancel_Oadd1,axiom,
% 11.11/6.12      ! [A2: rat,K: rat,A: rat,B: rat] :
% 11.11/6.12        ( ( A2
% 11.11/6.12          = ( plus_plus_rat @ K @ A ) )
% 11.11/6.12       => ( ( plus_plus_rat @ A2 @ B )
% 11.11/6.12          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_494_group__cancel_Oadd1,axiom,
% 11.11/6.12      ! [A2: nat,K: nat,A: nat,B: nat] :
% 11.11/6.12        ( ( A2
% 11.11/6.12          = ( plus_plus_nat @ K @ A ) )
% 11.11/6.12       => ( ( plus_plus_nat @ A2 @ B )
% 11.11/6.12          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_495_group__cancel_Oadd1,axiom,
% 11.11/6.12      ! [A2: int,K: int,A: int,B: int] :
% 11.11/6.12        ( ( A2
% 11.11/6.12          = ( plus_plus_int @ K @ A ) )
% 11.11/6.12       => ( ( plus_plus_int @ A2 @ B )
% 11.11/6.12          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_496_add__mono__thms__linordered__semiring_I4_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ( plus_plus_real @ I2 @ K )
% 11.11/6.12          = ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_497_add__mono__thms__linordered__semiring_I4_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ( plus_plus_rat @ I2 @ K )
% 11.11/6.12          = ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_498_add__mono__thms__linordered__semiring_I4_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ( plus_plus_nat @ I2 @ K )
% 11.11/6.12          = ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_499_add__mono__thms__linordered__semiring_I4_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ( plus_plus_int @ I2 @ K )
% 11.11/6.12          = ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_500_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_501_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_502_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_504_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_real,B3: set_real] :
% 11.11/6.12        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: real] :
% 11.11/6.12              ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 11.11/6.12             => ( member_real @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_505_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_complex,B3: set_complex] :
% 11.11/6.12        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: complex] :
% 11.11/6.12              ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 11.11/6.12             => ( member_complex @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_506_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_P6011104703257516679at_nat,B3: set_Pr1261947904930325089at_nat] :
% 11.11/6.12        ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: product_prod_nat_nat] :
% 11.11/6.12              ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.12             => ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_507_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 11.11/6.12        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: vEBT_VEBT] :
% 11.11/6.12              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.12             => ( member_VEBT_VEBT @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_508_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_nat,B3: set_nat] :
% 11.11/6.12        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: nat] :
% 11.11/6.12              ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 11.11/6.12             => ( member_nat @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_509_subset__code_I1_J,axiom,
% 11.11/6.12      ! [Xs: list_int,B3: set_int] :
% 11.11/6.12        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 11.11/6.12        = ( ! [X: int] :
% 11.11/6.12              ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 11.11/6.12             => ( member_int @ X @ B3 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_510_neq__if__length__neq,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 11.11/6.12        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 11.11/6.12         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 11.11/6.12       => ( Xs != Ys ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_511_neq__if__length__neq,axiom,
% 11.11/6.12      ! [Xs: list_o,Ys: list_o] :
% 11.11/6.12        ( ( ( size_size_list_o @ Xs )
% 11.11/6.12         != ( size_size_list_o @ Ys ) )
% 11.11/6.12       => ( Xs != Ys ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_512_neq__if__length__neq,axiom,
% 11.11/6.12      ! [Xs: list_nat,Ys: list_nat] :
% 11.11/6.12        ( ( ( size_size_list_nat @ Xs )
% 11.11/6.12         != ( size_size_list_nat @ Ys ) )
% 11.11/6.12       => ( Xs != Ys ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_513_neq__if__length__neq,axiom,
% 11.11/6.12      ! [Xs: list_int,Ys: list_int] :
% 11.11/6.12        ( ( ( size_size_list_int @ Xs )
% 11.11/6.12         != ( size_size_list_int @ Ys ) )
% 11.11/6.12       => ( Xs != Ys ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_514_Ex__list__of__length,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12      ? [Xs2: list_VEBT_VEBT] :
% 11.11/6.12        ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 11.11/6.12        = N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_515_Ex__list__of__length,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12      ? [Xs2: list_o] :
% 11.11/6.12        ( ( size_size_list_o @ Xs2 )
% 11.11/6.12        = N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_516_Ex__list__of__length,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12      ? [Xs2: list_nat] :
% 11.11/6.12        ( ( size_size_list_nat @ Xs2 )
% 11.11/6.12        = N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_517_Ex__list__of__length,axiom,
% 11.11/6.12      ! [N2: nat] :
% 11.11/6.12      ? [Xs2: list_int] :
% 11.11/6.12        ( ( size_size_list_int @ Xs2 )
% 11.11/6.12        = N2 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_518_add__le__imp__le__right,axiom,
% 11.11/6.12      ! [A: real,C: real,B: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.12       => ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_519_add__le__imp__le__right,axiom,
% 11.11/6.12      ! [A: rat,C: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.12       => ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_520_add__le__imp__le__right,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.12       => ( ord_less_eq_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_521_add__le__imp__le__right,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.12       => ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_522_add__le__imp__le__left,axiom,
% 11.11/6.12      ! [C: real,A: real,B: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 11.11/6.12       => ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_523_add__le__imp__le__left,axiom,
% 11.11/6.12      ! [C: rat,A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 11.11/6.12       => ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_524_add__le__imp__le__left,axiom,
% 11.11/6.12      ! [C: nat,A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 11.11/6.12       => ( ord_less_eq_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_525_add__le__imp__le__left,axiom,
% 11.11/6.12      ! [C: int,A: int,B: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 11.11/6.12       => ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_526_le__iff__add,axiom,
% 11.11/6.12      ( ord_less_eq_nat
% 11.11/6.12      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.12          ? [C2: nat] :
% 11.11/6.12            ( B2
% 11.11/6.12            = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_527_add__right__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.12       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_528_add__right__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.12       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_529_add__right__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_530_add__right__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.12       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_531_less__eqE,axiom,
% 11.11/6.12      ! [A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.12       => ~ ! [C3: nat] :
% 11.11/6.12              ( B
% 11.11/6.12             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_532_add__left__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.12       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_533_add__left__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.12       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_534_add__left__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_535_add__left__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.12       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_536_add__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.12         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_537_add__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_rat @ C @ D )
% 11.11/6.12         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_538_add__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_nat @ C @ D )
% 11.11/6.12         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_539_add__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_int @ C @ D )
% 11.11/6.12         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_540_add__mono__thms__linordered__semiring_I1_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_eq_real @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_541_add__mono__thms__linordered__semiring_I1_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_eq_rat @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_542_add__mono__thms__linordered__semiring_I1_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_543_add__mono__thms__linordered__semiring_I1_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_544_add__mono__thms__linordered__semiring_I2_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_eq_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_545_add__mono__thms__linordered__semiring_I2_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_eq_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_546_add__mono__thms__linordered__semiring_I2_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_eq_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_547_add__mono__thms__linordered__semiring_I2_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_eq_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_548_add__mono__thms__linordered__semiring_I3_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_eq_real @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_549_add__mono__thms__linordered__semiring_I3_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_eq_rat @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_550_add__mono__thms__linordered__semiring_I3_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_551_add__mono__thms__linordered__semiring_I3_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_552_add__less__imp__less__right,axiom,
% 11.11/6.12      ! [A: real,C: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.12       => ( ord_less_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_553_add__less__imp__less__right,axiom,
% 11.11/6.12      ! [A: rat,C: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.12       => ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_554_add__less__imp__less__right,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.12       => ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_555_add__less__imp__less__right,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.12       => ( ord_less_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_556_add__less__imp__less__left,axiom,
% 11.11/6.12      ! [C: real,A: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 11.11/6.12       => ( ord_less_real @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_557_add__less__imp__less__left,axiom,
% 11.11/6.12      ! [C: rat,A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 11.11/6.12       => ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_558_add__less__imp__less__left,axiom,
% 11.11/6.12      ! [C: nat,A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 11.11/6.12       => ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_559_add__less__imp__less__left,axiom,
% 11.11/6.12      ! [C: int,A: int,B: int] :
% 11.11/6.12        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 11.11/6.12       => ( ord_less_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_560_add__strict__right__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_561_add__strict__right__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_562_add__strict__right__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ord_less_nat @ A @ B )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_563_add__strict__right__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ord_less_int @ A @ B )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_564_add__strict__left__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_565_add__strict__left__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_566_add__strict__left__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( ord_less_nat @ A @ B )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_567_add__strict__left__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( ord_less_int @ A @ B )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_568_add__strict__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ( ord_less_real @ C @ D )
% 11.11/6.12         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_569_add__strict__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ( ord_less_rat @ C @ D )
% 11.11/6.12         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_570_add__strict__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.12        ( ( ord_less_nat @ A @ B )
% 11.11/6.12       => ( ( ord_less_nat @ C @ D )
% 11.11/6.12         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_571_add__strict__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.12        ( ( ord_less_int @ A @ B )
% 11.11/6.12       => ( ( ord_less_int @ C @ D )
% 11.11/6.12         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_572_add__mono__thms__linordered__field_I1_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_real @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_573_add__mono__thms__linordered__field_I1_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_rat @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_574_add__mono__thms__linordered__field_I1_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_575_add__mono__thms__linordered__field_I1_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_int @ I2 @ J )
% 11.11/6.12          & ( K = L ) )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_576_add__mono__thms__linordered__field_I2_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_577_add__mono__thms__linordered__field_I2_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_578_add__mono__thms__linordered__field_I2_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_579_add__mono__thms__linordered__field_I2_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( I2 = J )
% 11.11/6.12          & ( ord_less_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_580_add__mono__thms__linordered__field_I5_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_real @ I2 @ J )
% 11.11/6.12          & ( ord_less_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_581_add__mono__thms__linordered__field_I5_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_rat @ I2 @ J )
% 11.11/6.12          & ( ord_less_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_582_add__mono__thms__linordered__field_I5_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12          & ( ord_less_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_583_add__mono__thms__linordered__field_I5_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_int @ I2 @ J )
% 11.11/6.12          & ( ord_less_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_584_add__divide__distrib,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat] :
% 11.11/6.12        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_585_add__divide__distrib,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real] :
% 11.11/6.12        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_586_add__divide__distrib,axiom,
% 11.11/6.12      ! [A: complex,B: complex,C: complex] :
% 11.11/6.12        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 11.11/6.12        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_587_length__induct,axiom,
% 11.11/6.12      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 11.11/6.12        ( ! [Xs2: list_VEBT_VEBT] :
% 11.11/6.12            ( ! [Ys2: list_VEBT_VEBT] :
% 11.11/6.12                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 11.11/6.12               => ( P @ Ys2 ) )
% 11.11/6.12           => ( P @ Xs2 ) )
% 11.11/6.12       => ( P @ Xs ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_588_length__induct,axiom,
% 11.11/6.12      ! [P: list_o > $o,Xs: list_o] :
% 11.11/6.12        ( ! [Xs2: list_o] :
% 11.11/6.12            ( ! [Ys2: list_o] :
% 11.11/6.12                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 11.11/6.12               => ( P @ Ys2 ) )
% 11.11/6.12           => ( P @ Xs2 ) )
% 11.11/6.12       => ( P @ Xs ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_589_length__induct,axiom,
% 11.11/6.12      ! [P: list_nat > $o,Xs: list_nat] :
% 11.11/6.12        ( ! [Xs2: list_nat] :
% 11.11/6.12            ( ! [Ys2: list_nat] :
% 11.11/6.12                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 11.11/6.12               => ( P @ Ys2 ) )
% 11.11/6.12           => ( P @ Xs2 ) )
% 11.11/6.12       => ( P @ Xs ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_590_length__induct,axiom,
% 11.11/6.12      ! [P: list_int > $o,Xs: list_int] :
% 11.11/6.12        ( ! [Xs2: list_int] :
% 11.11/6.12            ( ! [Ys2: list_int] :
% 11.11/6.12                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 11.11/6.12               => ( P @ Ys2 ) )
% 11.11/6.12           => ( P @ Xs2 ) )
% 11.11/6.12       => ( P @ Xs ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_591_add__less__le__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.12         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_592_add__less__le__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_rat @ C @ D )
% 11.11/6.12         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_593_add__less__le__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.12        ( ( ord_less_nat @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_nat @ C @ D )
% 11.11/6.12         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_594_add__less__le__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.12        ( ( ord_less_int @ A @ B )
% 11.11/6.12       => ( ( ord_less_eq_int @ C @ D )
% 11.11/6.12         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_595_add__le__less__mono,axiom,
% 11.11/6.12      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.12        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.12       => ( ( ord_less_real @ C @ D )
% 11.11/6.12         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_596_add__le__less__mono,axiom,
% 11.11/6.12      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.12        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.12       => ( ( ord_less_rat @ C @ D )
% 11.11/6.12         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_597_add__le__less__mono,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.12        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.12       => ( ( ord_less_nat @ C @ D )
% 11.11/6.12         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_598_add__le__less__mono,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.12        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.12       => ( ( ord_less_int @ C @ D )
% 11.11/6.12         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_599_add__mono__thms__linordered__field_I3_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_real @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_600_add__mono__thms__linordered__field_I3_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_rat @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_601_add__mono__thms__linordered__field_I3_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_nat @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_602_add__mono__thms__linordered__field_I3_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_int @ I2 @ J )
% 11.11/6.12          & ( ord_less_eq_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_603_add__mono__thms__linordered__field_I4_J,axiom,
% 11.11/6.12      ! [I2: real,J: real,K: real,L: real] :
% 11.11/6.12        ( ( ( ord_less_eq_real @ I2 @ J )
% 11.11/6.12          & ( ord_less_real @ K @ L ) )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_604_add__mono__thms__linordered__field_I4_J,axiom,
% 11.11/6.12      ! [I2: rat,J: rat,K: rat,L: rat] :
% 11.11/6.12        ( ( ( ord_less_eq_rat @ I2 @ J )
% 11.11/6.12          & ( ord_less_rat @ K @ L ) )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_605_add__mono__thms__linordered__field_I4_J,axiom,
% 11.11/6.12      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.12        ( ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.12          & ( ord_less_nat @ K @ L ) )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_606_add__mono__thms__linordered__field_I4_J,axiom,
% 11.11/6.12      ! [I2: int,J: int,K: int,L: int] :
% 11.11/6.12        ( ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.12          & ( ord_less_int @ K @ L ) )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_607_add__mono1,axiom,
% 11.11/6.12      ! [A: real,B: real] :
% 11.11/6.12        ( ( ord_less_real @ A @ B )
% 11.11/6.12       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_608_add__mono1,axiom,
% 11.11/6.12      ! [A: rat,B: rat] :
% 11.11/6.12        ( ( ord_less_rat @ A @ B )
% 11.11/6.12       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_609_add__mono1,axiom,
% 11.11/6.12      ! [A: nat,B: nat] :
% 11.11/6.12        ( ( ord_less_nat @ A @ B )
% 11.11/6.12       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_610_add__mono1,axiom,
% 11.11/6.12      ! [A: int,B: int] :
% 11.11/6.12        ( ( ord_less_int @ A @ B )
% 11.11/6.12       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_611_less__add__one,axiom,
% 11.11/6.12      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_612_less__add__one,axiom,
% 11.11/6.12      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_613_less__add__one,axiom,
% 11.11/6.12      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_614_less__add__one,axiom,
% 11.11/6.12      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_615_list__eq__iff__nth__eq,axiom,
% 11.11/6.12      ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 11.11/6.12      = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 11.11/6.12            ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 11.11/6.12              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 11.11/6.12            & ! [I3: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 11.11/6.12               => ( ( nth_VEBT_VEBT @ Xs3 @ I3 )
% 11.11/6.12                  = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_616_list__eq__iff__nth__eq,axiom,
% 11.11/6.12      ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 11.11/6.12      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 11.11/6.12            ( ( ( size_size_list_o @ Xs3 )
% 11.11/6.12              = ( size_size_list_o @ Ys3 ) )
% 11.11/6.12            & ! [I3: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) )
% 11.11/6.12               => ( ( nth_o @ Xs3 @ I3 )
% 11.11/6.12                  = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_617_list__eq__iff__nth__eq,axiom,
% 11.11/6.12      ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 11.11/6.12      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 11.11/6.12            ( ( ( size_size_list_nat @ Xs3 )
% 11.11/6.12              = ( size_size_list_nat @ Ys3 ) )
% 11.11/6.12            & ! [I3: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) )
% 11.11/6.12               => ( ( nth_nat @ Xs3 @ I3 )
% 11.11/6.12                  = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_618_list__eq__iff__nth__eq,axiom,
% 11.11/6.12      ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 11.11/6.12      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 11.11/6.12            ( ( ( size_size_list_int @ Xs3 )
% 11.11/6.12              = ( size_size_list_int @ Ys3 ) )
% 11.11/6.12            & ! [I3: nat] :
% 11.11/6.12                ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) )
% 11.11/6.12               => ( ( nth_int @ Xs3 @ I3 )
% 11.11/6.12                  = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_619_Skolem__list__nth,axiom,
% 11.11/6.12      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 11.11/6.12        ( ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12             => ? [X3: vEBT_VEBT] : ( P @ I3 @ X3 ) ) )
% 11.11/6.12        = ( ? [Xs3: list_VEBT_VEBT] :
% 11.11/6.12              ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 11.11/6.12                = K )
% 11.11/6.12              & ! [I3: nat] :
% 11.11/6.12                  ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12                 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_620_Skolem__list__nth,axiom,
% 11.11/6.12      ! [K: nat,P: nat > $o > $o] :
% 11.11/6.12        ( ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12             => ? [X3: $o] : ( P @ I3 @ X3 ) ) )
% 11.11/6.12        = ( ? [Xs3: list_o] :
% 11.11/6.12              ( ( ( size_size_list_o @ Xs3 )
% 11.11/6.12                = K )
% 11.11/6.12              & ! [I3: nat] :
% 11.11/6.12                  ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12                 => ( P @ I3 @ ( nth_o @ Xs3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_621_Skolem__list__nth,axiom,
% 11.11/6.12      ! [K: nat,P: nat > nat > $o] :
% 11.11/6.12        ( ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12             => ? [X3: nat] : ( P @ I3 @ X3 ) ) )
% 11.11/6.12        = ( ? [Xs3: list_nat] :
% 11.11/6.12              ( ( ( size_size_list_nat @ Xs3 )
% 11.11/6.12                = K )
% 11.11/6.12              & ! [I3: nat] :
% 11.11/6.12                  ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12                 => ( P @ I3 @ ( nth_nat @ Xs3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_622_Skolem__list__nth,axiom,
% 11.11/6.12      ! [K: nat,P: nat > int > $o] :
% 11.11/6.12        ( ( ! [I3: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12             => ? [X3: int] : ( P @ I3 @ X3 ) ) )
% 11.11/6.12        = ( ? [Xs3: list_int] :
% 11.11/6.12              ( ( ( size_size_list_int @ Xs3 )
% 11.11/6.12                = K )
% 11.11/6.12              & ! [I3: nat] :
% 11.11/6.12                  ( ( ord_less_nat @ I3 @ K )
% 11.11/6.12                 => ( P @ I3 @ ( nth_int @ Xs3 @ I3 ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_623_nth__equalityI,axiom,
% 11.11/6.12      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 11.11/6.12        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 11.11/6.12          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 11.11/6.12       => ( ! [I4: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 11.11/6.12             => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 11.11/6.12                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 11.11/6.12         => ( Xs = Ys ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_624_nth__equalityI,axiom,
% 11.11/6.12      ! [Xs: list_o,Ys: list_o] :
% 11.11/6.12        ( ( ( size_size_list_o @ Xs )
% 11.11/6.12          = ( size_size_list_o @ Ys ) )
% 11.11/6.12       => ( ! [I4: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 11.11/6.12             => ( ( nth_o @ Xs @ I4 )
% 11.11/6.12                = ( nth_o @ Ys @ I4 ) ) )
% 11.11/6.12         => ( Xs = Ys ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_625_nth__equalityI,axiom,
% 11.11/6.12      ! [Xs: list_nat,Ys: list_nat] :
% 11.11/6.12        ( ( ( size_size_list_nat @ Xs )
% 11.11/6.12          = ( size_size_list_nat @ Ys ) )
% 11.11/6.12       => ( ! [I4: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 11.11/6.12             => ( ( nth_nat @ Xs @ I4 )
% 11.11/6.12                = ( nth_nat @ Ys @ I4 ) ) )
% 11.11/6.12         => ( Xs = Ys ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_626_nth__equalityI,axiom,
% 11.11/6.12      ! [Xs: list_int,Ys: list_int] :
% 11.11/6.12        ( ( ( size_size_list_int @ Xs )
% 11.11/6.12          = ( size_size_list_int @ Ys ) )
% 11.11/6.12       => ( ! [I4: nat] :
% 11.11/6.12              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 11.11/6.12             => ( ( nth_int @ Xs @ I4 )
% 11.11/6.12                = ( nth_int @ Ys @ I4 ) ) )
% 11.11/6.12         => ( Xs = Ys ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_627_discrete,axiom,
% 11.11/6.12      ( ord_less_nat
% 11.11/6.12      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_628_discrete,axiom,
% 11.11/6.12      ( ord_less_int
% 11.11/6.12      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_629_buildup__nothing__in__leaf,axiom,
% 11.11/6.12      ! [N2: nat,X4: nat] :
% 11.11/6.12        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_630_low__def,axiom,
% 11.11/6.12      ( vEBT_VEBT_low
% 11.11/6.12      = ( ^ [X: nat,N: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_631_buildup__nothing__in__min__max,axiom,
% 11.11/6.12      ! [N2: nat,X4: nat] :
% 11.11/6.12        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_632_invar__vebt_Ointros_I3_J,axiom,
% 11.11/6.12      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 11.11/6.12        ( ! [X5: vEBT_VEBT] :
% 11.11/6.12            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.12           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 11.11/6.12       => ( ( vEBT_invar_vebt @ Summary @ M )
% 11.11/6.12         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.12              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.12           => ( ( M
% 11.11/6.12                = ( suc @ N2 ) )
% 11.11/6.12             => ( ( Deg
% 11.11/6.12                  = ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.12               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 11.11/6.12                 => ( ! [X5: vEBT_VEBT] :
% 11.11/6.12                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.12                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 11.11/6.12                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_633_invar__vebt_Ointros_I2_J,axiom,
% 11.11/6.12      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 11.11/6.12        ( ! [X5: vEBT_VEBT] :
% 11.11/6.12            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.12           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 11.11/6.12       => ( ( vEBT_invar_vebt @ Summary @ M )
% 11.11/6.12         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.12              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.12           => ( ( M = N2 )
% 11.11/6.12             => ( ( Deg
% 11.11/6.12                  = ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.12               => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 11.11/6.12                 => ( ! [X5: vEBT_VEBT] :
% 11.11/6.12                        ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.12                       => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 11.11/6.12                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_634_dbl__simps_I3_J,axiom,
% 11.11/6.12      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 11.11/6.12      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_635_dbl__simps_I3_J,axiom,
% 11.11/6.12      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 11.11/6.12      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_636_dbl__simps_I3_J,axiom,
% 11.11/6.12      ( ( neg_numeral_dbl_real @ one_one_real )
% 11.11/6.12      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_637_dbl__simps_I3_J,axiom,
% 11.11/6.12      ( ( neg_numeral_dbl_int @ one_one_int )
% 11.11/6.12      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_638_power__numeral,axiom,
% 11.11/6.12      ! [K: num,L: num] :
% 11.11/6.12        ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.12        = ( numera1916890842035813515d_enat @ ( pow @ K @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_639_power__numeral,axiom,
% 11.11/6.12      ! [K: num,L: num] :
% 11.11/6.12        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.12        = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_640_power__numeral,axiom,
% 11.11/6.12      ! [K: num,L: num] :
% 11.11/6.12        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.12        = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_641_power__numeral,axiom,
% 11.11/6.12      ! [K: num,L: num] :
% 11.11/6.12        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.12        = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_642_power__numeral,axiom,
% 11.11/6.12      ! [K: num,L: num] :
% 11.11/6.12        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.12        = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_643_valid__eq2,axiom,
% 11.11/6.12      ! [T2: vEBT_VEBT,D: nat] :
% 11.11/6.12        ( ( vEBT_VEBT_valid @ T2 @ D )
% 11.11/6.12       => ( vEBT_invar_vebt @ T2 @ D ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_644_valid__eq,axiom,
% 11.11/6.12      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_645_valid__eq1,axiom,
% 11.11/6.12      ! [T2: vEBT_VEBT,D: nat] :
% 11.11/6.12        ( ( vEBT_invar_vebt @ T2 @ D )
% 11.11/6.12       => ( vEBT_VEBT_valid @ T2 @ D ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_646_zdiv__numeral__Bit0,axiom,
% 11.11/6.12      ! [V: num,W: num] :
% 11.11/6.12        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 11.11/6.12        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_647_mod__mod__trivial,axiom,
% 11.11/6.12      ! [A: nat,B: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 11.11/6.12        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_648_mod__mod__trivial,axiom,
% 11.11/6.12      ! [A: int,B: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 11.11/6.12        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_649_mod__mod__trivial,axiom,
% 11.11/6.12      ! [A: code_integer,B: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 11.11/6.12        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_650_mod__add__self1,axiom,
% 11.11/6.12      ! [B: nat,A: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 11.11/6.12        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_651_mod__add__self1,axiom,
% 11.11/6.12      ! [B: int,A: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 11.11/6.12        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_652_mod__add__self1,axiom,
% 11.11/6.12      ! [B: code_integer,A: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 11.11/6.12        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_653_mod__add__self2,axiom,
% 11.11/6.12      ! [A: nat,B: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 11.11/6.12        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_654_mod__add__self2,axiom,
% 11.11/6.12      ! [A: int,B: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.12        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_655_mod__add__self2,axiom,
% 11.11/6.12      ! [A: code_integer,B: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 11.11/6.12        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_656_mod__less,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.12       => ( ( modulo_modulo_nat @ M @ N2 )
% 11.11/6.12          = M ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_657_dbl__simps_I5_J,axiom,
% 11.11/6.12      ! [K: num] :
% 11.11/6.12        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 11.11/6.12        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_658_dbl__simps_I5_J,axiom,
% 11.11/6.12      ! [K: num] :
% 11.11/6.12        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 11.11/6.12        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_659_dbl__simps_I5_J,axiom,
% 11.11/6.12      ! [K: num] :
% 11.11/6.12        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 11.11/6.12        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_660_bits__one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_661_bits__one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_662_bits__one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_Code_integer ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_663_one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_nat ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_664_one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_int ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_665_one__mod__two__eq__one,axiom,
% 11.11/6.12      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.12      = one_one_Code_integer ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_666_mod2__Suc__Suc,axiom,
% 11.11/6.12      ! [M: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.12        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_667_mod__add__eq,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_668_mod__add__eq,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_669_mod__add__eq,axiom,
% 11.11/6.12      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_670_mod__add__cong,axiom,
% 11.11/6.12      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 11.11/6.12        ( ( ( modulo_modulo_nat @ A @ C )
% 11.11/6.12          = ( modulo_modulo_nat @ A4 @ C ) )
% 11.11/6.12       => ( ( ( modulo_modulo_nat @ B @ C )
% 11.11/6.12            = ( modulo_modulo_nat @ B4 @ C ) )
% 11.11/6.12         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.12            = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_671_mod__add__cong,axiom,
% 11.11/6.12      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 11.11/6.12        ( ( ( modulo_modulo_int @ A @ C )
% 11.11/6.12          = ( modulo_modulo_int @ A4 @ C ) )
% 11.11/6.12       => ( ( ( modulo_modulo_int @ B @ C )
% 11.11/6.12            = ( modulo_modulo_int @ B4 @ C ) )
% 11.11/6.12         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.12            = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_672_mod__add__cong,axiom,
% 11.11/6.12      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 11.11/6.12        ( ( ( modulo364778990260209775nteger @ A @ C )
% 11.11/6.12          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 11.11/6.12       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 11.11/6.12            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 11.11/6.12         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 11.11/6.12            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_673_mod__add__left__eq,axiom,
% 11.11/6.12      ! [A: nat,C: nat,B: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 11.11/6.12        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_674_mod__add__left__eq,axiom,
% 11.11/6.12      ! [A: int,C: int,B: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 11.11/6.12        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_675_mod__add__left__eq,axiom,
% 11.11/6.12      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 11.11/6.12        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_676_mod__add__right__eq,axiom,
% 11.11/6.12      ! [A: nat,B: nat,C: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_677_mod__add__right__eq,axiom,
% 11.11/6.12      ! [A: int,B: int,C: int] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_678_mod__add__right__eq,axiom,
% 11.11/6.12      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.12        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_679_power__mod,axiom,
% 11.11/6.12      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 11.11/6.12        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_680_power__mod,axiom,
% 11.11/6.12      ! [A: int,B: int,N2: nat] :
% 11.11/6.12        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 11.11/6.12        = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_681_power__mod,axiom,
% 11.11/6.12      ! [A: code_integer,B: code_integer,N2: nat] :
% 11.11/6.12        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N2 ) @ B )
% 11.11/6.12        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ B ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_682_mod__Suc__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.12        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 11.11/6.12        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.12  
% 11.11/6.12  thf(fact_683_mod__Suc__Suc__eq,axiom,
% 11.11/6.12      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 11.11/6.13        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_684_mod__less__eq__dividend,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_685_cong__exp__iff__simps_I9_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num,N2: num] :
% 11.11/6.13        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.13          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.13        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.13          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_686_cong__exp__iff__simps_I9_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num,N2: num] :
% 11.11/6.13        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.13          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.13        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 11.11/6.13          = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_687_cong__exp__iff__simps_I9_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num,N2: num] :
% 11.11/6.13        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.13          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.13        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 11.11/6.13          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_688_cong__exp__iff__simps_I4_J,axiom,
% 11.11/6.13      ! [M: num,N2: num] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 11.11/6.13        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_689_cong__exp__iff__simps_I4_J,axiom,
% 11.11/6.13      ! [M: num,N2: num] :
% 11.11/6.13        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 11.11/6.13        = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_690_cong__exp__iff__simps_I4_J,axiom,
% 11.11/6.13      ! [M: num,N2: num] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 11.11/6.13        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_691_cong__exp__iff__simps_I8_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_692_cong__exp__iff__simps_I8_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num] :
% 11.11/6.13        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_693_cong__exp__iff__simps_I8_J,axiom,
% 11.11/6.13      ! [M: num,Q3: num] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_694_cong__exp__iff__simps_I6_J,axiom,
% 11.11/6.13      ! [Q3: num,N2: num] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_695_cong__exp__iff__simps_I6_J,axiom,
% 11.11/6.13      ! [Q3: num,N2: num] :
% 11.11/6.13        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_696_cong__exp__iff__simps_I6_J,axiom,
% 11.11/6.13      ! [Q3: num,N2: num] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.13       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_697_div__add1__eq,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.13        = ( 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 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_698_div__add1__eq,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.13        = ( 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 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_699_div__add1__eq,axiom,
% 11.11/6.13      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 11.11/6.13        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_700_mod__induct,axiom,
% 11.11/6.13      ! [P: nat > $o,N2: nat,P2: nat,M: nat] :
% 11.11/6.13        ( ( P @ N2 )
% 11.11/6.13       => ( ( ord_less_nat @ N2 @ P2 )
% 11.11/6.13         => ( ( ord_less_nat @ M @ P2 )
% 11.11/6.13           => ( ! [N3: nat] :
% 11.11/6.13                  ( ( ord_less_nat @ N3 @ P2 )
% 11.11/6.13                 => ( ( P @ N3 )
% 11.11/6.13                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 11.11/6.13             => ( P @ M ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_701_mod__Suc__le__divisor,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_702_dbl__def,axiom,
% 11.11/6.13      ( neg_numeral_dbl_real
% 11.11/6.13      = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_703_dbl__def,axiom,
% 11.11/6.13      ( neg_numeral_dbl_rat
% 11.11/6.13      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_704_dbl__def,axiom,
% 11.11/6.13      ( neg_numeral_dbl_int
% 11.11/6.13      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_705_pow_Osimps_I1_J,axiom,
% 11.11/6.13      ! [X4: num] :
% 11.11/6.13        ( ( pow @ X4 @ one )
% 11.11/6.13        = X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_706_bounded__Max__nat,axiom,
% 11.11/6.13      ! [P: nat > $o,X4: nat,M7: nat] :
% 11.11/6.13        ( ( P @ X4 )
% 11.11/6.13       => ( ! [X5: nat] :
% 11.11/6.13              ( ( P @ X5 )
% 11.11/6.13             => ( ord_less_eq_nat @ X5 @ M7 ) )
% 11.11/6.13         => ~ ! [M5: nat] :
% 11.11/6.13                ( ( P @ M5 )
% 11.11/6.13               => ~ ! [X2: nat] :
% 11.11/6.13                      ( ( P @ X2 )
% 11.11/6.13                     => ( ord_less_eq_nat @ X2 @ M5 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_707_div__exp__mod__exp__eq,axiom,
% 11.11/6.13      ! [A: nat,N2: nat,M: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_708_div__exp__mod__exp__eq,axiom,
% 11.11/6.13      ! [A: int,N2: nat,M: nat] :
% 11.11/6.13        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_709_div__exp__mod__exp__eq,axiom,
% 11.11/6.13      ! [A: code_integer,N2: nat,M: nat] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_710_buildup__gives__valid,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_711_psubsetI,axiom,
% 11.11/6.13      ! [A2: set_int,B3: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.13       => ( ( A2 != B3 )
% 11.11/6.13         => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_712_subset__antisym,axiom,
% 11.11/6.13      ! [A2: set_int,B3: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 11.11/6.13         => ( A2 = B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_713_subsetI,axiom,
% 11.11/6.13      ! [A2: set_real,B3: set_real] :
% 11.11/6.13        ( ! [X5: real] :
% 11.11/6.13            ( ( member_real @ X5 @ A2 )
% 11.11/6.13           => ( member_real @ X5 @ B3 ) )
% 11.11/6.13       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_714_subsetI,axiom,
% 11.11/6.13      ! [A2: set_nat,B3: set_nat] :
% 11.11/6.13        ( ! [X5: nat] :
% 11.11/6.13            ( ( member_nat @ X5 @ A2 )
% 11.11/6.13           => ( member_nat @ X5 @ B3 ) )
% 11.11/6.13       => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_715_subsetI,axiom,
% 11.11/6.13      ! [A2: set_complex,B3: set_complex] :
% 11.11/6.13        ( ! [X5: complex] :
% 11.11/6.13            ( ( member_complex @ X5 @ A2 )
% 11.11/6.13           => ( member_complex @ X5 @ B3 ) )
% 11.11/6.13       => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_716_subsetI,axiom,
% 11.11/6.13      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 11.11/6.13        ( ! [X5: product_prod_nat_nat] :
% 11.11/6.13            ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 11.11/6.13           => ( member8440522571783428010at_nat @ X5 @ B3 ) )
% 11.11/6.13       => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_717_subsetI,axiom,
% 11.11/6.13      ! [A2: set_int,B3: set_int] :
% 11.11/6.13        ( ! [X5: int] :
% 11.11/6.13            ( ( member_int @ X5 @ A2 )
% 11.11/6.13           => ( member_int @ X5 @ B3 ) )
% 11.11/6.13       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_718_verit__eq__simplify_I8_J,axiom,
% 11.11/6.13      ! [X22: num,Y2: num] :
% 11.11/6.13        ( ( ( bit0 @ X22 )
% 11.11/6.13          = ( bit0 @ Y2 ) )
% 11.11/6.13        = ( X22 = Y2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_719_order__refl,axiom,
% 11.11/6.13      ! [X4: set_int] : ( ord_less_eq_set_int @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_720_order__refl,axiom,
% 11.11/6.13      ! [X4: rat] : ( ord_less_eq_rat @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_721_order__refl,axiom,
% 11.11/6.13      ! [X4: num] : ( ord_less_eq_num @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_722_order__refl,axiom,
% 11.11/6.13      ! [X4: nat] : ( ord_less_eq_nat @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_723_order__refl,axiom,
% 11.11/6.13      ! [X4: int] : ( ord_less_eq_int @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_724_dual__order_Orefl,axiom,
% 11.11/6.13      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_725_dual__order_Orefl,axiom,
% 11.11/6.13      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_726_dual__order_Orefl,axiom,
% 11.11/6.13      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_727_dual__order_Orefl,axiom,
% 11.11/6.13      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_728_dual__order_Orefl,axiom,
% 11.11/6.13      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_729_mod2__gr__0,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = one_one_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_730_length__subseqs,axiom,
% 11.11/6.13      ! [Xs: list_VEBT_VEBT] :
% 11.11/6.13        ( ( size_s8217280938318005548T_VEBT @ ( subseqs_VEBT_VEBT @ Xs ) )
% 11.11/6.13        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_731_length__subseqs,axiom,
% 11.11/6.13      ! [Xs: list_o] :
% 11.11/6.13        ( ( size_s2710708370519433104list_o @ ( subseqs_o @ Xs ) )
% 11.11/6.13        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_732_length__subseqs,axiom,
% 11.11/6.13      ! [Xs: list_nat] :
% 11.11/6.13        ( ( size_s3023201423986296836st_nat @ ( subseqs_nat @ Xs ) )
% 11.11/6.13        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_733_length__subseqs,axiom,
% 11.11/6.13      ! [Xs: list_int] :
% 11.11/6.13        ( ( size_s533118279054570080st_int @ ( subseqs_int @ Xs ) )
% 11.11/6.13        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_734_invar__vebt_Ointros_I5_J,axiom,
% 11.11/6.13      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 11.11/6.13        ( ! [X5: vEBT_VEBT] :
% 11.11/6.13            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.13           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 11.11/6.13       => ( ( vEBT_invar_vebt @ Summary @ M )
% 11.11/6.13         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.13              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13           => ( ( M
% 11.11/6.13                = ( suc @ N2 ) )
% 11.11/6.13             => ( ( Deg
% 11.11/6.13                  = ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.13               => ( ! [I4: nat] :
% 11.11/6.13                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 11.11/6.13                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 11.11/6.13                 => ( ( ( Mi = Ma )
% 11.11/6.13                     => ! [X5: vEBT_VEBT] :
% 11.11/6.13                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.13                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 11.11/6.13                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 11.11/6.13                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 11.11/6.13                       => ( ( ( Mi != Ma )
% 11.11/6.13                           => ! [I4: nat] :
% 11.11/6.13                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.13                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 11.11/6.13                                      = I4 )
% 11.11/6.13                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 11.11/6.13                                  & ! [X5: nat] :
% 11.11/6.13                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 11.11/6.13                                          = I4 )
% 11.11/6.13                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 11.11/6.13                                     => ( ( ord_less_nat @ Mi @ X5 )
% 11.11/6.13                                        & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 11.11/6.13                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_735_deg__not__0,axiom,
% 11.11/6.13      ! [T2: vEBT_VEBT,N2: nat] :
% 11.11/6.13        ( ( vEBT_invar_vebt @ T2 @ N2 )
% 11.11/6.13       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_736__C5_Ohyps_C_I12_J,axiom,
% 11.11/6.13      ( ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) )
% 11.11/6.13      = info ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_737_le__zero__eq,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_738_not__gr__zero,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_739_add__0,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_740_add__0,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ zero_zero_real @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_741_add__0,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_742_add__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_743_add__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ zero_zero_int @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_744_zero__eq__add__iff__both__eq__0,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( zero_zero_nat
% 11.11/6.13          = ( plus_plus_nat @ X4 @ Y ) )
% 11.11/6.13        = ( ( X4 = zero_zero_nat )
% 11.11/6.13          & ( Y = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_745_add__eq__0__iff__both__eq__0,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ X4 @ Y )
% 11.11/6.13          = zero_zero_nat )
% 11.11/6.13        = ( ( X4 = zero_zero_nat )
% 11.11/6.13          & ( Y = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_746_add__cancel__right__right,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_complex @ A @ B ) )
% 11.11/6.13        = ( B = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_747_add__cancel__right__right,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_real @ A @ B ) )
% 11.11/6.13        = ( B = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_748_add__cancel__right__right,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_rat @ A @ B ) )
% 11.11/6.13        = ( B = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_749_add__cancel__right__right,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_nat @ A @ B ) )
% 11.11/6.13        = ( B = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_750_add__cancel__right__right,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_int @ A @ B ) )
% 11.11/6.13        = ( B = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_751_add__cancel__right__left,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_complex @ B @ A ) )
% 11.11/6.13        = ( B = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_752_add__cancel__right__left,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_real @ B @ A ) )
% 11.11/6.13        = ( B = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_753_add__cancel__right__left,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_rat @ B @ A ) )
% 11.11/6.13        = ( B = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_754_add__cancel__right__left,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_nat @ B @ A ) )
% 11.11/6.13        = ( B = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_755_add__cancel__right__left,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( plus_plus_int @ B @ A ) )
% 11.11/6.13        = ( B = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_756_add__cancel__left__right,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( ( plus_plus_complex @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_757_add__cancel__left__right,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_758_add__cancel__left__right,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_759_add__cancel__left__right,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_760_add__cancel__left__right,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_761_add__cancel__left__left,axiom,
% 11.11/6.13      ! [B: complex,A: complex] :
% 11.11/6.13        ( ( ( plus_plus_complex @ B @ A )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_762_add__cancel__left__left,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( ( plus_plus_real @ B @ A )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_763_add__cancel__left__left,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ( plus_plus_rat @ B @ A )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_764_add__cancel__left__left,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ B @ A )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_765_add__cancel__left__left,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ( plus_plus_int @ B @ A )
% 11.11/6.13          = A )
% 11.11/6.13        = ( B = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_766_double__zero__sym,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( zero_zero_real
% 11.11/6.13          = ( plus_plus_real @ A @ A ) )
% 11.11/6.13        = ( A = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_767_double__zero__sym,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( zero_zero_rat
% 11.11/6.13          = ( plus_plus_rat @ A @ A ) )
% 11.11/6.13        = ( A = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_768_double__zero__sym,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( zero_zero_int
% 11.11/6.13          = ( plus_plus_int @ A @ A ) )
% 11.11/6.13        = ( A = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_769_add_Oright__neutral,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_770_add_Oright__neutral,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ A @ zero_zero_real )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_771_add_Oright__neutral,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_772_add_Oright__neutral,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_773_add_Oright__neutral,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ A @ zero_zero_int )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_774_division__ring__divide__zero,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 11.11/6.13        = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_775_division__ring__divide__zero,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( divide_divide_real @ A @ zero_zero_real )
% 11.11/6.13        = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_776_division__ring__divide__zero,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 11.11/6.13        = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_777_divide__cancel__right,axiom,
% 11.11/6.13      ! [A: rat,C: rat,B: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ A @ C )
% 11.11/6.13          = ( divide_divide_rat @ B @ C ) )
% 11.11/6.13        = ( ( C = zero_zero_rat )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_778_divide__cancel__right,axiom,
% 11.11/6.13      ! [A: real,C: real,B: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ A @ C )
% 11.11/6.13          = ( divide_divide_real @ B @ C ) )
% 11.11/6.13        = ( ( C = zero_zero_real )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_779_divide__cancel__right,axiom,
% 11.11/6.13      ! [A: complex,C: complex,B: complex] :
% 11.11/6.13        ( ( ( divide1717551699836669952omplex @ A @ C )
% 11.11/6.13          = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.13        = ( ( C = zero_zero_complex )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_780_divide__cancel__left,axiom,
% 11.11/6.13      ! [C: rat,A: rat,B: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ C @ A )
% 11.11/6.13          = ( divide_divide_rat @ C @ B ) )
% 11.11/6.13        = ( ( C = zero_zero_rat )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_781_divide__cancel__left,axiom,
% 11.11/6.13      ! [C: real,A: real,B: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ C @ A )
% 11.11/6.13          = ( divide_divide_real @ C @ B ) )
% 11.11/6.13        = ( ( C = zero_zero_real )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_782_divide__cancel__left,axiom,
% 11.11/6.13      ! [C: complex,A: complex,B: complex] :
% 11.11/6.13        ( ( ( divide1717551699836669952omplex @ C @ A )
% 11.11/6.13          = ( divide1717551699836669952omplex @ C @ B ) )
% 11.11/6.13        = ( ( C = zero_zero_complex )
% 11.11/6.13          | ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_783_div__by__0,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 11.11/6.13        = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_784_div__by__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_785_div__by__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( divide_divide_int @ A @ zero_zero_int )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_786_div__by__0,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( divide_divide_real @ A @ zero_zero_real )
% 11.11/6.13        = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_787_div__by__0,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 11.11/6.13        = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_788_div__by__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_789_divide__eq__0__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ A @ B )
% 11.11/6.13          = zero_zero_rat )
% 11.11/6.13        = ( ( A = zero_zero_rat )
% 11.11/6.13          | ( B = zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_790_divide__eq__0__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ A @ B )
% 11.11/6.13          = zero_zero_real )
% 11.11/6.13        = ( ( A = zero_zero_real )
% 11.11/6.13          | ( B = zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_791_divide__eq__0__iff,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( ( divide1717551699836669952omplex @ A @ B )
% 11.11/6.13          = zero_zero_complex )
% 11.11/6.13        = ( ( A = zero_zero_complex )
% 11.11/6.13          | ( B = zero_zero_complex ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_792_div__0,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 11.11/6.13        = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_793_div__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_794_div__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( divide_divide_int @ zero_zero_int @ A )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_795_div__0,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( divide_divide_real @ zero_zero_real @ A )
% 11.11/6.13        = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_796_div__0,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 11.11/6.13        = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_797_div__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_798_bits__div__by__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_799_bits__div__by__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( divide_divide_int @ A @ zero_zero_int )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_800_bits__div__by__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_801_bits__div__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_802_bits__div__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( divide_divide_int @ zero_zero_int @ A )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_803_bits__div__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_804_bits__mod__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_805_bits__mod__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_806_bits__mod__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_807_mod__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_808_mod__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_809_mod__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_810_mod__by__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_811_mod__by__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_812_mod__by__0,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_813_mod__self,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ A @ A )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_814_mod__self,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ A @ A )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_815_mod__self,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ A @ A )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_816_less__nat__zero__code,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_817_neq0__conv,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( N2 != zero_zero_nat )
% 11.11/6.13        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_818_bot__nat__0_Onot__eq__extremum,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( A != zero_zero_nat )
% 11.11/6.13        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_819_le0,axiom,
% 11.11/6.13      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_820_bot__nat__0_Oextremum,axiom,
% 11.11/6.13      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_821_Nat_Oadd__0__right,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 11.11/6.13        = M ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_822_add__is__0,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ M @ N2 )
% 11.11/6.13          = zero_zero_nat )
% 11.11/6.13        = ( ( M = zero_zero_nat )
% 11.11/6.13          & ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_823_dbl__simps_I2_J,axiom,
% 11.11/6.13      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 11.11/6.13      = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_824_dbl__simps_I2_J,axiom,
% 11.11/6.13      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 11.11/6.13      = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_825_dbl__simps_I2_J,axiom,
% 11.11/6.13      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 11.11/6.13      = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_826_dbl__simps_I2_J,axiom,
% 11.11/6.13      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 11.11/6.13      = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_827_mi__ma__2__deg,axiom,
% 11.11/6.13      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 11.11/6.13        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 11.11/6.13       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 11.11/6.13          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_828_add__le__same__cancel1,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_829_add__le__same__cancel1,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_830_add__le__same__cancel1,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_831_add__le__same__cancel1,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_832_add__le__same__cancel2,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_833_add__le__same__cancel2,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_834_add__le__same__cancel2,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_835_add__le__same__cancel2,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_836_le__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 11.11/6.13        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_837_le__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.13        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_838_le__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.13        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_839_le__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 11.11/6.13        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_840_le__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 11.11/6.13        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_841_le__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 11.11/6.13        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_842_le__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 11.11/6.13        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_843_le__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 11.11/6.13        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_844_double__add__le__zero__iff__single__add__le__zero,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 11.11/6.13        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_845_double__add__le__zero__iff__single__add__le__zero,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 11.11/6.13        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_846_double__add__le__zero__iff__single__add__le__zero,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 11.11/6.13        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_847_zero__le__double__add__iff__zero__le__single__add,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 11.11/6.13        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_848_zero__le__double__add__iff__zero__le__single__add,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 11.11/6.13        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_849_zero__le__double__add__iff__zero__le__single__add,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 11.11/6.13        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_850_zero__less__double__add__iff__zero__less__single__add,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 11.11/6.13        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_851_zero__less__double__add__iff__zero__less__single__add,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 11.11/6.13        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_852_zero__less__double__add__iff__zero__less__single__add,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 11.11/6.13        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_853_double__add__less__zero__iff__single__add__less__zero,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 11.11/6.13        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_854_double__add__less__zero__iff__single__add__less__zero,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 11.11/6.13        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_855_double__add__less__zero__iff__single__add__less__zero,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 11.11/6.13        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_856_less__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 11.11/6.13        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_857_less__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 11.11/6.13        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_858_less__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 11.11/6.13        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_859_less__add__same__cancel2,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 11.11/6.13        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_860_less__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 11.11/6.13        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_861_less__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.13        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_862_less__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.13        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_863_less__add__same__cancel1,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 11.11/6.13        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_864_add__less__same__cancel2,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_865_add__less__same__cancel2,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_866_add__less__same__cancel2,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_867_add__less__same__cancel2,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.13        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_868_add__less__same__cancel1,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_869_add__less__same__cancel1,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_870_add__less__same__cancel1,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_871_add__less__same__cancel1,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 11.11/6.13        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_872_zero__eq__1__divide__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( zero_zero_rat
% 11.11/6.13          = ( divide_divide_rat @ one_one_rat @ A ) )
% 11.11/6.13        = ( A = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_873_zero__eq__1__divide__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( zero_zero_real
% 11.11/6.13          = ( divide_divide_real @ one_one_real @ A ) )
% 11.11/6.13        = ( A = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_874_one__divide__eq__0__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 11.11/6.13          = zero_zero_rat )
% 11.11/6.13        = ( A = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_875_one__divide__eq__0__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ one_one_real @ A )
% 11.11/6.13          = zero_zero_real )
% 11.11/6.13        = ( A = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_876_eq__divide__eq__1,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( one_one_rat
% 11.11/6.13          = ( divide_divide_rat @ B @ A ) )
% 11.11/6.13        = ( ( A != zero_zero_rat )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_877_eq__divide__eq__1,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( one_one_real
% 11.11/6.13          = ( divide_divide_real @ B @ A ) )
% 11.11/6.13        = ( ( A != zero_zero_real )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_878_divide__eq__eq__1,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ B @ A )
% 11.11/6.13          = one_one_rat )
% 11.11/6.13        = ( ( A != zero_zero_rat )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_879_divide__eq__eq__1,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ B @ A )
% 11.11/6.13          = one_one_real )
% 11.11/6.13        = ( ( A != zero_zero_real )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_880_divide__self__if,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ( A = zero_zero_rat )
% 11.11/6.13         => ( ( divide_divide_rat @ A @ A )
% 11.11/6.13            = zero_zero_rat ) )
% 11.11/6.13        & ( ( A != zero_zero_rat )
% 11.11/6.13         => ( ( divide_divide_rat @ A @ A )
% 11.11/6.13            = one_one_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_881_divide__self__if,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ( A = zero_zero_real )
% 11.11/6.13         => ( ( divide_divide_real @ A @ A )
% 11.11/6.13            = zero_zero_real ) )
% 11.11/6.13        & ( ( A != zero_zero_real )
% 11.11/6.13         => ( ( divide_divide_real @ A @ A )
% 11.11/6.13            = one_one_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_882_divide__self__if,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( ( A = zero_zero_complex )
% 11.11/6.13         => ( ( divide1717551699836669952omplex @ A @ A )
% 11.11/6.13            = zero_zero_complex ) )
% 11.11/6.13        & ( ( A != zero_zero_complex )
% 11.11/6.13         => ( ( divide1717551699836669952omplex @ A @ A )
% 11.11/6.13            = one_one_complex ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_883_divide__self,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( A != zero_zero_rat )
% 11.11/6.13       => ( ( divide_divide_rat @ A @ A )
% 11.11/6.13          = one_one_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_884_divide__self,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( A != zero_zero_real )
% 11.11/6.13       => ( ( divide_divide_real @ A @ A )
% 11.11/6.13          = one_one_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_885_divide__self,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( A != zero_zero_complex )
% 11.11/6.13       => ( ( divide1717551699836669952omplex @ A @ A )
% 11.11/6.13          = one_one_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_886_one__eq__divide__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( one_one_rat
% 11.11/6.13          = ( divide_divide_rat @ A @ B ) )
% 11.11/6.13        = ( ( B != zero_zero_rat )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_887_one__eq__divide__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( one_one_real
% 11.11/6.13          = ( divide_divide_real @ A @ B ) )
% 11.11/6.13        = ( ( B != zero_zero_real )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_888_one__eq__divide__iff,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( one_one_complex
% 11.11/6.13          = ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.13        = ( ( B != zero_zero_complex )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_889_div__self,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( A != zero_zero_rat )
% 11.11/6.13       => ( ( divide_divide_rat @ A @ A )
% 11.11/6.13          = one_one_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_890_div__self,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( A != zero_zero_nat )
% 11.11/6.13       => ( ( divide_divide_nat @ A @ A )
% 11.11/6.13          = one_one_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_891_div__self,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( A != zero_zero_int )
% 11.11/6.13       => ( ( divide_divide_int @ A @ A )
% 11.11/6.13          = one_one_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_892_div__self,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( A != zero_zero_real )
% 11.11/6.13       => ( ( divide_divide_real @ A @ A )
% 11.11/6.13          = one_one_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_893_div__self,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( A != zero_zero_complex )
% 11.11/6.13       => ( ( divide1717551699836669952omplex @ A @ A )
% 11.11/6.13          = one_one_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_894_div__self,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.13       => ( ( divide6298287555418463151nteger @ A @ A )
% 11.11/6.13          = one_one_Code_integer ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_895_divide__eq__1__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ( divide_divide_rat @ A @ B )
% 11.11/6.13          = one_one_rat )
% 11.11/6.13        = ( ( B != zero_zero_rat )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_896_divide__eq__1__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ( divide_divide_real @ A @ B )
% 11.11/6.13          = one_one_real )
% 11.11/6.13        = ( ( B != zero_zero_real )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_897_divide__eq__1__iff,axiom,
% 11.11/6.13      ! [A: complex,B: complex] :
% 11.11/6.13        ( ( ( divide1717551699836669952omplex @ A @ B )
% 11.11/6.13          = one_one_complex )
% 11.11/6.13        = ( ( B != zero_zero_complex )
% 11.11/6.13          & ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_898_power__0__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 11.11/6.13        = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_899_power__0__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_900_power__0__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 11.11/6.13        = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_901_power__0__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_902_power__0__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 11.11/6.13        = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_903_power__zero__numeral,axiom,
% 11.11/6.13      ! [K: num] :
% 11.11/6.13        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.13        = zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_904_power__zero__numeral,axiom,
% 11.11/6.13      ! [K: num] :
% 11.11/6.13        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_905_power__zero__numeral,axiom,
% 11.11/6.13      ! [K: num] :
% 11.11/6.13        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 11.11/6.13        = zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_906_power__zero__numeral,axiom,
% 11.11/6.13      ! [K: num] :
% 11.11/6.13        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_907_power__zero__numeral,axiom,
% 11.11/6.13      ! [K: num] :
% 11.11/6.13        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 11.11/6.13        = zero_zero_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_908_mod__by__1,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_909_mod__by__1,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ A @ one_one_int )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_910_mod__by__1,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_911_bits__mod__by__1,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_912_bits__mod__by__1,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( modulo_modulo_int @ A @ one_one_int )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_913_bits__mod__by__1,axiom,
% 11.11/6.13      ! [A: code_integer] :
% 11.11/6.13        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_914_bits__mod__div__trivial,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_915_bits__mod__div__trivial,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_916_bits__mod__div__trivial,axiom,
% 11.11/6.13      ! [A: code_integer,B: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_917_mod__div__trivial,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_918_mod__div__trivial,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 11.11/6.13        = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_919_mod__div__trivial,axiom,
% 11.11/6.13      ! [A: code_integer,B: code_integer] :
% 11.11/6.13        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 11.11/6.13        = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_920_power__Suc0__right,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_921_power__Suc0__right,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_922_power__Suc0__right,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_923_power__Suc0__right,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_924_less__Suc0,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_925_zero__less__Suc,axiom,
% 11.11/6.13      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_926_add__gr__0,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.13        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.13          | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_927_less__one,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ N2 @ one_one_nat )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_928_div__by__Suc__0,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = M ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_929_div__less,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.13       => ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.13          = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_930_power__Suc__0,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.13        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_931_nat__power__eq__Suc__0__iff,axiom,
% 11.11/6.13      ! [X4: nat,M: nat] :
% 11.11/6.13        ( ( ( power_power_nat @ X4 @ M )
% 11.11/6.13          = ( suc @ zero_zero_nat ) )
% 11.11/6.13        = ( ( M = zero_zero_nat )
% 11.11/6.13          | ( X4
% 11.11/6.13            = ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_932_nat__zero__less__power__iff,axiom,
% 11.11/6.13      ! [X4: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X4 @ N2 ) )
% 11.11/6.13        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.13          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_933_mod__by__Suc__0,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_934_zero__le__divide__1__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 11.11/6.13        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_935_zero__le__divide__1__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 11.11/6.13        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_936_divide__le__0__1__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 11.11/6.13        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_937_divide__le__0__1__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 11.11/6.13        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_938_zero__less__divide__1__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 11.11/6.13        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_939_zero__less__divide__1__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 11.11/6.13        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_940_less__divide__eq__1__pos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.13          = ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_941_less__divide__eq__1__pos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.13          = ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_942_less__divide__eq__1__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.13          = ( ord_less_rat @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_943_less__divide__eq__1__neg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.13          = ( ord_less_real @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_944_divide__less__eq__1__pos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.13          = ( ord_less_rat @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_945_divide__less__eq__1__pos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.13          = ( ord_less_real @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_946_divide__less__eq__1__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.13          = ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_947_divide__less__eq__1__neg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.13          = ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_948_divide__less__0__1__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 11.11/6.13        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_949_divide__less__0__1__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 11.11/6.13        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_950_power__eq__0__iff,axiom,
% 11.11/6.13      ! [A: rat,N2: nat] :
% 11.11/6.13        ( ( ( power_power_rat @ A @ N2 )
% 11.11/6.13          = zero_zero_rat )
% 11.11/6.13        = ( ( A = zero_zero_rat )
% 11.11/6.13          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_951_power__eq__0__iff,axiom,
% 11.11/6.13      ! [A: nat,N2: nat] :
% 11.11/6.13        ( ( ( power_power_nat @ A @ N2 )
% 11.11/6.13          = zero_zero_nat )
% 11.11/6.13        = ( ( A = zero_zero_nat )
% 11.11/6.13          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_952_power__eq__0__iff,axiom,
% 11.11/6.13      ! [A: real,N2: nat] :
% 11.11/6.13        ( ( ( power_power_real @ A @ N2 )
% 11.11/6.13          = zero_zero_real )
% 11.11/6.13        = ( ( A = zero_zero_real )
% 11.11/6.13          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_953_power__eq__0__iff,axiom,
% 11.11/6.13      ! [A: int,N2: nat] :
% 11.11/6.13        ( ( ( power_power_int @ A @ N2 )
% 11.11/6.13          = zero_zero_int )
% 11.11/6.13        = ( ( A = zero_zero_int )
% 11.11/6.13          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_954_power__eq__0__iff,axiom,
% 11.11/6.13      ! [A: complex,N2: nat] :
% 11.11/6.13        ( ( ( power_power_complex @ A @ N2 )
% 11.11/6.13          = zero_zero_complex )
% 11.11/6.13        = ( ( A = zero_zero_complex )
% 11.11/6.13          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_955_le__divide__eq__1__pos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.13          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_956_le__divide__eq__1__pos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.13          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_957_le__divide__eq__1__neg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.13          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_958_le__divide__eq__1__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.13          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_959_divide__le__eq__1__pos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.13          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_960_divide__le__eq__1__pos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.13          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_961_divide__le__eq__1__neg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.13          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_962_divide__le__eq__1__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.13          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_963_power__strict__decreasing__iff,axiom,
% 11.11/6.13      ! [B: real,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.13       => ( ( ord_less_real @ B @ one_one_real )
% 11.11/6.13         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_964_power__strict__decreasing__iff,axiom,
% 11.11/6.13      ! [B: rat,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.13       => ( ( ord_less_rat @ B @ one_one_rat )
% 11.11/6.13         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_965_power__strict__decreasing__iff,axiom,
% 11.11/6.13      ! [B: nat,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.13       => ( ( ord_less_nat @ B @ one_one_nat )
% 11.11/6.13         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_966_power__strict__decreasing__iff,axiom,
% 11.11/6.13      ! [B: int,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.13       => ( ( ord_less_int @ B @ one_one_int )
% 11.11/6.13         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_967_power__mono__iff,axiom,
% 11.11/6.13      ! [A: real,B: real,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.13              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_968_power__mono__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 11.11/6.13              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_969_power__mono__iff,axiom,
% 11.11/6.13      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 11.11/6.13              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_970_power__mono__iff,axiom,
% 11.11/6.13      ! [A: int,B: int,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 11.11/6.13              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_971_zero__eq__power2,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = zero_zero_rat )
% 11.11/6.13        = ( A = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_972_zero__eq__power2,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = zero_zero_nat )
% 11.11/6.13        = ( A = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_973_zero__eq__power2,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = zero_zero_real )
% 11.11/6.13        = ( A = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_974_zero__eq__power2,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = zero_zero_int )
% 11.11/6.13        = ( A = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_975_zero__eq__power2,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13          = zero_zero_complex )
% 11.11/6.13        = ( A = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_976_one__div__two__eq__zero,axiom,
% 11.11/6.13      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_977_one__div__two__eq__zero,axiom,
% 11.11/6.13      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_978_one__div__two__eq__zero,axiom,
% 11.11/6.13      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_979_bits__1__div__2,axiom,
% 11.11/6.13      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_980_bits__1__div__2,axiom,
% 11.11/6.13      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_981_bits__1__div__2,axiom,
% 11.11/6.13      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.13      = zero_z3403309356797280102nteger ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_982_power__decreasing__iff,axiom,
% 11.11/6.13      ! [B: real,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.13       => ( ( ord_less_real @ B @ one_one_real )
% 11.11/6.13         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_983_power__decreasing__iff,axiom,
% 11.11/6.13      ! [B: rat,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.13       => ( ( ord_less_rat @ B @ one_one_rat )
% 11.11/6.13         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_984_power__decreasing__iff,axiom,
% 11.11/6.13      ! [B: nat,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.13       => ( ( ord_less_nat @ B @ one_one_nat )
% 11.11/6.13         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_985_power__decreasing__iff,axiom,
% 11.11/6.13      ! [B: int,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.13       => ( ( ord_less_int @ B @ one_one_int )
% 11.11/6.13         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 11.11/6.13            = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_986_power2__eq__iff__nonneg,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13            = ( X4 = Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_987_power2__eq__iff__nonneg,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13            = ( X4 = Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_988_power2__eq__iff__nonneg,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 11.11/6.13         => ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13            = ( X4 = Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_989_power2__eq__iff__nonneg,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.13         => ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13            = ( X4 = Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_990_power2__less__eq__zero__iff,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 11.11/6.13        = ( A = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_991_power2__less__eq__zero__iff,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 11.11/6.13        = ( A = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_992_power2__less__eq__zero__iff,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 11.11/6.13        = ( A = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_993_zero__less__power2,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13        = ( A != zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_994_zero__less__power2,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13        = ( A != zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_995_zero__less__power2,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13        = ( A != zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_996_sum__power2__eq__zero__iff,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13          = zero_zero_rat )
% 11.11/6.13        = ( ( X4 = zero_zero_rat )
% 11.11/6.13          & ( Y = zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_997_sum__power2__eq__zero__iff,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13          = zero_zero_real )
% 11.11/6.13        = ( ( X4 = zero_zero_real )
% 11.11/6.13          & ( Y = zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_998_sum__power2__eq__zero__iff,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.13          = zero_zero_int )
% 11.11/6.13        = ( ( X4 = zero_zero_int )
% 11.11/6.13          & ( Y = zero_zero_int ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_999_add__self__mod__2,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.13        = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1000_psubsetD,axiom,
% 11.11/6.13      ! [A2: set_real,B3: set_real,C: real] :
% 11.11/6.13        ( ( ord_less_set_real @ A2 @ B3 )
% 11.11/6.13       => ( ( member_real @ C @ A2 )
% 11.11/6.13         => ( member_real @ C @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1001_psubsetD,axiom,
% 11.11/6.13      ! [A2: set_nat,B3: set_nat,C: nat] :
% 11.11/6.13        ( ( ord_less_set_nat @ A2 @ B3 )
% 11.11/6.13       => ( ( member_nat @ C @ A2 )
% 11.11/6.13         => ( member_nat @ C @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1002_psubsetD,axiom,
% 11.11/6.13      ! [A2: set_complex,B3: set_complex,C: complex] :
% 11.11/6.13        ( ( ord_less_set_complex @ A2 @ B3 )
% 11.11/6.13       => ( ( member_complex @ C @ A2 )
% 11.11/6.13         => ( member_complex @ C @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1003_psubsetD,axiom,
% 11.11/6.13      ! [A2: set_int,B3: set_int,C: int] :
% 11.11/6.13        ( ( ord_less_set_int @ A2 @ B3 )
% 11.11/6.13       => ( ( member_int @ C @ A2 )
% 11.11/6.13         => ( member_int @ C @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1004_psubsetD,axiom,
% 11.11/6.13      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 11.11/6.13        ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 11.11/6.13       => ( ( member8440522571783428010at_nat @ C @ A2 )
% 11.11/6.13         => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1005_zero__reorient,axiom,
% 11.11/6.13      ! [X4: complex] :
% 11.11/6.13        ( ( zero_zero_complex = X4 )
% 11.11/6.13        = ( X4 = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1006_zero__reorient,axiom,
% 11.11/6.13      ! [X4: real] :
% 11.11/6.13        ( ( zero_zero_real = X4 )
% 11.11/6.13        = ( X4 = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1007_zero__reorient,axiom,
% 11.11/6.13      ! [X4: rat] :
% 11.11/6.13        ( ( zero_zero_rat = X4 )
% 11.11/6.13        = ( X4 = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1008_zero__reorient,axiom,
% 11.11/6.13      ! [X4: nat] :
% 11.11/6.13        ( ( zero_zero_nat = X4 )
% 11.11/6.13        = ( X4 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1009_zero__reorient,axiom,
% 11.11/6.13      ! [X4: int] :
% 11.11/6.13        ( ( zero_zero_int = X4 )
% 11.11/6.13        = ( X4 = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1010_verit__sum__simplify,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1011_verit__sum__simplify,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ A @ zero_zero_real )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1012_verit__sum__simplify,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1013_verit__sum__simplify,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1014_verit__sum__simplify,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ A @ zero_zero_int )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1015_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 11.11/6.13      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 11.11/6.13        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X4 )
% 11.11/6.13        = ( ( X4 = Mi )
% 11.11/6.13          | ( X4 = Ma ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1016_power__0__left,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ( N2 = zero_zero_nat )
% 11.11/6.13         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 11.11/6.13            = one_one_rat ) )
% 11.11/6.13        & ( ( N2 != zero_zero_nat )
% 11.11/6.13         => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 11.11/6.13            = zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1017_power__0__left,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ( N2 = zero_zero_nat )
% 11.11/6.13         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 11.11/6.13            = one_one_nat ) )
% 11.11/6.13        & ( ( N2 != zero_zero_nat )
% 11.11/6.13         => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 11.11/6.13            = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1018_power__0__left,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ( N2 = zero_zero_nat )
% 11.11/6.13         => ( ( power_power_real @ zero_zero_real @ N2 )
% 11.11/6.13            = one_one_real ) )
% 11.11/6.13        & ( ( N2 != zero_zero_nat )
% 11.11/6.13         => ( ( power_power_real @ zero_zero_real @ N2 )
% 11.11/6.13            = zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1019_power__0__left,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ( N2 = zero_zero_nat )
% 11.11/6.13         => ( ( power_power_int @ zero_zero_int @ N2 )
% 11.11/6.13            = one_one_int ) )
% 11.11/6.13        & ( ( N2 != zero_zero_nat )
% 11.11/6.13         => ( ( power_power_int @ zero_zero_int @ N2 )
% 11.11/6.13            = zero_zero_int ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1020_power__0__left,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ( N2 = zero_zero_nat )
% 11.11/6.13         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 11.11/6.13            = one_one_complex ) )
% 11.11/6.13        & ( ( N2 != zero_zero_nat )
% 11.11/6.13         => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 11.11/6.13            = zero_zero_complex ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1021_zero__power,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 11.11/6.13          = zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1022_zero__power,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 11.11/6.13          = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1023_zero__power,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( power_power_real @ zero_zero_real @ N2 )
% 11.11/6.13          = zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1024_zero__power,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( power_power_int @ zero_zero_int @ N2 )
% 11.11/6.13          = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1025_zero__power,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 11.11/6.13          = zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1026_zero__le,axiom,
% 11.11/6.13      ! [X4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1027_le__numeral__extra_I3_J,axiom,
% 11.11/6.13      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1028_le__numeral__extra_I3_J,axiom,
% 11.11/6.13      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1029_le__numeral__extra_I3_J,axiom,
% 11.11/6.13      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1030_le__numeral__extra_I3_J,axiom,
% 11.11/6.13      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1031_zero__less__iff__neq__zero,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13        = ( N2 != zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1032_gr__implies__not__zero,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.13       => ( N2 != zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1033_not__less__zero,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1034_gr__zeroI,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( N2 != zero_zero_nat )
% 11.11/6.13       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1035_less__numeral__extra_I3_J,axiom,
% 11.11/6.13      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1036_less__numeral__extra_I3_J,axiom,
% 11.11/6.13      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1037_less__numeral__extra_I3_J,axiom,
% 11.11/6.13      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1038_less__numeral__extra_I3_J,axiom,
% 11.11/6.13      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1039_field__lbound__gt__zero,axiom,
% 11.11/6.13      ! [D1: real,D2: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ D1 )
% 11.11/6.13       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 11.11/6.13         => ? [E: real] :
% 11.11/6.13              ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.13              & ( ord_less_real @ E @ D1 )
% 11.11/6.13              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1040_field__lbound__gt__zero,axiom,
% 11.11/6.13      ! [D1: rat,D2: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 11.11/6.13       => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 11.11/6.13         => ? [E: rat] :
% 11.11/6.13              ( ( ord_less_rat @ zero_zero_rat @ E )
% 11.11/6.13              & ( ord_less_rat @ E @ D1 )
% 11.11/6.13              & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1041_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_zero_rat
% 11.11/6.13       != ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1042_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_z5237406670263579293d_enat
% 11.11/6.13       != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1043_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_zero_complex
% 11.11/6.13       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1044_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_zero_real
% 11.11/6.13       != ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1045_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_zero_nat
% 11.11/6.13       != ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1046_zero__neq__numeral,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ( zero_zero_int
% 11.11/6.13       != ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1047_zero__neq__one,axiom,
% 11.11/6.13      zero_zero_complex != one_one_complex ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1048_zero__neq__one,axiom,
% 11.11/6.13      zero_zero_real != one_one_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1049_zero__neq__one,axiom,
% 11.11/6.13      zero_zero_rat != one_one_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1050_zero__neq__one,axiom,
% 11.11/6.13      zero_zero_nat != one_one_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1051_zero__neq__one,axiom,
% 11.11/6.13      zero_zero_int != one_one_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1052_add_Ogroup__left__neutral,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1053_add_Ogroup__left__neutral,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ zero_zero_real @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1054_add_Ogroup__left__neutral,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1055_add_Ogroup__left__neutral,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ zero_zero_int @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1056_add_Ocomm__neutral,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1057_add_Ocomm__neutral,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ A @ zero_zero_real )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1058_add_Ocomm__neutral,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1059_add_Ocomm__neutral,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1060_add_Ocomm__neutral,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ A @ zero_zero_int )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1061_comm__monoid__add__class_Oadd__0,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1062_comm__monoid__add__class_Oadd__0,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( plus_plus_real @ zero_zero_real @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1063_comm__monoid__add__class_Oadd__0,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1064_comm__monoid__add__class_Oadd__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1065_comm__monoid__add__class_Oadd__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( plus_plus_int @ zero_zero_int @ A )
% 11.11/6.13        = A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1066_power__not__zero,axiom,
% 11.11/6.13      ! [A: rat,N2: nat] :
% 11.11/6.13        ( ( A != zero_zero_rat )
% 11.11/6.13       => ( ( power_power_rat @ A @ N2 )
% 11.11/6.13         != zero_zero_rat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1067_power__not__zero,axiom,
% 11.11/6.13      ! [A: nat,N2: nat] :
% 11.11/6.13        ( ( A != zero_zero_nat )
% 11.11/6.13       => ( ( power_power_nat @ A @ N2 )
% 11.11/6.13         != zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1068_power__not__zero,axiom,
% 11.11/6.13      ! [A: real,N2: nat] :
% 11.11/6.13        ( ( A != zero_zero_real )
% 11.11/6.13       => ( ( power_power_real @ A @ N2 )
% 11.11/6.13         != zero_zero_real ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1069_power__not__zero,axiom,
% 11.11/6.13      ! [A: int,N2: nat] :
% 11.11/6.13        ( ( A != zero_zero_int )
% 11.11/6.13       => ( ( power_power_int @ A @ N2 )
% 11.11/6.13         != zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1070_power__not__zero,axiom,
% 11.11/6.13      ! [A: complex,N2: nat] :
% 11.11/6.13        ( ( A != zero_zero_complex )
% 11.11/6.13       => ( ( power_power_complex @ A @ N2 )
% 11.11/6.13         != zero_zero_complex ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1071_num_Osize_I4_J,axiom,
% 11.11/6.13      ( ( size_size_num @ one )
% 11.11/6.13      = zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1072_vebt__buildup_Ocases,axiom,
% 11.11/6.13      ! [X4: nat] :
% 11.11/6.13        ( ( X4 != zero_zero_nat )
% 11.11/6.13       => ( ( X4
% 11.11/6.13           != ( suc @ zero_zero_nat ) )
% 11.11/6.13         => ~ ! [Va2: nat] :
% 11.11/6.13                ( X4
% 11.11/6.13               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1073_not0__implies__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( N2 != zero_zero_nat )
% 11.11/6.13       => ? [M5: nat] :
% 11.11/6.13            ( N2
% 11.11/6.13            = ( suc @ M5 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1074_Zero__not__Suc,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( zero_zero_nat
% 11.11/6.13       != ( suc @ M ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1075_Zero__neq__Suc,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( zero_zero_nat
% 11.11/6.13       != ( suc @ M ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1076_Suc__neq__Zero,axiom,
% 11.11/6.13      ! [M: nat] :
% 11.11/6.13        ( ( suc @ M )
% 11.11/6.13       != zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1077_zero__induct,axiom,
% 11.11/6.13      ! [P: nat > $o,K: nat] :
% 11.11/6.13        ( ( P @ K )
% 11.11/6.13       => ( ! [N3: nat] :
% 11.11/6.13              ( ( P @ ( suc @ N3 ) )
% 11.11/6.13             => ( P @ N3 ) )
% 11.11/6.13         => ( P @ zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1078_diff__induct,axiom,
% 11.11/6.13      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 11.11/6.13        ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 11.11/6.13       => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( P @ X5 @ Y3 )
% 11.11/6.13               => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 11.11/6.13           => ( P @ M @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1079_nat__induct,axiom,
% 11.11/6.13      ! [P: nat > $o,N2: nat] :
% 11.11/6.13        ( ( P @ zero_zero_nat )
% 11.11/6.13       => ( ! [N3: nat] :
% 11.11/6.13              ( ( P @ N3 )
% 11.11/6.13             => ( P @ ( suc @ N3 ) ) )
% 11.11/6.13         => ( P @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1080_old_Onat_Oexhaust,axiom,
% 11.11/6.13      ! [Y: nat] :
% 11.11/6.13        ( ( Y != zero_zero_nat )
% 11.11/6.13       => ~ ! [Nat3: nat] :
% 11.11/6.13              ( Y
% 11.11/6.13             != ( suc @ Nat3 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1081_nat_OdiscI,axiom,
% 11.11/6.13      ! [Nat: nat,X22: nat] :
% 11.11/6.13        ( ( Nat
% 11.11/6.13          = ( suc @ X22 ) )
% 11.11/6.13       => ( Nat != zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1082_old_Onat_Odistinct_I1_J,axiom,
% 11.11/6.13      ! [Nat2: nat] :
% 11.11/6.13        ( zero_zero_nat
% 11.11/6.13       != ( suc @ Nat2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1083_old_Onat_Odistinct_I2_J,axiom,
% 11.11/6.13      ! [Nat2: nat] :
% 11.11/6.13        ( ( suc @ Nat2 )
% 11.11/6.13       != zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1084_nat_Odistinct_I1_J,axiom,
% 11.11/6.13      ! [X22: nat] :
% 11.11/6.13        ( zero_zero_nat
% 11.11/6.13       != ( suc @ X22 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1085_infinite__descent0,axiom,
% 11.11/6.13      ! [P: nat > $o,N2: nat] :
% 11.11/6.13        ( ( P @ zero_zero_nat )
% 11.11/6.13       => ( ! [N3: nat] :
% 11.11/6.13              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.13             => ( ~ ( P @ N3 )
% 11.11/6.13               => ? [M2: nat] :
% 11.11/6.13                    ( ( ord_less_nat @ M2 @ N3 )
% 11.11/6.13                    & ~ ( P @ M2 ) ) ) )
% 11.11/6.13         => ( P @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1086_gr__implies__not0,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.13       => ( N2 != zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1087_less__zeroE,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1088_not__less0,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1089_not__gr0,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1090_gr0I,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( N2 != zero_zero_nat )
% 11.11/6.13       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1091_bot__nat__0_Oextremum__strict,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1092_le__0__eq,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 11.11/6.13        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1093_bot__nat__0_Oextremum__uniqueI,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.13       => ( A = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1094_bot__nat__0_Oextremum__unique,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.13        = ( A = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1095_less__eq__nat_Osimps_I1_J,axiom,
% 11.11/6.13      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1096_add__eq__self__zero,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ M @ N2 )
% 11.11/6.13          = M )
% 11.11/6.13       => ( N2 = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1097_plus__nat_Oadd__0,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 11.11/6.13        = N2 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1098_power__eq__imp__eq__base,axiom,
% 11.11/6.13      ! [A: real,N2: nat,B: real] :
% 11.11/6.13        ( ( ( power_power_real @ A @ N2 )
% 11.11/6.13          = ( power_power_real @ B @ N2 ) )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.13           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13             => ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1099_power__eq__imp__eq__base,axiom,
% 11.11/6.13      ! [A: rat,N2: nat,B: rat] :
% 11.11/6.13        ( ( ( power_power_rat @ A @ N2 )
% 11.11/6.13          = ( power_power_rat @ B @ N2 ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.13           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13             => ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1100_power__eq__imp__eq__base,axiom,
% 11.11/6.13      ! [A: nat,N2: nat,B: nat] :
% 11.11/6.13        ( ( ( power_power_nat @ A @ N2 )
% 11.11/6.13          = ( power_power_nat @ B @ N2 ) )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.13           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13             => ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1101_power__eq__imp__eq__base,axiom,
% 11.11/6.13      ! [A: int,N2: nat,B: int] :
% 11.11/6.13        ( ( ( power_power_int @ A @ N2 )
% 11.11/6.13          = ( power_power_int @ B @ N2 ) )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.13           => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13             => ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1102_power__eq__iff__eq__base,axiom,
% 11.11/6.13      ! [N2: nat,A: real,B: real] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.13           => ( ( ( power_power_real @ A @ N2 )
% 11.11/6.13                = ( power_power_real @ B @ N2 ) )
% 11.11/6.13              = ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1103_power__eq__iff__eq__base,axiom,
% 11.11/6.13      ! [N2: nat,A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.13           => ( ( ( power_power_rat @ A @ N2 )
% 11.11/6.13                = ( power_power_rat @ B @ N2 ) )
% 11.11/6.13              = ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1104_power__eq__iff__eq__base,axiom,
% 11.11/6.13      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.13           => ( ( ( power_power_nat @ A @ N2 )
% 11.11/6.13                = ( power_power_nat @ B @ N2 ) )
% 11.11/6.13              = ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1105_power__eq__iff__eq__base,axiom,
% 11.11/6.13      ! [N2: nat,A: int,B: int] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.13           => ( ( ( power_power_int @ A @ N2 )
% 11.11/6.13                = ( power_power_int @ B @ N2 ) )
% 11.11/6.13              = ( A = B ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1106_power__strict__mono,axiom,
% 11.11/6.13      ! [A: real,B: real,N2: nat] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1107_power__strict__mono,axiom,
% 11.11/6.13      ! [A: rat,B: rat,N2: nat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1108_power__strict__mono,axiom,
% 11.11/6.13      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1109_power__strict__mono,axiom,
% 11.11/6.13      ! [A: int,B: int,N2: nat] :
% 11.11/6.13        ( ( ord_less_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13           => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1110_zero__le__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1111_zero__le__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1112_zero__le__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1113_zero__le__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1114_zero__le__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1115_not__numeral__le__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1116_not__numeral__le__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1117_not__numeral__le__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1118_not__numeral__le__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1119_not__numeral__le__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1120_not__numeral__less__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1121_not__numeral__less__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1122_not__numeral__less__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1123_not__numeral__less__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1124_not__numeral__less__zero,axiom,
% 11.11/6.13      ! [N2: num] :
% 11.11/6.13        ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1125_zero__less__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1126_zero__less__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1127_zero__less__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1128_zero__less__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1129_zero__less__numeral,axiom,
% 11.11/6.13      ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1130_zero__less__one__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1131_zero__less__one__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1132_zero__less__one__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1133_zero__less__one__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1134_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1135_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1136_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1137_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 11.11/6.13      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1138_not__one__le__zero,axiom,
% 11.11/6.13      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1139_not__one__le__zero,axiom,
% 11.11/6.13      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1140_not__one__le__zero,axiom,
% 11.11/6.13      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1141_not__one__le__zero,axiom,
% 11.11/6.13      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1142_add__decreasing,axiom,
% 11.11/6.13      ! [A: real,C: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ C @ B )
% 11.11/6.13         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1143_add__decreasing,axiom,
% 11.11/6.13      ! [A: rat,C: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ C @ B )
% 11.11/6.13         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1144_add__decreasing,axiom,
% 11.11/6.13      ! [A: nat,C: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.13       => ( ( ord_less_eq_nat @ C @ B )
% 11.11/6.13         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1145_add__decreasing,axiom,
% 11.11/6.13      ! [A: int,C: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_eq_int @ C @ B )
% 11.11/6.13         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1146_add__increasing,axiom,
% 11.11/6.13      ! [A: real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_eq_real @ B @ C )
% 11.11/6.13         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1147_add__increasing,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1148_add__increasing,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1149_add__increasing,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.13         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1150_add__decreasing2,axiom,
% 11.11/6.13      ! [C: real,A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.13         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1151_add__decreasing2,axiom,
% 11.11/6.13      ! [C: rat,A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1152_add__decreasing2,axiom,
% 11.11/6.13      ! [C: nat,A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 11.11/6.13       => ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1153_add__decreasing2,axiom,
% 11.11/6.13      ! [C: int,A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1154_add__increasing2,axiom,
% 11.11/6.13      ! [C: real,B: real,A: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.13       => ( ( ord_less_eq_real @ B @ A )
% 11.11/6.13         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1155_add__increasing2,axiom,
% 11.11/6.13      ! [C: rat,B: rat,A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.13         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1156_add__increasing2,axiom,
% 11.11/6.13      ! [C: nat,B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.13         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1157_add__increasing2,axiom,
% 11.11/6.13      ! [C: int,B: int,A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ A )
% 11.11/6.13         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1158_add__nonneg__nonneg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.13         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1159_add__nonneg__nonneg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.13         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1160_add__nonneg__nonneg,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.13         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1161_add__nonneg__nonneg,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.13         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1162_add__nonpos__nonpos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.13         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1163_add__nonpos__nonpos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1164_add__nonpos__nonpos,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 11.11/6.13         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1165_add__nonpos__nonpos,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.13         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1166_add__nonneg__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ( ( plus_plus_real @ X4 @ Y )
% 11.11/6.13              = zero_zero_real )
% 11.11/6.13            = ( ( X4 = zero_zero_real )
% 11.11/6.13              & ( Y = zero_zero_real ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1167_add__nonneg__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ( ( plus_plus_rat @ X4 @ Y )
% 11.11/6.13              = zero_zero_rat )
% 11.11/6.13            = ( ( X4 = zero_zero_rat )
% 11.11/6.13              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1168_add__nonneg__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 11.11/6.13         => ( ( ( plus_plus_nat @ X4 @ Y )
% 11.11/6.13              = zero_zero_nat )
% 11.11/6.13            = ( ( X4 = zero_zero_nat )
% 11.11/6.13              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1169_add__nonneg__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.13         => ( ( ( plus_plus_int @ X4 @ Y )
% 11.11/6.13              = zero_zero_int )
% 11.11/6.13            = ( ( X4 = zero_zero_int )
% 11.11/6.13              & ( Y = zero_zero_int ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1170_add__nonpos__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 11.11/6.13         => ( ( ( plus_plus_real @ X4 @ Y )
% 11.11/6.13              = zero_zero_real )
% 11.11/6.13            = ( ( X4 = zero_zero_real )
% 11.11/6.13              & ( Y = zero_zero_real ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1171_add__nonpos__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 11.11/6.13         => ( ( ( plus_plus_rat @ X4 @ Y )
% 11.11/6.13              = zero_zero_rat )
% 11.11/6.13            = ( ( X4 = zero_zero_rat )
% 11.11/6.13              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1172_add__nonpos__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ X4 @ zero_zero_nat )
% 11.11/6.13       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 11.11/6.13         => ( ( ( plus_plus_nat @ X4 @ Y )
% 11.11/6.13              = zero_zero_nat )
% 11.11/6.13            = ( ( X4 = zero_zero_nat )
% 11.11/6.13              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1173_add__nonpos__eq__0__iff,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 11.11/6.13         => ( ( ( plus_plus_int @ X4 @ Y )
% 11.11/6.13              = zero_zero_int )
% 11.11/6.13            = ( ( X4 = zero_zero_int )
% 11.11/6.13              & ( Y = zero_zero_int ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1174_not__one__less__zero,axiom,
% 11.11/6.13      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1175_not__one__less__zero,axiom,
% 11.11/6.13      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1176_not__one__less__zero,axiom,
% 11.11/6.13      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1177_not__one__less__zero,axiom,
% 11.11/6.13      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1178_zero__less__one,axiom,
% 11.11/6.13      ord_less_real @ zero_zero_real @ one_one_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1179_zero__less__one,axiom,
% 11.11/6.13      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1180_zero__less__one,axiom,
% 11.11/6.13      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1181_zero__less__one,axiom,
% 11.11/6.13      ord_less_int @ zero_zero_int @ one_one_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1182_less__numeral__extra_I1_J,axiom,
% 11.11/6.13      ord_less_real @ zero_zero_real @ one_one_real ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1183_less__numeral__extra_I1_J,axiom,
% 11.11/6.13      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1184_less__numeral__extra_I1_J,axiom,
% 11.11/6.13      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1185_less__numeral__extra_I1_J,axiom,
% 11.11/6.13      ord_less_int @ zero_zero_int @ one_one_int ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1186_pos__add__strict,axiom,
% 11.11/6.13      ! [A: real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1187_pos__add__strict,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1188_pos__add__strict,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ( ord_less_nat @ B @ C )
% 11.11/6.13         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1189_pos__add__strict,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ( ord_less_int @ B @ C )
% 11.11/6.13         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1190_canonically__ordered__monoid__add__class_OlessE,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ B )
% 11.11/6.13       => ~ ! [C3: nat] :
% 11.11/6.13              ( ( B
% 11.11/6.13                = ( plus_plus_nat @ A @ C3 ) )
% 11.11/6.13             => ( C3 = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1191_add__pos__pos,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.13         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1192_add__pos__pos,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.13         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1193_add__pos__pos,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.13         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1194_add__pos__pos,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.13         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1195_add__neg__neg,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.13         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1196_add__neg__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1197_add__neg__neg,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ zero_zero_nat )
% 11.11/6.13       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 11.11/6.13         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1198_add__neg__neg,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.13         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1199_add__less__zeroD,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.13          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1200_add__less__zeroD,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( plus_plus_rat @ X4 @ Y ) @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 11.11/6.13          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1201_add__less__zeroD,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ ( plus_plus_int @ X4 @ Y ) @ zero_zero_int )
% 11.11/6.13       => ( ( ord_less_int @ X4 @ zero_zero_int )
% 11.11/6.13          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1202_divide__le__0__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 11.11/6.13        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 11.11/6.13          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.13            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1203_divide__le__0__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.13        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 11.11/6.13          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.13            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1204_divide__right__mono,axiom,
% 11.11/6.13      ! [A: real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.13         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1205_divide__right__mono,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.13         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1206_zero__le__divide__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.13        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.13          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.13            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1207_zero__le__divide__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.13        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 11.11/6.13          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.13            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1208_divide__nonneg__nonneg,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1209_divide__nonneg__nonneg,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1210_divide__nonneg__nonpos,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 11.11/6.13         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1211_divide__nonneg__nonpos,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1212_divide__nonpos__nonneg,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1213_divide__nonpos__nonneg,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1214_divide__nonpos__nonpos,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 11.11/6.13         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1215_divide__nonpos__nonpos,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1216_divide__right__mono__neg,axiom,
% 11.11/6.13      ! [A: real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.13         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1217_divide__right__mono__neg,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1218_power__mono,axiom,
% 11.11/6.13      ! [A: real,B: real,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1219_power__mono,axiom,
% 11.11/6.13      ! [A: rat,B: rat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1220_power__mono,axiom,
% 11.11/6.13      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1221_power__mono,axiom,
% 11.11/6.13      ! [A: int,B: int,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1222_zero__le__power,axiom,
% 11.11/6.13      ! [A: real,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1223_zero__le__power,axiom,
% 11.11/6.13      ! [A: rat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1224_zero__le__power,axiom,
% 11.11/6.13      ! [A: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1225_zero__le__power,axiom,
% 11.11/6.13      ! [A: int,N2: nat] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1226_divide__strict__right__mono__neg,axiom,
% 11.11/6.13      ! [B: rat,A: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ B @ A )
% 11.11/6.13       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1227_divide__strict__right__mono__neg,axiom,
% 11.11/6.13      ! [B: real,A: real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ B @ A )
% 11.11/6.13       => ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.13         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1228_divide__strict__right__mono,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.13         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1229_divide__strict__right__mono,axiom,
% 11.11/6.13      ! [A: real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.13         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1230_zero__less__divide__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.13        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 11.11/6.13          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1231_zero__less__divide__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.13        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13            & ( ord_less_real @ zero_zero_real @ B ) )
% 11.11/6.13          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1232_divide__less__cancel,axiom,
% 11.11/6.13      ! [A: rat,C: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.13        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.13           => ( ord_less_rat @ A @ B ) )
% 11.11/6.13          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.13           => ( ord_less_rat @ B @ A ) )
% 11.11/6.13          & ( C != zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1233_divide__less__cancel,axiom,
% 11.11/6.13      ! [A: real,C: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.13        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.13           => ( ord_less_real @ A @ B ) )
% 11.11/6.13          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.13           => ( ord_less_real @ B @ A ) )
% 11.11/6.13          & ( C != zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1234_divide__less__0__iff,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.13        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 11.11/6.13          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.13            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1235_divide__less__0__iff,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 11.11/6.13        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13            & ( ord_less_real @ B @ zero_zero_real ) )
% 11.11/6.13          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.13            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1236_divide__pos__pos,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1237_divide__pos__pos,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1238_divide__pos__neg,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.13       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1239_divide__pos__neg,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.13       => ( ( ord_less_real @ Y @ zero_zero_real )
% 11.11/6.13         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1240_divide__neg__pos,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.13         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1241_divide__neg__pos,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.13         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1242_divide__neg__neg,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 11.11/6.13       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 11.11/6.13         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1243_divide__neg__neg,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.13       => ( ( ord_less_real @ Y @ zero_zero_real )
% 11.11/6.13         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1244_zero__less__power,axiom,
% 11.11/6.13      ! [A: real,N2: nat] :
% 11.11/6.13        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.13       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1245_zero__less__power,axiom,
% 11.11/6.13      ! [A: rat,N2: nat] :
% 11.11/6.13        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.13       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1246_zero__less__power,axiom,
% 11.11/6.13      ! [A: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1247_zero__less__power,axiom,
% 11.11/6.13      ! [A: int,N2: nat] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1248_right__inverse__eq,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( B != zero_zero_rat )
% 11.11/6.13       => ( ( ( divide_divide_rat @ A @ B )
% 11.11/6.13            = one_one_rat )
% 11.11/6.13          = ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1249_right__inverse__eq,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( B != zero_zero_real )
% 11.11/6.13       => ( ( ( divide_divide_real @ A @ B )
% 11.11/6.13            = one_one_real )
% 11.11/6.13          = ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1250_right__inverse__eq,axiom,
% 11.11/6.13      ! [B: complex,A: complex] :
% 11.11/6.13        ( ( B != zero_zero_complex )
% 11.11/6.13       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 11.11/6.13            = one_one_complex )
% 11.11/6.13          = ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1251_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 11.11/6.13      ! [A: code_integer,B: code_integer] :
% 11.11/6.13        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.13       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1252_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.13       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1253_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.13       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1254_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.13       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1255_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.13       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1256_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 11.11/6.13      ! [B: code_integer,A: code_integer] :
% 11.11/6.13        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.13       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1257_power__0,axiom,
% 11.11/6.13      ! [A: rat] :
% 11.11/6.13        ( ( power_power_rat @ A @ zero_zero_nat )
% 11.11/6.13        = one_one_rat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1258_power__0,axiom,
% 11.11/6.13      ! [A: nat] :
% 11.11/6.13        ( ( power_power_nat @ A @ zero_zero_nat )
% 11.11/6.13        = one_one_nat ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1259_power__0,axiom,
% 11.11/6.13      ! [A: real] :
% 11.11/6.13        ( ( power_power_real @ A @ zero_zero_nat )
% 11.11/6.13        = one_one_real ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1260_power__0,axiom,
% 11.11/6.13      ! [A: int] :
% 11.11/6.13        ( ( power_power_int @ A @ zero_zero_nat )
% 11.11/6.13        = one_one_int ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1261_power__0,axiom,
% 11.11/6.13      ! [A: complex] :
% 11.11/6.13        ( ( power_power_complex @ A @ zero_zero_nat )
% 11.11/6.13        = one_one_complex ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1262_mod__eq__self__iff__div__eq__0,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ( modulo_modulo_nat @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( ( divide_divide_nat @ A @ B )
% 11.11/6.13          = zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1263_mod__eq__self__iff__div__eq__0,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( ( divide_divide_int @ A @ B )
% 11.11/6.13          = zero_zero_int ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1264_mod__eq__self__iff__div__eq__0,axiom,
% 11.11/6.13      ! [A: code_integer,B: code_integer] :
% 11.11/6.13        ( ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.13          = A )
% 11.11/6.13        = ( ( divide6298287555418463151nteger @ A @ B )
% 11.11/6.13          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1265_Ex__less__Suc2,axiom,
% 11.11/6.13      ! [N2: nat,P: nat > $o] :
% 11.11/6.13        ( ( ? [I3: nat] :
% 11.11/6.13              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 11.11/6.13              & ( P @ I3 ) ) )
% 11.11/6.13        = ( ( P @ zero_zero_nat )
% 11.11/6.13          | ? [I3: nat] :
% 11.11/6.13              ( ( ord_less_nat @ I3 @ N2 )
% 11.11/6.13              & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1266_gr0__conv__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13        = ( ? [M6: nat] :
% 11.11/6.13              ( N2
% 11.11/6.13              = ( suc @ M6 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1267_All__less__Suc2,axiom,
% 11.11/6.13      ! [N2: nat,P: nat > $o] :
% 11.11/6.13        ( ( ! [I3: nat] :
% 11.11/6.13              ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 11.11/6.13             => ( P @ I3 ) ) )
% 11.11/6.13        = ( ( P @ zero_zero_nat )
% 11.11/6.13          & ! [I3: nat] :
% 11.11/6.13              ( ( ord_less_nat @ I3 @ N2 )
% 11.11/6.13             => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1268_gr0__implies__Suc,axiom,
% 11.11/6.13      ! [N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ? [M5: nat] :
% 11.11/6.13            ( N2
% 11.11/6.13            = ( suc @ M5 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1269_less__Suc__eq__0__disj,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 11.11/6.13        = ( ( M = zero_zero_nat )
% 11.11/6.13          | ? [J3: nat] :
% 11.11/6.13              ( ( M
% 11.11/6.13                = ( suc @ J3 ) )
% 11.11/6.13              & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1270_add__is__1,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( plus_plus_nat @ M @ N2 )
% 11.11/6.13          = ( suc @ zero_zero_nat ) )
% 11.11/6.13        = ( ( ( M
% 11.11/6.13              = ( suc @ zero_zero_nat ) )
% 11.11/6.13            & ( N2 = zero_zero_nat ) )
% 11.11/6.13          | ( ( M = zero_zero_nat )
% 11.11/6.13            & ( N2
% 11.11/6.13              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1271_one__is__add,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( suc @ zero_zero_nat )
% 11.11/6.13          = ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.13        = ( ( ( M
% 11.11/6.13              = ( suc @ zero_zero_nat ) )
% 11.11/6.13            & ( N2 = zero_zero_nat ) )
% 11.11/6.13          | ( ( M = zero_zero_nat )
% 11.11/6.13            & ( N2
% 11.11/6.13              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1272_ex__least__nat__le,axiom,
% 11.11/6.13      ! [P: nat > $o,N2: nat] :
% 11.11/6.13        ( ( P @ N2 )
% 11.11/6.13       => ( ~ ( P @ zero_zero_nat )
% 11.11/6.13         => ? [K2: nat] :
% 11.11/6.13              ( ( ord_less_eq_nat @ K2 @ N2 )
% 11.11/6.13              & ! [I: nat] :
% 11.11/6.13                  ( ( ord_less_nat @ I @ K2 )
% 11.11/6.13                 => ~ ( P @ I ) )
% 11.11/6.13              & ( P @ K2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1273_less__imp__add__positive,axiom,
% 11.11/6.13      ! [I2: nat,J: nat] :
% 11.11/6.13        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.13       => ? [K2: nat] :
% 11.11/6.13            ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 11.11/6.13            & ( ( plus_plus_nat @ I2 @ K2 )
% 11.11/6.13              = J ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1274_div__less__mono,axiom,
% 11.11/6.13      ! [A2: nat,B3: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A2 @ B3 )
% 11.11/6.13       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13         => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 11.11/6.13              = zero_zero_nat )
% 11.11/6.13           => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 11.11/6.13                = zero_zero_nat )
% 11.11/6.13             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1275_One__nat__def,axiom,
% 11.11/6.13      ( one_one_nat
% 11.11/6.13      = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1276_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.13          = zero_zero_nat )
% 11.11/6.13        = ( ( ord_less_nat @ M @ N2 )
% 11.11/6.13          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1277_nat__power__less__imp__less,axiom,
% 11.11/6.13      ! [I2: nat,M: nat,N2: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 11.11/6.13       => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 11.11/6.13         => ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1278_mod__Suc,axiom,
% 11.11/6.13      ! [M: nat,N2: nat] :
% 11.11/6.13        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.13            = N2 )
% 11.11/6.13         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 11.11/6.13            = zero_zero_nat ) )
% 11.11/6.13        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.13           != N2 )
% 11.11/6.13         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 11.11/6.13            = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1279_mod__less__divisor,axiom,
% 11.11/6.13      ! [N2: nat,M: nat] :
% 11.11/6.13        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.13       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1280_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 11.11/6.13      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 11.11/6.13        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1281_order__antisym__conv,axiom,
% 11.11/6.13      ! [Y: set_int,X4: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ Y @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.13          = ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1282_order__antisym__conv,axiom,
% 11.11/6.13      ! [Y: rat,X4: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13          = ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1283_order__antisym__conv,axiom,
% 11.11/6.13      ! [Y: num,X4: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ Y @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13          = ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1284_order__antisym__conv,axiom,
% 11.11/6.13      ! [Y: nat,X4: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13          = ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1285_order__antisym__conv,axiom,
% 11.11/6.13      ! [Y: int,X4: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ Y @ X4 )
% 11.11/6.13       => ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13          = ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1286_linorder__le__cases,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ~ ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13       => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1287_linorder__le__cases,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ~ ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13       => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1288_linorder__le__cases,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ~ ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13       => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1289_linorder__le__cases,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ~ ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13       => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1290_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1291_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1292_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1293_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1294_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1295_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1296_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1297_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1298_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1299_ord__le__eq__subst,axiom,
% 11.11/6.13      ! [A: nat,B: nat,F: nat > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1300_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1301_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: num,F: rat > num,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1302_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1303_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: int,F: rat > int,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1304_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: rat,F: num > rat,B: num,C: num] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1305_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: num,F: num > num,B: num,C: num] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1306_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: nat,F: num > nat,B: num,C: num] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1307_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: int,F: num > int,B: num,C: num] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1308_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1309_ord__eq__le__subst,axiom,
% 11.11/6.13      ! [A: num,F: nat > num,B: nat,C: nat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1310_linorder__linear,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13        | ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1311_linorder__linear,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13        | ( ord_less_eq_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1312_linorder__linear,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13        | ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1313_linorder__linear,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13        | ( ord_less_eq_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1314_verit__la__disequality,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13        | ~ ( ord_less_eq_rat @ A @ B )
% 11.11/6.13        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1315_verit__la__disequality,axiom,
% 11.11/6.13      ! [A: num,B: num] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13        | ~ ( ord_less_eq_num @ A @ B )
% 11.11/6.13        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1316_verit__la__disequality,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13        | ~ ( ord_less_eq_nat @ A @ B )
% 11.11/6.13        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1317_verit__la__disequality,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13        | ~ ( ord_less_eq_int @ A @ B )
% 11.11/6.13        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1318_order__eq__refl,axiom,
% 11.11/6.13      ! [X4: set_int,Y: set_int] :
% 11.11/6.13        ( ( X4 = Y )
% 11.11/6.13       => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1319_order__eq__refl,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( X4 = Y )
% 11.11/6.13       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1320_order__eq__refl,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( X4 = Y )
% 11.11/6.13       => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1321_order__eq__refl,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( X4 = Y )
% 11.11/6.13       => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1322_order__eq__refl,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( X4 = Y )
% 11.11/6.13       => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1323_order__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1324_order__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1325_order__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1326_order__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1327_order__subst2,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1328_order__subst2,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1329_order__subst2,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1330_order__subst2,axiom,
% 11.11/6.13      ! [A: num,B: num,F: num > int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1331_order__subst2,axiom,
% 11.11/6.13      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1332_order__subst2,axiom,
% 11.11/6.13      ! [A: nat,B: nat,F: nat > num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1333_order__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1334_order__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: num > rat,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1335_order__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1336_order__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: int > rat,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.13         => ( ! [X5: int,Y3: int] :
% 11.11/6.13                ( ( ord_less_eq_int @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1337_order__subst1,axiom,
% 11.11/6.13      ! [A: num,F: rat > num,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1338_order__subst1,axiom,
% 11.11/6.13      ! [A: num,F: num > num,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1339_order__subst1,axiom,
% 11.11/6.13      ! [A: num,F: nat > num,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_eq_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1340_order__subst1,axiom,
% 11.11/6.13      ! [A: num,F: int > num,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.13         => ( ! [X5: int,Y3: int] :
% 11.11/6.13                ( ( ord_less_eq_int @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1341_order__subst1,axiom,
% 11.11/6.13      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1342_order__subst1,axiom,
% 11.11/6.13      ! [A: nat,F: num > nat,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1343_Orderings_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: set_int,B2: set_int] :
% 11.11/6.13            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 11.11/6.13            & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1344_Orderings_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.13            ( ( ord_less_eq_rat @ A3 @ B2 )
% 11.11/6.13            & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1345_Orderings_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: num,B2: num] :
% 11.11/6.13            ( ( ord_less_eq_num @ A3 @ B2 )
% 11.11/6.13            & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1346_Orderings_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.13            ( ( ord_less_eq_nat @ A3 @ B2 )
% 11.11/6.13            & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1347_Orderings_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: int,B2: int] :
% 11.11/6.13            ( ( ord_less_eq_int @ A3 @ B2 )
% 11.11/6.13            & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1348_antisym,axiom,
% 11.11/6.13      ! [A: set_int,B: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ B @ A )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1349_antisym,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1350_antisym,axiom,
% 11.11/6.13      ! [A: num,B: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ A )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1351_antisym,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1352_antisym,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ A )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1353_dual__order_Otrans,axiom,
% 11.11/6.13      ! [B: set_int,A: set_int,C: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ C @ B )
% 11.11/6.13         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1354_dual__order_Otrans,axiom,
% 11.11/6.13      ! [B: rat,A: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ C @ B )
% 11.11/6.13         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1355_dual__order_Otrans,axiom,
% 11.11/6.13      ! [B: num,A: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_num @ C @ B )
% 11.11/6.13         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1356_dual__order_Otrans,axiom,
% 11.11/6.13      ! [B: nat,A: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_nat @ C @ B )
% 11.11/6.13         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1357_dual__order_Otrans,axiom,
% 11.11/6.13      ! [B: int,A: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_int @ C @ B )
% 11.11/6.13         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1358_dual__order_Oantisym,axiom,
% 11.11/6.13      ! [B: set_int,A: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1359_dual__order_Oantisym,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1360_dual__order_Oantisym,axiom,
% 11.11/6.13      ! [B: num,A: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1361_dual__order_Oantisym,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1362_dual__order_Oantisym,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.13       => ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13         => ( A = B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1363_dual__order_Oeq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: set_int,B2: set_int] :
% 11.11/6.13            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 11.11/6.13            & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1364_dual__order_Oeq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.13            ( ( ord_less_eq_rat @ B2 @ A3 )
% 11.11/6.13            & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1365_dual__order_Oeq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: num,B2: num] :
% 11.11/6.13            ( ( ord_less_eq_num @ B2 @ A3 )
% 11.11/6.13            & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1366_dual__order_Oeq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.13            ( ( ord_less_eq_nat @ B2 @ A3 )
% 11.11/6.13            & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1367_dual__order_Oeq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [A3: int,B2: int] :
% 11.11/6.13            ( ( ord_less_eq_int @ B2 @ A3 )
% 11.11/6.13            & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1368_linorder__wlog,axiom,
% 11.11/6.13      ! [P: rat > rat > $o,A: rat,B: rat] :
% 11.11/6.13        ( ! [A5: rat,B5: rat] :
% 11.11/6.13            ( ( ord_less_eq_rat @ A5 @ B5 )
% 11.11/6.13           => ( P @ A5 @ B5 ) )
% 11.11/6.13       => ( ! [A5: rat,B5: rat] :
% 11.11/6.13              ( ( P @ B5 @ A5 )
% 11.11/6.13             => ( P @ A5 @ B5 ) )
% 11.11/6.13         => ( P @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1369_linorder__wlog,axiom,
% 11.11/6.13      ! [P: num > num > $o,A: num,B: num] :
% 11.11/6.13        ( ! [A5: num,B5: num] :
% 11.11/6.13            ( ( ord_less_eq_num @ A5 @ B5 )
% 11.11/6.13           => ( P @ A5 @ B5 ) )
% 11.11/6.13       => ( ! [A5: num,B5: num] :
% 11.11/6.13              ( ( P @ B5 @ A5 )
% 11.11/6.13             => ( P @ A5 @ B5 ) )
% 11.11/6.13         => ( P @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1370_linorder__wlog,axiom,
% 11.11/6.13      ! [P: nat > nat > $o,A: nat,B: nat] :
% 11.11/6.13        ( ! [A5: nat,B5: nat] :
% 11.11/6.13            ( ( ord_less_eq_nat @ A5 @ B5 )
% 11.11/6.13           => ( P @ A5 @ B5 ) )
% 11.11/6.13       => ( ! [A5: nat,B5: nat] :
% 11.11/6.13              ( ( P @ B5 @ A5 )
% 11.11/6.13             => ( P @ A5 @ B5 ) )
% 11.11/6.13         => ( P @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1371_linorder__wlog,axiom,
% 11.11/6.13      ! [P: int > int > $o,A: int,B: int] :
% 11.11/6.13        ( ! [A5: int,B5: int] :
% 11.11/6.13            ( ( ord_less_eq_int @ A5 @ B5 )
% 11.11/6.13           => ( P @ A5 @ B5 ) )
% 11.11/6.13       => ( ! [A5: int,B5: int] :
% 11.11/6.13              ( ( P @ B5 @ A5 )
% 11.11/6.13             => ( P @ A5 @ B5 ) )
% 11.11/6.13         => ( P @ A @ B ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1372_order__trans,axiom,
% 11.11/6.13      ! [X4: set_int,Y: set_int,Z: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ Y @ Z )
% 11.11/6.13         => ( ord_less_eq_set_int @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1373_order__trans,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_rat @ Y @ Z )
% 11.11/6.13         => ( ord_less_eq_rat @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1374_order__trans,axiom,
% 11.11/6.13      ! [X4: num,Y: num,Z: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_num @ Y @ Z )
% 11.11/6.13         => ( ord_less_eq_num @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1375_order__trans,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat,Z: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_nat @ Y @ Z )
% 11.11/6.13         => ( ord_less_eq_nat @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1376_order__trans,axiom,
% 11.11/6.13      ! [X4: int,Y: int,Z: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_int @ Y @ Z )
% 11.11/6.13         => ( ord_less_eq_int @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1377_order_Otrans,axiom,
% 11.11/6.13      ! [A: set_int,B: set_int,C: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ B @ C )
% 11.11/6.13         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1378_order_Otrans,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1379_order_Otrans,axiom,
% 11.11/6.13      ! [A: num,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1380_order_Otrans,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1381_order_Otrans,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.13         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1382_order__antisym,axiom,
% 11.11/6.13      ! [X4: set_int,Y: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ Y @ X4 )
% 11.11/6.13         => ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1383_order__antisym,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.13         => ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1384_order__antisym,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_num @ Y @ X4 )
% 11.11/6.13         => ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1385_order__antisym,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.13         => ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1386_order__antisym,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_eq_int @ Y @ X4 )
% 11.11/6.13         => ( X4 = Y ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1387_ord__le__eq__trans,axiom,
% 11.11/6.13      ! [A: set_int,B: set_int,C: set_int] :
% 11.11/6.13        ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.13       => ( ( B = C )
% 11.11/6.13         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1388_ord__le__eq__trans,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.13       => ( ( B = C )
% 11.11/6.13         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1389_ord__le__eq__trans,axiom,
% 11.11/6.13      ! [A: num,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.13       => ( ( B = C )
% 11.11/6.13         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1390_ord__le__eq__trans,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.13       => ( ( B = C )
% 11.11/6.13         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1391_ord__le__eq__trans,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.13       => ( ( B = C )
% 11.11/6.13         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1392_ord__eq__le__trans,axiom,
% 11.11/6.13      ! [A: set_int,B: set_int,C: set_int] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13       => ( ( ord_less_eq_set_int @ B @ C )
% 11.11/6.13         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1393_ord__eq__le__trans,axiom,
% 11.11/6.13      ! [A: rat,B: rat,C: rat] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1394_ord__eq__le__trans,axiom,
% 11.11/6.13      ! [A: num,B: num,C: num] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.13         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1395_ord__eq__le__trans,axiom,
% 11.11/6.13      ! [A: nat,B: nat,C: nat] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.13         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1396_ord__eq__le__trans,axiom,
% 11.11/6.13      ! [A: int,B: int,C: int] :
% 11.11/6.13        ( ( A = B )
% 11.11/6.13       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.13         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1397_order__class_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [X: set_int,Y5: set_int] :
% 11.11/6.13            ( ( ord_less_eq_set_int @ X @ Y5 )
% 11.11/6.13            & ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1398_order__class_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [X: rat,Y5: rat] :
% 11.11/6.13            ( ( ord_less_eq_rat @ X @ Y5 )
% 11.11/6.13            & ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1399_order__class_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [X: num,Y5: num] :
% 11.11/6.13            ( ( ord_less_eq_num @ X @ Y5 )
% 11.11/6.13            & ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1400_order__class_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [X: nat,Y5: nat] :
% 11.11/6.13            ( ( ord_less_eq_nat @ X @ Y5 )
% 11.11/6.13            & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1401_order__class_Oorder__eq__iff,axiom,
% 11.11/6.13      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 11.11/6.13      = ( ^ [X: int,Y5: int] :
% 11.11/6.13            ( ( ord_less_eq_int @ X @ Y5 )
% 11.11/6.13            & ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1402_le__cases3,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.13        ( ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.13         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 11.11/6.13       => ( ( ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.13           => ~ ( ord_less_eq_rat @ X4 @ Z ) )
% 11.11/6.13         => ( ( ( ord_less_eq_rat @ X4 @ Z )
% 11.11/6.13             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 11.11/6.13           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 11.11/6.13               => ~ ( ord_less_eq_rat @ Y @ X4 ) )
% 11.11/6.13             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 11.11/6.13                 => ~ ( ord_less_eq_rat @ Z @ X4 ) )
% 11.11/6.13               => ~ ( ( ord_less_eq_rat @ Z @ X4 )
% 11.11/6.13                   => ~ ( ord_less_eq_rat @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1403_le__cases3,axiom,
% 11.11/6.13      ! [X4: num,Y: num,Z: num] :
% 11.11/6.13        ( ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.13         => ~ ( ord_less_eq_num @ Y @ Z ) )
% 11.11/6.13       => ( ( ( ord_less_eq_num @ Y @ X4 )
% 11.11/6.13           => ~ ( ord_less_eq_num @ X4 @ Z ) )
% 11.11/6.13         => ( ( ( ord_less_eq_num @ X4 @ Z )
% 11.11/6.13             => ~ ( ord_less_eq_num @ Z @ Y ) )
% 11.11/6.13           => ( ( ( ord_less_eq_num @ Z @ Y )
% 11.11/6.13               => ~ ( ord_less_eq_num @ Y @ X4 ) )
% 11.11/6.13             => ( ( ( ord_less_eq_num @ Y @ Z )
% 11.11/6.13                 => ~ ( ord_less_eq_num @ Z @ X4 ) )
% 11.11/6.13               => ~ ( ( ord_less_eq_num @ Z @ X4 )
% 11.11/6.13                   => ~ ( ord_less_eq_num @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1404_le__cases3,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat,Z: nat] :
% 11.11/6.13        ( ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.13         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 11.11/6.13       => ( ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.13           => ~ ( ord_less_eq_nat @ X4 @ Z ) )
% 11.11/6.13         => ( ( ( ord_less_eq_nat @ X4 @ Z )
% 11.11/6.13             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 11.11/6.13           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 11.11/6.13               => ~ ( ord_less_eq_nat @ Y @ X4 ) )
% 11.11/6.13             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 11.11/6.13                 => ~ ( ord_less_eq_nat @ Z @ X4 ) )
% 11.11/6.13               => ~ ( ( ord_less_eq_nat @ Z @ X4 )
% 11.11/6.13                   => ~ ( ord_less_eq_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1405_le__cases3,axiom,
% 11.11/6.13      ! [X4: int,Y: int,Z: int] :
% 11.11/6.13        ( ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.13         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 11.11/6.13       => ( ( ( ord_less_eq_int @ Y @ X4 )
% 11.11/6.13           => ~ ( ord_less_eq_int @ X4 @ Z ) )
% 11.11/6.13         => ( ( ( ord_less_eq_int @ X4 @ Z )
% 11.11/6.13             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 11.11/6.13           => ( ( ( ord_less_eq_int @ Z @ Y )
% 11.11/6.13               => ~ ( ord_less_eq_int @ Y @ X4 ) )
% 11.11/6.13             => ( ( ( ord_less_eq_int @ Y @ Z )
% 11.11/6.13                 => ~ ( ord_less_eq_int @ Z @ X4 ) )
% 11.11/6.13               => ~ ( ( ord_less_eq_int @ Z @ X4 )
% 11.11/6.13                   => ~ ( ord_less_eq_int @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1406_nle__le,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.13        = ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.13          & ( B != A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1407_nle__le,axiom,
% 11.11/6.13      ! [A: num,B: num] :
% 11.11/6.13        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 11.11/6.13        = ( ( ord_less_eq_num @ B @ A )
% 11.11/6.13          & ( B != A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1408_nle__le,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 11.11/6.13        = ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.13          & ( B != A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1409_nle__le,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 11.11/6.13        = ( ( ord_less_eq_int @ B @ A )
% 11.11/6.13          & ( B != A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1410_verit__comp__simplify1_I2_J,axiom,
% 11.11/6.13      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1411_verit__comp__simplify1_I2_J,axiom,
% 11.11/6.13      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1412_verit__comp__simplify1_I2_J,axiom,
% 11.11/6.13      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1413_verit__comp__simplify1_I2_J,axiom,
% 11.11/6.13      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1414_verit__comp__simplify1_I2_J,axiom,
% 11.11/6.13      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1415_order__less__imp__not__less,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1416_order__less__imp__not__less,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1417_order__less__imp__not__less,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1418_order__less__imp__not__less,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1419_order__less__imp__not__less,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1420_order__less__imp__not__eq2,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ( Y != X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1421_order__less__imp__not__eq2,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ( Y != X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1422_order__less__imp__not__eq2,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ( Y != X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1423_order__less__imp__not__eq2,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ( Y != X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1424_order__less__imp__not__eq2,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ( Y != X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1425_order__less__imp__not__eq,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ( X4 != Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1426_order__less__imp__not__eq,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ( X4 != Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1427_order__less__imp__not__eq,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ( X4 != Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1428_order__less__imp__not__eq,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ( X4 != Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1429_order__less__imp__not__eq,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ( X4 != Y ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1430_linorder__less__linear,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13        | ( X4 = Y )
% 11.11/6.13        | ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1431_linorder__less__linear,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13        | ( X4 = Y )
% 11.11/6.13        | ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1432_linorder__less__linear,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13        | ( X4 = Y )
% 11.11/6.13        | ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1433_linorder__less__linear,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13        | ( X4 = Y )
% 11.11/6.13        | ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1434_linorder__less__linear,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13        | ( X4 = Y )
% 11.11/6.13        | ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1435_order__less__imp__triv,axiom,
% 11.11/6.13      ! [X4: real,Y: real,P: $o] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.13         => P ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1436_order__less__imp__triv,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat,P: $o] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_rat @ Y @ X4 )
% 11.11/6.13         => P ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1437_order__less__imp__triv,axiom,
% 11.11/6.13      ! [X4: num,Y: num,P: $o] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_num @ Y @ X4 )
% 11.11/6.13         => P ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1438_order__less__imp__triv,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat,P: $o] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_nat @ Y @ X4 )
% 11.11/6.13         => P ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1439_order__less__imp__triv,axiom,
% 11.11/6.13      ! [X4: int,Y: int,P: $o] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_int @ Y @ X4 )
% 11.11/6.13         => P ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1440_order__less__not__sym,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1441_order__less__not__sym,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1442_order__less__not__sym,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1443_order__less__not__sym,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1444_order__less__not__sym,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1445_order__less__subst2,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_real @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1446_order__less__subst2,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1447_order__less__subst2,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > num,C: num] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_num @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1448_order__less__subst2,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1449_order__less__subst2,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > int,C: int] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ord_less_int @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1450_order__less__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > real,C: real] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_real @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1451_order__less__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1452_order__less__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > num,C: num] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_num @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1453_order__less__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1454_order__less__subst2,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > int,C: int] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ord_less_int @ ( F @ B ) @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1455_order__less__subst1,axiom,
% 11.11/6.13      ! [A: real,F: real > real,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1456_order__less__subst1,axiom,
% 11.11/6.13      ! [A: real,F: rat > real,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1457_order__less__subst1,axiom,
% 11.11/6.13      ! [A: real,F: num > real,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1458_order__less__subst1,axiom,
% 11.11/6.13      ! [A: real,F: nat > real,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1459_order__less__subst1,axiom,
% 11.11/6.13      ! [A: real,F: int > real,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_int @ B @ C )
% 11.11/6.13         => ( ! [X5: int,Y3: int] :
% 11.11/6.13                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1460_order__less__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: real > rat,B: real,C: real] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1461_order__less__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1462_order__less__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: num > rat,B: num,C: num] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_num @ B @ C )
% 11.11/6.13         => ( ! [X5: num,Y3: num] :
% 11.11/6.13                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1463_order__less__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_nat @ B @ C )
% 11.11/6.13         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.13                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1464_order__less__subst1,axiom,
% 11.11/6.13      ! [A: rat,F: int > rat,B: int,C: int] :
% 11.11/6.13        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_int @ B @ C )
% 11.11/6.13         => ( ! [X5: int,Y3: int] :
% 11.11/6.13                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1465_order__less__irrefl,axiom,
% 11.11/6.13      ! [X4: real] :
% 11.11/6.13        ~ ( ord_less_real @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1466_order__less__irrefl,axiom,
% 11.11/6.13      ! [X4: rat] :
% 11.11/6.13        ~ ( ord_less_rat @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1467_order__less__irrefl,axiom,
% 11.11/6.13      ! [X4: num] :
% 11.11/6.13        ~ ( ord_less_num @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1468_order__less__irrefl,axiom,
% 11.11/6.13      ! [X4: nat] :
% 11.11/6.13        ~ ( ord_less_nat @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1469_order__less__irrefl,axiom,
% 11.11/6.13      ! [X4: int] :
% 11.11/6.13        ~ ( ord_less_int @ X4 @ X4 ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1470_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1471_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1472_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > num,C: num] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1473_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1474_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: real,B: real,F: real > int,C: int] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1475_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > real,C: real] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1476_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1477_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > num,C: num] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1478_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1479_ord__less__eq__subst,axiom,
% 11.11/6.13      ! [A: rat,B: rat,F: rat > int,C: int] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( ( ( F @ B )
% 11.11/6.13            = C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1480_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: real,F: real > real,B: real,C: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1481_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: rat,F: real > rat,B: real,C: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1482_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: num,F: real > num,B: real,C: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1483_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: nat,F: real > nat,B: real,C: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1484_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: int,F: real > int,B: real,C: real] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_real @ B @ C )
% 11.11/6.13         => ( ! [X5: real,Y3: real] :
% 11.11/6.13                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1485_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: real,F: rat > real,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1486_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1487_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: num,F: rat > num,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1488_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1489_ord__eq__less__subst,axiom,
% 11.11/6.13      ! [A: int,F: rat > int,B: rat,C: rat] :
% 11.11/6.13        ( ( A
% 11.11/6.13          = ( F @ B ) )
% 11.11/6.13       => ( ( ord_less_rat @ B @ C )
% 11.11/6.13         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.13                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.13               => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.13           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1490_order__less__trans,axiom,
% 11.11/6.13      ! [X4: real,Y: real,Z: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_real @ Y @ Z )
% 11.11/6.13         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1491_order__less__trans,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_rat @ Y @ Z )
% 11.11/6.13         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1492_order__less__trans,axiom,
% 11.11/6.13      ! [X4: num,Y: num,Z: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_num @ Y @ Z )
% 11.11/6.13         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1493_order__less__trans,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat,Z: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_nat @ Y @ Z )
% 11.11/6.13         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1494_order__less__trans,axiom,
% 11.11/6.13      ! [X4: int,Y: int,Z: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ( ( ord_less_int @ Y @ Z )
% 11.11/6.13         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1495_order__less__asym_H,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ~ ( ord_less_real @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1496_order__less__asym_H,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ~ ( ord_less_rat @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1497_order__less__asym_H,axiom,
% 11.11/6.13      ! [A: num,B: num] :
% 11.11/6.13        ( ( ord_less_num @ A @ B )
% 11.11/6.13       => ~ ( ord_less_num @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1498_order__less__asym_H,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ B )
% 11.11/6.13       => ~ ( ord_less_nat @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1499_order__less__asym_H,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ A @ B )
% 11.11/6.13       => ~ ( ord_less_int @ B @ A ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1500_linorder__neq__iff,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13        = ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13          | ( ord_less_real @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1501_linorder__neq__iff,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13        = ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13          | ( ord_less_rat @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1502_linorder__neq__iff,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13        = ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13          | ( ord_less_num @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1503_linorder__neq__iff,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13        = ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13          | ( ord_less_nat @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1504_linorder__neq__iff,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13        = ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13          | ( ord_less_int @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1505_order__less__asym,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1506_order__less__asym,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1507_order__less__asym,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1508_order__less__asym,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1509_order__less__asym,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.13       => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1510_linorder__neqE,axiom,
% 11.11/6.13      ! [X4: real,Y: real] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13       => ( ~ ( ord_less_real @ X4 @ Y )
% 11.11/6.13         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1511_linorder__neqE,axiom,
% 11.11/6.13      ! [X4: rat,Y: rat] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13       => ( ~ ( ord_less_rat @ X4 @ Y )
% 11.11/6.13         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1512_linorder__neqE,axiom,
% 11.11/6.13      ! [X4: num,Y: num] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13       => ( ~ ( ord_less_num @ X4 @ Y )
% 11.11/6.13         => ( ord_less_num @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1513_linorder__neqE,axiom,
% 11.11/6.13      ! [X4: nat,Y: nat] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13       => ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.13         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1514_linorder__neqE,axiom,
% 11.11/6.13      ! [X4: int,Y: int] :
% 11.11/6.13        ( ( X4 != Y )
% 11.11/6.13       => ( ~ ( ord_less_int @ X4 @ Y )
% 11.11/6.13         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1515_dual__order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [B: real,A: real] :
% 11.11/6.13        ( ( ord_less_real @ B @ A )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1516_dual__order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [B: rat,A: rat] :
% 11.11/6.13        ( ( ord_less_rat @ B @ A )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1517_dual__order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [B: num,A: num] :
% 11.11/6.13        ( ( ord_less_num @ B @ A )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1518_dual__order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [B: nat,A: nat] :
% 11.11/6.13        ( ( ord_less_nat @ B @ A )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1519_dual__order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [B: int,A: int] :
% 11.11/6.13        ( ( ord_less_int @ B @ A )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1520_order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [A: real,B: real] :
% 11.11/6.13        ( ( ord_less_real @ A @ B )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1521_order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [A: rat,B: rat] :
% 11.11/6.13        ( ( ord_less_rat @ A @ B )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1522_order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [A: num,B: num] :
% 11.11/6.13        ( ( ord_less_num @ A @ B )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1523_order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [A: nat,B: nat] :
% 11.11/6.13        ( ( ord_less_nat @ A @ B )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1524_order_Ostrict__implies__not__eq,axiom,
% 11.11/6.13      ! [A: int,B: int] :
% 11.11/6.13        ( ( ord_less_int @ A @ B )
% 11.11/6.13       => ( A != B ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1525_dual__order_Ostrict__trans,axiom,
% 11.11/6.13      ! [B: real,A: real,C: real] :
% 11.11/6.13        ( ( ord_less_real @ B @ A )
% 11.11/6.13       => ( ( ord_less_real @ C @ B )
% 11.11/6.13         => ( ord_less_real @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1526_dual__order_Ostrict__trans,axiom,
% 11.11/6.13      ! [B: rat,A: rat,C: rat] :
% 11.11/6.13        ( ( ord_less_rat @ B @ A )
% 11.11/6.13       => ( ( ord_less_rat @ C @ B )
% 11.11/6.13         => ( ord_less_rat @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1527_dual__order_Ostrict__trans,axiom,
% 11.11/6.13      ! [B: num,A: num,C: num] :
% 11.11/6.13        ( ( ord_less_num @ B @ A )
% 11.11/6.13       => ( ( ord_less_num @ C @ B )
% 11.11/6.13         => ( ord_less_num @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1528_dual__order_Ostrict__trans,axiom,
% 11.11/6.13      ! [B: nat,A: nat,C: nat] :
% 11.11/6.13        ( ( ord_less_nat @ B @ A )
% 11.11/6.13       => ( ( ord_less_nat @ C @ B )
% 11.11/6.13         => ( ord_less_nat @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1529_dual__order_Ostrict__trans,axiom,
% 11.11/6.13      ! [B: int,A: int,C: int] :
% 11.11/6.13        ( ( ord_less_int @ B @ A )
% 11.11/6.13       => ( ( ord_less_int @ C @ B )
% 11.11/6.13         => ( ord_less_int @ C @ A ) ) ) ).
% 11.11/6.13  
% 11.11/6.13  thf(fact_1530_not__less__iff__gr__or__eq,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 11.11/6.14        = ( ( ord_less_real @ Y @ X4 )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1531_not__less__iff__gr__or__eq,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 11.11/6.14        = ( ( ord_less_rat @ Y @ X4 )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1532_not__less__iff__gr__or__eq,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 11.11/6.14        = ( ( ord_less_num @ Y @ X4 )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1533_not__less__iff__gr__or__eq,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 11.11/6.14        = ( ( ord_less_nat @ Y @ X4 )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1534_not__less__iff__gr__or__eq,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 11.11/6.14        = ( ( ord_less_int @ Y @ X4 )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1535_order_Ostrict__trans,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1536_order_Ostrict__trans,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1537_order_Ostrict__trans,axiom,
% 11.11/6.14      ! [A: num,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_num @ B @ C )
% 11.11/6.14         => ( ord_less_num @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1538_order_Ostrict__trans,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1539_order_Ostrict__trans,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1540_linorder__less__wlog,axiom,
% 11.11/6.14      ! [P: real > real > $o,A: real,B: real] :
% 11.11/6.14        ( ! [A5: real,B5: real] :
% 11.11/6.14            ( ( ord_less_real @ A5 @ B5 )
% 11.11/6.14           => ( P @ A5 @ B5 ) )
% 11.11/6.14       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 11.11/6.14         => ( ! [A5: real,B5: real] :
% 11.11/6.14                ( ( P @ B5 @ A5 )
% 11.11/6.14               => ( P @ A5 @ B5 ) )
% 11.11/6.14           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1541_linorder__less__wlog,axiom,
% 11.11/6.14      ! [P: rat > rat > $o,A: rat,B: rat] :
% 11.11/6.14        ( ! [A5: rat,B5: rat] :
% 11.11/6.14            ( ( ord_less_rat @ A5 @ B5 )
% 11.11/6.14           => ( P @ A5 @ B5 ) )
% 11.11/6.14       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 11.11/6.14         => ( ! [A5: rat,B5: rat] :
% 11.11/6.14                ( ( P @ B5 @ A5 )
% 11.11/6.14               => ( P @ A5 @ B5 ) )
% 11.11/6.14           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1542_linorder__less__wlog,axiom,
% 11.11/6.14      ! [P: num > num > $o,A: num,B: num] :
% 11.11/6.14        ( ! [A5: num,B5: num] :
% 11.11/6.14            ( ( ord_less_num @ A5 @ B5 )
% 11.11/6.14           => ( P @ A5 @ B5 ) )
% 11.11/6.14       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 11.11/6.14         => ( ! [A5: num,B5: num] :
% 11.11/6.14                ( ( P @ B5 @ A5 )
% 11.11/6.14               => ( P @ A5 @ B5 ) )
% 11.11/6.14           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1543_linorder__less__wlog,axiom,
% 11.11/6.14      ! [P: nat > nat > $o,A: nat,B: nat] :
% 11.11/6.14        ( ! [A5: nat,B5: nat] :
% 11.11/6.14            ( ( ord_less_nat @ A5 @ B5 )
% 11.11/6.14           => ( P @ A5 @ B5 ) )
% 11.11/6.14       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 11.11/6.14         => ( ! [A5: nat,B5: nat] :
% 11.11/6.14                ( ( P @ B5 @ A5 )
% 11.11/6.14               => ( P @ A5 @ B5 ) )
% 11.11/6.14           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1544_linorder__less__wlog,axiom,
% 11.11/6.14      ! [P: int > int > $o,A: int,B: int] :
% 11.11/6.14        ( ! [A5: int,B5: int] :
% 11.11/6.14            ( ( ord_less_int @ A5 @ B5 )
% 11.11/6.14           => ( P @ A5 @ B5 ) )
% 11.11/6.14       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 11.11/6.14         => ( ! [A5: int,B5: int] :
% 11.11/6.14                ( ( P @ B5 @ A5 )
% 11.11/6.14               => ( P @ A5 @ B5 ) )
% 11.11/6.14           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1545_exists__least__iff,axiom,
% 11.11/6.14      ( ( ^ [P3: nat > $o] :
% 11.11/6.14          ? [X6: nat] : ( P3 @ X6 ) )
% 11.11/6.14      = ( ^ [P4: nat > $o] :
% 11.11/6.14          ? [N: nat] :
% 11.11/6.14            ( ( P4 @ N )
% 11.11/6.14            & ! [M6: nat] :
% 11.11/6.14                ( ( ord_less_nat @ M6 @ N )
% 11.11/6.14               => ~ ( P4 @ M6 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1546_dual__order_Oirrefl,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ~ ( ord_less_real @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1547_dual__order_Oirrefl,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ~ ( ord_less_rat @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1548_dual__order_Oirrefl,axiom,
% 11.11/6.14      ! [A: num] :
% 11.11/6.14        ~ ( ord_less_num @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1549_dual__order_Oirrefl,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ~ ( ord_less_nat @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1550_dual__order_Oirrefl,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ~ ( ord_less_int @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1551_dual__order_Oasym,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_real @ B @ A )
% 11.11/6.14       => ~ ( ord_less_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1552_dual__order_Oasym,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ B @ A )
% 11.11/6.14       => ~ ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1553_dual__order_Oasym,axiom,
% 11.11/6.14      ! [B: num,A: num] :
% 11.11/6.14        ( ( ord_less_num @ B @ A )
% 11.11/6.14       => ~ ( ord_less_num @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1554_dual__order_Oasym,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_nat @ B @ A )
% 11.11/6.14       => ~ ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1555_dual__order_Oasym,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ B @ A )
% 11.11/6.14       => ~ ( ord_less_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1556_linorder__cases,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ~ ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ( X4 != Y )
% 11.11/6.14         => ( ord_less_real @ Y @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1557_linorder__cases,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ~ ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ( X4 != Y )
% 11.11/6.14         => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1558_linorder__cases,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ~ ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( ( X4 != Y )
% 11.11/6.14         => ( ord_less_num @ Y @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1559_linorder__cases,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( ( X4 != Y )
% 11.11/6.14         => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1560_linorder__cases,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ~ ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( ( X4 != Y )
% 11.11/6.14         => ( ord_less_int @ Y @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1561_antisym__conv3,axiom,
% 11.11/6.14      ! [Y: real,X4: real] :
% 11.11/6.14        ( ~ ( ord_less_real @ Y @ X4 )
% 11.11/6.14       => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1562_antisym__conv3,axiom,
% 11.11/6.14      ! [Y: rat,X4: rat] :
% 11.11/6.14        ( ~ ( ord_less_rat @ Y @ X4 )
% 11.11/6.14       => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1563_antisym__conv3,axiom,
% 11.11/6.14      ! [Y: num,X4: num] :
% 11.11/6.14        ( ~ ( ord_less_num @ Y @ X4 )
% 11.11/6.14       => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1564_antisym__conv3,axiom,
% 11.11/6.14      ! [Y: nat,X4: nat] :
% 11.11/6.14        ( ~ ( ord_less_nat @ Y @ X4 )
% 11.11/6.14       => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1565_antisym__conv3,axiom,
% 11.11/6.14      ! [Y: int,X4: int] :
% 11.11/6.14        ( ~ ( ord_less_int @ Y @ X4 )
% 11.11/6.14       => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1566_less__induct,axiom,
% 11.11/6.14      ! [P: nat > $o,A: nat] :
% 11.11/6.14        ( ! [X5: nat] :
% 11.11/6.14            ( ! [Y4: nat] :
% 11.11/6.14                ( ( ord_less_nat @ Y4 @ X5 )
% 11.11/6.14               => ( P @ Y4 ) )
% 11.11/6.14           => ( P @ X5 ) )
% 11.11/6.14       => ( P @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1567_ord__less__eq__trans,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ( B = C )
% 11.11/6.14         => ( ord_less_real @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1568_ord__less__eq__trans,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ( B = C )
% 11.11/6.14         => ( ord_less_rat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1569_ord__less__eq__trans,axiom,
% 11.11/6.14      ! [A: num,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ( B = C )
% 11.11/6.14         => ( ord_less_num @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1570_ord__less__eq__trans,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ( B = C )
% 11.11/6.14         => ( ord_less_nat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1571_ord__less__eq__trans,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ( B = C )
% 11.11/6.14         => ( ord_less_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1572_ord__eq__less__trans,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( A = B )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1573_ord__eq__less__trans,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( A = B )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1574_ord__eq__less__trans,axiom,
% 11.11/6.14      ! [A: num,B: num,C: num] :
% 11.11/6.14        ( ( A = B )
% 11.11/6.14       => ( ( ord_less_num @ B @ C )
% 11.11/6.14         => ( ord_less_num @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1575_ord__eq__less__trans,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( A = B )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1576_ord__eq__less__trans,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( A = B )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1577_order_Oasym,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ~ ( ord_less_real @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1578_order_Oasym,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ~ ( ord_less_rat @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1579_order_Oasym,axiom,
% 11.11/6.14      ! [A: num,B: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ~ ( ord_less_num @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1580_order_Oasym,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ~ ( ord_less_nat @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1581_order_Oasym,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ~ ( ord_less_int @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1582_less__imp__neq,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( X4 != Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1583_less__imp__neq,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( X4 != Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1584_less__imp__neq,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( X4 != Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1585_less__imp__neq,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( X4 != Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1586_less__imp__neq,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( X4 != Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1587_dense,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ? [Z2: real] :
% 11.11/6.14            ( ( ord_less_real @ X4 @ Z2 )
% 11.11/6.14            & ( ord_less_real @ Z2 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1588_dense,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ? [Z2: rat] :
% 11.11/6.14            ( ( ord_less_rat @ X4 @ Z2 )
% 11.11/6.14            & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1589_gt__ex,axiom,
% 11.11/6.14      ! [X4: real] :
% 11.11/6.14      ? [X_12: real] : ( ord_less_real @ X4 @ X_12 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1590_gt__ex,axiom,
% 11.11/6.14      ! [X4: rat] :
% 11.11/6.14      ? [X_12: rat] : ( ord_less_rat @ X4 @ X_12 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1591_gt__ex,axiom,
% 11.11/6.14      ! [X4: nat] :
% 11.11/6.14      ? [X_12: nat] : ( ord_less_nat @ X4 @ X_12 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1592_gt__ex,axiom,
% 11.11/6.14      ! [X4: int] :
% 11.11/6.14      ? [X_12: int] : ( ord_less_int @ X4 @ X_12 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1593_lt__ex,axiom,
% 11.11/6.14      ! [X4: real] :
% 11.11/6.14      ? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1594_lt__ex,axiom,
% 11.11/6.14      ! [X4: rat] :
% 11.11/6.14      ? [Y3: rat] : ( ord_less_rat @ Y3 @ X4 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1595_lt__ex,axiom,
% 11.11/6.14      ! [X4: int] :
% 11.11/6.14      ? [Y3: int] : ( ord_less_int @ Y3 @ X4 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1596_verit__comp__simplify1_I1_J,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ~ ( ord_less_real @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1597_verit__comp__simplify1_I1_J,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ~ ( ord_less_rat @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1598_verit__comp__simplify1_I1_J,axiom,
% 11.11/6.14      ! [A: num] :
% 11.11/6.14        ~ ( ord_less_num @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1599_verit__comp__simplify1_I1_J,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ~ ( ord_less_nat @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1600_verit__comp__simplify1_I1_J,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ~ ( ord_less_int @ A @ A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1601_add__strict__increasing2,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1602_add__strict__increasing2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1603_add__strict__increasing2,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1604_add__strict__increasing2,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1605_add__strict__increasing,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_eq_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1606_add__strict__increasing,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1607_add__strict__increasing,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1608_add__strict__increasing,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1609_add__pos__nonneg,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.14         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1610_add__pos__nonneg,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.14         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1611_add__pos__nonneg,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.14         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1612_add__pos__nonneg,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1613_add__nonpos__neg,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.14       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.14         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1614_add__nonpos__neg,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.14       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.14         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1615_add__nonpos__neg,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.14       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 11.11/6.14         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1616_add__nonpos__neg,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.14         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1617_add__nonneg__pos,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.14         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1618_add__nonneg__pos,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.14         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1619_add__nonneg__pos,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.14         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1620_add__nonneg__pos,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1621_add__neg__nonpos,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.14       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.14         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1622_add__neg__nonpos,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 11.11/6.14         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1623_add__neg__nonpos,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ zero_zero_nat )
% 11.11/6.14       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 11.11/6.14         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1624_add__neg__nonpos,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.14         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1625_field__le__epsilon,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ! [E: real] :
% 11.11/6.14            ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.14           => ( ord_less_eq_real @ X4 @ ( plus_plus_real @ Y @ E ) ) )
% 11.11/6.14       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1626_field__le__epsilon,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ! [E: rat] :
% 11.11/6.14            ( ( ord_less_rat @ zero_zero_rat @ E )
% 11.11/6.14           => ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ Y @ E ) ) )
% 11.11/6.14       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1627_divide__nonpos__pos,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.14         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1628_divide__nonpos__pos,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.14       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.14         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1629_divide__nonpos__neg,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.14       => ( ( ord_less_real @ Y @ zero_zero_real )
% 11.11/6.14         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1630_divide__nonpos__neg,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.14       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 11.11/6.14         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1631_divide__nonneg__pos,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.14         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1632_divide__nonneg__pos,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.14       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.14         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1633_divide__nonneg__neg,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.14       => ( ( ord_less_real @ Y @ zero_zero_real )
% 11.11/6.14         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1634_divide__nonneg__neg,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.14       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 11.11/6.14         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1635_divide__le__cancel,axiom,
% 11.11/6.14      ! [A: real,C: real,B: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.14        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.14           => ( ord_less_eq_real @ A @ B ) )
% 11.11/6.14          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.14           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1636_divide__le__cancel,axiom,
% 11.11/6.14      ! [A: rat,C: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.14        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.14           => ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.14          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.14           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1637_frac__less2,axiom,
% 11.11/6.14      ! [X4: real,Y: real,W: real,Z: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.14       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_real @ zero_zero_real @ W )
% 11.11/6.14           => ( ( ord_less_real @ W @ Z )
% 11.11/6.14             => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1638_frac__less2,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.14       => ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 11.11/6.14           => ( ( ord_less_rat @ W @ Z )
% 11.11/6.14             => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1639_frac__less,axiom,
% 11.11/6.14      ! [X4: real,Y: real,W: real,Z: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.14       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_real @ zero_zero_real @ W )
% 11.11/6.14           => ( ( ord_less_eq_real @ W @ Z )
% 11.11/6.14             => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1640_frac__less,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.14       => ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 11.11/6.14           => ( ( ord_less_eq_rat @ W @ Z )
% 11.11/6.14             => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1641_frac__le,axiom,
% 11.11/6.14      ! [Y: real,X4: real,W: real,Z: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.14       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_real @ zero_zero_real @ W )
% 11.11/6.14           => ( ( ord_less_eq_real @ W @ Z )
% 11.11/6.14             => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1642_frac__le,axiom,
% 11.11/6.14      ! [Y: rat,X4: rat,W: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.14       => ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 11.11/6.14           => ( ( ord_less_eq_rat @ W @ Z )
% 11.11/6.14             => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1643_div__positive,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.14       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 11.11/6.14         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1644_div__positive,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.14       => ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.14         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1645_div__positive,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14       => ( ( ord_less_eq_int @ B @ A )
% 11.11/6.14         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1646_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.14       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 11.11/6.14         => ( ( divide6298287555418463151nteger @ A @ B )
% 11.11/6.14            = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1647_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ A @ B )
% 11.11/6.14         => ( ( divide_divide_nat @ A @ B )
% 11.11/6.14            = zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1648_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ A @ B )
% 11.11/6.14         => ( ( divide_divide_int @ A @ B )
% 11.11/6.14            = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1649_power__less__imp__less__base,axiom,
% 11.11/6.14      ! [A: real,N2: nat,B: real] :
% 11.11/6.14        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.14         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1650_power__less__imp__less__base,axiom,
% 11.11/6.14      ! [A: rat,N2: nat,B: rat] :
% 11.11/6.14        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.14         => ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1651_power__less__imp__less__base,axiom,
% 11.11/6.14      ! [A: nat,N2: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.14         => ( ord_less_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1652_power__less__imp__less__base,axiom,
% 11.11/6.14      ! [A: int,N2: nat,B: int] :
% 11.11/6.14        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1653_zero__less__two,axiom,
% 11.11/6.14      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1654_zero__less__two,axiom,
% 11.11/6.14      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1655_zero__less__two,axiom,
% 11.11/6.14      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1656_zero__less__two,axiom,
% 11.11/6.14      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1657_power__le__one,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.14         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1658_power__le__one,axiom,
% 11.11/6.14      ! [A: rat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 11.11/6.14         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1659_power__le__one,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 11.11/6.14         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1660_power__le__one,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_eq_int @ A @ one_one_int )
% 11.11/6.14         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1661_less__divide__eq__1,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.14        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14            & ( ord_less_rat @ A @ B ) )
% 11.11/6.14          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.14            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1662_less__divide__eq__1,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.14        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14            & ( ord_less_real @ A @ B ) )
% 11.11/6.14          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.14            & ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1663_divide__less__eq__1,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.14        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14            & ( ord_less_rat @ B @ A ) )
% 11.11/6.14          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.14            & ( ord_less_rat @ A @ B ) )
% 11.11/6.14          | ( A = zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1664_divide__less__eq__1,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.14        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14            & ( ord_less_real @ B @ A ) )
% 11.11/6.14          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.14            & ( ord_less_real @ A @ B ) )
% 11.11/6.14          | ( A = zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1665_div__add__self2,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( B != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 11.11/6.14          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1666_div__add__self2,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( B != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.14          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1667_div__add__self2,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 11.11/6.14          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1668_div__add__self1,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( B != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 11.11/6.14          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1669_div__add__self1,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( B != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 11.11/6.14          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1670_div__add__self1,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 11.11/6.14          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1671_power__inject__base,axiom,
% 11.11/6.14      ! [A: real,N2: nat,B: real] :
% 11.11/6.14        ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 11.11/6.14          = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.14           => ( A = B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1672_power__inject__base,axiom,
% 11.11/6.14      ! [A: rat,N2: nat,B: rat] :
% 11.11/6.14        ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 11.11/6.14          = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.14           => ( A = B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1673_power__inject__base,axiom,
% 11.11/6.14      ! [A: nat,N2: nat,B: nat] :
% 11.11/6.14        ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 11.11/6.14          = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.14           => ( A = B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1674_power__inject__base,axiom,
% 11.11/6.14      ! [A: int,N2: nat,B: int] :
% 11.11/6.14        ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 11.11/6.14          = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.14           => ( A = B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1675_power__le__imp__le__base,axiom,
% 11.11/6.14      ! [A: real,N2: nat,B: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.14         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1676_power__le__imp__le__base,axiom,
% 11.11/6.14      ! [A: rat,N2: nat,B: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.14         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1677_power__le__imp__le__base,axiom,
% 11.11/6.14      ! [A: nat,N2: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.14         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1678_power__le__imp__le__base,axiom,
% 11.11/6.14      ! [A: int,N2: nat,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1679_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.14       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 11.11/6.14         => ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.14            = A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1680_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ A @ B )
% 11.11/6.14         => ( ( modulo_modulo_nat @ A @ B )
% 11.11/6.14            = A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1681_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ A @ B )
% 11.11/6.14         => ( ( modulo_modulo_int @ A @ B )
% 11.11/6.14            = A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1682_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.14       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1683_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.14       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1684_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1685_in__mono,axiom,
% 11.11/6.14      ! [A2: set_real,B3: set_real,X4: real] :
% 11.11/6.14        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 11.11/6.14       => ( ( member_real @ X4 @ A2 )
% 11.11/6.14         => ( member_real @ X4 @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1686_in__mono,axiom,
% 11.11/6.14      ! [A2: set_nat,B3: set_nat,X4: nat] :
% 11.11/6.14        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 11.11/6.14       => ( ( member_nat @ X4 @ A2 )
% 11.11/6.14         => ( member_nat @ X4 @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1687_in__mono,axiom,
% 11.11/6.14      ! [A2: set_complex,B3: set_complex,X4: complex] :
% 11.11/6.14        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 11.11/6.14       => ( ( member_complex @ X4 @ A2 )
% 11.11/6.14         => ( member_complex @ X4 @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1688_in__mono,axiom,
% 11.11/6.14      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] :
% 11.11/6.14        ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 11.11/6.14       => ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 11.11/6.14         => ( member8440522571783428010at_nat @ X4 @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1689_in__mono,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int,X4: int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ( member_int @ X4 @ A2 )
% 11.11/6.14         => ( member_int @ X4 @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1690_subsetD,axiom,
% 11.11/6.14      ! [A2: set_real,B3: set_real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 11.11/6.14       => ( ( member_real @ C @ A2 )
% 11.11/6.14         => ( member_real @ C @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1691_subsetD,axiom,
% 11.11/6.14      ! [A2: set_nat,B3: set_nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 11.11/6.14       => ( ( member_nat @ C @ A2 )
% 11.11/6.14         => ( member_nat @ C @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1692_subsetD,axiom,
% 11.11/6.14      ! [A2: set_complex,B3: set_complex,C: complex] :
% 11.11/6.14        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 11.11/6.14       => ( ( member_complex @ C @ A2 )
% 11.11/6.14         => ( member_complex @ C @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1693_subsetD,axiom,
% 11.11/6.14      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 11.11/6.14        ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 11.11/6.14       => ( ( member8440522571783428010at_nat @ C @ A2 )
% 11.11/6.14         => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1694_subsetD,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ( member_int @ C @ A2 )
% 11.11/6.14         => ( member_int @ C @ B3 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1695_equalityE,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int] :
% 11.11/6.14        ( ( A2 = B3 )
% 11.11/6.14       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14           => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1696_subset__eq,axiom,
% 11.11/6.14      ( ord_less_eq_set_real
% 11.11/6.14      = ( ^ [A6: set_real,B6: set_real] :
% 11.11/6.14          ! [X: real] :
% 11.11/6.14            ( ( member_real @ X @ A6 )
% 11.11/6.14           => ( member_real @ X @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1697_subset__eq,axiom,
% 11.11/6.14      ( ord_less_eq_set_nat
% 11.11/6.14      = ( ^ [A6: set_nat,B6: set_nat] :
% 11.11/6.14          ! [X: nat] :
% 11.11/6.14            ( ( member_nat @ X @ A6 )
% 11.11/6.14           => ( member_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1698_subset__eq,axiom,
% 11.11/6.14      ( ord_le211207098394363844omplex
% 11.11/6.14      = ( ^ [A6: set_complex,B6: set_complex] :
% 11.11/6.14          ! [X: complex] :
% 11.11/6.14            ( ( member_complex @ X @ A6 )
% 11.11/6.14           => ( member_complex @ X @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1699_subset__eq,axiom,
% 11.11/6.14      ( ord_le3146513528884898305at_nat
% 11.11/6.14      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 11.11/6.14          ! [X: product_prod_nat_nat] :
% 11.11/6.14            ( ( member8440522571783428010at_nat @ X @ A6 )
% 11.11/6.14           => ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1700_subset__eq,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14          ! [X: int] :
% 11.11/6.14            ( ( member_int @ X @ A6 )
% 11.11/6.14           => ( member_int @ X @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1701_equalityD1,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int] :
% 11.11/6.14        ( ( A2 = B3 )
% 11.11/6.14       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1702_equalityD2,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int] :
% 11.11/6.14        ( ( A2 = B3 )
% 11.11/6.14       => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1703_subset__iff,axiom,
% 11.11/6.14      ( ord_less_eq_set_real
% 11.11/6.14      = ( ^ [A6: set_real,B6: set_real] :
% 11.11/6.14          ! [T: real] :
% 11.11/6.14            ( ( member_real @ T @ A6 )
% 11.11/6.14           => ( member_real @ T @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1704_subset__iff,axiom,
% 11.11/6.14      ( ord_less_eq_set_nat
% 11.11/6.14      = ( ^ [A6: set_nat,B6: set_nat] :
% 11.11/6.14          ! [T: nat] :
% 11.11/6.14            ( ( member_nat @ T @ A6 )
% 11.11/6.14           => ( member_nat @ T @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1705_subset__iff,axiom,
% 11.11/6.14      ( ord_le211207098394363844omplex
% 11.11/6.14      = ( ^ [A6: set_complex,B6: set_complex] :
% 11.11/6.14          ! [T: complex] :
% 11.11/6.14            ( ( member_complex @ T @ A6 )
% 11.11/6.14           => ( member_complex @ T @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1706_subset__iff,axiom,
% 11.11/6.14      ( ord_le3146513528884898305at_nat
% 11.11/6.14      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 11.11/6.14          ! [T: product_prod_nat_nat] :
% 11.11/6.14            ( ( member8440522571783428010at_nat @ T @ A6 )
% 11.11/6.14           => ( member8440522571783428010at_nat @ T @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1707_subset__iff,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14          ! [T: int] :
% 11.11/6.14            ( ( member_int @ T @ A6 )
% 11.11/6.14           => ( member_int @ T @ B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1708_subset__refl,axiom,
% 11.11/6.14      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1709_Collect__mono,axiom,
% 11.11/6.14      ! [P: complex > $o,Q: complex > $o] :
% 11.11/6.14        ( ! [X5: complex] :
% 11.11/6.14            ( ( P @ X5 )
% 11.11/6.14           => ( Q @ X5 ) )
% 11.11/6.14       => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1710_Collect__mono,axiom,
% 11.11/6.14      ! [P: real > $o,Q: real > $o] :
% 11.11/6.14        ( ! [X5: real] :
% 11.11/6.14            ( ( P @ X5 )
% 11.11/6.14           => ( Q @ X5 ) )
% 11.11/6.14       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1711_Collect__mono,axiom,
% 11.11/6.14      ! [P: list_nat > $o,Q: list_nat > $o] :
% 11.11/6.14        ( ! [X5: list_nat] :
% 11.11/6.14            ( ( P @ X5 )
% 11.11/6.14           => ( Q @ X5 ) )
% 11.11/6.14       => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1712_Collect__mono,axiom,
% 11.11/6.14      ! [P: nat > $o,Q: nat > $o] :
% 11.11/6.14        ( ! [X5: nat] :
% 11.11/6.14            ( ( P @ X5 )
% 11.11/6.14           => ( Q @ X5 ) )
% 11.11/6.14       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1713_Collect__mono,axiom,
% 11.11/6.14      ! [P: int > $o,Q: int > $o] :
% 11.11/6.14        ( ! [X5: int] :
% 11.11/6.14            ( ( P @ X5 )
% 11.11/6.14           => ( Q @ X5 ) )
% 11.11/6.14       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1714_subset__trans,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int,C4: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 11.11/6.14         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1715_set__eq__subset,axiom,
% 11.11/6.14      ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 11.11/6.14            & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1716_Collect__mono__iff,axiom,
% 11.11/6.14      ! [P: complex > $o,Q: complex > $o] :
% 11.11/6.14        ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 11.11/6.14        = ( ! [X: complex] :
% 11.11/6.14              ( ( P @ X )
% 11.11/6.14             => ( Q @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1717_Collect__mono__iff,axiom,
% 11.11/6.14      ! [P: real > $o,Q: real > $o] :
% 11.11/6.14        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 11.11/6.14        = ( ! [X: real] :
% 11.11/6.14              ( ( P @ X )
% 11.11/6.14             => ( Q @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1718_Collect__mono__iff,axiom,
% 11.11/6.14      ! [P: list_nat > $o,Q: list_nat > $o] :
% 11.11/6.14        ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 11.11/6.14        = ( ! [X: list_nat] :
% 11.11/6.14              ( ( P @ X )
% 11.11/6.14             => ( Q @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1719_Collect__mono__iff,axiom,
% 11.11/6.14      ! [P: nat > $o,Q: nat > $o] :
% 11.11/6.14        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 11.11/6.14        = ( ! [X: nat] :
% 11.11/6.14              ( ( P @ X )
% 11.11/6.14             => ( Q @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1720_Collect__mono__iff,axiom,
% 11.11/6.14      ! [P: int > $o,Q: int > $o] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 11.11/6.14        = ( ! [X: int] :
% 11.11/6.14              ( ( P @ X )
% 11.11/6.14             => ( Q @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1721_subset__iff__psubset__eq,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14            ( ( ord_less_set_int @ A6 @ B6 )
% 11.11/6.14            | ( A6 = B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1722_subset__psubset__trans,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int,C4: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_set_int @ B3 @ C4 )
% 11.11/6.14         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1723_subset__not__subset__eq,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 11.11/6.14            & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1724_psubset__subset__trans,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int,C4: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 11.11/6.14         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1725_psubset__imp__subset,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ A2 @ B3 )
% 11.11/6.14       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1726_psubset__eq,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 11.11/6.14            & ( A6 != B6 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1727_psubsetE,axiom,
% 11.11/6.14      ! [A2: set_int,B3: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ A2 @ B3 )
% 11.11/6.14       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.14           => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1728_cong__exp__iff__simps_I2_J,axiom,
% 11.11/6.14      ! [N2: num,Q3: num] :
% 11.11/6.14        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.14          = zero_zero_nat )
% 11.11/6.14        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.14          = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1729_cong__exp__iff__simps_I2_J,axiom,
% 11.11/6.14      ! [N2: num,Q3: num] :
% 11.11/6.14        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 11.11/6.14          = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1730_cong__exp__iff__simps_I2_J,axiom,
% 11.11/6.14      ! [N2: num,Q3: num] :
% 11.11/6.14        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.14          = zero_z3403309356797280102nteger )
% 11.11/6.14        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 11.11/6.14          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1731_cong__exp__iff__simps_I1_J,axiom,
% 11.11/6.14      ! [N2: num] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1732_cong__exp__iff__simps_I1_J,axiom,
% 11.11/6.14      ! [N2: num] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 11.11/6.14        = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1733_cong__exp__iff__simps_I1_J,axiom,
% 11.11/6.14      ! [N2: num] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 11.11/6.14        = zero_z3403309356797280102nteger ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1734_numeral__1__eq__Suc__0,axiom,
% 11.11/6.14      ( ( numeral_numeral_nat @ one )
% 11.11/6.14      = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1735_num_Osize_I5_J,axiom,
% 11.11/6.14      ! [X22: num] :
% 11.11/6.14        ( ( size_size_num @ ( bit0 @ X22 ) )
% 11.11/6.14        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1736_ex__least__nat__less,axiom,
% 11.11/6.14      ! [P: nat > $o,N2: nat] :
% 11.11/6.14        ( ( P @ N2 )
% 11.11/6.14       => ( ~ ( P @ zero_zero_nat )
% 11.11/6.14         => ? [K2: nat] :
% 11.11/6.14              ( ( ord_less_nat @ K2 @ N2 )
% 11.11/6.14              & ! [I: nat] :
% 11.11/6.14                  ( ( ord_less_eq_nat @ I @ K2 )
% 11.11/6.14                 => ~ ( P @ I ) )
% 11.11/6.14              & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1737_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: real,Xs: list_real] :
% 11.11/6.14        ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1738_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: complex,Xs: list_complex] :
% 11.11/6.14        ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1739_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 11.11/6.14        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1740_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 11.11/6.14        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1741_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: $o,Xs: list_o] :
% 11.11/6.14        ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1742_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: nat,Xs: list_nat] :
% 11.11/6.14        ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1743_length__pos__if__in__set,axiom,
% 11.11/6.14      ! [X4: int,Xs: list_int] :
% 11.11/6.14        ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1744_nat__induct__non__zero,axiom,
% 11.11/6.14      ! [N2: nat,P: nat > $o] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14       => ( ( P @ one_one_nat )
% 11.11/6.14         => ( ! [N3: nat] :
% 11.11/6.14                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.14               => ( ( P @ N3 )
% 11.11/6.14                 => ( P @ ( suc @ N3 ) ) ) )
% 11.11/6.14           => ( P @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1745_power__gt__expt,axiom,
% 11.11/6.14      ! [N2: nat,K: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.14       => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1746_div__greater__zero__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.14        = ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.14          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1747_div__le__mono2,axiom,
% 11.11/6.14      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.14       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.14         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1748_nat__one__le__power,axiom,
% 11.11/6.14      ! [I2: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 11.11/6.14       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1749_mod__le__divisor,axiom,
% 11.11/6.14      ! [N2: nat,M: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1750_div__eq__dividend__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.14       => ( ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.14            = M )
% 11.11/6.14          = ( N2 = one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1751_div__less__dividend,axiom,
% 11.11/6.14      ! [N2: nat,M: nat] :
% 11.11/6.14        ( ( ord_less_nat @ one_one_nat @ N2 )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.14         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1752_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 11.11/6.14      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 11.11/6.14        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1753_le__divide__eq__1,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 11.11/6.14        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14            & ( ord_less_eq_real @ A @ B ) )
% 11.11/6.14          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.14            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1754_le__divide__eq__1,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 11.11/6.14        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14            & ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.14          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.14            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1755_divide__le__eq__1,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 11.11/6.14        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14            & ( ord_less_eq_real @ B @ A ) )
% 11.11/6.14          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.14            & ( ord_less_eq_real @ A @ B ) )
% 11.11/6.14          | ( A = zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1756_divide__le__eq__1,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 11.11/6.14        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14            & ( ord_less_eq_rat @ B @ A ) )
% 11.11/6.14          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.14            & ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.14          | ( A = zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1757_power__Suc__le__self,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.14         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1758_power__Suc__le__self,axiom,
% 11.11/6.14      ! [A: rat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 11.11/6.14         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1759_power__Suc__le__self,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 11.11/6.14         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1760_power__Suc__le__self,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_eq_int @ A @ one_one_int )
% 11.11/6.14         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1761_power__Suc__less__one,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ( ord_less_real @ A @ one_one_real )
% 11.11/6.14         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1762_power__Suc__less__one,axiom,
% 11.11/6.14      ! [A: rat,N2: nat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ( ord_less_rat @ A @ one_one_rat )
% 11.11/6.14         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1763_power__Suc__less__one,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ A @ one_one_nat )
% 11.11/6.14         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1764_power__Suc__less__one,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ A @ one_one_int )
% 11.11/6.14         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1765_power__strict__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: real] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14         => ( ( ord_less_real @ A @ one_one_real )
% 11.11/6.14           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1766_power__strict__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: rat] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14         => ( ( ord_less_rat @ A @ one_one_rat )
% 11.11/6.14           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1767_power__strict__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.14         => ( ( ord_less_nat @ A @ one_one_nat )
% 11.11/6.14           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1768_power__strict__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: int] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.14         => ( ( ord_less_int @ A @ one_one_int )
% 11.11/6.14           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1769_power__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: real] :
% 11.11/6.14        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.14         => ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.14           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1770_power__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: rat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.14         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 11.11/6.14           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1771_power__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 11.11/6.14           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1772_power__decreasing,axiom,
% 11.11/6.14      ! [N2: nat,N4: nat,A: int] :
% 11.11/6.14        ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14         => ( ( ord_less_eq_int @ A @ one_one_int )
% 11.11/6.14           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1773_zero__power2,axiom,
% 11.11/6.14      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14      = zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1774_zero__power2,axiom,
% 11.11/6.14      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14      = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1775_zero__power2,axiom,
% 11.11/6.14      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14      = zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1776_zero__power2,axiom,
% 11.11/6.14      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14      = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1777_zero__power2,axiom,
% 11.11/6.14      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14      = zero_zero_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1778_self__le__power,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_real @ one_one_real @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1779_self__le__power,axiom,
% 11.11/6.14      ! [A: rat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1780_self__le__power,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1781_self__le__power,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_int @ one_one_int @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1782_one__less__power,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1783_one__less__power,axiom,
% 11.11/6.14      ! [A: rat,N2: nat] :
% 11.11/6.14        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1784_one__less__power,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1785_one__less__power,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1786_numeral__2__eq__2,axiom,
% 11.11/6.14      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 11.11/6.14      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1787_verit__le__mono__div,axiom,
% 11.11/6.14      ! [A2: nat,B3: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ord_less_eq_nat
% 11.11/6.14            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 11.11/6.14              @ ( if_nat
% 11.11/6.14                @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 11.11/6.14                  = zero_zero_nat )
% 11.11/6.14                @ one_one_nat
% 11.11/6.14                @ zero_zero_nat ) )
% 11.11/6.14            @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1788_half__gt__zero__iff,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 11.11/6.14        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1789_half__gt__zero__iff,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.14        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1790_half__gt__zero,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.14       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1791_half__gt__zero,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1792_power2__le__imp__le,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.14         => ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1793_power2__le__imp__le,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.14         => ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1794_power2__le__imp__le,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 11.11/6.14         => ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1795_power2__le__imp__le,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.14         => ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1796_power2__eq__imp__eq,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.14           => ( X4 = Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1797_power2__eq__imp__eq,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.14           => ( X4 = Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1798_power2__eq__imp__eq,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 11.11/6.14           => ( X4 = Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1799_power2__eq__imp__eq,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.14           => ( X4 = Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1800_zero__le__power2,axiom,
% 11.11/6.14      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1801_zero__le__power2,axiom,
% 11.11/6.14      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1802_zero__le__power2,axiom,
% 11.11/6.14      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1803_power2__less__0,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1804_power2__less__0,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1805_power2__less__0,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1806_exp__add__not__zero__imp__right,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.14         != zero_zero_nat )
% 11.11/6.14       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.14         != zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1807_exp__add__not__zero__imp__right,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.14         != zero_zero_int )
% 11.11/6.14       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.14         != zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1808_exp__add__not__zero__imp__left,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.14         != zero_zero_nat )
% 11.11/6.14       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 11.11/6.14         != zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1809_exp__add__not__zero__imp__left,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.14         != zero_zero_int )
% 11.11/6.14       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 11.11/6.14         != zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1810_less__2__cases__iff,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14        = ( ( N2 = zero_zero_nat )
% 11.11/6.14          | ( N2
% 11.11/6.14            = ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1811_less__2__cases,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14       => ( ( N2 = zero_zero_nat )
% 11.11/6.14          | ( N2
% 11.11/6.14            = ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1812_power2__less__imp__less,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.14         => ( ord_less_real @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1813_power2__less__imp__less,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.14         => ( ord_less_rat @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1814_power2__less__imp__less,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 11.11/6.14         => ( ord_less_nat @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1815_power2__less__imp__less,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.14         => ( ord_less_int @ X4 @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1816_sum__power2__le__zero__iff,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 11.11/6.14        = ( ( X4 = zero_zero_real )
% 11.11/6.14          & ( Y = zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1817_sum__power2__le__zero__iff,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 11.11/6.14        = ( ( X4 = zero_zero_rat )
% 11.11/6.14          & ( Y = zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1818_sum__power2__le__zero__iff,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 11.11/6.14        = ( ( X4 = zero_zero_int )
% 11.11/6.14          & ( Y = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1819_sum__power2__ge__zero,axiom,
% 11.11/6.14      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1820_sum__power2__ge__zero,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1821_sum__power2__ge__zero,axiom,
% 11.11/6.14      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1822_sum__power2__gt__zero__iff,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.14        = ( ( X4 != zero_zero_real )
% 11.11/6.14          | ( Y != zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1823_sum__power2__gt__zero__iff,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.14        = ( ( X4 != zero_zero_rat )
% 11.11/6.14          | ( Y != zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1824_sum__power2__gt__zero__iff,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.14        = ( ( X4 != zero_zero_int )
% 11.11/6.14          | ( Y != zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1825_not__sum__power2__lt__zero,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1826_not__sum__power2__lt__zero,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1827_not__sum__power2__lt__zero,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1828_bits__stable__imp__add__self,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = A )
% 11.11/6.14       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.14          = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1829_bits__stable__imp__add__self,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.14          = A )
% 11.11/6.14       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 11.11/6.14          = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1830_bits__stable__imp__add__self,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.14          = A )
% 11.11/6.14       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 11.11/6.14          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1831_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1832_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_set_int @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1833_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1834_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_num @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1835_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1836_order__le__imp__less__or__eq,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_int @ X4 @ Y )
% 11.11/6.14          | ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1837_linorder__le__less__linear,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14        | ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1838_linorder__le__less__linear,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14        | ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1839_linorder__le__less__linear,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.14        | ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1840_linorder__le__less__linear,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.14        | ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1841_linorder__le__less__linear,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.14        | ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1842_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: real,B: real,F: real > real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: real,Y3: real] :
% 11.11/6.14                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1843_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > real,C: real] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1844_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > real,C: real] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1845_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: nat,B: nat,F: nat > real,C: real] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.14                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1846_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: int,B: int,F: int > real,C: real] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: int,Y3: int] :
% 11.11/6.14                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1847_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: real,B: real,F: real > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: real,Y3: real] :
% 11.11/6.14                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1848_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1849_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1850_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.14                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1851_order__less__le__subst2,axiom,
% 11.11/6.14      ! [A: int,B: int,F: int > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: int,Y3: int] :
% 11.11/6.14                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1852_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: real,F: rat > real,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1853_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1854_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: num,F: rat > num,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_num @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1855_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1856_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: int,F: rat > int,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_int @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1857_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: real,F: num > real,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1858_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: num > rat,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1859_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: num,F: num > num,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1860_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: nat,F: num > nat,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_nat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1861_order__less__le__subst1,axiom,
% 11.11/6.14      ! [A: int,F: num > int,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_int @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1862_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1863_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1864_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_num @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1865_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1866_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,F: rat > int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_int @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_eq_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1867_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_real @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1868_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1869_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_num @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1870_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1871_order__le__less__subst2,axiom,
% 11.11/6.14      ! [A: num,B: num,F: num > int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_int @ ( F @ B ) @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_eq_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1872_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: real,F: real > real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ! [X5: real,Y3: real] :
% 11.11/6.14                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1873_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: real,F: rat > real,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1874_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: real,F: num > real,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1875_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: real,F: nat > real,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.14                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1876_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: real,F: int > real,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ! [X5: int,Y3: int] :
% 11.11/6.14                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1877_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: real > rat,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ! [X5: real,Y3: real] :
% 11.11/6.14                ( ( ord_less_real @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1878_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ! [X5: rat,Y3: rat] :
% 11.11/6.14                ( ( ord_less_rat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1879_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: num > rat,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_num @ B @ C )
% 11.11/6.14         => ( ! [X5: num,Y3: num] :
% 11.11/6.14                ( ( ord_less_num @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1880_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ! [X5: nat,Y3: nat] :
% 11.11/6.14                ( ( ord_less_nat @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1881_order__le__less__subst1,axiom,
% 11.11/6.14      ! [A: rat,F: int > rat,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ! [X5: int,Y3: int] :
% 11.11/6.14                ( ( ord_less_int @ X5 @ Y3 )
% 11.11/6.14               => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 11.11/6.14           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1882_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: real,Y: real,Z: real] :
% 11.11/6.14        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_real @ Y @ Z )
% 11.11/6.14         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1883_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int,Z: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ Y @ Z )
% 11.11/6.14         => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1884_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_rat @ Y @ Z )
% 11.11/6.14         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1885_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: num,Y: num,Z: num] :
% 11.11/6.14        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_num @ Y @ Z )
% 11.11/6.14         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1886_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat,Z: nat] :
% 11.11/6.14        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_nat @ Y @ Z )
% 11.11/6.14         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1887_order__less__le__trans,axiom,
% 11.11/6.14      ! [X4: int,Y: int,Z: int] :
% 11.11/6.14        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_int @ Y @ Z )
% 11.11/6.14         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1888_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: real,Y: real,Z: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_real @ Y @ Z )
% 11.11/6.14         => ( ord_less_real @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1889_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int,Z: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_set_int @ Y @ Z )
% 11.11/6.14         => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1890_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_rat @ Y @ Z )
% 11.11/6.14         => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1891_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: num,Y: num,Z: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_num @ Y @ Z )
% 11.11/6.14         => ( ord_less_num @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1892_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat,Z: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_nat @ Y @ Z )
% 11.11/6.14         => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1893_order__le__less__trans,axiom,
% 11.11/6.14      ! [X4: int,Y: int,Z: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_int @ Y @ Z )
% 11.11/6.14         => ( ord_less_int @ X4 @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1894_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.14         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1895_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.14         => ( ord_less_set_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1896_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14         => ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1897_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: num,B: num] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14         => ( ord_less_num @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1898_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.14         => ( ord_less_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1899_order__neq__le__trans,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( A != B )
% 11.11/6.14       => ( ( ord_less_eq_int @ A @ B )
% 11.11/6.14         => ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1900_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1901_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_set_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1902_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1903_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: num,B: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_num @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1904_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1905_order__le__neq__trans,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.14       => ( ( A != B )
% 11.11/6.14         => ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1906_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1907_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1908_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1909_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1910_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1911_order__less__imp__le,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1912_linorder__not__less,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_eq_real @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1913_linorder__not__less,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1914_linorder__not__less,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_eq_num @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1915_linorder__not__less,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1916_linorder__not__less,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_eq_int @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1917_linorder__not__le,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_real @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_real @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1918_linorder__not__le,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_rat @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_rat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1919_linorder__not__le,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_num @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_num @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1920_linorder__not__le,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_nat @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_nat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1921_linorder__not__le,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_int @ X4 @ Y ) )
% 11.11/6.14        = ( ord_less_int @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1922_order__less__le,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [X: real,Y5: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1923_order__less__le,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [X: set_int,Y5: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1924_order__less__le,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [X: rat,Y5: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1925_order__less__le,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [X: num,Y5: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1926_order__less__le,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [X: nat,Y5: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1927_order__less__le,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [X: int,Y5: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ X @ Y5 )
% 11.11/6.14            & ( X != Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1928_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_real
% 11.11/6.14      = ( ^ [X: real,Y5: real] :
% 11.11/6.14            ( ( ord_less_real @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1929_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [X: set_int,Y5: set_int] :
% 11.11/6.14            ( ( ord_less_set_int @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1930_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_rat
% 11.11/6.14      = ( ^ [X: rat,Y5: rat] :
% 11.11/6.14            ( ( ord_less_rat @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1931_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_num
% 11.11/6.14      = ( ^ [X: num,Y5: num] :
% 11.11/6.14            ( ( ord_less_num @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1932_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_nat
% 11.11/6.14      = ( ^ [X: nat,Y5: nat] :
% 11.11/6.14            ( ( ord_less_nat @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1933_order__le__less,axiom,
% 11.11/6.14      ( ord_less_eq_int
% 11.11/6.14      = ( ^ [X: int,Y5: int] :
% 11.11/6.14            ( ( ord_less_int @ X @ Y5 )
% 11.11/6.14            | ( X = Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1934_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( ord_less_real @ B @ A )
% 11.11/6.14       => ( ord_less_eq_real @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1935_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: set_int,A: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ B @ A )
% 11.11/6.14       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1936_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( ord_less_rat @ B @ A )
% 11.11/6.14       => ( ord_less_eq_rat @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1937_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: num,A: num] :
% 11.11/6.14        ( ( ord_less_num @ B @ A )
% 11.11/6.14       => ( ord_less_eq_num @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1938_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( ord_less_nat @ B @ A )
% 11.11/6.14       => ( ord_less_eq_nat @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1939_dual__order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ B @ A )
% 11.11/6.14       => ( ord_less_eq_int @ B @ A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1940_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1941_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ A @ B )
% 11.11/6.14       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1942_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1943_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: num,B: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ord_less_eq_num @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1944_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ord_less_eq_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1945_order_Ostrict__implies__order,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1946_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [B2: real,A3: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1947_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [B2: set_int,A3: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1948_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [B2: rat,A3: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1949_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [B2: num,A3: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1950_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [B2: nat,A3: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1951_dual__order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [B2: int,A3: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ B2 @ A3 )
% 11.11/6.14            & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1952_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: real,A: real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_real @ C @ B )
% 11.11/6.14         => ( ord_less_real @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1953_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: set_int,A: set_int,C: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ C @ B )
% 11.11/6.14         => ( ord_less_set_int @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1954_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: rat,A: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_rat @ C @ B )
% 11.11/6.14         => ( ord_less_rat @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1955_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: num,A: num,C: num] :
% 11.11/6.14        ( ( ord_less_num @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_num @ C @ B )
% 11.11/6.14         => ( ord_less_num @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1956_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: nat,A: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_nat @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_nat @ C @ B )
% 11.11/6.14         => ( ord_less_nat @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1957_dual__order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [B: int,A: int,C: int] :
% 11.11/6.14        ( ( ord_less_int @ B @ A )
% 11.11/6.14       => ( ( ord_less_eq_int @ C @ B )
% 11.11/6.14         => ( ord_less_int @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1958_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: real,A: real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.14       => ( ( ord_less_real @ C @ B )
% 11.11/6.14         => ( ord_less_real @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1959_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: set_int,A: set_int,C: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ B @ A )
% 11.11/6.14       => ( ( ord_less_set_int @ C @ B )
% 11.11/6.14         => ( ord_less_set_int @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1960_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: rat,A: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.14       => ( ( ord_less_rat @ C @ B )
% 11.11/6.14         => ( ord_less_rat @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1961_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: num,A: num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ B @ A )
% 11.11/6.14       => ( ( ord_less_num @ C @ B )
% 11.11/6.14         => ( ord_less_num @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1962_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: nat,A: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.14       => ( ( ord_less_nat @ C @ B )
% 11.11/6.14         => ( ord_less_nat @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1963_dual__order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [B: int,A: int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.14       => ( ( ord_less_int @ C @ B )
% 11.11/6.14         => ( ord_less_int @ C @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1964_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [B2: real,A3: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1965_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [B2: set_int,A3: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1966_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [B2: rat,A3: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1967_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [B2: num,A3: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1968_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [B2: nat,A3: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1969_dual__order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [B2: int,A3: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ B2 @ A3 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1970_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_real
% 11.11/6.14      = ( ^ [B2: real,A3: real] :
% 11.11/6.14            ( ( ord_less_real @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1971_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [B2: set_int,A3: set_int] :
% 11.11/6.14            ( ( ord_less_set_int @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1972_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_rat
% 11.11/6.14      = ( ^ [B2: rat,A3: rat] :
% 11.11/6.14            ( ( ord_less_rat @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1973_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_num
% 11.11/6.14      = ( ^ [B2: num,A3: num] :
% 11.11/6.14            ( ( ord_less_num @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1974_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_nat
% 11.11/6.14      = ( ^ [B2: nat,A3: nat] :
% 11.11/6.14            ( ( ord_less_nat @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1975_dual__order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_int
% 11.11/6.14      = ( ^ [B2: int,A3: int] :
% 11.11/6.14            ( ( ord_less_int @ B2 @ A3 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1976_dense__le__bounded,axiom,
% 11.11/6.14      ! [X4: real,Y: real,Z: real] :
% 11.11/6.14        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ! [W2: real] :
% 11.11/6.14              ( ( ord_less_real @ X4 @ W2 )
% 11.11/6.14             => ( ( ord_less_real @ W2 @ Y )
% 11.11/6.14               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 11.11/6.14         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1977_dense__le__bounded,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.14        ( ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ! [W2: rat] :
% 11.11/6.14              ( ( ord_less_rat @ X4 @ W2 )
% 11.11/6.14             => ( ( ord_less_rat @ W2 @ Y )
% 11.11/6.14               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 11.11/6.14         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1978_dense__ge__bounded,axiom,
% 11.11/6.14      ! [Z: real,X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_real @ Z @ X4 )
% 11.11/6.14       => ( ! [W2: real] :
% 11.11/6.14              ( ( ord_less_real @ Z @ W2 )
% 11.11/6.14             => ( ( ord_less_real @ W2 @ X4 )
% 11.11/6.14               => ( ord_less_eq_real @ Y @ W2 ) ) )
% 11.11/6.14         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1979_dense__ge__bounded,axiom,
% 11.11/6.14      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_rat @ Z @ X4 )
% 11.11/6.14       => ( ! [W2: rat] :
% 11.11/6.14              ( ( ord_less_rat @ Z @ W2 )
% 11.11/6.14             => ( ( ord_less_rat @ W2 @ X4 )
% 11.11/6.14               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 11.11/6.14         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1980_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [A3: real,B2: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1981_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [A3: set_int,B2: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1982_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1983_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [A3: num,B2: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1984_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1985_order_Ostrict__iff__not,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [A3: int,B2: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ A3 @ B2 )
% 11.11/6.14            & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1986_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_real @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1987_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int,C: set_int] :
% 11.11/6.14        ( ( ord_less_set_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ B @ C )
% 11.11/6.14         => ( ord_less_set_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1988_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1989_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: num,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_num @ B @ C )
% 11.11/6.14         => ( ord_less_num @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1990_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_nat @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1991_order_Ostrict__trans2,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_eq_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1992_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.14       => ( ( ord_less_real @ B @ C )
% 11.11/6.14         => ( ord_less_real @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1993_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int,C: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_set_int @ B @ C )
% 11.11/6.14         => ( ord_less_set_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1994_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.14       => ( ( ord_less_rat @ B @ C )
% 11.11/6.14         => ( ord_less_rat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1995_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: num,B: num,C: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ A @ B )
% 11.11/6.14       => ( ( ord_less_num @ B @ C )
% 11.11/6.14         => ( ord_less_num @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1996_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.14       => ( ( ord_less_nat @ B @ C )
% 11.11/6.14         => ( ord_less_nat @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1997_order_Ostrict__trans1,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.14       => ( ( ord_less_int @ B @ C )
% 11.11/6.14         => ( ord_less_int @ A @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1998_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [A3: real,B2: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_1999_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [A3: set_int,B2: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2000_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2001_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [A3: num,B2: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2002_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2003_order_Ostrict__iff__order,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [A3: int,B2: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ A3 @ B2 )
% 11.11/6.14            & ( A3 != B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2004_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_real
% 11.11/6.14      = ( ^ [A3: real,B2: real] :
% 11.11/6.14            ( ( ord_less_real @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2005_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_set_int
% 11.11/6.14      = ( ^ [A3: set_int,B2: set_int] :
% 11.11/6.14            ( ( ord_less_set_int @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2006_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_rat
% 11.11/6.14      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.14            ( ( ord_less_rat @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2007_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_num
% 11.11/6.14      = ( ^ [A3: num,B2: num] :
% 11.11/6.14            ( ( ord_less_num @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2008_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_nat
% 11.11/6.14      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.14            ( ( ord_less_nat @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2009_order_Oorder__iff__strict,axiom,
% 11.11/6.14      ( ord_less_eq_int
% 11.11/6.14      = ( ^ [A3: int,B2: int] :
% 11.11/6.14            ( ( ord_less_int @ A3 @ B2 )
% 11.11/6.14            | ( A3 = B2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2010_not__le__imp__less,axiom,
% 11.11/6.14      ! [Y: real,X4: real] :
% 11.11/6.14        ( ~ ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.14       => ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2011_not__le__imp__less,axiom,
% 11.11/6.14      ! [Y: rat,X4: rat] :
% 11.11/6.14        ( ~ ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.14       => ( ord_less_rat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2012_not__le__imp__less,axiom,
% 11.11/6.14      ! [Y: num,X4: num] :
% 11.11/6.14        ( ~ ( ord_less_eq_num @ Y @ X4 )
% 11.11/6.14       => ( ord_less_num @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2013_not__le__imp__less,axiom,
% 11.11/6.14      ! [Y: nat,X4: nat] :
% 11.11/6.14        ( ~ ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.14       => ( ord_less_nat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2014_not__le__imp__less,axiom,
% 11.11/6.14      ! [Y: int,X4: int] :
% 11.11/6.14        ( ~ ( ord_less_eq_int @ Y @ X4 )
% 11.11/6.14       => ( ord_less_int @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2015_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_real
% 11.11/6.14      = ( ^ [X: real,Y5: real] :
% 11.11/6.14            ( ( ord_less_eq_real @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2016_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_set_int
% 11.11/6.14      = ( ^ [X: set_int,Y5: set_int] :
% 11.11/6.14            ( ( ord_less_eq_set_int @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2017_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_rat
% 11.11/6.14      = ( ^ [X: rat,Y5: rat] :
% 11.11/6.14            ( ( ord_less_eq_rat @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2018_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_num
% 11.11/6.14      = ( ^ [X: num,Y5: num] :
% 11.11/6.14            ( ( ord_less_eq_num @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2019_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_nat
% 11.11/6.14      = ( ^ [X: nat,Y5: nat] :
% 11.11/6.14            ( ( ord_less_eq_nat @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2020_less__le__not__le,axiom,
% 11.11/6.14      ( ord_less_int
% 11.11/6.14      = ( ^ [X: int,Y5: int] :
% 11.11/6.14            ( ( ord_less_eq_int @ X @ Y5 )
% 11.11/6.14            & ~ ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2021_dense__le,axiom,
% 11.11/6.14      ! [Y: real,Z: real] :
% 11.11/6.14        ( ! [X5: real] :
% 11.11/6.14            ( ( ord_less_real @ X5 @ Y )
% 11.11/6.14           => ( ord_less_eq_real @ X5 @ Z ) )
% 11.11/6.14       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2022_dense__le,axiom,
% 11.11/6.14      ! [Y: rat,Z: rat] :
% 11.11/6.14        ( ! [X5: rat] :
% 11.11/6.14            ( ( ord_less_rat @ X5 @ Y )
% 11.11/6.14           => ( ord_less_eq_rat @ X5 @ Z ) )
% 11.11/6.14       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2023_dense__ge,axiom,
% 11.11/6.14      ! [Z: real,Y: real] :
% 11.11/6.14        ( ! [X5: real] :
% 11.11/6.14            ( ( ord_less_real @ Z @ X5 )
% 11.11/6.14           => ( ord_less_eq_real @ Y @ X5 ) )
% 11.11/6.14       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2024_dense__ge,axiom,
% 11.11/6.14      ! [Z: rat,Y: rat] :
% 11.11/6.14        ( ! [X5: rat] :
% 11.11/6.14            ( ( ord_less_rat @ Z @ X5 )
% 11.11/6.14           => ( ord_less_eq_rat @ Y @ X5 ) )
% 11.11/6.14       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2025_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2026_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_set_int @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2027_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2028_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2029_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2030_antisym__conv2,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.14       => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2031_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ~ ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2032_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: set_int,Y: set_int] :
% 11.11/6.14        ( ~ ( ord_less_set_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2033_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ~ ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2034_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ~ ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_num @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2035_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_nat @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2036_antisym__conv1,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ~ ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.14          = ( X4 = Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2037_nless__le,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ~ ( ord_less_real @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_real @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2038_nless__le,axiom,
% 11.11/6.14      ! [A: set_int,B: set_int] :
% 11.11/6.14        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2039_nless__le,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ~ ( ord_less_rat @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_rat @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2040_nless__le,axiom,
% 11.11/6.14      ! [A: num,B: num] :
% 11.11/6.14        ( ( ~ ( ord_less_num @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_num @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2041_nless__le,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ~ ( ord_less_nat @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_nat @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2042_nless__le,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ~ ( ord_less_int @ A @ B ) )
% 11.11/6.14        = ( ~ ( ord_less_eq_int @ A @ B )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2043_leI,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ~ ( ord_less_real @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_real @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2044_leI,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ~ ( ord_less_rat @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2045_leI,axiom,
% 11.11/6.14      ! [X4: num,Y: num] :
% 11.11/6.14        ( ~ ( ord_less_num @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2046_leI,axiom,
% 11.11/6.14      ! [X4: nat,Y: nat] :
% 11.11/6.14        ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2047_leI,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ~ ( ord_less_int @ X4 @ Y )
% 11.11/6.14       => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2048_leD,axiom,
% 11.11/6.14      ! [Y: real,X4: real] :
% 11.11/6.14        ( ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2049_leD,axiom,
% 11.11/6.14      ! [Y: set_int,X4: set_int] :
% 11.11/6.14        ( ( ord_less_eq_set_int @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_set_int @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2050_leD,axiom,
% 11.11/6.14      ! [Y: rat,X4: rat] :
% 11.11/6.14        ( ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_rat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2051_leD,axiom,
% 11.11/6.14      ! [Y: num,X4: num] :
% 11.11/6.14        ( ( ord_less_eq_num @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_num @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2052_leD,axiom,
% 11.11/6.14      ! [Y: nat,X4: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_nat @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2053_leD,axiom,
% 11.11/6.14      ! [Y: int,X4: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ Y @ X4 )
% 11.11/6.14       => ~ ( ord_less_int @ X4 @ Y ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2054_verit__comp__simplify1_I3_J,axiom,
% 11.11/6.14      ! [B4: real,A4: real] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 11.11/6.14        = ( ord_less_real @ A4 @ B4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2055_verit__comp__simplify1_I3_J,axiom,
% 11.11/6.14      ! [B4: rat,A4: rat] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 11.11/6.14        = ( ord_less_rat @ A4 @ B4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2056_verit__comp__simplify1_I3_J,axiom,
% 11.11/6.14      ! [B4: num,A4: num] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 11.11/6.14        = ( ord_less_num @ A4 @ B4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2057_verit__comp__simplify1_I3_J,axiom,
% 11.11/6.14      ! [B4: nat,A4: nat] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 11.11/6.14        = ( ord_less_nat @ A4 @ B4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2058_verit__comp__simplify1_I3_J,axiom,
% 11.11/6.14      ! [B4: int,A4: int] :
% 11.11/6.14        ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 11.11/6.14        = ( ord_less_int @ A4 @ B4 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2059_Suc__n__div__2__gt__zero,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2060_div__2__gt__zero,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.14       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2061_verit__eq__simplify_I10_J,axiom,
% 11.11/6.14      ! [X22: num] :
% 11.11/6.14        ( one
% 11.11/6.14       != ( bit0 @ X22 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2062_invar__vebt_Ointros_I4_J,axiom,
% 11.11/6.14      ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 11.11/6.14        ( ! [X5: vEBT_VEBT] :
% 11.11/6.14            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.14           => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 11.11/6.14       => ( ( vEBT_invar_vebt @ Summary @ M )
% 11.11/6.14         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.14              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.14           => ( ( M = N2 )
% 11.11/6.14             => ( ( Deg
% 11.11/6.14                  = ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.14               => ( ! [I4: nat] :
% 11.11/6.14                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.14                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 11.11/6.14                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 11.11/6.14                 => ( ( ( Mi = Ma )
% 11.11/6.14                     => ! [X5: vEBT_VEBT] :
% 11.11/6.14                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.14                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 11.11/6.14                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 11.11/6.14                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 11.11/6.14                       => ( ( ( Mi != Ma )
% 11.11/6.14                           => ! [I4: nat] :
% 11.11/6.14                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.14                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 11.11/6.14                                      = I4 )
% 11.11/6.14                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 11.11/6.14                                  & ! [X5: nat] :
% 11.11/6.14                                      ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 11.11/6.14                                          = I4 )
% 11.11/6.14                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 11.11/6.14                                     => ( ( ord_less_nat @ Mi @ X5 )
% 11.11/6.14                                        & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 11.11/6.14                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2063_not__mod2__eq__Suc__0__eq__0,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14         != ( suc @ zero_zero_nat ) )
% 11.11/6.14        = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2064_not__mod__2__eq__1__eq__0,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14         != one_one_nat )
% 11.11/6.14        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2065_not__mod__2__eq__1__eq__0,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.14         != one_one_int )
% 11.11/6.14        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.14          = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2066_not__mod__2__eq__1__eq__0,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.14         != one_one_Code_integer )
% 11.11/6.14        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.14          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2067_not__mod__2__eq__0__eq__1,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14         != zero_zero_nat )
% 11.11/6.14        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = one_one_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2068_not__mod__2__eq__0__eq__1,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.14         != zero_zero_int )
% 11.11/6.14        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.14          = one_one_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2069_not__mod__2__eq__0__eq__1,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.14         != zero_z3403309356797280102nteger )
% 11.11/6.14        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.14          = one_one_Code_integer ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2070_invar__vebt_Osimps,axiom,
% 11.11/6.14      ( vEBT_invar_vebt
% 11.11/6.14      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 11.11/6.14            ( ( ? [A3: $o,B2: $o] :
% 11.11/6.14                  ( A1
% 11.11/6.14                  = ( vEBT_Leaf @ A3 @ B2 ) )
% 11.11/6.14              & ( A22
% 11.11/6.14                = ( suc @ zero_zero_nat ) ) )
% 11.11/6.14            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 11.11/6.14                ( ( A1
% 11.11/6.14                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ( vEBT_invar_vebt @ X @ N ) )
% 11.11/6.14                & ( vEBT_invar_vebt @ Summary2 @ N )
% 11.11/6.14                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 11.11/6.14                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.14                & ( A22
% 11.11/6.14                  = ( plus_plus_nat @ N @ N ) )
% 11.11/6.14                & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.14            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 11.11/6.14                ( ( A1
% 11.11/6.14                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ( vEBT_invar_vebt @ X @ N ) )
% 11.11/6.14                & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 11.11/6.14                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 11.11/6.14                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 11.11/6.14                & ( A22
% 11.11/6.14                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 11.11/6.14                & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.14            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 11.11/6.14                ( ( A1
% 11.11/6.14                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ( vEBT_invar_vebt @ X @ N ) )
% 11.11/6.14                & ( vEBT_invar_vebt @ Summary2 @ N )
% 11.11/6.14                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 11.11/6.14                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.14                & ( A22
% 11.11/6.14                  = ( plus_plus_nat @ N @ N ) )
% 11.11/6.14                & ! [I3: nat] :
% 11.11/6.14                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.14                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 11.11/6.14                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 11.11/6.14                & ( ( Mi2 = Ma2 )
% 11.11/6.14                 => ! [X: vEBT_VEBT] :
% 11.11/6.14                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.14                & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.14                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 11.11/6.14                & ( ( Mi2 != Ma2 )
% 11.11/6.14                 => ! [I3: nat] :
% 11.11/6.14                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.14                     => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 11.11/6.14                            = I3 )
% 11.11/6.14                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 11.11/6.14                        & ! [X: nat] :
% 11.11/6.14                            ( ( ( ( vEBT_VEBT_high @ X @ N )
% 11.11/6.14                                = I3 )
% 11.11/6.14                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 11.11/6.14                           => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.14                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) )
% 11.11/6.14            | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 11.11/6.14                ( ( A1
% 11.11/6.14                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 11.11/6.14                & ! [X: vEBT_VEBT] :
% 11.11/6.14                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                   => ( vEBT_invar_vebt @ X @ N ) )
% 11.11/6.14                & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 11.11/6.14                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 11.11/6.14                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 11.11/6.14                & ( A22
% 11.11/6.14                  = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 11.11/6.14                & ! [I3: nat] :
% 11.11/6.14                    ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 11.11/6.14                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 11.11/6.14                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 11.11/6.14                & ( ( Mi2 = Ma2 )
% 11.11/6.14                 => ! [X: vEBT_VEBT] :
% 11.11/6.14                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 11.11/6.14                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.14                & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.14                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 11.11/6.14                & ( ( Mi2 != Ma2 )
% 11.11/6.14                 => ! [I3: nat] :
% 11.11/6.14                      ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 11.11/6.14                     => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 11.11/6.14                            = I3 )
% 11.11/6.14                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 11.11/6.14                        & ! [X: nat] :
% 11.11/6.14                            ( ( ( ( vEBT_VEBT_high @ X @ N )
% 11.11/6.14                                = I3 )
% 11.11/6.14                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 11.11/6.14                           => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.14                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2071_invar__vebt_Ocases,axiom,
% 11.11/6.14      ! [A12: vEBT_VEBT,A23: nat] :
% 11.11/6.14        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 11.11/6.14       => ( ( ? [A5: $o,B5: $o] :
% 11.11/6.14                ( A12
% 11.11/6.14                = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.14           => ( A23
% 11.11/6.14             != ( suc @ zero_zero_nat ) ) )
% 11.11/6.14         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 11.11/6.14                ( ( A12
% 11.11/6.14                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.14               => ( ( A23 = Deg2 )
% 11.11/6.14                 => ( ! [X2: vEBT_VEBT] :
% 11.11/6.14                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                       => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 11.11/6.14                   => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 11.11/6.14                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.14                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                       => ( ( M5 = N3 )
% 11.11/6.14                         => ( ( Deg2
% 11.11/6.14                              = ( plus_plus_nat @ N3 @ M5 ) )
% 11.11/6.14                           => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 11.11/6.14                             => ~ ! [X2: vEBT_VEBT] :
% 11.11/6.14                                    ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                                   => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 11.11/6.14           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 11.11/6.14                  ( ( A12
% 11.11/6.14                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.14                 => ( ( A23 = Deg2 )
% 11.11/6.14                   => ( ! [X2: vEBT_VEBT] :
% 11.11/6.14                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                         => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 11.11/6.14                     => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 11.11/6.14                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.14                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                         => ( ( M5
% 11.11/6.14                              = ( suc @ N3 ) )
% 11.11/6.14                           => ( ( Deg2
% 11.11/6.14                                = ( plus_plus_nat @ N3 @ M5 ) )
% 11.11/6.14                             => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 11.11/6.14                               => ~ ! [X2: vEBT_VEBT] :
% 11.11/6.14                                      ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                                     => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 11.11/6.14             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 11.11/6.14                    ( ( A12
% 11.11/6.14                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.14                   => ( ( A23 = Deg2 )
% 11.11/6.14                     => ( ! [X2: vEBT_VEBT] :
% 11.11/6.14                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                           => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 11.11/6.14                       => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 11.11/6.14                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.14                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                           => ( ( M5 = N3 )
% 11.11/6.14                             => ( ( Deg2
% 11.11/6.14                                  = ( plus_plus_nat @ N3 @ M5 ) )
% 11.11/6.14                               => ( ! [I: nat] :
% 11.11/6.14                                      ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 11.11/6.14                                        = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 11.11/6.14                                 => ( ( ( Mi3 = Ma3 )
% 11.11/6.14                                     => ! [X2: vEBT_VEBT] :
% 11.11/6.14                                          ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 11.11/6.14                                   => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 11.11/6.14                                     => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.14                                       => ~ ( ( Mi3 != Ma3 )
% 11.11/6.14                                           => ! [I: nat] :
% 11.11/6.14                                                ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                                               => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 11.11/6.14                                                      = I )
% 11.11/6.14                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 11.11/6.14                                                  & ! [X2: nat] :
% 11.11/6.14                                                      ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 11.11/6.14                                                          = I )
% 11.11/6.14                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 11.11/6.14                                                     => ( ( ord_less_nat @ Mi3 @ X2 )
% 11.11/6.14                                                        & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 11.11/6.14               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 11.11/6.14                      ( ( A12
% 11.11/6.14                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.14                     => ( ( A23 = Deg2 )
% 11.11/6.14                       => ( ! [X2: vEBT_VEBT] :
% 11.11/6.14                              ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                             => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 11.11/6.14                         => ( ( vEBT_invar_vebt @ Summary3 @ M5 )
% 11.11/6.14                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.14                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                             => ( ( M5
% 11.11/6.14                                  = ( suc @ N3 ) )
% 11.11/6.14                               => ( ( Deg2
% 11.11/6.14                                    = ( plus_plus_nat @ N3 @ M5 ) )
% 11.11/6.14                                 => ( ! [I: nat] :
% 11.11/6.14                                        ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                                       => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 11.11/6.14                                          = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 11.11/6.14                                   => ( ( ( Mi3 = Ma3 )
% 11.11/6.14                                       => ! [X2: vEBT_VEBT] :
% 11.11/6.14                                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.14                                           => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 11.11/6.14                                     => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 11.11/6.14                                       => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.14                                         => ~ ( ( Mi3 != Ma3 )
% 11.11/6.14                                             => ! [I: nat] :
% 11.11/6.14                                                  ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 11.11/6.14                                                 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 11.11/6.14                                                        = I )
% 11.11/6.14                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 11.11/6.14                                                    & ! [X2: nat] :
% 11.11/6.14                                                        ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 11.11/6.14                                                            = I )
% 11.11/6.14                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 11.11/6.14                                                       => ( ( ord_less_nat @ Mi3 @ X2 )
% 11.11/6.14                                                          & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2072_nat__induct2,axiom,
% 11.11/6.14      ! [P: nat > $o,N2: nat] :
% 11.11/6.14        ( ( P @ zero_zero_nat )
% 11.11/6.14       => ( ( P @ one_one_nat )
% 11.11/6.14         => ( ! [N3: nat] :
% 11.11/6.14                ( ( P @ N3 )
% 11.11/6.14               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.14           => ( P @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2073_not__Some__eq,axiom,
% 11.11/6.14      ! [X4: option4927543243414619207at_nat] :
% 11.11/6.14        ( ( ! [Y5: product_prod_nat_nat] :
% 11.11/6.14              ( X4
% 11.11/6.14             != ( some_P7363390416028606310at_nat @ Y5 ) ) )
% 11.11/6.14        = ( X4 = none_P5556105721700978146at_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2074_not__Some__eq,axiom,
% 11.11/6.14      ! [X4: option_num] :
% 11.11/6.14        ( ( ! [Y5: num] :
% 11.11/6.14              ( X4
% 11.11/6.14             != ( some_num @ Y5 ) ) )
% 11.11/6.14        = ( X4 = none_num ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2075_not__None__eq,axiom,
% 11.11/6.14      ! [X4: option4927543243414619207at_nat] :
% 11.11/6.14        ( ( X4 != none_P5556105721700978146at_nat )
% 11.11/6.14        = ( ? [Y5: product_prod_nat_nat] :
% 11.11/6.14              ( X4
% 11.11/6.14              = ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2076_not__None__eq,axiom,
% 11.11/6.14      ! [X4: option_num] :
% 11.11/6.14        ( ( X4 != none_num )
% 11.11/6.14        = ( ? [Y5: num] :
% 11.11/6.14              ( X4
% 11.11/6.14              = ( some_num @ Y5 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2077_pos2,axiom,
% 11.11/6.14      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2078_double__eq__0__iff,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( ( plus_plus_real @ A @ A )
% 11.11/6.14          = zero_zero_real )
% 11.11/6.14        = ( A = zero_zero_real ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2079_double__eq__0__iff,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( ( plus_plus_rat @ A @ A )
% 11.11/6.14          = zero_zero_rat )
% 11.11/6.14        = ( A = zero_zero_rat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2080_double__eq__0__iff,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( ( plus_plus_int @ A @ A )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ( A = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2081_div__pos__pos__trivial,axiom,
% 11.11/6.14      ! [K: int,L: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.14       => ( ( ord_less_int @ K @ L )
% 11.11/6.14         => ( ( divide_divide_int @ K @ L )
% 11.11/6.14            = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2082_div__neg__neg__trivial,axiom,
% 11.11/6.14      ! [K: int,L: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ L @ K )
% 11.11/6.14         => ( ( divide_divide_int @ K @ L )
% 11.11/6.14            = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2083_VEBT_Oinject_I2_J,axiom,
% 11.11/6.14      ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 11.11/6.14        ( ( ( vEBT_Leaf @ X21 @ X222 )
% 11.11/6.14          = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 11.11/6.14        = ( ( X21 = Y21 )
% 11.11/6.14          & ( X222 = Y22 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2084_i0__less,axiom,
% 11.11/6.14      ! [N2: extended_enat] :
% 11.11/6.14        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 11.11/6.14        = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2085_half__nonnegative__int__iff,axiom,
% 11.11/6.14      ! [K: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 11.11/6.14        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2086_half__negative__int__iff,axiom,
% 11.11/6.14      ! [K: int] :
% 11.11/6.14        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 11.11/6.14        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2087_VEBT_Osize_I4_J,axiom,
% 11.11/6.14      ! [X21: $o,X222: $o] :
% 11.11/6.14        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2088_VEBT_Oexhaust,axiom,
% 11.11/6.14      ! [Y: vEBT_VEBT] :
% 11.11/6.14        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 11.11/6.14            ( Y
% 11.11/6.14           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 11.11/6.14       => ~ ! [X212: $o,X223: $o] :
% 11.11/6.14              ( Y
% 11.11/6.14             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2089_VEBT_Odistinct_I1_J,axiom,
% 11.11/6.14      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 11.11/6.14        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 11.11/6.14       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2090_zdiv__mono__strict,axiom,
% 11.11/6.14      ! [A2: int,B3: int,N2: int] :
% 11.11/6.14        ( ( ord_less_int @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 11.11/6.14         => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 11.11/6.14              = zero_zero_int )
% 11.11/6.14           => ( ( ( modulo_modulo_int @ B3 @ N2 )
% 11.11/6.14                = zero_zero_int )
% 11.11/6.14             => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2091_div__neg__pos__less0,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2092_neg__imp__zdiv__neg__iff,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 11.11/6.14          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2093_pos__imp__zdiv__neg__iff,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 11.11/6.14          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2094_nonneg1__imp__zdiv__pos__iff,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 11.11/6.14          = ( ( ord_less_eq_int @ B @ A )
% 11.11/6.14            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2095_pos__imp__zdiv__nonneg__iff,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 11.11/6.14          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2096_neg__imp__zdiv__nonneg__iff,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 11.11/6.14          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2097_pos__imp__zdiv__pos__iff,axiom,
% 11.11/6.14      ! [K: int,I2: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 11.11/6.14          = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2098_div__nonpos__pos__le0,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2099_div__nonneg__neg__le0,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.14         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2100_verit__le__mono__div__int,axiom,
% 11.11/6.14      ! [A2: int,B3: int,N2: int] :
% 11.11/6.14        ( ( ord_less_int @ A2 @ B3 )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 11.11/6.14         => ( ord_less_eq_int
% 11.11/6.14            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 11.11/6.14              @ ( if_int
% 11.11/6.14                @ ( ( modulo_modulo_int @ B3 @ N2 )
% 11.11/6.14                  = zero_zero_int )
% 11.11/6.14                @ one_one_int
% 11.11/6.14                @ zero_zero_int ) )
% 11.11/6.14            @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2101_int__div__less__self,axiom,
% 11.11/6.14      ! [X4: int,K: int] :
% 11.11/6.14        ( ( ord_less_int @ zero_zero_int @ X4 )
% 11.11/6.14       => ( ( ord_less_int @ one_one_int @ K )
% 11.11/6.14         => ( ord_less_int @ ( divide_divide_int @ X4 @ K ) @ X4 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2102_div__positive__int,axiom,
% 11.11/6.14      ! [L: int,K: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ L @ K )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.14         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2103_div__int__pos__iff,axiom,
% 11.11/6.14      ! [K: int,L: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 11.11/6.14        = ( ( K = zero_zero_int )
% 11.11/6.14          | ( L = zero_zero_int )
% 11.11/6.14          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.14            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 11.11/6.14          | ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.14            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2104_zdiv__mono2__neg,axiom,
% 11.11/6.14      ! [A: int,B4: int,B: int] :
% 11.11/6.14        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 11.11/6.14         => ( ( ord_less_eq_int @ B4 @ B )
% 11.11/6.14           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2105_zdiv__mono1__neg,axiom,
% 11.11/6.14      ! [A: int,A4: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ A4 )
% 11.11/6.14       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.14         => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2106_zdiv__eq__0__iff,axiom,
% 11.11/6.14      ! [I2: int,K: int] :
% 11.11/6.14        ( ( ( divide_divide_int @ I2 @ K )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ( ( K = zero_zero_int )
% 11.11/6.14          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 11.11/6.14            & ( ord_less_int @ I2 @ K ) )
% 11.11/6.14          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 11.11/6.14            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2107_zdiv__mono2,axiom,
% 11.11/6.14      ! [A: int,B4: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 11.11/6.14         => ( ( ord_less_eq_int @ B4 @ B )
% 11.11/6.14           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2108_zdiv__mono1,axiom,
% 11.11/6.14      ! [A: int,A4: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ A @ A4 )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2109_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 11.11/6.14      ! [Uu: $o,Uv: $o,Uw: nat] :
% 11.11/6.14        ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2110_not__iless0,axiom,
% 11.11/6.14      ! [N2: extended_enat] :
% 11.11/6.14        ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2111_i0__lb,axiom,
% 11.11/6.14      ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2112_ile0__eq,axiom,
% 11.11/6.14      ! [N2: extended_enat] :
% 11.11/6.14        ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 11.11/6.14        = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2113_realpow__pos__nth2,axiom,
% 11.11/6.14      ! [A: real,N2: nat] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14       => ? [R2: real] :
% 11.11/6.14            ( ( ord_less_real @ zero_zero_real @ R2 )
% 11.11/6.14            & ( ( power_power_real @ R2 @ ( suc @ N2 ) )
% 11.11/6.14              = A ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2114_vebt__buildup_Osimps_I1_J,axiom,
% 11.11/6.14      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 11.11/6.14      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2115_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 11.11/6.14      ! [Uu: $o,Uv: $o,D: nat] :
% 11.11/6.14        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 11.11/6.14        = ( D = one_one_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2116_realpow__pos__nth__unique,axiom,
% 11.11/6.14      ! [N2: nat,A: real] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14         => ? [X5: real] :
% 11.11/6.14              ( ( ord_less_real @ zero_zero_real @ X5 )
% 11.11/6.14              & ( ( power_power_real @ X5 @ N2 )
% 11.11/6.14                = A )
% 11.11/6.14              & ! [Y4: real] :
% 11.11/6.14                  ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 11.11/6.14                    & ( ( power_power_real @ Y4 @ N2 )
% 11.11/6.14                      = A ) )
% 11.11/6.14                 => ( Y4 = X5 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2117_realpow__pos__nth,axiom,
% 11.11/6.14      ! [N2: nat,A: real] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.14         => ? [R2: real] :
% 11.11/6.14              ( ( ord_less_real @ zero_zero_real @ R2 )
% 11.11/6.14              & ( ( power_power_real @ R2 @ N2 )
% 11.11/6.14                = A ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2118_invar__vebt_Ointros_I1_J,axiom,
% 11.11/6.14      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2119_not__exp__less__eq__0__int,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2120_vebt__buildup_Osimps_I2_J,axiom,
% 11.11/6.14      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 11.11/6.14      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2121_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 11.11/6.14      ! [A: $o,B: $o,X4: nat] :
% 11.11/6.14        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X4 )
% 11.11/6.14        = ( ( ( X4 = zero_zero_nat )
% 11.11/6.14           => A )
% 11.11/6.14          & ( ( X4 != zero_zero_nat )
% 11.11/6.14           => ( ( ( X4 = one_one_nat )
% 11.11/6.14               => B )
% 11.11/6.14              & ( X4 = one_one_nat ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2122_real__arch__pow__inv,axiom,
% 11.11/6.14      ! [Y: real,X4: real] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.14       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.14         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X4 @ N3 ) @ Y ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2123_option_Odistinct_I1_J,axiom,
% 11.11/6.14      ! [X22: product_prod_nat_nat] :
% 11.11/6.14        ( none_P5556105721700978146at_nat
% 11.11/6.14       != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2124_option_Odistinct_I1_J,axiom,
% 11.11/6.14      ! [X22: num] :
% 11.11/6.14        ( none_num
% 11.11/6.14       != ( some_num @ X22 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2125_option_OdiscI,axiom,
% 11.11/6.14      ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 11.11/6.14        ( ( Option
% 11.11/6.14          = ( some_P7363390416028606310at_nat @ X22 ) )
% 11.11/6.14       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2126_option_OdiscI,axiom,
% 11.11/6.14      ! [Option: option_num,X22: num] :
% 11.11/6.14        ( ( Option
% 11.11/6.14          = ( some_num @ X22 ) )
% 11.11/6.14       => ( Option != none_num ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2127_option_Oexhaust,axiom,
% 11.11/6.14      ! [Y: option4927543243414619207at_nat] :
% 11.11/6.14        ( ( Y != none_P5556105721700978146at_nat )
% 11.11/6.14       => ~ ! [X23: product_prod_nat_nat] :
% 11.11/6.14              ( Y
% 11.11/6.14             != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2128_option_Oexhaust,axiom,
% 11.11/6.14      ! [Y: option_num] :
% 11.11/6.14        ( ( Y != none_num )
% 11.11/6.14       => ~ ! [X23: num] :
% 11.11/6.14              ( Y
% 11.11/6.14             != ( some_num @ X23 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2129_split__option__ex,axiom,
% 11.11/6.14      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 11.11/6.14          ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 11.11/6.14      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 11.11/6.14            ( ( P4 @ none_P5556105721700978146at_nat )
% 11.11/6.14            | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2130_split__option__ex,axiom,
% 11.11/6.14      ( ( ^ [P3: option_num > $o] :
% 11.11/6.14          ? [X6: option_num] : ( P3 @ X6 ) )
% 11.11/6.14      = ( ^ [P4: option_num > $o] :
% 11.11/6.14            ( ( P4 @ none_num )
% 11.11/6.14            | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2131_split__option__all,axiom,
% 11.11/6.14      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 11.11/6.14          ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 11.11/6.14      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 11.11/6.14            ( ( P4 @ none_P5556105721700978146at_nat )
% 11.11/6.14            & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2132_split__option__all,axiom,
% 11.11/6.14      ( ( ^ [P3: option_num > $o] :
% 11.11/6.14          ! [X6: option_num] : ( P3 @ X6 ) )
% 11.11/6.14      = ( ^ [P4: option_num > $o] :
% 11.11/6.14            ( ( P4 @ none_num )
% 11.11/6.14            & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2133_combine__options__cases,axiom,
% 11.11/6.14      ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 11.11/6.14        ( ( ( X4 = none_P5556105721700978146at_nat )
% 11.11/6.14         => ( P @ X4 @ Y ) )
% 11.11/6.14       => ( ( ( Y = none_P5556105721700978146at_nat )
% 11.11/6.14           => ( P @ X4 @ Y ) )
% 11.11/6.14         => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 11.11/6.14                ( ( X4
% 11.11/6.14                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 11.11/6.14               => ( ( Y
% 11.11/6.14                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 11.11/6.14                 => ( P @ X4 @ Y ) ) )
% 11.11/6.14           => ( P @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2134_combine__options__cases,axiom,
% 11.11/6.14      ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 11.11/6.14        ( ( ( X4 = none_P5556105721700978146at_nat )
% 11.11/6.14         => ( P @ X4 @ Y ) )
% 11.11/6.14       => ( ( ( Y = none_num )
% 11.11/6.14           => ( P @ X4 @ Y ) )
% 11.11/6.14         => ( ! [A5: product_prod_nat_nat,B5: num] :
% 11.11/6.14                ( ( X4
% 11.11/6.14                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 11.11/6.14               => ( ( Y
% 11.11/6.14                    = ( some_num @ B5 ) )
% 11.11/6.14                 => ( P @ X4 @ Y ) ) )
% 11.11/6.14           => ( P @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2135_combine__options__cases,axiom,
% 11.11/6.14      ! [X4: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 11.11/6.14        ( ( ( X4 = none_num )
% 11.11/6.14         => ( P @ X4 @ Y ) )
% 11.11/6.14       => ( ( ( Y = none_P5556105721700978146at_nat )
% 11.11/6.14           => ( P @ X4 @ Y ) )
% 11.11/6.14         => ( ! [A5: num,B5: product_prod_nat_nat] :
% 11.11/6.14                ( ( X4
% 11.11/6.14                  = ( some_num @ A5 ) )
% 11.11/6.14               => ( ( Y
% 11.11/6.14                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 11.11/6.14                 => ( P @ X4 @ Y ) ) )
% 11.11/6.14           => ( P @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2136_combine__options__cases,axiom,
% 11.11/6.14      ! [X4: option_num,P: option_num > option_num > $o,Y: option_num] :
% 11.11/6.14        ( ( ( X4 = none_num )
% 11.11/6.14         => ( P @ X4 @ Y ) )
% 11.11/6.14       => ( ( ( Y = none_num )
% 11.11/6.14           => ( P @ X4 @ Y ) )
% 11.11/6.14         => ( ! [A5: num,B5: num] :
% 11.11/6.14                ( ( X4
% 11.11/6.14                  = ( some_num @ A5 ) )
% 11.11/6.14               => ( ( Y
% 11.11/6.14                    = ( some_num @ B5 ) )
% 11.11/6.14                 => ( P @ X4 @ Y ) ) )
% 11.11/6.14           => ( P @ X4 @ Y ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2137_option_Osize_I3_J,axiom,
% 11.11/6.14      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 11.11/6.14      = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2138_option_Osize_I3_J,axiom,
% 11.11/6.14      ( ( size_size_option_num @ none_num )
% 11.11/6.14      = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2139_option_Osize_I4_J,axiom,
% 11.11/6.14      ! [X22: product_prod_nat_nat] :
% 11.11/6.14        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 11.11/6.14        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2140_option_Osize_I4_J,axiom,
% 11.11/6.14      ! [X22: num] :
% 11.11/6.14        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 11.11/6.14        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2141_divides__aux__eq,axiom,
% 11.11/6.14      ! [Q3: nat,R3: nat] :
% 11.11/6.14        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 11.11/6.14        = ( R3 = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2142_divides__aux__eq,axiom,
% 11.11/6.14      ! [Q3: int,R3: int] :
% 11.11/6.14        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.14        = ( R3 = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2143_gcd__nat__induct,axiom,
% 11.11/6.14      ! [P: nat > nat > $o,M: nat,N2: nat] :
% 11.11/6.14        ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 11.11/6.14       => ( ! [M5: nat,N3: nat] :
% 11.11/6.14              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.14             => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 11.11/6.14               => ( P @ M5 @ N3 ) ) )
% 11.11/6.14         => ( P @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2144_option_Osize__gen_I2_J,axiom,
% 11.11/6.14      ! [X4: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 11.11/6.14        ( ( size_o8335143837870341156at_nat @ X4 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 11.11/6.14        = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2145_option_Osize__gen_I2_J,axiom,
% 11.11/6.14      ! [X4: num > nat,X22: num] :
% 11.11/6.14        ( ( size_option_num @ X4 @ ( some_num @ X22 ) )
% 11.11/6.14        = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2146_even__succ__mod__exp,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2147_even__succ__mod__exp,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2148_even__succ__mod__exp,axiom,
% 11.11/6.14      ! [A: code_integer,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2149_even__succ__div__exp,axiom,
% 11.11/6.14      ! [A: nat,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2150_even__succ__div__exp,axiom,
% 11.11/6.14      ! [A: int,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2151_even__succ__div__exp,axiom,
% 11.11/6.14      ! [A: code_integer,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.14         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2152_divmod__digit__1_I1_J,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.14       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.14         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.14           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 11.11/6.14              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2153_divmod__digit__1_I1_J,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.14       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.14         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.14           => ( ( 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 )
% 11.11/6.14              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2154_divmod__digit__1_I1_J,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.14       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.14         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.14           => ( ( 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 )
% 11.11/6.14              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2155_num_Osize__gen_I2_J,axiom,
% 11.11/6.14      ! [X22: num] :
% 11.11/6.14        ( ( size_num @ ( bit0 @ X22 ) )
% 11.11/6.14        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2156_power__le__zero__eq__numeral,axiom,
% 11.11/6.14      ! [A: real,W: num] :
% 11.11/6.14        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 11.11/6.14            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( A = zero_zero_real ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2157_power__le__zero__eq__numeral,axiom,
% 11.11/6.14      ! [A: rat,W: num] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 11.11/6.14            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( A = zero_zero_rat ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2158_power__le__zero__eq__numeral,axiom,
% 11.11/6.14      ! [A: int,W: num] :
% 11.11/6.14        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 11.11/6.14            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.14              & ( A = zero_zero_int ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2159_one__mod__2__pow__eq,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2160_one__mod__2__pow__eq,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2161_one__mod__2__pow__eq,axiom,
% 11.11/6.14      ! [N2: nat] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.14        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2162_arith__geo__mean,axiom,
% 11.11/6.14      ! [U: real,X4: real,Y: real] :
% 11.11/6.14        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( times_times_real @ X4 @ Y ) )
% 11.11/6.14       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.14           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2163_arith__geo__mean,axiom,
% 11.11/6.14      ! [U: rat,X4: rat,Y: rat] :
% 11.11/6.14        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.14          = ( times_times_rat @ X4 @ Y ) )
% 11.11/6.14       => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.14         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.14           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2164_semiring__norm_I13_J,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.14        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2165_semiring__norm_I11_J,axiom,
% 11.11/6.14      ! [M: num] :
% 11.11/6.14        ( ( times_times_num @ M @ one )
% 11.11/6.14        = M ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2166_semiring__norm_I12_J,axiom,
% 11.11/6.14      ! [N2: num] :
% 11.11/6.14        ( ( times_times_num @ one @ N2 )
% 11.11/6.14        = N2 ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2167_mult__is__0,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ M @ N2 )
% 11.11/6.14          = zero_zero_nat )
% 11.11/6.14        = ( ( M = zero_zero_nat )
% 11.11/6.14          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2168_mult__0__right,axiom,
% 11.11/6.14      ! [M: nat] :
% 11.11/6.14        ( ( times_times_nat @ M @ zero_zero_nat )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2169_mult__cancel1,axiom,
% 11.11/6.14      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ K @ M )
% 11.11/6.14          = ( times_times_nat @ K @ N2 ) )
% 11.11/6.14        = ( ( M = N2 )
% 11.11/6.14          | ( K = zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2170_mult__cancel2,axiom,
% 11.11/6.14      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ M @ K )
% 11.11/6.14          = ( times_times_nat @ N2 @ K ) )
% 11.11/6.14        = ( ( M = N2 )
% 11.11/6.14          | ( K = zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2171_nat__mult__eq__1__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ M @ N2 )
% 11.11/6.14          = one_one_nat )
% 11.11/6.14        = ( ( M = one_one_nat )
% 11.11/6.14          & ( N2 = one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2172_nat__1__eq__mult__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( one_one_nat
% 11.11/6.14          = ( times_times_nat @ M @ N2 ) )
% 11.11/6.14        = ( ( M = one_one_nat )
% 11.11/6.14          & ( N2 = one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2173_mult__zero__left,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( times_times_rat @ zero_zero_rat @ A )
% 11.11/6.14        = zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2174_mult__zero__left,axiom,
% 11.11/6.14      ! [A: complex] :
% 11.11/6.14        ( ( times_times_complex @ zero_zero_complex @ A )
% 11.11/6.14        = zero_zero_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2175_mult__zero__left,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( times_times_real @ zero_zero_real @ A )
% 11.11/6.14        = zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2176_mult__zero__left,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( times_times_nat @ zero_zero_nat @ A )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2177_mult__zero__left,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( times_times_int @ zero_zero_int @ A )
% 11.11/6.14        = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2178_mult__zero__right,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( times_times_rat @ A @ zero_zero_rat )
% 11.11/6.14        = zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2179_mult__zero__right,axiom,
% 11.11/6.14      ! [A: complex] :
% 11.11/6.14        ( ( times_times_complex @ A @ zero_zero_complex )
% 11.11/6.14        = zero_zero_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2180_mult__zero__right,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( times_times_real @ A @ zero_zero_real )
% 11.11/6.14        = zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2181_mult__zero__right,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( times_times_nat @ A @ zero_zero_nat )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2182_mult__zero__right,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( times_times_int @ A @ zero_zero_int )
% 11.11/6.14        = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2183_mult__eq__0__iff,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( ( times_times_rat @ A @ B )
% 11.11/6.14          = zero_zero_rat )
% 11.11/6.14        = ( ( A = zero_zero_rat )
% 11.11/6.14          | ( B = zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2184_mult__eq__0__iff,axiom,
% 11.11/6.14      ! [A: complex,B: complex] :
% 11.11/6.14        ( ( ( times_times_complex @ A @ B )
% 11.11/6.14          = zero_zero_complex )
% 11.11/6.14        = ( ( A = zero_zero_complex )
% 11.11/6.14          | ( B = zero_zero_complex ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2185_mult__eq__0__iff,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( ( times_times_real @ A @ B )
% 11.11/6.14          = zero_zero_real )
% 11.11/6.14        = ( ( A = zero_zero_real )
% 11.11/6.14          | ( B = zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2186_mult__eq__0__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ A @ B )
% 11.11/6.14          = zero_zero_nat )
% 11.11/6.14        = ( ( A = zero_zero_nat )
% 11.11/6.14          | ( B = zero_zero_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2187_mult__eq__0__iff,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( ( times_times_int @ A @ B )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ( ( A = zero_zero_int )
% 11.11/6.14          | ( B = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2188_mult__cancel__left,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( ( times_times_rat @ C @ A )
% 11.11/6.14          = ( times_times_rat @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2189_mult__cancel__left,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( ( times_times_complex @ C @ A )
% 11.11/6.14          = ( times_times_complex @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2190_mult__cancel__left,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( ( times_times_real @ C @ A )
% 11.11/6.14          = ( times_times_real @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2191_mult__cancel__left,axiom,
% 11.11/6.14      ! [C: nat,A: nat,B: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ C @ A )
% 11.11/6.14          = ( times_times_nat @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_nat )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2192_mult__cancel__left,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( ( times_times_int @ C @ A )
% 11.11/6.14          = ( times_times_int @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2193_mult__cancel__right,axiom,
% 11.11/6.14      ! [A: rat,C: rat,B: rat] :
% 11.11/6.14        ( ( ( times_times_rat @ A @ C )
% 11.11/6.14          = ( times_times_rat @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2194_mult__cancel__right,axiom,
% 11.11/6.14      ! [A: complex,C: complex,B: complex] :
% 11.11/6.14        ( ( ( times_times_complex @ A @ C )
% 11.11/6.14          = ( times_times_complex @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2195_mult__cancel__right,axiom,
% 11.11/6.14      ! [A: real,C: real,B: real] :
% 11.11/6.14        ( ( ( times_times_real @ A @ C )
% 11.11/6.14          = ( times_times_real @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2196_mult__cancel__right,axiom,
% 11.11/6.14      ! [A: nat,C: nat,B: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ A @ C )
% 11.11/6.14          = ( times_times_nat @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_nat )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2197_mult__cancel__right,axiom,
% 11.11/6.14      ! [A: int,C: int,B: int] :
% 11.11/6.14        ( ( ( times_times_int @ A @ C )
% 11.11/6.14          = ( times_times_int @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( A = B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2198_numeral__times__numeral,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 11.11/6.14        = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2199_numeral__times__numeral,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.14        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2200_numeral__times__numeral,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.14        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2201_numeral__times__numeral,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.14        = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2202_numeral__times__numeral,axiom,
% 11.11/6.14      ! [M: num,N2: num] :
% 11.11/6.14        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.14        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2203_mult__numeral__left__semiring__numeral,axiom,
% 11.11/6.14      ! [V: num,W: num,Z: extended_enat] :
% 11.11/6.14        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 11.11/6.14        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2204_mult__numeral__left__semiring__numeral,axiom,
% 11.11/6.14      ! [V: num,W: num,Z: complex] :
% 11.11/6.14        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 11.11/6.14        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2205_mult__numeral__left__semiring__numeral,axiom,
% 11.11/6.14      ! [V: num,W: num,Z: real] :
% 11.11/6.14        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 11.11/6.14        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2206_mult__numeral__left__semiring__numeral,axiom,
% 11.11/6.14      ! [V: num,W: num,Z: nat] :
% 11.11/6.14        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 11.11/6.14        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2207_mult__numeral__left__semiring__numeral,axiom,
% 11.11/6.14      ! [V: num,W: num,Z: int] :
% 11.11/6.14        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 11.11/6.14        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2208_mult__1,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( times_times_rat @ one_one_rat @ A )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2209_mult__1,axiom,
% 11.11/6.14      ! [A: complex] :
% 11.11/6.14        ( ( times_times_complex @ one_one_complex @ A )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2210_mult__1,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( times_times_real @ one_one_real @ A )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2211_mult__1,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( times_times_nat @ one_one_nat @ A )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2212_mult__1,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( times_times_int @ one_one_int @ A )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2213_mult_Oright__neutral,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( times_times_rat @ A @ one_one_rat )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2214_mult_Oright__neutral,axiom,
% 11.11/6.14      ! [A: complex] :
% 11.11/6.14        ( ( times_times_complex @ A @ one_one_complex )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2215_mult_Oright__neutral,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( times_times_real @ A @ one_one_real )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2216_mult_Oright__neutral,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( times_times_nat @ A @ one_one_nat )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2217_mult_Oright__neutral,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( times_times_int @ A @ one_one_int )
% 11.11/6.14        = A ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2218_num__double,axiom,
% 11.11/6.14      ! [N2: num] :
% 11.11/6.14        ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 11.11/6.14        = ( bit0 @ N2 ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2219_times__divide__eq__right,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.14        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2220_times__divide__eq__right,axiom,
% 11.11/6.14      ! [A: complex,B: complex,C: complex] :
% 11.11/6.14        ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.14        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2221_divide__divide__eq__right,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.14        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2222_divide__divide__eq__right,axiom,
% 11.11/6.14      ! [A: complex,B: complex,C: complex] :
% 11.11/6.14        ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.14        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2223_divide__divide__eq__left,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 11.11/6.14        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2224_divide__divide__eq__left,axiom,
% 11.11/6.14      ! [A: complex,B: complex,C: complex] :
% 11.11/6.14        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 11.11/6.14        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2225_times__divide__eq__left,axiom,
% 11.11/6.14      ! [B: real,C: real,A: real] :
% 11.11/6.14        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.14        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2226_times__divide__eq__left,axiom,
% 11.11/6.14      ! [B: complex,C: complex,A: complex] :
% 11.11/6.14        ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 11.11/6.14        = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2227_dvd__0__right,axiom,
% 11.11/6.14      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2228_dvd__0__right,axiom,
% 11.11/6.14      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2229_dvd__0__right,axiom,
% 11.11/6.14      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2230_dvd__0__right,axiom,
% 11.11/6.14      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2231_dvd__0__right,axiom,
% 11.11/6.14      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2232_dvd__0__right,axiom,
% 11.11/6.14      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2233_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 11.11/6.14        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2234_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: complex] :
% 11.11/6.14        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 11.11/6.14        = ( A = zero_zero_complex ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2235_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 11.11/6.14        = ( A = zero_zero_real ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2236_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 11.11/6.14        = ( A = zero_zero_rat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2237_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 11.11/6.14        = ( A = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2238_dvd__0__left__iff,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 11.11/6.14        = ( A = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2239_dvd__add__triv__right__iff,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 11.11/6.14        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2240_dvd__add__triv__right__iff,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 11.11/6.14        = ( dvd_dvd_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2241_dvd__add__triv__right__iff,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 11.11/6.14        = ( dvd_dvd_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2242_dvd__add__triv__right__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 11.11/6.14        = ( dvd_dvd_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2243_dvd__add__triv__right__iff,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 11.11/6.14        = ( dvd_dvd_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2244_dvd__add__triv__left__iff,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.14        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2245_dvd__add__triv__left__iff,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 11.11/6.14        = ( dvd_dvd_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2246_dvd__add__triv__left__iff,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.14        = ( dvd_dvd_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2247_dvd__add__triv__left__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.14        = ( dvd_dvd_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2248_dvd__add__triv__left__iff,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 11.11/6.14        = ( dvd_dvd_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2249_mult__eq__1__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( times_times_nat @ M @ N2 )
% 11.11/6.14          = ( suc @ zero_zero_nat ) )
% 11.11/6.14        = ( ( M
% 11.11/6.14            = ( suc @ zero_zero_nat ) )
% 11.11/6.14          & ( N2
% 11.11/6.14            = ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2250_one__eq__mult__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ( suc @ zero_zero_nat )
% 11.11/6.14          = ( times_times_nat @ M @ N2 ) )
% 11.11/6.14        = ( ( M
% 11.11/6.14            = ( suc @ zero_zero_nat ) )
% 11.11/6.14          & ( N2
% 11.11/6.14            = ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2251_div__dvd__div,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.14       => ( ( dvd_dvd_nat @ A @ C )
% 11.11/6.14         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 11.11/6.14            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2252_div__dvd__div,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.14       => ( ( dvd_dvd_int @ A @ C )
% 11.11/6.14         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 11.11/6.14            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2253_div__dvd__div,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ A @ C )
% 11.11/6.14         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 11.11/6.14            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2254_power__mult__numeral,axiom,
% 11.11/6.14      ! [A: nat,M: num,N2: num] :
% 11.11/6.14        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.14        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2255_power__mult__numeral,axiom,
% 11.11/6.14      ! [A: real,M: num,N2: num] :
% 11.11/6.14        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.14        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2256_power__mult__numeral,axiom,
% 11.11/6.14      ! [A: int,M: num,N2: num] :
% 11.11/6.14        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.14        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2257_power__mult__numeral,axiom,
% 11.11/6.14      ! [A: complex,M: num,N2: num] :
% 11.11/6.14        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.14        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2258_nat__mult__less__cancel__disj,axiom,
% 11.11/6.14      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.14          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2259_nat__0__less__mult__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.14          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2260_mult__less__cancel2,axiom,
% 11.11/6.14      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.14          & ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2261_not__real__square__gt__zero,axiom,
% 11.11/6.14      ! [X4: real] :
% 11.11/6.14        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X4 @ X4 ) ) )
% 11.11/6.14        = ( X4 = zero_zero_real ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2262_mult__Suc__right,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 11.11/6.14        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2263_nat__mult__dvd__cancel__disj,axiom,
% 11.11/6.14      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.14        = ( ( K = zero_zero_nat )
% 11.11/6.14          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2264_of__bool__less__eq__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 11.11/6.14        = ( P
% 11.11/6.14         => Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2265_of__bool__less__eq__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 11.11/6.14        = ( P
% 11.11/6.14         => Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2266_of__bool__less__eq__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 11.11/6.14        = ( P
% 11.11/6.14         => Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2267_of__bool__less__eq__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 11.11/6.14        = ( P
% 11.11/6.14         => Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2268_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n1201886186963655149omplex @ $false )
% 11.11/6.14      = zero_zero_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2269_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n3304061248610475627l_real @ $false )
% 11.11/6.14      = zero_zero_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2270_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n2052037380579107095ol_rat @ $false )
% 11.11/6.14      = zero_zero_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2271_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n2687167440665602831ol_nat @ $false )
% 11.11/6.14      = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2272_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n2684676970156552555ol_int @ $false )
% 11.11/6.14      = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2273_of__bool__eq_I1_J,axiom,
% 11.11/6.14      ( ( zero_n356916108424825756nteger @ $false )
% 11.11/6.14      = zero_z3403309356797280102nteger ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2274_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n1201886186963655149omplex @ P )
% 11.11/6.14          = zero_zero_complex )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2275_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n3304061248610475627l_real @ P )
% 11.11/6.14          = zero_zero_real )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2276_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 11.11/6.14          = zero_zero_rat )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2277_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 11.11/6.14          = zero_zero_nat )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2278_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2684676970156552555ol_int @ P )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2279_of__bool__eq__0__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n356916108424825756nteger @ P )
% 11.11/6.14          = zero_z3403309356797280102nteger )
% 11.11/6.14        = ~ P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2280_nat__mult__div__cancel__disj,axiom,
% 11.11/6.14      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.14        ( ( ( K = zero_zero_nat )
% 11.11/6.14         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.14            = zero_zero_nat ) )
% 11.11/6.14        & ( ( K != zero_zero_nat )
% 11.11/6.14         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.14            = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2281_of__bool__less__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 11.11/6.14        = ( ~ P
% 11.11/6.14          & Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2282_of__bool__less__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 11.11/6.14        = ( ~ P
% 11.11/6.14          & Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2283_of__bool__less__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 11.11/6.14        = ( ~ P
% 11.11/6.14          & Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2284_of__bool__less__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 11.11/6.14        = ( ~ P
% 11.11/6.14          & Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2285_of__bool__less__iff,axiom,
% 11.11/6.14      ! [P: $o,Q: $o] :
% 11.11/6.14        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 11.11/6.14        = ( ~ P
% 11.11/6.14          & Q ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2286_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n1201886186963655149omplex @ P )
% 11.11/6.14          = one_one_complex )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2287_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n3304061248610475627l_real @ P )
% 11.11/6.14          = one_one_real )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2288_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 11.11/6.14          = one_one_rat )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2289_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 11.11/6.14          = one_one_nat )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2290_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n2684676970156552555ol_int @ P )
% 11.11/6.14          = one_one_int )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2291_of__bool__eq__1__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ( zero_n356916108424825756nteger @ P )
% 11.11/6.14          = one_one_Code_integer )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2292_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n1201886186963655149omplex @ $true )
% 11.11/6.14      = one_one_complex ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2293_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n3304061248610475627l_real @ $true )
% 11.11/6.14      = one_one_real ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2294_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n2052037380579107095ol_rat @ $true )
% 11.11/6.14      = one_one_rat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2295_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n2687167440665602831ol_nat @ $true )
% 11.11/6.14      = one_one_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2296_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n2684676970156552555ol_int @ $true )
% 11.11/6.14      = one_one_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2297_of__bool__eq_I2_J,axiom,
% 11.11/6.14      ( ( zero_n356916108424825756nteger @ $true )
% 11.11/6.14      = one_one_Code_integer ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2298_nat__dvd__1__iff__1,axiom,
% 11.11/6.14      ! [M: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 11.11/6.14        = ( M = one_one_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2299_mult__cancel__right2,axiom,
% 11.11/6.14      ! [A: rat,C: rat] :
% 11.11/6.14        ( ( ( times_times_rat @ A @ C )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( A = one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2300_mult__cancel__right2,axiom,
% 11.11/6.14      ! [A: complex,C: complex] :
% 11.11/6.14        ( ( ( times_times_complex @ A @ C )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( A = one_one_complex ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2301_mult__cancel__right2,axiom,
% 11.11/6.14      ! [A: real,C: real] :
% 11.11/6.14        ( ( ( times_times_real @ A @ C )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( A = one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2302_mult__cancel__right2,axiom,
% 11.11/6.14      ! [A: int,C: int] :
% 11.11/6.14        ( ( ( times_times_int @ A @ C )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( A = one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2303_mult__cancel__right1,axiom,
% 11.11/6.14      ! [C: rat,B: rat] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_rat @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( B = one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2304_mult__cancel__right1,axiom,
% 11.11/6.14      ! [C: complex,B: complex] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_complex @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( B = one_one_complex ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2305_mult__cancel__right1,axiom,
% 11.11/6.14      ! [C: real,B: real] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_real @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( B = one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2306_mult__cancel__right1,axiom,
% 11.11/6.14      ! [C: int,B: int] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_int @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( B = one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2307_mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: rat,A: rat] :
% 11.11/6.14        ( ( ( times_times_rat @ C @ A )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( A = one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2308_mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: complex,A: complex] :
% 11.11/6.14        ( ( ( times_times_complex @ C @ A )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( A = one_one_complex ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2309_mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: real,A: real] :
% 11.11/6.14        ( ( ( times_times_real @ C @ A )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( A = one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2310_mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: int,A: int] :
% 11.11/6.14        ( ( ( times_times_int @ C @ A )
% 11.11/6.14          = C )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( A = one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2311_mult__cancel__left1,axiom,
% 11.11/6.14      ! [C: rat,B: rat] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_rat @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( B = one_one_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2312_mult__cancel__left1,axiom,
% 11.11/6.14      ! [C: complex,B: complex] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_complex @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( B = one_one_complex ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2313_mult__cancel__left1,axiom,
% 11.11/6.14      ! [C: real,B: real] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_real @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( B = one_one_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2314_mult__cancel__left1,axiom,
% 11.11/6.14      ! [C: int,B: int] :
% 11.11/6.14        ( ( C
% 11.11/6.14          = ( times_times_int @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( B = one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2315_sum__squares__eq__zero__iff,axiom,
% 11.11/6.14      ! [X4: rat,Y: rat] :
% 11.11/6.14        ( ( ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 11.11/6.14          = zero_zero_rat )
% 11.11/6.14        = ( ( X4 = zero_zero_rat )
% 11.11/6.14          & ( Y = zero_zero_rat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2316_sum__squares__eq__zero__iff,axiom,
% 11.11/6.14      ! [X4: real,Y: real] :
% 11.11/6.14        ( ( ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 11.11/6.14          = zero_zero_real )
% 11.11/6.14        = ( ( X4 = zero_zero_real )
% 11.11/6.14          & ( Y = zero_zero_real ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2317_sum__squares__eq__zero__iff,axiom,
% 11.11/6.14      ! [X4: int,Y: int] :
% 11.11/6.14        ( ( ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 11.11/6.14          = zero_zero_int )
% 11.11/6.14        = ( ( X4 = zero_zero_int )
% 11.11/6.14          & ( Y = zero_zero_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2318_nonzero__mult__divide__mult__cancel__right2,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( C != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.14          = ( divide_divide_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2319_nonzero__mult__divide__mult__cancel__right2,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( C != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 11.11/6.14          = ( divide_divide_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2320_nonzero__mult__divide__mult__cancel__right2,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( C != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 11.11/6.14          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2321_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: rat,A: rat] :
% 11.11/6.14        ( ( B != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2322_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( B != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2323_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( B != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2324_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: real,A: real] :
% 11.11/6.14        ( ( B != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2325_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: complex,A: complex] :
% 11.11/6.14        ( ( B != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2326_nonzero__mult__div__cancel__right,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2327_nonzero__mult__divide__mult__cancel__right,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( C != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.14          = ( divide_divide_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2328_nonzero__mult__divide__mult__cancel__right,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( C != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.14          = ( divide_divide_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2329_nonzero__mult__divide__mult__cancel__right,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( C != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 11.11/6.14          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2330_nonzero__mult__divide__mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( C != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.14          = ( divide_divide_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2331_nonzero__mult__divide__mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( C != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 11.11/6.14          = ( divide_divide_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2332_nonzero__mult__divide__mult__cancel__left2,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( C != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 11.11/6.14          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2333_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: rat,B: rat] :
% 11.11/6.14        ( ( A != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2334_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( A != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2335_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( A != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2336_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: real,B: real] :
% 11.11/6.14        ( ( A != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2337_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: complex,B: complex] :
% 11.11/6.14        ( ( A != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2338_nonzero__mult__div__cancel__left,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2339_nonzero__mult__divide__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( C != zero_zero_rat )
% 11.11/6.14       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.14          = ( divide_divide_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2340_nonzero__mult__divide__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( C != zero_zero_real )
% 11.11/6.14       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.14          = ( divide_divide_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2341_nonzero__mult__divide__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( C != zero_zero_complex )
% 11.11/6.14       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 11.11/6.14          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2342_mult__divide__mult__cancel__left__if,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( ( C = zero_zero_rat )
% 11.11/6.14         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.14            = zero_zero_rat ) )
% 11.11/6.14        & ( ( C != zero_zero_rat )
% 11.11/6.14         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.14            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2343_mult__divide__mult__cancel__left__if,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( ( C = zero_zero_real )
% 11.11/6.14         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.14            = zero_zero_real ) )
% 11.11/6.14        & ( ( C != zero_zero_real )
% 11.11/6.14         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.14            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2344_mult__divide__mult__cancel__left__if,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( ( C = zero_zero_complex )
% 11.11/6.14         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 11.11/6.14            = zero_zero_complex ) )
% 11.11/6.14        & ( ( C != zero_zero_complex )
% 11.11/6.14         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 11.11/6.14            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2345_div__mult__mult1,axiom,
% 11.11/6.14      ! [C: nat,A: nat,B: nat] :
% 11.11/6.14        ( ( C != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 11.11/6.14          = ( divide_divide_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2346_div__mult__mult1,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( C != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.14          = ( divide_divide_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2347_div__mult__mult1,axiom,
% 11.11/6.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( C != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 11.11/6.14          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2348_div__mult__mult2,axiom,
% 11.11/6.14      ! [C: nat,A: nat,B: nat] :
% 11.11/6.14        ( ( C != zero_zero_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 11.11/6.14          = ( divide_divide_nat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2349_div__mult__mult2,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( C != zero_zero_int )
% 11.11/6.14       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.14          = ( divide_divide_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2350_div__mult__mult2,axiom,
% 11.11/6.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( C != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.14          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2351_div__mult__mult1__if,axiom,
% 11.11/6.14      ! [C: nat,A: nat,B: nat] :
% 11.11/6.14        ( ( ( C = zero_zero_nat )
% 11.11/6.14         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 11.11/6.14            = zero_zero_nat ) )
% 11.11/6.14        & ( ( C != zero_zero_nat )
% 11.11/6.14         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 11.11/6.14            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2352_div__mult__mult1__if,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( ( C = zero_zero_int )
% 11.11/6.14         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.14            = zero_zero_int ) )
% 11.11/6.14        & ( ( C != zero_zero_int )
% 11.11/6.14         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.14            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2353_div__mult__mult1__if,axiom,
% 11.11/6.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( ( C = zero_z3403309356797280102nteger )
% 11.11/6.14         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 11.11/6.14            = zero_z3403309356797280102nteger ) )
% 11.11/6.14        & ( ( C != zero_z3403309356797280102nteger )
% 11.11/6.14         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 11.11/6.14            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2354_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: rat,B: rat,V: num] :
% 11.11/6.14        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 11.11/6.14        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2355_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: extended_enat,B: extended_enat,V: num] :
% 11.11/6.14        ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 11.11/6.14        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2356_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: complex,B: complex,V: num] :
% 11.11/6.14        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 11.11/6.14        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2357_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: real,B: real,V: num] :
% 11.11/6.14        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 11.11/6.14        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2358_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: nat,B: nat,V: num] :
% 11.11/6.14        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 11.11/6.14        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2359_distrib__right__numeral,axiom,
% 11.11/6.14      ! [A: int,B: int,V: num] :
% 11.11/6.14        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.14        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2360_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: rat,C: rat] :
% 11.11/6.14        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.14        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2361_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: extended_enat,C: extended_enat] :
% 11.11/6.14        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 11.11/6.14        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2362_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: complex,C: complex] :
% 11.11/6.14        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 11.11/6.14        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2363_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: real,C: real] :
% 11.11/6.14        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.14        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2364_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: nat,C: nat] :
% 11.11/6.14        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.14        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2365_distrib__left__numeral,axiom,
% 11.11/6.14      ! [V: num,B: int,C: int] :
% 11.11/6.14        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.14        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2366_dvd__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_z3403309356797280102nteger )
% 11.11/6.14          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2367_dvd__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: rat,A: rat,B: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2368_dvd__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: complex,A: complex,B: complex] :
% 11.11/6.14        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2369_dvd__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: real,A: real,B: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2370_dvd__mult__cancel__left,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2371_dvd__mult__cancel__right,axiom,
% 11.11/6.14      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_z3403309356797280102nteger )
% 11.11/6.14          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2372_dvd__mult__cancel__right,axiom,
% 11.11/6.14      ! [A: rat,C: rat,B: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_rat )
% 11.11/6.14          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2373_dvd__mult__cancel__right,axiom,
% 11.11/6.14      ! [A: complex,C: complex,B: complex] :
% 11.11/6.14        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_complex )
% 11.11/6.14          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2374_dvd__mult__cancel__right,axiom,
% 11.11/6.14      ! [A: real,C: real,B: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_real )
% 11.11/6.14          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2375_dvd__mult__cancel__right,axiom,
% 11.11/6.14      ! [A: int,C: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.14        = ( ( C = zero_zero_int )
% 11.11/6.14          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2376_dvd__times__left__cancel__iff,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.14        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 11.11/6.14          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2377_dvd__times__left__cancel__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( A != zero_zero_nat )
% 11.11/6.14       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 11.11/6.14          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2378_dvd__times__left__cancel__iff,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( A != zero_zero_int )
% 11.11/6.14       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 11.11/6.14          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2379_dvd__times__right__cancel__iff,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.14        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 11.11/6.14          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2380_dvd__times__right__cancel__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( A != zero_zero_nat )
% 11.11/6.14       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 11.11/6.14          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2381_dvd__times__right__cancel__iff,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( A != zero_zero_int )
% 11.11/6.14       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 11.11/6.14          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2382_unit__prod,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.14         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2383_unit__prod,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.14       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.14         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2384_unit__prod,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.14       => ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.14         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2385_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2386_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: rat,B: rat,C: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2387_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: complex,B: complex,C: complex] :
% 11.11/6.14        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_complex @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2388_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: real,B: real,C: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2389_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2390_dvd__add__times__triv__right__iff,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 11.11/6.14        = ( dvd_dvd_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2391_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2392_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: rat,C: rat,B: rat] :
% 11.11/6.14        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_rat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2393_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: complex,C: complex,B: complex] :
% 11.11/6.14        ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_complex @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2394_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: real,C: real,B: real] :
% 11.11/6.14        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_real @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2395_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: nat,C: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2396_dvd__add__times__triv__left__iff,axiom,
% 11.11/6.14      ! [A: int,C: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 11.11/6.14        = ( dvd_dvd_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2397_mod__mult__self1__is__0,axiom,
% 11.11/6.14      ! [B: nat,A: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2398_mod__mult__self1__is__0,axiom,
% 11.11/6.14      ! [B: int,A: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 11.11/6.14        = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2399_mod__mult__self1__is__0,axiom,
% 11.11/6.14      ! [B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 11.11/6.14        = zero_z3403309356797280102nteger ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2400_mod__mult__self2__is__0,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 11.11/6.14        = zero_zero_nat ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2401_mod__mult__self2__is__0,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 11.11/6.14        = zero_zero_int ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2402_mod__mult__self2__is__0,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 11.11/6.14        = zero_z3403309356797280102nteger ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2403_dvd__mult__div__cancel,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.14       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2404_dvd__mult__div__cancel,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.14       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2405_dvd__mult__div__cancel,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.14       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2406_dvd__div__mult__self,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.14       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2407_dvd__div__mult__self,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.14       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2408_dvd__div__mult__self,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.14       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 11.11/6.14          = B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2409_unit__div__1__div__1,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.14       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2410_unit__div__1__div__1,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.14       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2411_unit__div__1__div__1,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.14       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 11.11/6.14          = A ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2412_unit__div__1__unit,axiom,
% 11.11/6.14      ! [A: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.14       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2413_unit__div__1__unit,axiom,
% 11.11/6.14      ! [A: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.14       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2414_unit__div__1__unit,axiom,
% 11.11/6.14      ! [A: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.14       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2415_unit__div,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.14       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.14         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2416_unit__div,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.14       => ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.14         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2417_unit__div,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.14         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2418_div__add,axiom,
% 11.11/6.14      ! [C: nat,A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ C @ A )
% 11.11/6.14       => ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.14         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.14            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2419_div__add,axiom,
% 11.11/6.14      ! [C: int,A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ C @ A )
% 11.11/6.14       => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.14         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.14            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2420_div__add,axiom,
% 11.11/6.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ C @ A )
% 11.11/6.14       => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.14         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 11.11/6.14            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2421_mod__mult__self1,axiom,
% 11.11/6.14      ! [A: nat,C: nat,B: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 11.11/6.14        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2422_mod__mult__self1,axiom,
% 11.11/6.14      ! [A: int,C: int,B: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 11.11/6.14        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2423_mod__mult__self1,axiom,
% 11.11/6.14      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 11.11/6.14        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2424_mod__mult__self2,axiom,
% 11.11/6.14      ! [A: nat,B: nat,C: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 11.11/6.14        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2425_mod__mult__self2,axiom,
% 11.11/6.14      ! [A: int,B: int,C: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 11.11/6.14        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2426_mod__mult__self2,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 11.11/6.14        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2427_mod__mult__self3,axiom,
% 11.11/6.14      ! [C: nat,B: nat,A: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 11.11/6.14        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2428_mod__mult__self3,axiom,
% 11.11/6.14      ! [C: int,B: int,A: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 11.11/6.14        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2429_mod__mult__self3,axiom,
% 11.11/6.14      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 11.11/6.14        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2430_mod__mult__self4,axiom,
% 11.11/6.14      ! [B: nat,C: nat,A: nat] :
% 11.11/6.14        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 11.11/6.14        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2431_mod__mult__self4,axiom,
% 11.11/6.14      ! [B: int,C: int,A: int] :
% 11.11/6.14        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 11.11/6.14        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2432_mod__mult__self4,axiom,
% 11.11/6.14      ! [B: code_integer,C: code_integer,A: code_integer] :
% 11.11/6.14        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 11.11/6.14        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2433_dvd__imp__mod__0,axiom,
% 11.11/6.14      ! [A: nat,B: nat] :
% 11.11/6.14        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.14       => ( ( modulo_modulo_nat @ B @ A )
% 11.11/6.14          = zero_zero_nat ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2434_dvd__imp__mod__0,axiom,
% 11.11/6.14      ! [A: int,B: int] :
% 11.11/6.14        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.14       => ( ( modulo_modulo_int @ B @ A )
% 11.11/6.14          = zero_zero_int ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2435_dvd__imp__mod__0,axiom,
% 11.11/6.14      ! [A: code_integer,B: code_integer] :
% 11.11/6.14        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.14       => ( ( modulo364778990260209775nteger @ B @ A )
% 11.11/6.14          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2436_one__le__mult__iff,axiom,
% 11.11/6.14      ! [M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.14        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 11.11/6.14          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2437_mult__le__cancel2,axiom,
% 11.11/6.14      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.14         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2438_nat__mult__le__cancel__disj,axiom,
% 11.11/6.14      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.14        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.14        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.14         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2439_zero__less__of__bool__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2440_zero__less__of__bool__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 11.11/6.14        = P ) ).
% 11.11/6.14  
% 11.11/6.14  thf(fact_2441_zero__less__of__bool__iff,axiom,
% 11.11/6.14      ! [P: $o] :
% 11.11/6.14        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 11.11/6.14        = P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2442_zero__less__of__bool__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 11.11/6.15        = P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2443_zero__less__of__bool__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 11.11/6.15        = P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2444_of__bool__less__one__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 11.11/6.15        = ~ P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2445_of__bool__less__one__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 11.11/6.15        = ~ P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2446_of__bool__less__one__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 11.11/6.15        = ~ P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2447_of__bool__less__one__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 11.11/6.15        = ~ P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2448_of__bool__less__one__iff,axiom,
% 11.11/6.15      ! [P: $o] :
% 11.11/6.15        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 11.11/6.15        = ~ P ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2449_dvd__1__left,axiom,
% 11.11/6.15      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2450_dvd__1__iff__1,axiom,
% 11.11/6.15      ! [M: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 11.11/6.15        = ( M
% 11.11/6.15          = ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2451_div__mult__self1__is__m,axiom,
% 11.11/6.15      ! [N2: nat,M: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.15       => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 11.11/6.15          = M ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2452_div__mult__self__is__m,axiom,
% 11.11/6.15      ! [N2: nat,M: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.15       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 11.11/6.15          = M ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2453_Suc__0__mod__eq,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.15        = ( zero_n2687167440665602831ol_nat
% 11.11/6.15          @ ( N2
% 11.11/6.15           != ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2454_Suc__mod__mult__self1,axiom,
% 11.11/6.15      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 11.11/6.15        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2455_Suc__mod__mult__self2,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 11.11/6.15        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2456_Suc__mod__mult__self3,axiom,
% 11.11/6.15      ! [K: nat,N2: nat,M: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 11.11/6.15        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2457_Suc__mod__mult__self4,axiom,
% 11.11/6.15      ! [N2: nat,K: nat,M: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 11.11/6.15        = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2458_le__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: real,B: real,W: num] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.15        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2459_le__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: rat,B: rat,W: num] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.15        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2460_divide__le__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: real,W: num,A: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 11.11/6.15        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2461_divide__le__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: rat,W: num,A: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 11.11/6.15        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2462_eq__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: rat,B: rat,W: num] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.15        = ( ( ( ( numeral_numeral_rat @ W )
% 11.11/6.15             != zero_zero_rat )
% 11.11/6.15           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( ( numeral_numeral_rat @ W )
% 11.11/6.15              = zero_zero_rat )
% 11.11/6.15           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2463_eq__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: real,B: real,W: num] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.15        = ( ( ( ( numeral_numeral_real @ W )
% 11.11/6.15             != zero_zero_real )
% 11.11/6.15           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( ( numeral_numeral_real @ W )
% 11.11/6.15              = zero_zero_real )
% 11.11/6.15           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2464_eq__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: complex,B: complex,W: num] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.15        = ( ( ( ( numera6690914467698888265omplex @ W )
% 11.11/6.15             != zero_zero_complex )
% 11.11/6.15           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( ( numera6690914467698888265omplex @ W )
% 11.11/6.15              = zero_zero_complex )
% 11.11/6.15           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2465_divide__eq__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: rat,W: num,A: rat] :
% 11.11/6.15        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( ( numeral_numeral_rat @ W )
% 11.11/6.15             != zero_zero_rat )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 11.11/6.15          & ( ( ( numeral_numeral_rat @ W )
% 11.11/6.15              = zero_zero_rat )
% 11.11/6.15           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2466_divide__eq__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: real,W: num,A: real] :
% 11.11/6.15        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( ( numeral_numeral_real @ W )
% 11.11/6.15             != zero_zero_real )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 11.11/6.15          & ( ( ( numeral_numeral_real @ W )
% 11.11/6.15              = zero_zero_real )
% 11.11/6.15           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2467_divide__eq__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: complex,W: num,A: complex] :
% 11.11/6.15        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( ( numera6690914467698888265omplex @ W )
% 11.11/6.15             != zero_zero_complex )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 11.11/6.15          & ( ( ( numera6690914467698888265omplex @ W )
% 11.11/6.15              = zero_zero_complex )
% 11.11/6.15           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2468_less__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: rat,B: rat,W: num] :
% 11.11/6.15        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.15        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2469_less__divide__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [A: real,B: real,W: num] :
% 11.11/6.15        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.15        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2470_divide__less__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: rat,W: num,A: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 11.11/6.15        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2471_divide__less__eq__numeral1_I1_J,axiom,
% 11.11/6.15      ! [B: real,W: num,A: real] :
% 11.11/6.15        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 11.11/6.15        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2472_nonzero__divide__mult__cancel__right,axiom,
% 11.11/6.15      ! [B: rat,A: rat] :
% 11.11/6.15        ( ( B != zero_zero_rat )
% 11.11/6.15       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 11.11/6.15          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2473_nonzero__divide__mult__cancel__right,axiom,
% 11.11/6.15      ! [B: real,A: real] :
% 11.11/6.15        ( ( B != zero_zero_real )
% 11.11/6.15       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 11.11/6.15          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2474_nonzero__divide__mult__cancel__right,axiom,
% 11.11/6.15      ! [B: complex,A: complex] :
% 11.11/6.15        ( ( B != zero_zero_complex )
% 11.11/6.15       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 11.11/6.15          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2475_nonzero__divide__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( A != zero_zero_rat )
% 11.11/6.15       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 11.11/6.15          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2476_nonzero__divide__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( A != zero_zero_real )
% 11.11/6.15       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 11.11/6.15          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2477_nonzero__divide__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: complex,B: complex] :
% 11.11/6.15        ( ( A != zero_zero_complex )
% 11.11/6.15       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 11.11/6.15          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2478_div__mult__self4,axiom,
% 11.11/6.15      ! [B: nat,C: nat,A: nat] :
% 11.11/6.15        ( ( B != zero_zero_nat )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 11.11/6.15          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2479_div__mult__self4,axiom,
% 11.11/6.15      ! [B: int,C: int,A: int] :
% 11.11/6.15        ( ( B != zero_zero_int )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 11.11/6.15          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2480_div__mult__self4,axiom,
% 11.11/6.15      ! [B: code_integer,C: code_integer,A: code_integer] :
% 11.11/6.15        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2481_div__mult__self3,axiom,
% 11.11/6.15      ! [B: nat,C: nat,A: nat] :
% 11.11/6.15        ( ( B != zero_zero_nat )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 11.11/6.15          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2482_div__mult__self3,axiom,
% 11.11/6.15      ! [B: int,C: int,A: int] :
% 11.11/6.15        ( ( B != zero_zero_int )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 11.11/6.15          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2483_div__mult__self3,axiom,
% 11.11/6.15      ! [B: code_integer,C: code_integer,A: code_integer] :
% 11.11/6.15        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2484_div__mult__self2,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( B != zero_zero_nat )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 11.11/6.15          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2485_div__mult__self2,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( B != zero_zero_int )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 11.11/6.15          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2486_div__mult__self2,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2487_div__mult__self1,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( B != zero_zero_nat )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 11.11/6.15          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2488_div__mult__self1,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( B != zero_zero_int )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 11.11/6.15          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2489_div__mult__self1,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2490_unit__div__mult__self,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 11.11/6.15          = B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2491_unit__div__mult__self,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 11.11/6.15          = B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2492_unit__div__mult__self,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 11.11/6.15          = B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2493_unit__mult__div__div,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 11.11/6.15          = ( divide_divide_nat @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2494_unit__mult__div__div,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 11.11/6.15          = ( divide_divide_int @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2495_unit__mult__div__div,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2496_pow__divides__pow__iff,axiom,
% 11.11/6.15      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2497_pow__divides__pow__iff,axiom,
% 11.11/6.15      ! [N2: nat,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.15       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2498_zmod__numeral__Bit0,axiom,
% 11.11/6.15      ! [V: num,W: num] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 11.11/6.15        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2499_power__add__numeral2,axiom,
% 11.11/6.15      ! [A: complex,M: num,N2: num,B: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 11.11/6.15        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2500_power__add__numeral2,axiom,
% 11.11/6.15      ! [A: real,M: num,N2: num,B: real] :
% 11.11/6.15        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 11.11/6.15        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2501_power__add__numeral2,axiom,
% 11.11/6.15      ! [A: nat,M: num,N2: num,B: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 11.11/6.15        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2502_power__add__numeral2,axiom,
% 11.11/6.15      ! [A: int,M: num,N2: num,B: int] :
% 11.11/6.15        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 11.11/6.15        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2503_power__add__numeral,axiom,
% 11.11/6.15      ! [A: complex,M: num,N2: num] :
% 11.11/6.15        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 11.11/6.15        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2504_power__add__numeral,axiom,
% 11.11/6.15      ! [A: real,M: num,N2: num] :
% 11.11/6.15        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 11.11/6.15        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2505_power__add__numeral,axiom,
% 11.11/6.15      ! [A: nat,M: num,N2: num] :
% 11.11/6.15        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 11.11/6.15        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2506_power__add__numeral,axiom,
% 11.11/6.15      ! [A: int,M: num,N2: num] :
% 11.11/6.15        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 11.11/6.15        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2507_Suc__times__numeral__mod__eq,axiom,
% 11.11/6.15      ! [K: num,N2: nat] :
% 11.11/6.15        ( ( ( numeral_numeral_nat @ K )
% 11.11/6.15         != one_one_nat )
% 11.11/6.15       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.15          = one_one_nat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2508_zle__add1__eq__le,axiom,
% 11.11/6.15      ! [W: int,Z: int] :
% 11.11/6.15        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 11.11/6.15        = ( ord_less_eq_int @ W @ Z ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2509_mod__neg__neg__trivial,axiom,
% 11.11/6.15      ! [K: int,L: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_int @ L @ K )
% 11.11/6.15         => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.15            = K ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2510_mod__pos__pos__trivial,axiom,
% 11.11/6.15      ! [K: int,L: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.15       => ( ( ord_less_int @ K @ L )
% 11.11/6.15         => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.15            = K ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2511_even__mult__iff,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2512_even__mult__iff,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2513_even__mult__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2514_even__add,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2515_even__add,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2516_even__add,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 11.11/6.15        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2517_odd__add,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 11.11/6.15        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2518_odd__add,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 11.11/6.15        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2519_odd__add,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 11.11/6.15        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2520_even__mod__2__iff,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.15        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2521_even__mod__2__iff,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 11.11/6.15        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2522_even__mod__2__iff,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 11.11/6.15        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2523_even__Suc__Suc__iff,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 11.11/6.15        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2524_even__Suc,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2525_odd__of__bool__self,axiom,
% 11.11/6.15      ! [P2: $o] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 11.11/6.15        = P2 ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2526_odd__of__bool__self,axiom,
% 11.11/6.15      ! [P2: $o] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 11.11/6.15        = P2 ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2527_odd__of__bool__self,axiom,
% 11.11/6.15      ! [P2: $o] :
% 11.11/6.15        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 11.11/6.15        = P2 ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2528_even__plus__one__iff,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 11.11/6.15        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2529_even__plus__one__iff,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2530_even__plus__one__iff,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 11.11/6.15        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2531_of__bool__half__eq__0,axiom,
% 11.11/6.15      ! [B: $o] :
% 11.11/6.15        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15        = zero_zero_nat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2532_of__bool__half__eq__0,axiom,
% 11.11/6.15      ! [B: $o] :
% 11.11/6.15        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15        = zero_zero_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2533_of__bool__half__eq__0,axiom,
% 11.11/6.15      ! [B: $o] :
% 11.11/6.15        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15        = zero_z3403309356797280102nteger ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2534_even__Suc__div__two,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.15       => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2535_odd__Suc__div__two,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.15       => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2536_even__succ__div__2,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2537_even__succ__div__2,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2538_even__succ__div__2,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2539_even__succ__div__two,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2540_even__succ__div__two,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2541_even__succ__div__two,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2542_odd__succ__div__two,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2543_odd__succ__div__two,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2544_odd__succ__div__two,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2545_zero__le__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: real,W: num] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2546_zero__le__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: rat,W: num] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2547_zero__le__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: int,W: num] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2548_even__power,axiom,
% 11.11/6.15      ! [A: code_integer,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 11.11/6.15        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2549_even__power,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 11.11/6.15        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2550_even__power,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 11.11/6.15        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15          & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2551_power__less__zero__eq__numeral,axiom,
% 11.11/6.15      ! [A: real,W: num] :
% 11.11/6.15        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2552_power__less__zero__eq__numeral,axiom,
% 11.11/6.15      ! [A: rat,W: num] :
% 11.11/6.15        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2553_power__less__zero__eq__numeral,axiom,
% 11.11/6.15      ! [A: int,W: num] :
% 11.11/6.15        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2554_power__less__zero__eq,axiom,
% 11.11/6.15      ! [A: real,N2: nat] :
% 11.11/6.15        ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.15          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2555_power__less__zero__eq,axiom,
% 11.11/6.15      ! [A: rat,N2: nat] :
% 11.11/6.15        ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.15          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2556_power__less__zero__eq,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 11.11/6.15        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.15          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2557_odd__two__times__div__two__succ,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2558_odd__two__times__div__two__succ,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2559_odd__two__times__div__two__succ,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2560_zero__less__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: real,W: num] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( ( numeral_numeral_nat @ W )
% 11.11/6.15            = zero_zero_nat )
% 11.11/6.15          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( A != zero_zero_real ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2561_zero__less__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: rat,W: num] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( ( numeral_numeral_nat @ W )
% 11.11/6.15            = zero_zero_nat )
% 11.11/6.15          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( A != zero_zero_rat ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2562_zero__less__power__eq__numeral,axiom,
% 11.11/6.15      ! [A: int,W: num] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 11.11/6.15        = ( ( ( numeral_numeral_nat @ W )
% 11.11/6.15            = zero_zero_nat )
% 11.11/6.15          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( A != zero_zero_int ) )
% 11.11/6.15          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.15            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2563_one__div__2__pow__eq,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2564_one__div__2__pow__eq,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2565_one__div__2__pow__eq,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2566_bits__1__div__exp,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2567_bits__1__div__exp,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2568_bits__1__div__exp,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2569_add1__zle__eq,axiom,
% 11.11/6.15      ! [W: int,Z: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 11.11/6.15        = ( ord_less_int @ W @ Z ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2570_zdvd__imp__le,axiom,
% 11.11/6.15      ! [Z: int,N2: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ Z @ N2 )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ N2 )
% 11.11/6.15         => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2571_int__gr__induct,axiom,
% 11.11/6.15      ! [K: int,I2: int,P: int > $o] :
% 11.11/6.15        ( ( ord_less_int @ K @ I2 )
% 11.11/6.15       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 11.11/6.15         => ( ! [I4: int] :
% 11.11/6.15                ( ( ord_less_int @ K @ I4 )
% 11.11/6.15               => ( ( P @ I4 )
% 11.11/6.15                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.15           => ( P @ I2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2572_le__imp__0__less,axiom,
% 11.11/6.15      ! [Z: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.15       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2573_zless__add1__eq,axiom,
% 11.11/6.15      ! [W: int,Z: int] :
% 11.11/6.15        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 11.11/6.15        = ( ( ord_less_int @ W @ Z )
% 11.11/6.15          | ( W = Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2574_split__zmod,axiom,
% 11.11/6.15      ! [P: int > $o,N2: int,K: int] :
% 11.11/6.15        ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 11.11/6.15        = ( ( ( K = zero_zero_int )
% 11.11/6.15           => ( P @ N2 ) )
% 11.11/6.15          & ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.15           => ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 11.11/6.15                  & ( ord_less_int @ J3 @ K )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ J3 ) ) )
% 11.11/6.15          & ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.15           => ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_int @ K @ J3 )
% 11.11/6.15                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ J3 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2575_odd__less__0__iff,axiom,
% 11.11/6.15      ! [Z: int] :
% 11.11/6.15        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 11.11/6.15        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2576_q__pos__lemma,axiom,
% 11.11/6.15      ! [B4: int,Q4: int,R4: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 11.11/6.15       => ( ( ord_less_int @ R4 @ B4 )
% 11.11/6.15         => ( ( ord_less_int @ zero_zero_int @ B4 )
% 11.11/6.15           => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2577_neg__mod__conj,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 11.11/6.15          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2578_pos__mod__conj,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.15          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2579_int__mod__neg__eq,axiom,
% 11.11/6.15      ! [A: int,B: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 11.11/6.15         => ( ( ord_less_int @ B @ R3 )
% 11.11/6.15           => ( ( modulo_modulo_int @ A @ B )
% 11.11/6.15              = R3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2580_int__mod__pos__eq,axiom,
% 11.11/6.15      ! [A: int,B: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 11.11/6.15         => ( ( ord_less_int @ R3 @ B )
% 11.11/6.15           => ( ( modulo_modulo_int @ A @ B )
% 11.11/6.15              = R3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2581_pos__zmult__eq__1__iff,axiom,
% 11.11/6.15      ! [M: int,N2: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ M )
% 11.11/6.15       => ( ( ( times_times_int @ M @ N2 )
% 11.11/6.15            = one_one_int )
% 11.11/6.15          = ( ( M = one_one_int )
% 11.11/6.15            & ( N2 = one_one_int ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2582_zless__imp__add1__zle,axiom,
% 11.11/6.15      ! [W: int,Z: int] :
% 11.11/6.15        ( ( ord_less_int @ W @ Z )
% 11.11/6.15       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2583_mod__int__pos__iff,axiom,
% 11.11/6.15      ! [K: int,L: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 11.11/6.15        = ( ( dvd_dvd_int @ L @ K )
% 11.11/6.15          | ( ( L = zero_zero_int )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 11.11/6.15          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2584_zdiv__mono2__lemma,axiom,
% 11.11/6.15      ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 11.11/6.15        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 11.11/6.15         => ( ( ord_less_int @ R4 @ B4 )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 11.11/6.15             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 11.11/6.15               => ( ( ord_less_eq_int @ B4 @ B )
% 11.11/6.15                 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2585_zmod__trivial__iff,axiom,
% 11.11/6.15      ! [I2: int,K: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ I2 @ K )
% 11.11/6.15          = I2 )
% 11.11/6.15        = ( ( K = zero_zero_int )
% 11.11/6.15          | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 11.11/6.15            & ( ord_less_int @ I2 @ K ) )
% 11.11/6.15          | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 11.11/6.15            & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2586_zdiv__mono2__neg__lemma,axiom,
% 11.11/6.15      ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 11.11/6.15        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 11.11/6.15       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) @ zero_zero_int )
% 11.11/6.15         => ( ( ord_less_int @ R3 @ B )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 11.11/6.15             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 11.11/6.15               => ( ( ord_less_eq_int @ B4 @ B )
% 11.11/6.15                 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2587_int__one__le__iff__zero__less,axiom,
% 11.11/6.15      ! [Z: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ one_one_int @ Z )
% 11.11/6.15        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2588_unique__quotient__lemma,axiom,
% 11.11/6.15      ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 11.11/6.15         => ( ( ord_less_int @ R4 @ B )
% 11.11/6.15           => ( ( ord_less_int @ R3 @ B )
% 11.11/6.15             => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2589_neg__mod__sign,axiom,
% 11.11/6.15      ! [L: int,K: int] :
% 11.11/6.15        ( ( ord_less_int @ L @ zero_zero_int )
% 11.11/6.15       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2590_Euclidean__Division_Opos__mod__sign,axiom,
% 11.11/6.15      ! [L: int,K: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.15       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2591_unique__quotient__lemma__neg,axiom,
% 11.11/6.15      ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 11.11/6.15         => ( ( ord_less_int @ B @ R3 )
% 11.11/6.15           => ( ( ord_less_int @ B @ R4 )
% 11.11/6.15             => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2592_mod__pos__neg__trivial,axiom,
% 11.11/6.15      ! [K: int,L: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.15       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 11.11/6.15         => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.15            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2593_zmod__le__nonneg__dividend,axiom,
% 11.11/6.15      ! [M: int,K: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 11.11/6.15       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2594_zdvd__antisym__nonneg,axiom,
% 11.11/6.15      ! [M: int,N2: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 11.11/6.15         => ( ( dvd_dvd_int @ M @ N2 )
% 11.11/6.15           => ( ( dvd_dvd_int @ N2 @ M )
% 11.11/6.15             => ( M = N2 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2595_verit__la__generic,axiom,
% 11.11/6.15      ! [A: int,X4: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ X4 )
% 11.11/6.15        | ( A = X4 )
% 11.11/6.15        | ( ord_less_eq_int @ X4 @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2596_less__eq__int__code_I1_J,axiom,
% 11.11/6.15      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2597_zmod__eq__0D,axiom,
% 11.11/6.15      ! [M: int,D: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ M @ D )
% 11.11/6.15          = zero_zero_int )
% 11.11/6.15       => ? [Q2: int] :
% 11.11/6.15            ( M
% 11.11/6.15            = ( times_times_int @ D @ Q2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2598_zmod__eq__0__iff,axiom,
% 11.11/6.15      ! [M: int,D: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ M @ D )
% 11.11/6.15          = zero_zero_int )
% 11.11/6.15        = ( ? [Q5: int] :
% 11.11/6.15              ( M
% 11.11/6.15              = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2599_Euclidean__Division_Opos__mod__bound,axiom,
% 11.11/6.15      ! [L: int,K: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.15       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2600_neg__mod__bound,axiom,
% 11.11/6.15      ! [L: int,K: int] :
% 11.11/6.15        ( ( ord_less_int @ L @ zero_zero_int )
% 11.11/6.15       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2601_zmult__zless__mono2,axiom,
% 11.11/6.15      ! [I2: int,J: int,K: int] :
% 11.11/6.15        ( ( ord_less_int @ I2 @ J )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2602_zdvd__not__zless,axiom,
% 11.11/6.15      ! [M: int,N2: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ M )
% 11.11/6.15       => ( ( ord_less_int @ M @ N2 )
% 11.11/6.15         => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2603_less__int__code_I1_J,axiom,
% 11.11/6.15      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2604_iadd__is__0,axiom,
% 11.11/6.15      ! [M: extended_enat,N2: extended_enat] :
% 11.11/6.15        ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 11.11/6.15          = zero_z5237406670263579293d_enat )
% 11.11/6.15        = ( ( M = zero_z5237406670263579293d_enat )
% 11.11/6.15          & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2605_imult__is__0,axiom,
% 11.11/6.15      ! [M: extended_enat,N2: extended_enat] :
% 11.11/6.15        ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 11.11/6.15          = zero_z5237406670263579293d_enat )
% 11.11/6.15        = ( ( M = zero_z5237406670263579293d_enat )
% 11.11/6.15          | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2606_zero__one__enat__neq_I1_J,axiom,
% 11.11/6.15      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2607_int__ge__induct,axiom,
% 11.11/6.15      ! [K: int,I2: int,P: int > $o] :
% 11.11/6.15        ( ( ord_less_eq_int @ K @ I2 )
% 11.11/6.15       => ( ( P @ K )
% 11.11/6.15         => ( ! [I4: int] :
% 11.11/6.15                ( ( ord_less_eq_int @ K @ I4 )
% 11.11/6.15               => ( ( P @ I4 )
% 11.11/6.15                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.15           => ( P @ I2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2608_is__unit__mult__iff,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 11.11/6.15        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2609_is__unit__mult__iff,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 11.11/6.15        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2610_is__unit__mult__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 11.11/6.15        = ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2611_dvd__mult__unit__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2612_dvd__mult__unit__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2613_dvd__mult__unit__iff,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2614_mult__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2615_mult__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2616_mult__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2617_dvd__mult__unit__iff_H,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2618_dvd__mult__unit__iff_H,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2619_dvd__mult__unit__iff_H,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2620_mult__unit__dvd__iff_H,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2621_mult__unit__dvd__iff_H,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2622_mult__unit__dvd__iff_H,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2623_unit__mult__left__cancel,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 11.11/6.15            = ( times_3573771949741848930nteger @ A @ C ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2624_unit__mult__left__cancel,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( ( times_times_nat @ A @ B )
% 11.11/6.15            = ( times_times_nat @ A @ C ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2625_unit__mult__left__cancel,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( ( times_times_int @ A @ B )
% 11.11/6.15            = ( times_times_int @ A @ C ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2626_unit__mult__right__cancel,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 11.11/6.15            = ( times_3573771949741848930nteger @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2627_unit__mult__right__cancel,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( ( times_times_nat @ B @ A )
% 11.11/6.15            = ( times_times_nat @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2628_unit__mult__right__cancel,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( ( times_times_int @ B @ A )
% 11.11/6.15            = ( times_times_int @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2629_dvd__div__mult,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 11.11/6.15          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2630_dvd__div__mult,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 11.11/6.15          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2631_dvd__div__mult,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2632_div__mult__swap,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 11.11/6.15          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2633_div__mult__swap,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 11.11/6.15          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2634_div__mult__swap,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2635_div__div__eq__right,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 11.11/6.15            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2636_div__div__eq__right,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 11.11/6.15            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2637_div__div__eq__right,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2638_dvd__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: nat,C: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 11.11/6.15       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.15          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2639_dvd__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: int,C: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 11.11/6.15       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2640_dvd__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: code_integer,C: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2641_dvd__mult__imp__div,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 11.11/6.15       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2642_dvd__mult__imp__div,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 11.11/6.15       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2643_dvd__mult__imp__div,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2644_div__mult__div__if__dvd,axiom,
% 11.11/6.15      ! [B: nat,A: nat,D: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15       => ( ( dvd_dvd_nat @ D @ C )
% 11.11/6.15         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 11.11/6.15            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2645_div__mult__div__if__dvd,axiom,
% 11.11/6.15      ! [B: int,A: int,D: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15       => ( ( dvd_dvd_int @ D @ C )
% 11.11/6.15         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 11.11/6.15            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2646_div__mult__div__if__dvd,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ D @ C )
% 11.11/6.15         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2647_dvd__antisym,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ M @ N2 )
% 11.11/6.15       => ( ( dvd_dvd_nat @ N2 @ M )
% 11.11/6.15         => ( M = N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2648_bezout__lemma__nat,axiom,
% 11.11/6.15      ! [D: nat,A: nat,B: nat,X4: nat,Y: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ D @ A )
% 11.11/6.15       => ( ( dvd_dvd_nat @ D @ B )
% 11.11/6.15         => ( ( ( ( times_times_nat @ A @ X4 )
% 11.11/6.15                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 11.11/6.15              | ( ( times_times_nat @ B @ X4 )
% 11.11/6.15                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 11.11/6.15           => ? [X5: nat,Y3: nat] :
% 11.11/6.15                ( ( dvd_dvd_nat @ D @ A )
% 11.11/6.15                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.15                & ( ( ( times_times_nat @ A @ X5 )
% 11.11/6.15                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 11.11/6.15                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 11.11/6.15                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2649_bezout__add__nat,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15      ? [D3: nat,X5: nat,Y3: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ D3 @ A )
% 11.11/6.15        & ( dvd_dvd_nat @ D3 @ B )
% 11.11/6.15        & ( ( ( times_times_nat @ A @ X5 )
% 11.11/6.15            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 11.11/6.15          | ( ( times_times_nat @ B @ X5 )
% 11.11/6.15            = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2650_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2651_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2652_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2653_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2654_dvdE,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15       => ~ ! [K2: code_integer] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2655_dvdE,axiom,
% 11.11/6.15      ! [B: complex,A: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ B @ A )
% 11.11/6.15       => ~ ! [K2: complex] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_complex @ B @ K2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2656_dvdE,axiom,
% 11.11/6.15      ! [B: real,A: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ B @ A )
% 11.11/6.15       => ~ ! [K2: real] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_real @ B @ K2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2657_dvdE,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15       => ~ ! [K2: nat] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_nat @ B @ K2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2658_dvdE,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15       => ~ ! [K2: int] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_int @ B @ K2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2659_dvdI,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,K: code_integer] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( times_3573771949741848930nteger @ B @ K ) )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2660_dvdI,axiom,
% 11.11/6.15      ! [A: complex,B: complex,K: complex] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( times_times_complex @ B @ K ) )
% 11.11/6.15       => ( dvd_dvd_complex @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2661_dvdI,axiom,
% 11.11/6.15      ! [A: real,B: real,K: real] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( times_times_real @ B @ K ) )
% 11.11/6.15       => ( dvd_dvd_real @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2662_dvdI,axiom,
% 11.11/6.15      ! [A: nat,B: nat,K: nat] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( times_times_nat @ B @ K ) )
% 11.11/6.15       => ( dvd_dvd_nat @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2663_dvdI,axiom,
% 11.11/6.15      ! [A: int,B: int,K: int] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( times_times_int @ B @ K ) )
% 11.11/6.15       => ( dvd_dvd_int @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2664_dvd__def,axiom,
% 11.11/6.15      ( dvd_dvd_Code_integer
% 11.11/6.15      = ( ^ [B2: code_integer,A3: code_integer] :
% 11.11/6.15          ? [K3: code_integer] :
% 11.11/6.15            ( A3
% 11.11/6.15            = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2665_dvd__def,axiom,
% 11.11/6.15      ( dvd_dvd_complex
% 11.11/6.15      = ( ^ [B2: complex,A3: complex] :
% 11.11/6.15          ? [K3: complex] :
% 11.11/6.15            ( A3
% 11.11/6.15            = ( times_times_complex @ B2 @ K3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2666_dvd__def,axiom,
% 11.11/6.15      ( dvd_dvd_real
% 11.11/6.15      = ( ^ [B2: real,A3: real] :
% 11.11/6.15          ? [K3: real] :
% 11.11/6.15            ( A3
% 11.11/6.15            = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2667_dvd__def,axiom,
% 11.11/6.15      ( dvd_dvd_nat
% 11.11/6.15      = ( ^ [B2: nat,A3: nat] :
% 11.11/6.15          ? [K3: nat] :
% 11.11/6.15            ( A3
% 11.11/6.15            = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2668_dvd__def,axiom,
% 11.11/6.15      ( dvd_dvd_int
% 11.11/6.15      = ( ^ [B2: int,A3: int] :
% 11.11/6.15          ? [K3: int] :
% 11.11/6.15            ( A3
% 11.11/6.15            = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2669_of__bool__conj,axiom,
% 11.11/6.15      ! [P: $o,Q: $o] :
% 11.11/6.15        ( ( zero_n1201886186963655149omplex
% 11.11/6.15          @ ( P
% 11.11/6.15            & Q ) )
% 11.11/6.15        = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2670_of__bool__conj,axiom,
% 11.11/6.15      ! [P: $o,Q: $o] :
% 11.11/6.15        ( ( zero_n3304061248610475627l_real
% 11.11/6.15          @ ( P
% 11.11/6.15            & Q ) )
% 11.11/6.15        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2671_of__bool__conj,axiom,
% 11.11/6.15      ! [P: $o,Q: $o] :
% 11.11/6.15        ( ( zero_n2687167440665602831ol_nat
% 11.11/6.15          @ ( P
% 11.11/6.15            & Q ) )
% 11.11/6.15        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2672_of__bool__conj,axiom,
% 11.11/6.15      ! [P: $o,Q: $o] :
% 11.11/6.15        ( ( zero_n2684676970156552555ol_int
% 11.11/6.15          @ ( P
% 11.11/6.15            & Q ) )
% 11.11/6.15        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2673_of__bool__conj,axiom,
% 11.11/6.15      ! [P: $o,Q: $o] :
% 11.11/6.15        ( ( zero_n356916108424825756nteger
% 11.11/6.15          @ ( P
% 11.11/6.15            & Q ) )
% 11.11/6.15        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2674_dvd__mult,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ C )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2675_dvd__mult,axiom,
% 11.11/6.15      ! [A: complex,C: complex,B: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ A @ C )
% 11.11/6.15       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2676_dvd__mult,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ C )
% 11.11/6.15       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2677_dvd__mult,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ C )
% 11.11/6.15       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2678_dvd__mult,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ C )
% 11.11/6.15       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2679_dvd__refl,axiom,
% 11.11/6.15      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2680_dvd__refl,axiom,
% 11.11/6.15      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2681_dvd__refl,axiom,
% 11.11/6.15      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2682_mult_Oassoc,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2683_mult_Oassoc,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2684_mult_Oassoc,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2685_mult_Oassoc,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2686_dvd__mult2,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2687_dvd__mult2,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ A @ B )
% 11.11/6.15       => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2688_dvd__mult2,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ B )
% 11.11/6.15       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2689_dvd__mult2,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2690_dvd__mult2,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2691_dvd__trans,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ C )
% 11.11/6.15         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2692_dvd__trans,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ C )
% 11.11/6.15         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2693_dvd__trans,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ C )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2694_of__bool__eq__iff,axiom,
% 11.11/6.15      ! [P2: $o,Q3: $o] :
% 11.11/6.15        ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 11.11/6.15          = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 11.11/6.15        = ( P2 = Q3 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2695_of__bool__eq__iff,axiom,
% 11.11/6.15      ! [P2: $o,Q3: $o] :
% 11.11/6.15        ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 11.11/6.15          = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 11.11/6.15        = ( P2 = Q3 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2696_of__bool__eq__iff,axiom,
% 11.11/6.15      ! [P2: $o,Q3: $o] :
% 11.11/6.15        ( ( ( zero_n356916108424825756nteger @ P2 )
% 11.11/6.15          = ( zero_n356916108424825756nteger @ Q3 ) )
% 11.11/6.15        = ( P2 = Q3 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2697_dvd__mult__left,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2698_dvd__mult__left,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_complex @ A @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2699_dvd__mult__left,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_real @ A @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2700_dvd__mult__left,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_nat @ A @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2701_dvd__mult__left,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_int @ A @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2702_dvd__triv__left,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2703_dvd__triv__left,axiom,
% 11.11/6.15      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2704_dvd__triv__left,axiom,
% 11.11/6.15      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2705_dvd__triv__left,axiom,
% 11.11/6.15      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2706_dvd__triv__left,axiom,
% 11.11/6.15      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2707_mult__dvd__mono,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ D )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2708_mult__dvd__mono,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex,D: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_complex @ C @ D )
% 11.11/6.15         => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2709_mult__dvd__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_real @ C @ D )
% 11.11/6.15         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2710_mult__dvd__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ D )
% 11.11/6.15         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2711_mult__dvd__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ D )
% 11.11/6.15         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2712_mult_Ocommute,axiom,
% 11.11/6.15      ( times_times_complex
% 11.11/6.15      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ B2 @ A3 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2713_mult_Ocommute,axiom,
% 11.11/6.15      ( times_times_real
% 11.11/6.15      = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2714_mult_Ocommute,axiom,
% 11.11/6.15      ( times_times_nat
% 11.11/6.15      = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2715_mult_Ocommute,axiom,
% 11.11/6.15      ( times_times_int
% 11.11/6.15      = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2716_dvd__mult__right,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2717_dvd__mult__right,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_complex @ B @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2718_dvd__mult__right,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_real @ B @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2719_dvd__mult__right,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_nat @ B @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2720_dvd__mult__right,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15       => ( dvd_dvd_int @ B @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2721_dvd__triv__right,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2722_dvd__triv__right,axiom,
% 11.11/6.15      ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2723_dvd__triv__right,axiom,
% 11.11/6.15      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2724_dvd__triv__right,axiom,
% 11.11/6.15      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2725_dvd__triv__right,axiom,
% 11.11/6.15      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2726_mult_Oleft__commute,axiom,
% 11.11/6.15      ! [B: complex,A: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 11.11/6.15        = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2727_mult_Oleft__commute,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 11.11/6.15        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2728_mult_Oleft__commute,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 11.11/6.15        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2729_mult_Oleft__commute,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 11.11/6.15        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2730_bezout__add__strong__nat,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ? [D3: nat,X5: nat,Y3: nat] :
% 11.11/6.15            ( ( dvd_dvd_nat @ D3 @ A )
% 11.11/6.15            & ( dvd_dvd_nat @ D3 @ B )
% 11.11/6.15            & ( ( times_times_nat @ A @ X5 )
% 11.11/6.15              = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2731_unit__dvdE,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ~ ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15           => ! [C3: code_integer] :
% 11.11/6.15                ( B
% 11.11/6.15               != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2732_unit__dvdE,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ~ ( ( A != zero_zero_nat )
% 11.11/6.15           => ! [C3: nat] :
% 11.11/6.15                ( B
% 11.11/6.15               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2733_unit__dvdE,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ~ ( ( A != zero_zero_int )
% 11.11/6.15           => ! [C3: int] :
% 11.11/6.15                ( B
% 11.11/6.15               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2734_dvd__div__eq__mult,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15         => ( ( ( divide_divide_nat @ B @ A )
% 11.11/6.15              = C )
% 11.11/6.15            = ( B
% 11.11/6.15              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2735_dvd__div__eq__mult,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( A != zero_zero_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15         => ( ( ( divide_divide_int @ B @ A )
% 11.11/6.15              = C )
% 11.11/6.15            = ( B
% 11.11/6.15              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2736_dvd__div__eq__mult,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 11.11/6.15              = C )
% 11.11/6.15            = ( B
% 11.11/6.15              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2737_div__dvd__iff__mult,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( B != zero_zero_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 11.11/6.15            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2738_div__dvd__iff__mult,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( B != zero_zero_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 11.11/6.15            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2739_div__dvd__iff__mult,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( B != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 11.11/6.15            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2740_dvd__div__iff__mult,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( C != zero_zero_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 11.11/6.15            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2741_dvd__div__iff__mult,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( C != zero_zero_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 11.11/6.15            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2742_dvd__div__iff__mult,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( C != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2743_dvd__div__div__eq__mult,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat,D: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ( ( C != zero_zero_nat )
% 11.11/6.15         => ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15           => ( ( dvd_dvd_nat @ C @ D )
% 11.11/6.15             => ( ( ( divide_divide_nat @ B @ A )
% 11.11/6.15                  = ( divide_divide_nat @ D @ C ) )
% 11.11/6.15                = ( ( times_times_nat @ B @ C )
% 11.11/6.15                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2744_dvd__div__div__eq__mult,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int,D: int] :
% 11.11/6.15        ( ( A != zero_zero_int )
% 11.11/6.15       => ( ( C != zero_zero_int )
% 11.11/6.15         => ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15           => ( ( dvd_dvd_int @ C @ D )
% 11.11/6.15             => ( ( ( divide_divide_int @ B @ A )
% 11.11/6.15                  = ( divide_divide_int @ D @ C ) )
% 11.11/6.15                = ( ( times_times_int @ B @ C )
% 11.11/6.15                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2745_dvd__div__div__eq__mult,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 11.11/6.15        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( C != zero_z3403309356797280102nteger )
% 11.11/6.15         => ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15           => ( ( dvd_dvd_Code_integer @ C @ D )
% 11.11/6.15             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 11.11/6.15                  = ( divide6298287555418463151nteger @ D @ C ) )
% 11.11/6.15                = ( ( times_3573771949741848930nteger @ B @ C )
% 11.11/6.15                  = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2746_is__unit__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: nat,C: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 11.11/6.15         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.15            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2747_is__unit__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: int,C: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ one_one_int )
% 11.11/6.15         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2748_is__unit__div__mult2__eq,axiom,
% 11.11/6.15      ! [B: code_integer,C: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2749_unit__div__mult__swap,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 11.11/6.15       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 11.11/6.15          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2750_unit__div__mult__swap,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ one_one_int )
% 11.11/6.15       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 11.11/6.15          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2751_unit__div__mult__swap,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2752_unit__div__commute,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 11.11/6.15          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2753_unit__div__commute,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 11.11/6.15          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2754_unit__div__commute,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2755_div__mult__unit2,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.15            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2756_div__mult__unit2,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2757_div__mult__unit2,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2758_unit__eq__div2,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide_divide_nat @ C @ B ) )
% 11.11/6.15          = ( ( times_times_nat @ A @ B )
% 11.11/6.15            = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2759_unit__eq__div2,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide_divide_int @ C @ B ) )
% 11.11/6.15          = ( ( times_times_int @ A @ B )
% 11.11/6.15            = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2760_unit__eq__div2,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide6298287555418463151nteger @ C @ B ) )
% 11.11/6.15          = ( ( times_3573771949741848930nteger @ A @ B )
% 11.11/6.15            = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2761_unit__eq__div1,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( ( divide_divide_nat @ A @ B )
% 11.11/6.15            = C )
% 11.11/6.15          = ( A
% 11.11/6.15            = ( times_times_nat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2762_unit__eq__div1,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( ( divide_divide_int @ A @ B )
% 11.11/6.15            = C )
% 11.11/6.15          = ( A
% 11.11/6.15            = ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2763_unit__eq__div1,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 11.11/6.15            = C )
% 11.11/6.15          = ( A
% 11.11/6.15            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2764_nat__mult__dvd__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.15          = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2765_dvd__mult__cancel,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15         => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2766_dvd__field__iff,axiom,
% 11.11/6.15      ( dvd_dvd_complex
% 11.11/6.15      = ( ^ [A3: complex,B2: complex] :
% 11.11/6.15            ( ( A3 = zero_zero_complex )
% 11.11/6.15           => ( B2 = zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2767_dvd__field__iff,axiom,
% 11.11/6.15      ( dvd_dvd_real
% 11.11/6.15      = ( ^ [A3: real,B2: real] :
% 11.11/6.15            ( ( A3 = zero_zero_real )
% 11.11/6.15           => ( B2 = zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2768_dvd__field__iff,axiom,
% 11.11/6.15      ( dvd_dvd_rat
% 11.11/6.15      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.15            ( ( A3 = zero_zero_rat )
% 11.11/6.15           => ( B2 = zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2769_dvd__0__left,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 11.11/6.15       => ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2770_dvd__0__left,axiom,
% 11.11/6.15      ! [A: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 11.11/6.15       => ( A = zero_zero_complex ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2771_dvd__0__left,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 11.11/6.15       => ( A = zero_zero_real ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2772_dvd__0__left,axiom,
% 11.11/6.15      ! [A: rat] :
% 11.11/6.15        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( A = zero_zero_rat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2773_dvd__0__left,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( A = zero_zero_nat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2774_dvd__0__left,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 11.11/6.15       => ( A = zero_zero_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2775_dvd__unit__imp__unit,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2776_dvd__unit__imp__unit,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2777_dvd__unit__imp__unit,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2778_unit__imp__dvd,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2779_unit__imp__dvd,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( dvd_dvd_nat @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2780_unit__imp__dvd,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( dvd_dvd_int @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2781_one__dvd,axiom,
% 11.11/6.15      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2782_one__dvd,axiom,
% 11.11/6.15      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2783_one__dvd,axiom,
% 11.11/6.15      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2784_one__dvd,axiom,
% 11.11/6.15      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2785_one__dvd,axiom,
% 11.11/6.15      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2786_one__dvd,axiom,
% 11.11/6.15      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2787_dvd__add__right__iff,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2788_dvd__add__right__iff,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2789_dvd__add__right__iff,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( dvd_dvd_rat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2790_dvd__add__right__iff,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2791_dvd__add__right__iff,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2792_dvd__add__left__iff,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ C )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2793_dvd__add__left__iff,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ C )
% 11.11/6.15       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2794_dvd__add__left__iff,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( dvd_dvd_rat @ A @ C )
% 11.11/6.15       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2795_dvd__add__left__iff,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ C )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2796_dvd__add__left__iff,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ C )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2797_dvd__add,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ C )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2798_dvd__add,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_real @ A @ C )
% 11.11/6.15         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2799_dvd__add,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( dvd_dvd_rat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_rat @ A @ C )
% 11.11/6.15         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2800_dvd__add,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ C )
% 11.11/6.15         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2801_dvd__add,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ C )
% 11.11/6.15         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2802_div__div__div__same,axiom,
% 11.11/6.15      ! [D: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ D @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 11.11/6.15            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2803_div__div__div__same,axiom,
% 11.11/6.15      ! [D: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ D @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 11.11/6.15            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2804_div__div__div__same,axiom,
% 11.11/6.15      ! [D: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ D @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2805_dvd__div__eq__cancel,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( ( divide_divide_nat @ A @ C )
% 11.11/6.15          = ( divide_divide_nat @ B @ C ) )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ A )
% 11.11/6.15         => ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15           => ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2806_dvd__div__eq__cancel,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ( divide_divide_int @ A @ C )
% 11.11/6.15          = ( divide_divide_int @ B @ C ) )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ A )
% 11.11/6.15         => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15           => ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2807_dvd__div__eq__cancel,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ( divide_divide_real @ A @ C )
% 11.11/6.15          = ( divide_divide_real @ B @ C ) )
% 11.11/6.15       => ( ( dvd_dvd_real @ C @ A )
% 11.11/6.15         => ( ( dvd_dvd_real @ C @ B )
% 11.11/6.15           => ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2808_dvd__div__eq__cancel,axiom,
% 11.11/6.15      ! [A: complex,C: complex,B: complex] :
% 11.11/6.15        ( ( ( divide1717551699836669952omplex @ A @ C )
% 11.11/6.15          = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.15       => ( ( dvd_dvd_complex @ C @ A )
% 11.11/6.15         => ( ( dvd_dvd_complex @ C @ B )
% 11.11/6.15           => ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2809_dvd__div__eq__cancel,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ( divide6298287555418463151nteger @ A @ C )
% 11.11/6.15          = ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ A )
% 11.11/6.15         => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15           => ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2810_dvd__div__eq__iff,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ A )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15         => ( ( ( divide_divide_nat @ A @ C )
% 11.11/6.15              = ( divide_divide_nat @ B @ C ) )
% 11.11/6.15            = ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2811_dvd__div__eq__iff,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ A )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15         => ( ( ( divide_divide_int @ A @ C )
% 11.11/6.15              = ( divide_divide_int @ B @ C ) )
% 11.11/6.15            = ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2812_dvd__div__eq__iff,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ C @ A )
% 11.11/6.15       => ( ( dvd_dvd_real @ C @ B )
% 11.11/6.15         => ( ( ( divide_divide_real @ A @ C )
% 11.11/6.15              = ( divide_divide_real @ B @ C ) )
% 11.11/6.15            = ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2813_dvd__div__eq__iff,axiom,
% 11.11/6.15      ! [C: complex,A: complex,B: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ C @ A )
% 11.11/6.15       => ( ( dvd_dvd_complex @ C @ B )
% 11.11/6.15         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 11.11/6.15              = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.15            = ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2814_dvd__div__eq__iff,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ A )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 11.11/6.15              = ( divide6298287555418463151nteger @ B @ C ) )
% 11.11/6.15            = ( A = B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2815_dvd__power__same,axiom,
% 11.11/6.15      ! [X4: code_integer,Y: code_integer,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2816_dvd__power__same,axiom,
% 11.11/6.15      ! [X4: nat,Y: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ X4 @ Y )
% 11.11/6.15       => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2817_dvd__power__same,axiom,
% 11.11/6.15      ! [X4: real,Y: real,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_real @ X4 @ Y )
% 11.11/6.15       => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2818_dvd__power__same,axiom,
% 11.11/6.15      ! [X4: int,Y: int,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ X4 @ Y )
% 11.11/6.15       => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2819_dvd__power__same,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_complex @ X4 @ Y )
% 11.11/6.15       => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2820_mult__not__zero,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ( times_times_rat @ A @ B )
% 11.11/6.15         != zero_zero_rat )
% 11.11/6.15       => ( ( A != zero_zero_rat )
% 11.11/6.15          & ( B != zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2821_mult__not__zero,axiom,
% 11.11/6.15      ! [A: complex,B: complex] :
% 11.11/6.15        ( ( ( times_times_complex @ A @ B )
% 11.11/6.15         != zero_zero_complex )
% 11.11/6.15       => ( ( A != zero_zero_complex )
% 11.11/6.15          & ( B != zero_zero_complex ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2822_mult__not__zero,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ( times_times_real @ A @ B )
% 11.11/6.15         != zero_zero_real )
% 11.11/6.15       => ( ( A != zero_zero_real )
% 11.11/6.15          & ( B != zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2823_mult__not__zero,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ A @ B )
% 11.11/6.15         != zero_zero_nat )
% 11.11/6.15       => ( ( A != zero_zero_nat )
% 11.11/6.15          & ( B != zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2824_mult__not__zero,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( times_times_int @ A @ B )
% 11.11/6.15         != zero_zero_int )
% 11.11/6.15       => ( ( A != zero_zero_int )
% 11.11/6.15          & ( B != zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2825_divisors__zero,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ( times_times_rat @ A @ B )
% 11.11/6.15          = zero_zero_rat )
% 11.11/6.15       => ( ( A = zero_zero_rat )
% 11.11/6.15          | ( B = zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2826_divisors__zero,axiom,
% 11.11/6.15      ! [A: complex,B: complex] :
% 11.11/6.15        ( ( ( times_times_complex @ A @ B )
% 11.11/6.15          = zero_zero_complex )
% 11.11/6.15       => ( ( A = zero_zero_complex )
% 11.11/6.15          | ( B = zero_zero_complex ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2827_divisors__zero,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ( times_times_real @ A @ B )
% 11.11/6.15          = zero_zero_real )
% 11.11/6.15       => ( ( A = zero_zero_real )
% 11.11/6.15          | ( B = zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2828_divisors__zero,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ A @ B )
% 11.11/6.15          = zero_zero_nat )
% 11.11/6.15       => ( ( A = zero_zero_nat )
% 11.11/6.15          | ( B = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2829_divisors__zero,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( times_times_int @ A @ B )
% 11.11/6.15          = zero_zero_int )
% 11.11/6.15       => ( ( A = zero_zero_int )
% 11.11/6.15          | ( B = zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2830_no__zero__divisors,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( A != zero_zero_rat )
% 11.11/6.15       => ( ( B != zero_zero_rat )
% 11.11/6.15         => ( ( times_times_rat @ A @ B )
% 11.11/6.15           != zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2831_no__zero__divisors,axiom,
% 11.11/6.15      ! [A: complex,B: complex] :
% 11.11/6.15        ( ( A != zero_zero_complex )
% 11.11/6.15       => ( ( B != zero_zero_complex )
% 11.11/6.15         => ( ( times_times_complex @ A @ B )
% 11.11/6.15           != zero_zero_complex ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2832_no__zero__divisors,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( A != zero_zero_real )
% 11.11/6.15       => ( ( B != zero_zero_real )
% 11.11/6.15         => ( ( times_times_real @ A @ B )
% 11.11/6.15           != zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2833_no__zero__divisors,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ( ( B != zero_zero_nat )
% 11.11/6.15         => ( ( times_times_nat @ A @ B )
% 11.11/6.15           != zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2834_no__zero__divisors,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( A != zero_zero_int )
% 11.11/6.15       => ( ( B != zero_zero_int )
% 11.11/6.15         => ( ( times_times_int @ A @ B )
% 11.11/6.15           != zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2835_mult__left__cancel,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( ( times_times_rat @ C @ A )
% 11.11/6.15            = ( times_times_rat @ C @ B ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2836_mult__left__cancel,axiom,
% 11.11/6.15      ! [C: complex,A: complex,B: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( ( times_times_complex @ C @ A )
% 11.11/6.15            = ( times_times_complex @ C @ B ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2837_mult__left__cancel,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( ( times_times_real @ C @ A )
% 11.11/6.15            = ( times_times_real @ C @ B ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2838_mult__left__cancel,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( C != zero_zero_nat )
% 11.11/6.15       => ( ( ( times_times_nat @ C @ A )
% 11.11/6.15            = ( times_times_nat @ C @ B ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2839_mult__left__cancel,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( C != zero_zero_int )
% 11.11/6.15       => ( ( ( times_times_int @ C @ A )
% 11.11/6.15            = ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2840_mult__right__cancel,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( ( times_times_rat @ A @ C )
% 11.11/6.15            = ( times_times_rat @ B @ C ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2841_mult__right__cancel,axiom,
% 11.11/6.15      ! [C: complex,A: complex,B: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( ( times_times_complex @ A @ C )
% 11.11/6.15            = ( times_times_complex @ B @ C ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2842_mult__right__cancel,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( ( times_times_real @ A @ C )
% 11.11/6.15            = ( times_times_real @ B @ C ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2843_mult__right__cancel,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( C != zero_zero_nat )
% 11.11/6.15       => ( ( ( times_times_nat @ A @ C )
% 11.11/6.15            = ( times_times_nat @ B @ C ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2844_mult__right__cancel,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( C != zero_zero_int )
% 11.11/6.15       => ( ( ( times_times_int @ A @ C )
% 11.11/6.15            = ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( A = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2845_mult_Ocomm__neutral,axiom,
% 11.11/6.15      ! [A: rat] :
% 11.11/6.15        ( ( times_times_rat @ A @ one_one_rat )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2846_mult_Ocomm__neutral,axiom,
% 11.11/6.15      ! [A: complex] :
% 11.11/6.15        ( ( times_times_complex @ A @ one_one_complex )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2847_mult_Ocomm__neutral,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ( ( times_times_real @ A @ one_one_real )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2848_mult_Ocomm__neutral,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( times_times_nat @ A @ one_one_nat )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2849_mult_Ocomm__neutral,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( times_times_int @ A @ one_one_int )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2850_comm__monoid__mult__class_Omult__1,axiom,
% 11.11/6.15      ! [A: rat] :
% 11.11/6.15        ( ( times_times_rat @ one_one_rat @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2851_comm__monoid__mult__class_Omult__1,axiom,
% 11.11/6.15      ! [A: complex] :
% 11.11/6.15        ( ( times_times_complex @ one_one_complex @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2852_comm__monoid__mult__class_Omult__1,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ( ( times_times_real @ one_one_real @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2853_comm__monoid__mult__class_Omult__1,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( times_times_nat @ one_one_nat @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2854_comm__monoid__mult__class_Omult__1,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( times_times_int @ one_one_int @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2855_combine__common__factor,axiom,
% 11.11/6.15      ! [A: rat,E2: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2856_combine__common__factor,axiom,
% 11.11/6.15      ! [A: complex,E2: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ C ) )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E2 ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2857_combine__common__factor,axiom,
% 11.11/6.15      ! [A: real,E2: real,B: real,C: real] :
% 11.11/6.15        ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2858_combine__common__factor,axiom,
% 11.11/6.15      ! [A: nat,E2: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2859_combine__common__factor,axiom,
% 11.11/6.15      ! [A: int,E2: int,B: int,C: int] :
% 11.11/6.15        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2860_distrib__right,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2861_distrib__right,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2862_distrib__right,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2863_distrib__right,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2864_distrib__right,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2865_distrib__left,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2866_distrib__left,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2867_distrib__left,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2868_distrib__left,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2869_distrib__left,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2870_comm__semiring__class_Odistrib,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2871_comm__semiring__class_Odistrib,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2872_comm__semiring__class_Odistrib,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2873_comm__semiring__class_Odistrib,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2874_comm__semiring__class_Odistrib,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2875_ring__class_Oring__distribs_I1_J,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2876_ring__class_Oring__distribs_I1_J,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2877_ring__class_Oring__distribs_I1_J,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2878_ring__class_Oring__distribs_I1_J,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2879_ring__class_Oring__distribs_I2_J,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2880_ring__class_Oring__distribs_I2_J,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2881_ring__class_Oring__distribs_I2_J,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2882_ring__class_Oring__distribs_I2_J,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2883_dvd__mod,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ K @ M )
% 11.11/6.15       => ( ( dvd_dvd_nat @ K @ N2 )
% 11.11/6.15         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2884_dvd__mod,axiom,
% 11.11/6.15      ! [K: int,M: int,N2: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ K @ M )
% 11.11/6.15       => ( ( dvd_dvd_int @ K @ N2 )
% 11.11/6.15         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2885_dvd__mod,axiom,
% 11.11/6.15      ! [K: code_integer,M: code_integer,N2: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ K @ M )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2886_mod__mod__cancel,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 11.11/6.15          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2887_mod__mod__cancel,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 11.11/6.15          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2888_mod__mod__cancel,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 11.11/6.15          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2889_dvd__mod__iff,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.15          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2890_dvd__mod__iff,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.15          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2891_dvd__mod__iff,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2892_dvd__mod__imp__dvd,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.15       => ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2893_dvd__mod__imp__dvd,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.15       => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2894_dvd__mod__imp__dvd,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2895_divide__divide__eq__left_H,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 11.11/6.15        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2896_divide__divide__eq__left_H,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 11.11/6.15        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2897_divide__divide__times__eq,axiom,
% 11.11/6.15      ! [X4: real,Y: real,Z: real,W: real] :
% 11.11/6.15        ( ( divide_divide_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 11.11/6.15        = ( divide_divide_real @ ( times_times_real @ X4 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2898_divide__divide__times__eq,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 11.11/6.15        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 11.11/6.15        = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2899_times__divide__times__eq,axiom,
% 11.11/6.15      ! [X4: real,Y: real,Z: real,W: real] :
% 11.11/6.15        ( ( times_times_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 11.11/6.15        = ( divide_divide_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2900_times__divide__times__eq,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 11.11/6.15        = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2901_power__commuting__commutes,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,N2: nat] :
% 11.11/6.15        ( ( ( times_times_complex @ X4 @ Y )
% 11.11/6.15          = ( times_times_complex @ Y @ X4 ) )
% 11.11/6.15       => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ Y )
% 11.11/6.15          = ( times_times_complex @ Y @ ( power_power_complex @ X4 @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2902_power__commuting__commutes,axiom,
% 11.11/6.15      ! [X4: real,Y: real,N2: nat] :
% 11.11/6.15        ( ( ( times_times_real @ X4 @ Y )
% 11.11/6.15          = ( times_times_real @ Y @ X4 ) )
% 11.11/6.15       => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ Y )
% 11.11/6.15          = ( times_times_real @ Y @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2903_power__commuting__commutes,axiom,
% 11.11/6.15      ! [X4: nat,Y: nat,N2: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ X4 @ Y )
% 11.11/6.15          = ( times_times_nat @ Y @ X4 ) )
% 11.11/6.15       => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ Y )
% 11.11/6.15          = ( times_times_nat @ Y @ ( power_power_nat @ X4 @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2904_power__commuting__commutes,axiom,
% 11.11/6.15      ! [X4: int,Y: int,N2: nat] :
% 11.11/6.15        ( ( ( times_times_int @ X4 @ Y )
% 11.11/6.15          = ( times_times_int @ Y @ X4 ) )
% 11.11/6.15       => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ Y )
% 11.11/6.15          = ( times_times_int @ Y @ ( power_power_int @ X4 @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2905_power__mult__distrib,axiom,
% 11.11/6.15      ! [A: complex,B: complex,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 11.11/6.15        = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2906_power__mult__distrib,axiom,
% 11.11/6.15      ! [A: real,B: real,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 11.11/6.15        = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2907_power__mult__distrib,axiom,
% 11.11/6.15      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 11.11/6.15        = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2908_power__mult__distrib,axiom,
% 11.11/6.15      ! [A: int,B: int,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 11.11/6.15        = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2909_power__commutes,axiom,
% 11.11/6.15      ! [A: complex,N2: nat] :
% 11.11/6.15        ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 11.11/6.15        = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2910_power__commutes,axiom,
% 11.11/6.15      ! [A: real,N2: nat] :
% 11.11/6.15        ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 11.11/6.15        = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2911_power__commutes,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 11.11/6.15        = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2912_power__commutes,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 11.11/6.15        = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2913_Suc__mult__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 11.11/6.15          = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 11.11/6.15        = ( M = N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2914_power__mult,axiom,
% 11.11/6.15      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.15        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2915_power__mult,axiom,
% 11.11/6.15      ! [A: real,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.15        = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2916_power__mult,axiom,
% 11.11/6.15      ! [A: int,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.15        = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2917_power__mult,axiom,
% 11.11/6.15      ! [A: complex,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.15        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2918_fold__atLeastAtMost__nat_Ocases,axiom,
% 11.11/6.15      ! [X4: produc3368934014287244435at_num] :
% 11.11/6.15        ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 11.11/6.15            ( X4
% 11.11/6.15           != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2919_fold__atLeastAtMost__nat_Ocases,axiom,
% 11.11/6.15      ! [X4: produc4471711990508489141at_nat] :
% 11.11/6.15        ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 11.11/6.15            ( X4
% 11.11/6.15           != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2920_mult__0,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ zero_zero_nat @ N2 )
% 11.11/6.15        = zero_zero_nat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2921_nat__mult__eq__cancel__disj,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ K @ M )
% 11.11/6.15          = ( times_times_nat @ K @ N2 ) )
% 11.11/6.15        = ( ( K = zero_zero_nat )
% 11.11/6.15          | ( M = N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2922_mult__le__mono2,axiom,
% 11.11/6.15      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.15       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2923_mult__le__mono1,axiom,
% 11.11/6.15      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.15       => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2924_mult__le__mono,axiom,
% 11.11/6.15      ! [I2: nat,J: nat,K: nat,L: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.15       => ( ( ord_less_eq_nat @ K @ L )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2925_le__square,axiom,
% 11.11/6.15      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2926_le__cube,axiom,
% 11.11/6.15      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2927_mod__mult__eq,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2928_mod__mult__eq,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2929_mod__mult__eq,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2930_mod__mult__cong,axiom,
% 11.11/6.15      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 11.11/6.15        ( ( ( modulo_modulo_nat @ A @ C )
% 11.11/6.15          = ( modulo_modulo_nat @ A4 @ C ) )
% 11.11/6.15       => ( ( ( modulo_modulo_nat @ B @ C )
% 11.11/6.15            = ( modulo_modulo_nat @ B4 @ C ) )
% 11.11/6.15         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.15            = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2931_mod__mult__cong,axiom,
% 11.11/6.15      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ A @ C )
% 11.11/6.15          = ( modulo_modulo_int @ A4 @ C ) )
% 11.11/6.15       => ( ( ( modulo_modulo_int @ B @ C )
% 11.11/6.15            = ( modulo_modulo_int @ B4 @ C ) )
% 11.11/6.15         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.15            = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2932_mod__mult__cong,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 11.11/6.15        ( ( ( modulo364778990260209775nteger @ A @ C )
% 11.11/6.15          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 11.11/6.15       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 11.11/6.15            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 11.11/6.15         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.15            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2933_mod__mult__mult2,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 11.11/6.15        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2934_mod__mult__mult2,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2935_mod__mult__mult2,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2936_mult__mod__right,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.15        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2937_mult__mod__right,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.15        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2938_mult__mod__right,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.15        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2939_mod__mult__left__eq,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 11.11/6.15        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2940_mod__mult__left__eq,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 11.11/6.15        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2941_mod__mult__left__eq,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 11.11/6.15        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2942_mod__mult__right__eq,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2943_mod__mult__right__eq,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2944_mod__mult__right__eq,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.15        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2945_left__add__mult__distrib,axiom,
% 11.11/6.15      ! [I2: nat,U: nat,J: nat,K: nat] :
% 11.11/6.15        ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2946_add__mult__distrib2,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2947_add__mult__distrib,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 11.11/6.15        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2948_nat__mult__1__right,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ N2 @ one_one_nat )
% 11.11/6.15        = N2 ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2949_nat__mult__1,axiom,
% 11.11/6.15      ! [N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ one_one_nat @ N2 )
% 11.11/6.15        = N2 ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2950_div__mult2__eq,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.15        ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 11.11/6.15        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2951_div__mod__decomp__int,axiom,
% 11.11/6.15      ! [A2: int,N2: int] :
% 11.11/6.15        ( A2
% 11.11/6.15        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2952_split__zdiv,axiom,
% 11.11/6.15      ! [P: int > $o,N2: int,K: int] :
% 11.11/6.15        ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 11.11/6.15        = ( ( ( K = zero_zero_int )
% 11.11/6.15           => ( P @ zero_zero_int ) )
% 11.11/6.15          & ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.15           => ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 11.11/6.15                  & ( ord_less_int @ J3 @ K )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ I3 ) ) )
% 11.11/6.15          & ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.15           => ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_int @ K @ J3 )
% 11.11/6.15                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ I3 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2953_int__div__neg__eq,axiom,
% 11.11/6.15      ! [A: int,B: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 11.11/6.15         => ( ( ord_less_int @ B @ R3 )
% 11.11/6.15           => ( ( divide_divide_int @ A @ B )
% 11.11/6.15              = Q3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2954_int__div__pos__eq,axiom,
% 11.11/6.15      ! [A: int,B: int,Q3: int,R3: int] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 11.11/6.15         => ( ( ord_less_int @ R3 @ B )
% 11.11/6.15           => ( ( divide_divide_int @ A @ B )
% 11.11/6.15              = Q3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2955_split__neg__lemma,axiom,
% 11.11/6.15      ! [K: int,P: int > int > $o,N2: int] :
% 11.11/6.15        ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.15       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 11.11/6.15          = ( ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_int @ K @ J3 )
% 11.11/6.15                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2956_split__pos__lemma,axiom,
% 11.11/6.15      ! [K: int,P: int > int > $o,N2: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.15       => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 11.11/6.15          = ( ! [I3: int,J3: int] :
% 11.11/6.15                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 11.11/6.15                  & ( ord_less_int @ J3 @ K )
% 11.11/6.15                  & ( N2
% 11.11/6.15                    = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 11.11/6.15               => ( P @ I3 @ J3 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2957_zdiv__zmult2__eq,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2958_zmod__zmult2__eq,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2959_dvd__pos__nat,axiom,
% 11.11/6.15      ! [N2: nat,M: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.15       => ( ( dvd_dvd_nat @ M @ N2 )
% 11.11/6.15         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2960_enat__0__less__mult__iff,axiom,
% 11.11/6.15      ! [M: extended_enat,N2: extended_enat] :
% 11.11/6.15        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 11.11/6.15        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 11.11/6.15          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2961_is__unit__div__mult__cancel__right,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 11.11/6.15            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2962_is__unit__div__mult__cancel__right,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( A != zero_zero_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 11.11/6.15            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2963_is__unit__div__mult__cancel__right,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2964_is__unit__div__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( A != zero_zero_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 11.11/6.15            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2965_is__unit__div__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( A != zero_zero_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 11.11/6.15            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2966_is__unit__div__mult__cancel__left,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 11.11/6.15            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2967_is__unitE,axiom,
% 11.11/6.15      ! [A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ~ ( ( A != zero_zero_nat )
% 11.11/6.15           => ! [B5: nat] :
% 11.11/6.15                ( ( B5 != zero_zero_nat )
% 11.11/6.15               => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 11.11/6.15                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 11.11/6.15                      = B5 )
% 11.11/6.15                   => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 11.11/6.15                        = A )
% 11.11/6.15                     => ( ( ( times_times_nat @ A @ B5 )
% 11.11/6.15                          = one_one_nat )
% 11.11/6.15                       => ( ( divide_divide_nat @ C @ A )
% 11.11/6.15                         != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2968_is__unitE,axiom,
% 11.11/6.15      ! [A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ~ ( ( A != zero_zero_int )
% 11.11/6.15           => ! [B5: int] :
% 11.11/6.15                ( ( B5 != zero_zero_int )
% 11.11/6.15               => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 11.11/6.15                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 11.11/6.15                      = B5 )
% 11.11/6.15                   => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 11.11/6.15                        = A )
% 11.11/6.15                     => ( ( ( times_times_int @ A @ B5 )
% 11.11/6.15                          = one_one_int )
% 11.11/6.15                       => ( ( divide_divide_int @ C @ A )
% 11.11/6.15                         != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2969_is__unitE,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ~ ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.15           => ! [B5: code_integer] :
% 11.11/6.15                ( ( B5 != zero_z3403309356797280102nteger )
% 11.11/6.15               => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 11.11/6.15                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 11.11/6.15                      = B5 )
% 11.11/6.15                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 11.11/6.15                        = A )
% 11.11/6.15                     => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 11.11/6.15                          = one_one_Code_integer )
% 11.11/6.15                       => ( ( divide6298287555418463151nteger @ C @ A )
% 11.11/6.15                         != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2970_evenE,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: code_integer] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2971_evenE,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: nat] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2972_evenE,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: int] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2973_dvd__mult__cancel2,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 11.11/6.15          = ( N2 = one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2974_dvd__mult__cancel1,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 11.11/6.15          = ( N2 = one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2975_of__bool__odd__eq__mod__2,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( zero_n2687167440665602831ol_nat
% 11.11/6.15          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2976_of__bool__odd__eq__mod__2,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( zero_n2684676970156552555ol_int
% 11.11/6.15          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2977_of__bool__odd__eq__mod__2,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( zero_n356916108424825756nteger
% 11.11/6.15          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.15        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2978_even__two__times__div__two,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2979_even__two__times__div__two,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2980_even__two__times__div__two,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 11.11/6.15          = A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2981_zero__less__eq__of__bool,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2982_zero__less__eq__of__bool,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2983_zero__less__eq__of__bool,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2984_zero__less__eq__of__bool,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2985_zero__less__eq__of__bool,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2986_of__bool__less__eq__one,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2987_of__bool__less__eq__one,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2988_of__bool__less__eq__one,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2989_of__bool__less__eq__one,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2990_of__bool__less__eq__one,axiom,
% 11.11/6.15      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2991_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: complex > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_complex ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2992_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: real > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_real ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2993_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: rat > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_rat ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2994_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: nat > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_nat ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2995_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: int > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_int ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2996_split__of__bool__asm,axiom,
% 11.11/6.15      ! [P: code_integer > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 11.11/6.15        = ( ~ ( ( P2
% 11.11/6.15                & ~ ( P @ one_one_Code_integer ) )
% 11.11/6.15              | ( ~ P2
% 11.11/6.15                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2997_split__of__bool,axiom,
% 11.11/6.15      ! [P: complex > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_complex ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2998_split__of__bool,axiom,
% 11.11/6.15      ! [P: real > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_real ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_2999_split__of__bool,axiom,
% 11.11/6.15      ! [P: rat > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_rat ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3000_split__of__bool,axiom,
% 11.11/6.15      ! [P: nat > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_nat ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_zero_nat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3001_split__of__bool,axiom,
% 11.11/6.15      ! [P: int > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_int ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_zero_int ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3002_split__of__bool,axiom,
% 11.11/6.15      ! [P: code_integer > $o,P2: $o] :
% 11.11/6.15        ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 11.11/6.15        = ( ( P2
% 11.11/6.15           => ( P @ one_one_Code_integer ) )
% 11.11/6.15          & ( ~ P2
% 11.11/6.15           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3003_of__bool__def,axiom,
% 11.11/6.15      ( zero_n1201886186963655149omplex
% 11.11/6.15      = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3004_of__bool__def,axiom,
% 11.11/6.15      ( zero_n3304061248610475627l_real
% 11.11/6.15      = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3005_of__bool__def,axiom,
% 11.11/6.15      ( zero_n2052037380579107095ol_rat
% 11.11/6.15      = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3006_of__bool__def,axiom,
% 11.11/6.15      ( zero_n2687167440665602831ol_nat
% 11.11/6.15      = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3007_of__bool__def,axiom,
% 11.11/6.15      ( zero_n2684676970156552555ol_int
% 11.11/6.15      = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3008_of__bool__def,axiom,
% 11.11/6.15      ( zero_n356916108424825756nteger
% 11.11/6.15      = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3009_not__is__unit__0,axiom,
% 11.11/6.15      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3010_not__is__unit__0,axiom,
% 11.11/6.15      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3011_not__is__unit__0,axiom,
% 11.11/6.15      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3012_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: rat,A: rat] :
% 11.11/6.15        ( ( dvd_dvd_rat @ B @ A )
% 11.11/6.15       => ( ( ( divide_divide_rat @ A @ B )
% 11.11/6.15            = zero_zero_rat )
% 11.11/6.15          = ( A = zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3013_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15       => ( ( ( divide_divide_nat @ A @ B )
% 11.11/6.15            = zero_zero_nat )
% 11.11/6.15          = ( A = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3014_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15       => ( ( ( divide_divide_int @ A @ B )
% 11.11/6.15            = zero_zero_int )
% 11.11/6.15          = ( A = zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3015_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: real,A: real] :
% 11.11/6.15        ( ( dvd_dvd_real @ B @ A )
% 11.11/6.15       => ( ( ( divide_divide_real @ A @ B )
% 11.11/6.15            = zero_zero_real )
% 11.11/6.15          = ( A = zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3016_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: complex,A: complex] :
% 11.11/6.15        ( ( dvd_dvd_complex @ B @ A )
% 11.11/6.15       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 11.11/6.15            = zero_zero_complex )
% 11.11/6.15          = ( A = zero_zero_complex ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3017_dvd__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 11.11/6.15            = zero_z3403309356797280102nteger )
% 11.11/6.15          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3018_dvd__div__unit__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3019_dvd__div__unit__iff,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3020_dvd__div__unit__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3021_div__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3022_div__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3023_div__unit__dvd__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 11.11/6.15          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3024_unit__div__cancel,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( ( divide_divide_nat @ B @ A )
% 11.11/6.15            = ( divide_divide_nat @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3025_unit__div__cancel,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15       => ( ( ( divide_divide_int @ B @ A )
% 11.11/6.15            = ( divide_divide_int @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3026_unit__div__cancel,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 11.11/6.15            = ( divide6298287555418463151nteger @ C @ A ) )
% 11.11/6.15          = ( B = C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3027_div__plus__div__distrib__dvd__right,axiom,
% 11.11/6.15      ! [C: nat,B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ B )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.15          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3028_div__plus__div__distrib__dvd__right,axiom,
% 11.11/6.15      ! [C: int,B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ B )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.15          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3029_div__plus__div__distrib__dvd__right,axiom,
% 11.11/6.15      ! [C: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3030_div__plus__div__distrib__dvd__left,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ C @ A )
% 11.11/6.15       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 11.11/6.15          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3031_div__plus__div__distrib__dvd__left,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ C @ A )
% 11.11/6.15       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 11.11/6.15          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3032_div__plus__div__distrib__dvd__left,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ C @ A )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 11.11/6.15          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3033_div__power,axiom,
% 11.11/6.15      ! [B: nat,A: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ A )
% 11.11/6.15       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 11.11/6.15          = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3034_div__power,axiom,
% 11.11/6.15      ! [B: int,A: int,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.15       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 11.11/6.15          = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3035_div__power,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.15       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3036_mod__0__imp__dvd,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ( modulo_modulo_nat @ A @ B )
% 11.11/6.15          = zero_zero_nat )
% 11.11/6.15       => ( dvd_dvd_nat @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3037_mod__0__imp__dvd,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.15          = zero_zero_int )
% 11.11/6.15       => ( dvd_dvd_int @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3038_mod__0__imp__dvd,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.15          = zero_z3403309356797280102nteger )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3039_dvd__eq__mod__eq__0,axiom,
% 11.11/6.15      ( dvd_dvd_nat
% 11.11/6.15      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.15            ( ( modulo_modulo_nat @ B2 @ A3 )
% 11.11/6.15            = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3040_dvd__eq__mod__eq__0,axiom,
% 11.11/6.15      ( dvd_dvd_int
% 11.11/6.15      = ( ^ [A3: int,B2: int] :
% 11.11/6.15            ( ( modulo_modulo_int @ B2 @ A3 )
% 11.11/6.15            = zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3041_dvd__eq__mod__eq__0,axiom,
% 11.11/6.15      ( dvd_dvd_Code_integer
% 11.11/6.15      = ( ^ [A3: code_integer,B2: code_integer] :
% 11.11/6.15            ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 11.11/6.15            = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3042_mod__eq__0__iff__dvd,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ( modulo_modulo_nat @ A @ B )
% 11.11/6.15          = zero_zero_nat )
% 11.11/6.15        = ( dvd_dvd_nat @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3043_mod__eq__0__iff__dvd,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.15          = zero_zero_int )
% 11.11/6.15        = ( dvd_dvd_int @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3044_mod__eq__0__iff__dvd,axiom,
% 11.11/6.15      ! [A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.15          = zero_z3403309356797280102nteger )
% 11.11/6.15        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3045_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3046_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3047_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3048_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3049_zero__le__mult__iff,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3050_zero__le__mult__iff,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3051_zero__le__mult__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3052_mult__nonneg__nonpos2,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3053_mult__nonneg__nonpos2,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3054_mult__nonneg__nonpos2,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3055_mult__nonneg__nonpos2,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3056_mult__nonpos__nonneg,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3057_mult__nonpos__nonneg,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3058_mult__nonpos__nonneg,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3059_mult__nonpos__nonneg,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3060_mult__nonneg__nonpos,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3061_mult__nonneg__nonpos,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3062_mult__nonneg__nonpos,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3063_mult__nonneg__nonpos,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3064_mult__nonneg__nonneg,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.15         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3065_mult__nonneg__nonneg,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.15         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3066_mult__nonneg__nonneg,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.15         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3067_mult__nonneg__nonneg,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.15         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3068_split__mult__neg__le,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 11.11/6.15          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 11.11/6.15       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3069_split__mult__neg__le,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 11.11/6.15          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 11.11/6.15       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3070_split__mult__neg__le,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 11.11/6.15          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 11.11/6.15            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 11.11/6.15       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3071_split__mult__neg__le,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 11.11/6.15          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 11.11/6.15       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3072_mult__le__0__iff,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 11.11/6.15        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 11.11/6.15          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3073_mult__le__0__iff,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.15        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 11.11/6.15          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3074_mult__le__0__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 11.11/6.15        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 11.11/6.15          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3075_mult__right__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3076_mult__right__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3077_mult__right__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3078_mult__right__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3079_mult__right__mono__neg,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3080_mult__right__mono__neg,axiom,
% 11.11/6.15      ! [B: rat,A: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3081_mult__right__mono__neg,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3082_mult__left__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3083_mult__left__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3084_mult__left__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3085_mult__left__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3086_mult__nonpos__nonpos,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3087_mult__nonpos__nonpos,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3088_mult__nonpos__nonpos,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3089_mult__left__mono__neg,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3090_mult__left__mono__neg,axiom,
% 11.11/6.15      ! [B: rat,A: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3091_mult__left__mono__neg,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.15       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3092_split__mult__pos__le,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 11.11/6.15       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3093_split__mult__pos__le,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 11.11/6.15       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3094_split__mult__pos__le,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 11.11/6.15          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 11.11/6.15       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3095_zero__le__square,axiom,
% 11.11/6.15      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3096_zero__le__square,axiom,
% 11.11/6.15      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3097_zero__le__square,axiom,
% 11.11/6.15      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3098_mult__mono_H,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3099_mult__mono_H,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3100_mult__mono_H,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3101_mult__mono_H,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3102_mult__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.15           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3103_mult__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.15           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3104_mult__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.15           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3105_mult__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3106_mult__neg__neg,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3107_mult__neg__neg,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3108_mult__neg__neg,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3109_not__square__less__zero,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3110_not__square__less__zero,axiom,
% 11.11/6.15      ! [A: rat] :
% 11.11/6.15        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3111_not__square__less__zero,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3112_mult__less__0__iff,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_real @ B @ zero_zero_real ) )
% 11.11/6.15          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3113_mult__less__0__iff,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 11.11/6.15          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3114_mult__less__0__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_int @ B @ zero_zero_int ) )
% 11.11/6.15          | ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3115_mult__neg__pos,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3116_mult__neg__pos,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3117_mult__neg__pos,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ zero_zero_nat )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3118_mult__neg__pos,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3119_mult__pos__neg,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3120_mult__pos__neg,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3121_mult__pos__neg,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3122_mult__pos__neg,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3123_mult__pos__pos,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.15         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3124_mult__pos__pos,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.15         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3125_mult__pos__pos,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.15         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3126_mult__pos__pos,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.15         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3127_mult__pos__neg2,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3128_mult__pos__neg2,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3129_mult__pos__neg2,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3130_mult__pos__neg2,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15       => ( ( ord_less_int @ B @ zero_zero_int )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3131_zero__less__mult__iff,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15            & ( ord_less_real @ zero_zero_real @ B ) )
% 11.11/6.15          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.15            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3132_zero__less__mult__iff,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 11.11/6.15          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3133_zero__less__mult__iff,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15            & ( ord_less_int @ zero_zero_int @ B ) )
% 11.11/6.15          | ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.15            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3134_zero__less__mult__pos,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3135_zero__less__mult__pos,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3136_zero__less__mult__pos,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3137_zero__less__mult__pos,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3138_zero__less__mult__pos2,axiom,
% 11.11/6.15      ! [B: real,A: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3139_zero__less__mult__pos2,axiom,
% 11.11/6.15      ! [B: rat,A: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3140_zero__less__mult__pos2,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3141_zero__less__mult__pos2,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3142_mult__less__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15          = ( ord_less_real @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3143_mult__less__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15          = ( ord_less_rat @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3144_mult__less__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( ord_less_int @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3145_mult__less__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15          = ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3146_mult__less__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15          = ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3147_mult__less__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3148_mult__strict__left__mono__neg,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ B @ A )
% 11.11/6.15       => ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3149_mult__strict__left__mono__neg,axiom,
% 11.11/6.15      ! [B: rat,A: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ B @ A )
% 11.11/6.15       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3150_mult__strict__left__mono__neg,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( ord_less_int @ B @ A )
% 11.11/6.15       => ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3151_mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3152_mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3153_mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3154_mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3155_mult__less__cancel__left__disj,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15            & ( ord_less_real @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15            & ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3156_mult__less__cancel__left__disj,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15            & ( ord_less_rat @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3157_mult__less__cancel__left__disj,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15            & ( ord_less_int @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15            & ( ord_less_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3158_mult__strict__right__mono__neg,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ B @ A )
% 11.11/6.15       => ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3159_mult__strict__right__mono__neg,axiom,
% 11.11/6.15      ! [B: rat,A: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ B @ A )
% 11.11/6.15       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3160_mult__strict__right__mono__neg,axiom,
% 11.11/6.15      ! [B: int,A: int,C: int] :
% 11.11/6.15        ( ( ord_less_int @ B @ A )
% 11.11/6.15       => ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3161_mult__strict__right__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3162_mult__strict__right__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3163_mult__strict__right__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3164_mult__strict__right__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3165_mult__less__cancel__right__disj,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15            & ( ord_less_real @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15            & ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3166_mult__less__cancel__right__disj,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15            & ( ord_less_rat @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3167_mult__less__cancel__right__disj,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15            & ( ord_less_int @ A @ B ) )
% 11.11/6.15          | ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15            & ( ord_less_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3168_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3169_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3170_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3171_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3172_dvd__power__le,axiom,
% 11.11/6.15      ! [X4: code_integer,Y: code_integer,N2: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 11.11/6.15       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3173_dvd__power__le,axiom,
% 11.11/6.15      ! [X4: nat,Y: nat,N2: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ X4 @ Y )
% 11.11/6.15       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.15         => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3174_dvd__power__le,axiom,
% 11.11/6.15      ! [X4: real,Y: real,N2: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_real @ X4 @ Y )
% 11.11/6.15       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.15         => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3175_dvd__power__le,axiom,
% 11.11/6.15      ! [X4: int,Y: int,N2: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ X4 @ Y )
% 11.11/6.15       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.15         => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3176_dvd__power__le,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,N2: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_complex @ X4 @ Y )
% 11.11/6.15       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.15         => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3177_power__le__dvd,axiom,
% 11.11/6.15      ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3178_power__le__dvd,axiom,
% 11.11/6.15      ! [A: nat,N2: nat,B: nat,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3179_power__le__dvd,axiom,
% 11.11/6.15      ! [A: real,N2: nat,B: real,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3180_power__le__dvd,axiom,
% 11.11/6.15      ! [A: int,N2: nat,B: int,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3181_power__le__dvd,axiom,
% 11.11/6.15      ! [A: complex,N2: nat,B: complex,M: nat] :
% 11.11/6.15        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3182_le__imp__power__dvd,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,A: code_integer] :
% 11.11/6.15        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3183_le__imp__power__dvd,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,A: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3184_le__imp__power__dvd,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,A: real] :
% 11.11/6.15        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3185_le__imp__power__dvd,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,A: int] :
% 11.11/6.15        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3186_le__imp__power__dvd,axiom,
% 11.11/6.15      ! [M: nat,N2: nat,A: complex] :
% 11.11/6.15        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.15       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3187_less__1__mult,axiom,
% 11.11/6.15      ! [M: real,N2: real] :
% 11.11/6.15        ( ( ord_less_real @ one_one_real @ M )
% 11.11/6.15       => ( ( ord_less_real @ one_one_real @ N2 )
% 11.11/6.15         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3188_less__1__mult,axiom,
% 11.11/6.15      ! [M: rat,N2: rat] :
% 11.11/6.15        ( ( ord_less_rat @ one_one_rat @ M )
% 11.11/6.15       => ( ( ord_less_rat @ one_one_rat @ N2 )
% 11.11/6.15         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3189_less__1__mult,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ one_one_nat @ M )
% 11.11/6.15       => ( ( ord_less_nat @ one_one_nat @ N2 )
% 11.11/6.15         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3190_less__1__mult,axiom,
% 11.11/6.15      ! [M: int,N2: int] :
% 11.11/6.15        ( ( ord_less_int @ one_one_int @ M )
% 11.11/6.15       => ( ( ord_less_int @ one_one_int @ N2 )
% 11.11/6.15         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3191_nonzero__eq__divide__eq,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide_divide_rat @ B @ C ) )
% 11.11/6.15          = ( ( times_times_rat @ A @ C )
% 11.11/6.15            = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3192_nonzero__eq__divide__eq,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide_divide_real @ B @ C ) )
% 11.11/6.15          = ( ( times_times_real @ A @ C )
% 11.11/6.15            = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3193_nonzero__eq__divide__eq,axiom,
% 11.11/6.15      ! [C: complex,A: complex,B: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( A
% 11.11/6.15            = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.15          = ( ( times_times_complex @ A @ C )
% 11.11/6.15            = B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3194_nonzero__divide__eq__eq,axiom,
% 11.11/6.15      ! [C: rat,B: rat,A: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( ( divide_divide_rat @ B @ C )
% 11.11/6.15            = A )
% 11.11/6.15          = ( B
% 11.11/6.15            = ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3195_nonzero__divide__eq__eq,axiom,
% 11.11/6.15      ! [C: real,B: real,A: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( ( divide_divide_real @ B @ C )
% 11.11/6.15            = A )
% 11.11/6.15          = ( B
% 11.11/6.15            = ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3196_nonzero__divide__eq__eq,axiom,
% 11.11/6.15      ! [C: complex,B: complex,A: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 11.11/6.15            = A )
% 11.11/6.15          = ( B
% 11.11/6.15            = ( times_times_complex @ A @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3197_eq__divide__imp,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( ( times_times_rat @ A @ C )
% 11.11/6.15            = B )
% 11.11/6.15         => ( A
% 11.11/6.15            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3198_eq__divide__imp,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( ( times_times_real @ A @ C )
% 11.11/6.15            = B )
% 11.11/6.15         => ( A
% 11.11/6.15            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3199_eq__divide__imp,axiom,
% 11.11/6.15      ! [C: complex,A: complex,B: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( ( times_times_complex @ A @ C )
% 11.11/6.15            = B )
% 11.11/6.15         => ( A
% 11.11/6.15            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3200_divide__eq__imp,axiom,
% 11.11/6.15      ! [C: rat,B: rat,A: rat] :
% 11.11/6.15        ( ( C != zero_zero_rat )
% 11.11/6.15       => ( ( B
% 11.11/6.15            = ( times_times_rat @ A @ C ) )
% 11.11/6.15         => ( ( divide_divide_rat @ B @ C )
% 11.11/6.15            = A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3201_divide__eq__imp,axiom,
% 11.11/6.15      ! [C: real,B: real,A: real] :
% 11.11/6.15        ( ( C != zero_zero_real )
% 11.11/6.15       => ( ( B
% 11.11/6.15            = ( times_times_real @ A @ C ) )
% 11.11/6.15         => ( ( divide_divide_real @ B @ C )
% 11.11/6.15            = A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3202_divide__eq__imp,axiom,
% 11.11/6.15      ! [C: complex,B: complex,A: complex] :
% 11.11/6.15        ( ( C != zero_zero_complex )
% 11.11/6.15       => ( ( B
% 11.11/6.15            = ( times_times_complex @ A @ C ) )
% 11.11/6.15         => ( ( divide1717551699836669952omplex @ B @ C )
% 11.11/6.15            = A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3203_eq__divide__eq,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide_divide_rat @ B @ C ) )
% 11.11/6.15        = ( ( ( C != zero_zero_rat )
% 11.11/6.15           => ( ( times_times_rat @ A @ C )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( C = zero_zero_rat )
% 11.11/6.15           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3204_eq__divide__eq,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide_divide_real @ B @ C ) )
% 11.11/6.15        = ( ( ( C != zero_zero_real )
% 11.11/6.15           => ( ( times_times_real @ A @ C )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( C = zero_zero_real )
% 11.11/6.15           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3205_eq__divide__eq,axiom,
% 11.11/6.15      ! [A: complex,B: complex,C: complex] :
% 11.11/6.15        ( ( A
% 11.11/6.15          = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.15        = ( ( ( C != zero_zero_complex )
% 11.11/6.15           => ( ( times_times_complex @ A @ C )
% 11.11/6.15              = B ) )
% 11.11/6.15          & ( ( C = zero_zero_complex )
% 11.11/6.15           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3206_divide__eq__eq,axiom,
% 11.11/6.15      ! [B: rat,C: rat,A: rat] :
% 11.11/6.15        ( ( ( divide_divide_rat @ B @ C )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( C != zero_zero_rat )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_rat @ A @ C ) ) )
% 11.11/6.15          & ( ( C = zero_zero_rat )
% 11.11/6.15           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3207_divide__eq__eq,axiom,
% 11.11/6.15      ! [B: real,C: real,A: real] :
% 11.11/6.15        ( ( ( divide_divide_real @ B @ C )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( C != zero_zero_real )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_real @ A @ C ) ) )
% 11.11/6.15          & ( ( C = zero_zero_real )
% 11.11/6.15           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3208_divide__eq__eq,axiom,
% 11.11/6.15      ! [B: complex,C: complex,A: complex] :
% 11.11/6.15        ( ( ( divide1717551699836669952omplex @ B @ C )
% 11.11/6.15          = A )
% 11.11/6.15        = ( ( ( C != zero_zero_complex )
% 11.11/6.15           => ( B
% 11.11/6.15              = ( times_times_complex @ A @ C ) ) )
% 11.11/6.15          & ( ( C = zero_zero_complex )
% 11.11/6.15           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3209_frac__eq__eq,axiom,
% 11.11/6.15      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 11.11/6.15        ( ( Y != zero_zero_rat )
% 11.11/6.15       => ( ( Z != zero_zero_rat )
% 11.11/6.15         => ( ( ( divide_divide_rat @ X4 @ Y )
% 11.11/6.15              = ( divide_divide_rat @ W @ Z ) )
% 11.11/6.15            = ( ( times_times_rat @ X4 @ Z )
% 11.11/6.15              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3210_frac__eq__eq,axiom,
% 11.11/6.15      ! [Y: real,Z: real,X4: real,W: real] :
% 11.11/6.15        ( ( Y != zero_zero_real )
% 11.11/6.15       => ( ( Z != zero_zero_real )
% 11.11/6.15         => ( ( ( divide_divide_real @ X4 @ Y )
% 11.11/6.15              = ( divide_divide_real @ W @ Z ) )
% 11.11/6.15            = ( ( times_times_real @ X4 @ Z )
% 11.11/6.15              = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3211_frac__eq__eq,axiom,
% 11.11/6.15      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 11.11/6.15        ( ( Y != zero_zero_complex )
% 11.11/6.15       => ( ( Z != zero_zero_complex )
% 11.11/6.15         => ( ( ( divide1717551699836669952omplex @ X4 @ Y )
% 11.11/6.15              = ( divide1717551699836669952omplex @ W @ Z ) )
% 11.11/6.15            = ( ( times_times_complex @ X4 @ Z )
% 11.11/6.15              = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3212_mult__numeral__1__right,axiom,
% 11.11/6.15      ! [A: extended_enat] :
% 11.11/6.15        ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3213_mult__numeral__1__right,axiom,
% 11.11/6.15      ! [A: complex] :
% 11.11/6.15        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3214_mult__numeral__1__right,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3215_mult__numeral__1__right,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3216_mult__numeral__1__right,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3217_mult__numeral__1,axiom,
% 11.11/6.15      ! [A: extended_enat] :
% 11.11/6.15        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3218_mult__numeral__1,axiom,
% 11.11/6.15      ! [A: complex] :
% 11.11/6.15        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3219_mult__numeral__1,axiom,
% 11.11/6.15      ! [A: real] :
% 11.11/6.15        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3220_mult__numeral__1,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3221_mult__numeral__1,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 11.11/6.15        = A ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3222_nat__dvd__not__less,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.15       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.15         => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3223_div__mult2__numeral__eq,axiom,
% 11.11/6.15      ! [A: nat,K: num,L: num] :
% 11.11/6.15        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 11.11/6.15        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3224_div__mult2__numeral__eq,axiom,
% 11.11/6.15      ! [A: int,K: num,L: num] :
% 11.11/6.15        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 11.11/6.15        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3225_div__mult2__numeral__eq,axiom,
% 11.11/6.15      ! [A: code_integer,K: num,L: num] :
% 11.11/6.15        ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ L ) )
% 11.11/6.15        = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( times_times_num @ K @ L ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3226_left__right__inverse__power,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat,N2: nat] :
% 11.11/6.15        ( ( ( times_times_rat @ X4 @ Y )
% 11.11/6.15          = one_one_rat )
% 11.11/6.15       => ( ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 11.11/6.15          = one_one_rat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3227_left__right__inverse__power,axiom,
% 11.11/6.15      ! [X4: complex,Y: complex,N2: nat] :
% 11.11/6.15        ( ( ( times_times_complex @ X4 @ Y )
% 11.11/6.15          = one_one_complex )
% 11.11/6.15       => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 11.11/6.15          = one_one_complex ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3228_left__right__inverse__power,axiom,
% 11.11/6.15      ! [X4: real,Y: real,N2: nat] :
% 11.11/6.15        ( ( ( times_times_real @ X4 @ Y )
% 11.11/6.15          = one_one_real )
% 11.11/6.15       => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 11.11/6.15          = one_one_real ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3229_left__right__inverse__power,axiom,
% 11.11/6.15      ! [X4: nat,Y: nat,N2: nat] :
% 11.11/6.15        ( ( ( times_times_nat @ X4 @ Y )
% 11.11/6.15          = one_one_nat )
% 11.11/6.15       => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 11.11/6.15          = one_one_nat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3230_left__right__inverse__power,axiom,
% 11.11/6.15      ! [X4: int,Y: int,N2: nat] :
% 11.11/6.15        ( ( ( times_times_int @ X4 @ Y )
% 11.11/6.15          = one_one_int )
% 11.11/6.15       => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 11.11/6.15          = one_one_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3231_power__Suc,axiom,
% 11.11/6.15      ! [A: complex,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3232_power__Suc,axiom,
% 11.11/6.15      ! [A: real,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3233_power__Suc,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3234_power__Suc,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3235_power__Suc2,axiom,
% 11.11/6.15      ! [A: complex,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3236_power__Suc2,axiom,
% 11.11/6.15      ! [A: real,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3237_power__Suc2,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3238_power__Suc2,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ A @ ( suc @ N2 ) )
% 11.11/6.15        = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3239_mod__eqE,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ( modulo_modulo_int @ A @ C )
% 11.11/6.15          = ( modulo_modulo_int @ B @ C ) )
% 11.11/6.15       => ~ ! [D3: int] :
% 11.11/6.15              ( B
% 11.11/6.15             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3240_mod__eqE,axiom,
% 11.11/6.15      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ( modulo364778990260209775nteger @ A @ C )
% 11.11/6.15          = ( modulo364778990260209775nteger @ B @ C ) )
% 11.11/6.15       => ~ ! [D3: code_integer] :
% 11.11/6.15              ( B
% 11.11/6.15             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3241_Suc__mult__less__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 11.11/6.15        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3242_power__add,axiom,
% 11.11/6.15      ! [A: complex,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.15        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3243_power__add,axiom,
% 11.11/6.15      ! [A: real,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.15        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3244_power__add,axiom,
% 11.11/6.15      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.15        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3245_power__add,axiom,
% 11.11/6.15      ! [A: int,M: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.15        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3246_nat__mult__less__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.15          = ( ord_less_nat @ M @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3247_nat__mult__eq__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15       => ( ( ( times_times_nat @ K @ M )
% 11.11/6.15            = ( times_times_nat @ K @ N2 ) )
% 11.11/6.15          = ( M = N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3248_mult__less__mono2,axiom,
% 11.11/6.15      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.15        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3249_mult__less__mono1,axiom,
% 11.11/6.15      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.15        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.15         => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3250_Suc__mult__le__cancel1,axiom,
% 11.11/6.15      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 11.11/6.15        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3251_mult__Suc,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 11.11/6.15        = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3252_mult__eq__self__implies__10,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( M
% 11.11/6.15          = ( times_times_nat @ M @ N2 ) )
% 11.11/6.15       => ( ( N2 = one_one_nat )
% 11.11/6.15          | ( M = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3253_less__mult__imp__div__less,axiom,
% 11.11/6.15      ! [M: nat,I2: nat,N2: nat] :
% 11.11/6.15        ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 11.11/6.15       => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3254_div__times__less__eq__dividend,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3255_times__div__less__eq__dividend,axiom,
% 11.11/6.15      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3256_mod__eq__0D,axiom,
% 11.11/6.15      ! [M: nat,D: nat] :
% 11.11/6.15        ( ( ( modulo_modulo_nat @ M @ D )
% 11.11/6.15          = zero_zero_nat )
% 11.11/6.15       => ? [Q2: nat] :
% 11.11/6.15            ( M
% 11.11/6.15            = ( times_times_nat @ D @ Q2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3257_nat__mod__eq__iff,axiom,
% 11.11/6.15      ! [X4: nat,N2: nat,Y: nat] :
% 11.11/6.15        ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 11.11/6.15          = ( modulo_modulo_nat @ Y @ N2 ) )
% 11.11/6.15        = ( ? [Q1: nat,Q22: nat] :
% 11.11/6.15              ( ( plus_plus_nat @ X4 @ ( times_times_nat @ N2 @ Q1 ) )
% 11.11/6.15              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3258_bits__induct,axiom,
% 11.11/6.15      ! [P: nat > $o,A: nat] :
% 11.11/6.15        ( ! [A5: nat] :
% 11.11/6.15            ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15              = A5 )
% 11.11/6.15           => ( P @ A5 ) )
% 11.11/6.15       => ( ! [A5: nat,B5: $o] :
% 11.11/6.15              ( ( P @ A5 )
% 11.11/6.15             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.15                  = A5 )
% 11.11/6.15               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 11.11/6.15         => ( P @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3259_bits__induct,axiom,
% 11.11/6.15      ! [P: int > $o,A: int] :
% 11.11/6.15        ( ! [A5: int] :
% 11.11/6.15            ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15              = A5 )
% 11.11/6.15           => ( P @ A5 ) )
% 11.11/6.15       => ( ! [A5: int,B5: $o] :
% 11.11/6.15              ( ( P @ A5 )
% 11.11/6.15             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.15                  = A5 )
% 11.11/6.15               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 11.11/6.15         => ( P @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3260_bits__induct,axiom,
% 11.11/6.15      ! [P: code_integer > $o,A: code_integer] :
% 11.11/6.15        ( ! [A5: code_integer] :
% 11.11/6.15            ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15              = A5 )
% 11.11/6.15           => ( P @ A5 ) )
% 11.11/6.15       => ( ! [A5: code_integer,B5: $o] :
% 11.11/6.15              ( ( P @ A5 )
% 11.11/6.15             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.15                  = A5 )
% 11.11/6.15               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 11.11/6.15         => ( P @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3261_oddE,axiom,
% 11.11/6.15      ! [A: code_integer] :
% 11.11/6.15        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: code_integer] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3262_oddE,axiom,
% 11.11/6.15      ! [A: nat] :
% 11.11/6.15        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: nat] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3263_oddE,axiom,
% 11.11/6.15      ! [A: int] :
% 11.11/6.15        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.15       => ~ ! [B5: int] :
% 11.11/6.15              ( A
% 11.11/6.15             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3264_VEBT__internal_Ovalid_H_Ocases,axiom,
% 11.11/6.15      ! [X4: produc9072475918466114483BT_nat] :
% 11.11/6.15        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 11.11/6.15            ( X4
% 11.11/6.15           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 11.11/6.15       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Deg3: nat] :
% 11.11/6.15              ( X4
% 11.11/6.15             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Deg3 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3265_power__odd__eq,axiom,
% 11.11/6.15      ! [A: complex,N2: nat] :
% 11.11/6.15        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.15        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3266_power__odd__eq,axiom,
% 11.11/6.15      ! [A: real,N2: nat] :
% 11.11/6.15        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.15        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3267_power__odd__eq,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.15        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3268_power__odd__eq,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.15        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3269_exp__mod__exp,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3270_exp__mod__exp,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3271_exp__mod__exp,axiom,
% 11.11/6.15      ! [M: nat,N2: nat] :
% 11.11/6.15        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.15        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3272_unit__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( ( divide_divide_nat @ A @ B )
% 11.11/6.15            = zero_zero_nat )
% 11.11/6.15          = ( A = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3273_unit__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( ( divide_divide_int @ A @ B )
% 11.11/6.15            = zero_zero_int )
% 11.11/6.15          = ( A = zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3274_unit__div__eq__0__iff,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 11.11/6.15            = zero_z3403309356797280102nteger )
% 11.11/6.15          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3275_even__numeral,axiom,
% 11.11/6.15      ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3276_even__numeral,axiom,
% 11.11/6.15      ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3277_even__numeral,axiom,
% 11.11/6.15      ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3278_unit__imp__mod__eq__0,axiom,
% 11.11/6.15      ! [B: nat,A: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 11.11/6.15       => ( ( modulo_modulo_nat @ A @ B )
% 11.11/6.15          = zero_zero_nat ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3279_unit__imp__mod__eq__0,axiom,
% 11.11/6.15      ! [B: int,A: int] :
% 11.11/6.15        ( ( dvd_dvd_int @ B @ one_one_int )
% 11.11/6.15       => ( ( modulo_modulo_int @ A @ B )
% 11.11/6.15          = zero_zero_int ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3280_unit__imp__mod__eq__0,axiom,
% 11.11/6.15      ! [B: code_integer,A: code_integer] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 11.11/6.15       => ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.15          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3281_is__unit__power__iff,axiom,
% 11.11/6.15      ! [A: code_integer,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 11.11/6.15        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 11.11/6.15          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3282_is__unit__power__iff,axiom,
% 11.11/6.15      ! [A: nat,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 11.11/6.15        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 11.11/6.15          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3283_is__unit__power__iff,axiom,
% 11.11/6.15      ! [A: int,N2: nat] :
% 11.11/6.15        ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 11.11/6.15        = ( ( dvd_dvd_int @ A @ one_one_int )
% 11.11/6.15          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3284_mult__le__cancel__left,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15           => ( ord_less_eq_real @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3285_mult__le__cancel__left,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15           => ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3286_mult__le__cancel__left,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15           => ( ord_less_eq_int @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3287_mult__le__cancel__right,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15           => ( ord_less_eq_real @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3288_mult__le__cancel__right,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15           => ( ord_less_eq_rat @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3289_mult__le__cancel__right,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15           => ( ord_less_eq_int @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3290_mult__left__less__imp__less,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3291_mult__left__less__imp__less,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3292_mult__left__less__imp__less,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3293_mult__left__less__imp__less,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3294_mult__strict__mono,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.15           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3295_mult__strict__mono,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.15           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3296_mult__strict__mono,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.15           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3297_mult__strict__mono,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3298_mult__less__cancel__left,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15           => ( ord_less_real @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.15           => ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3299_mult__less__cancel__left,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15           => ( ord_less_rat @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.15           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3300_mult__less__cancel__left,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15           => ( ord_less_int @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.15           => ( ord_less_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3301_mult__right__less__imp__less,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3302_mult__right__less__imp__less,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3303_mult__right__less__imp__less,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3304_mult__right__less__imp__less,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3305_mult__strict__mono_H,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3306_mult__strict__mono_H,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3307_mult__strict__mono_H,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3308_mult__strict__mono_H,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3309_mult__less__cancel__right,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15           => ( ord_less_real @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.15           => ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3310_mult__less__cancel__right,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15           => ( ord_less_rat @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.15           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3311_mult__less__cancel__right,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15           => ( ord_less_int @ A @ B ) )
% 11.11/6.15          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.15           => ( ord_less_int @ B @ A ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3312_mult__le__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3313_mult__le__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3314_mult__le__cancel__left__neg,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3315_mult__le__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3316_mult__le__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3317_mult__le__cancel__left__pos,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3318_mult__left__le__imp__le,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3319_mult__left__le__imp__le,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3320_mult__left__le__imp__le,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3321_mult__left__le__imp__le,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3322_mult__right__le__imp__le,axiom,
% 11.11/6.15      ! [A: real,C: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3323_mult__right__le__imp__le,axiom,
% 11.11/6.15      ! [A: rat,C: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3324_mult__right__le__imp__le,axiom,
% 11.11/6.15      ! [A: nat,C: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3325_mult__right__le__imp__le,axiom,
% 11.11/6.15      ! [A: int,C: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 11.11/6.15       => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3326_mult__le__less__imp__less,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.15           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3327_mult__le__less__imp__less,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.15           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3328_mult__le__less__imp__less,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.15           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3329_mult__le__less__imp__less,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.15           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3330_mult__less__le__imp__less,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15           => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3331_mult__less__le__imp__less,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_rat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3332_mult__less__le__imp__less,axiom,
% 11.11/6.15      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.15        ( ( ord_less_nat @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_nat @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.15             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3333_mult__less__le__imp__less,axiom,
% 11.11/6.15      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.15        ( ( ord_less_int @ A @ B )
% 11.11/6.15       => ( ( ord_less_eq_int @ C @ D )
% 11.11/6.15         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15           => ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.15             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3334_mult__left__le__one__le,axiom,
% 11.11/6.15      ! [X4: real,Y: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.15         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.15           => ( ord_less_eq_real @ ( times_times_real @ Y @ X4 ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3335_mult__left__le__one__le,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.15         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 11.11/6.15           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X4 ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3336_mult__left__le__one__le,axiom,
% 11.11/6.15      ! [X4: int,Y: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.15         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 11.11/6.15           => ( ord_less_eq_int @ ( times_times_int @ Y @ X4 ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3337_mult__right__le__one__le,axiom,
% 11.11/6.15      ! [X4: real,Y: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.15         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.15           => ( ord_less_eq_real @ ( times_times_real @ X4 @ Y ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3338_mult__right__le__one__le,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.15         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 11.11/6.15           => ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Y ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3339_mult__right__le__one__le,axiom,
% 11.11/6.15      ! [X4: int,Y: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.15         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 11.11/6.15           => ( ord_less_eq_int @ ( times_times_int @ X4 @ Y ) @ X4 ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3340_mult__le__one,axiom,
% 11.11/6.15      ! [A: real,B: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.15         => ( ( ord_less_eq_real @ B @ one_one_real )
% 11.11/6.15           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3341_mult__le__one,axiom,
% 11.11/6.15      ! [A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.15         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 11.11/6.15           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3342_mult__le__one,axiom,
% 11.11/6.15      ! [A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 11.11/6.15         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 11.11/6.15           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3343_mult__le__one,axiom,
% 11.11/6.15      ! [A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ A @ one_one_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.15         => ( ( ord_less_eq_int @ B @ one_one_int )
% 11.11/6.15           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3344_mult__left__le,axiom,
% 11.11/6.15      ! [C: real,A: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ C @ one_one_real )
% 11.11/6.15       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.15         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3345_mult__left__le,axiom,
% 11.11/6.15      ! [C: rat,A: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 11.11/6.15       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.15         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3346_mult__left__le,axiom,
% 11.11/6.15      ! [C: nat,A: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 11.11/6.15       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.15         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3347_mult__left__le,axiom,
% 11.11/6.15      ! [C: int,A: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ C @ one_one_int )
% 11.11/6.15       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.15         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3348_sum__squares__ge__zero,axiom,
% 11.11/6.15      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3349_sum__squares__ge__zero,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3350_sum__squares__ge__zero,axiom,
% 11.11/6.15      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3351_sum__squares__le__zero__iff,axiom,
% 11.11/6.15      ! [X4: real,Y: real] :
% 11.11/6.15        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 11.11/6.15        = ( ( X4 = zero_zero_real )
% 11.11/6.15          & ( Y = zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3352_sum__squares__le__zero__iff,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] :
% 11.11/6.15        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 11.11/6.15        = ( ( X4 = zero_zero_rat )
% 11.11/6.15          & ( Y = zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3353_sum__squares__le__zero__iff,axiom,
% 11.11/6.15      ! [X4: int,Y: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 11.11/6.15        = ( ( X4 = zero_zero_int )
% 11.11/6.15          & ( Y = zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3354_not__sum__squares__lt__zero,axiom,
% 11.11/6.15      ! [X4: real,Y: real] :
% 11.11/6.15        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3355_not__sum__squares__lt__zero,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] :
% 11.11/6.15        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3356_not__sum__squares__lt__zero,axiom,
% 11.11/6.15      ! [X4: int,Y: int] :
% 11.11/6.15        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3357_sum__squares__gt__zero__iff,axiom,
% 11.11/6.15      ! [X4: real,Y: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) )
% 11.11/6.15        = ( ( X4 != zero_zero_real )
% 11.11/6.15          | ( Y != zero_zero_real ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3358_sum__squares__gt__zero__iff,axiom,
% 11.11/6.15      ! [X4: rat,Y: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) )
% 11.11/6.15        = ( ( X4 != zero_zero_rat )
% 11.11/6.15          | ( Y != zero_zero_rat ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3359_sum__squares__gt__zero__iff,axiom,
% 11.11/6.15      ! [X4: int,Y: int] :
% 11.11/6.15        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) )
% 11.11/6.15        = ( ( X4 != zero_zero_int )
% 11.11/6.15          | ( Y != zero_zero_int ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3360_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 11.11/6.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.15        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 11.11/6.15       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.15          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3361_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 11.11/6.15      ! [C: nat,A: nat,B: nat] :
% 11.11/6.15        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.15       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.15          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3362_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 11.11/6.15      ! [C: int,A: int,B: int] :
% 11.11/6.15        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.15       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.15          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3363_divide__strict__left__mono__neg,axiom,
% 11.11/6.15      ! [A: rat,B: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ A @ B )
% 11.11/6.15       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.15         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.15           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3364_divide__strict__left__mono__neg,axiom,
% 11.11/6.15      ! [A: real,B: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ A @ B )
% 11.11/6.15       => ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.15         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.15           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3365_divide__strict__left__mono,axiom,
% 11.11/6.15      ! [B: rat,A: rat,C: rat] :
% 11.11/6.15        ( ( ord_less_rat @ B @ A )
% 11.11/6.15       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.15           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3366_divide__strict__left__mono,axiom,
% 11.11/6.15      ! [B: real,A: real,C: real] :
% 11.11/6.15        ( ( ord_less_real @ B @ A )
% 11.11/6.15       => ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.15           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3367_mult__imp__less__div__pos,axiom,
% 11.11/6.15      ! [Y: rat,Z: rat,X4: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.15       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 11.11/6.15         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3368_mult__imp__less__div__pos,axiom,
% 11.11/6.15      ! [Y: real,Z: real,X4: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.15       => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 11.11/6.15         => ( ord_less_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3369_mult__imp__div__pos__less,axiom,
% 11.11/6.15      ! [Y: rat,X4: rat,Z: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.15       => ( ( ord_less_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 11.11/6.15         => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3370_mult__imp__div__pos__less,axiom,
% 11.11/6.15      ! [Y: real,X4: real,Z: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.15       => ( ( ord_less_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 11.11/6.15         => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3371_pos__less__divide__eq,axiom,
% 11.11/6.15      ! [C: rat,A: rat,B: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.15          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3372_pos__less__divide__eq,axiom,
% 11.11/6.15      ! [C: real,A: real,B: real] :
% 11.11/6.15        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.15       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.15          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.15  
% 11.11/6.15  thf(fact_3373_pos__divide__less__eq,axiom,
% 11.11/6.15      ! [C: rat,B: rat,A: rat] :
% 11.11/6.15        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.15       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3374_pos__divide__less__eq,axiom,
% 11.11/6.16      ! [C: real,B: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3375_neg__less__divide__eq,axiom,
% 11.11/6.16      ! [C: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3376_neg__less__divide__eq,axiom,
% 11.11/6.16      ! [C: real,A: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3377_neg__divide__less__eq,axiom,
% 11.11/6.16      ! [C: rat,B: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3378_neg__divide__less__eq,axiom,
% 11.11/6.16      ! [C: real,B: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3379_less__divide__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3380_less__divide__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3381_divide__less__eq,axiom,
% 11.11/6.16      ! [B: rat,C: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3382_divide__less__eq,axiom,
% 11.11/6.16      ! [B: real,C: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3383_eq__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: rat,C: rat] :
% 11.11/6.16        ( ( ( numeral_numeral_rat @ W )
% 11.11/6.16          = ( divide_divide_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( C != zero_zero_rat )
% 11.11/6.16           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 11.11/6.16              = B ) )
% 11.11/6.16          & ( ( C = zero_zero_rat )
% 11.11/6.16           => ( ( numeral_numeral_rat @ W )
% 11.11/6.16              = zero_zero_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3384_eq__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: real,C: real] :
% 11.11/6.16        ( ( ( numeral_numeral_real @ W )
% 11.11/6.16          = ( divide_divide_real @ B @ C ) )
% 11.11/6.16        = ( ( ( C != zero_zero_real )
% 11.11/6.16           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 11.11/6.16              = B ) )
% 11.11/6.16          & ( ( C = zero_zero_real )
% 11.11/6.16           => ( ( numeral_numeral_real @ W )
% 11.11/6.16              = zero_zero_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3385_eq__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: complex,C: complex] :
% 11.11/6.16        ( ( ( numera6690914467698888265omplex @ W )
% 11.11/6.16          = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.16        = ( ( ( C != zero_zero_complex )
% 11.11/6.16           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 11.11/6.16              = B ) )
% 11.11/6.16          & ( ( C = zero_zero_complex )
% 11.11/6.16           => ( ( numera6690914467698888265omplex @ W )
% 11.11/6.16              = zero_zero_complex ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3386_divide__eq__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: rat,C: rat,W: num] :
% 11.11/6.16        ( ( ( divide_divide_rat @ B @ C )
% 11.11/6.16          = ( numeral_numeral_rat @ W ) )
% 11.11/6.16        = ( ( ( C != zero_zero_rat )
% 11.11/6.16           => ( B
% 11.11/6.16              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 11.11/6.16          & ( ( C = zero_zero_rat )
% 11.11/6.16           => ( ( numeral_numeral_rat @ W )
% 11.11/6.16              = zero_zero_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3387_divide__eq__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: real,C: real,W: num] :
% 11.11/6.16        ( ( ( divide_divide_real @ B @ C )
% 11.11/6.16          = ( numeral_numeral_real @ W ) )
% 11.11/6.16        = ( ( ( C != zero_zero_real )
% 11.11/6.16           => ( B
% 11.11/6.16              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 11.11/6.16          & ( ( C = zero_zero_real )
% 11.11/6.16           => ( ( numeral_numeral_real @ W )
% 11.11/6.16              = zero_zero_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3388_divide__eq__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: complex,C: complex,W: num] :
% 11.11/6.16        ( ( ( divide1717551699836669952omplex @ B @ C )
% 11.11/6.16          = ( numera6690914467698888265omplex @ W ) )
% 11.11/6.16        = ( ( ( C != zero_zero_complex )
% 11.11/6.16           => ( B
% 11.11/6.16              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 11.11/6.16          & ( ( C = zero_zero_complex )
% 11.11/6.16           => ( ( numera6690914467698888265omplex @ W )
% 11.11/6.16              = zero_zero_complex ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3389_divide__add__eq__iff,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( Z != zero_zero_rat )
% 11.11/6.16       => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3390_divide__add__eq__iff,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( Z != zero_zero_real )
% 11.11/6.16       => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3391_divide__add__eq__iff,axiom,
% 11.11/6.16      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.16        ( ( Z != zero_zero_complex )
% 11.11/6.16       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3392_add__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( Z != zero_zero_rat )
% 11.11/6.16       => ( ( plus_plus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 11.11/6.16          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3393_add__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( Z != zero_zero_real )
% 11.11/6.16       => ( ( plus_plus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 11.11/6.16          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3394_add__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.16        ( ( Z != zero_zero_complex )
% 11.11/6.16       => ( ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3395_add__num__frac,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) )
% 11.11/6.16          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3396_add__num__frac,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.16          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3397_add__num__frac,axiom,
% 11.11/6.16      ! [Y: complex,Z: complex,X4: complex] :
% 11.11/6.16        ( ( Y != zero_zero_complex )
% 11.11/6.16       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3398_add__frac__num,axiom,
% 11.11/6.16      ! [Y: rat,X4: rat,Z: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z )
% 11.11/6.16          = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3399_add__frac__num,axiom,
% 11.11/6.16      ! [Y: real,X4: real,Z: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ Z )
% 11.11/6.16          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3400_add__frac__num,axiom,
% 11.11/6.16      ! [Y: complex,X4: complex,Z: complex] :
% 11.11/6.16        ( ( Y != zero_zero_complex )
% 11.11/6.16       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ Z )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3401_add__frac__eq,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 11.11/6.16            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3402_add__frac__eq,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real,W: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 11.11/6.16            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3403_add__frac__eq,axiom,
% 11.11/6.16      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 11.11/6.16        ( ( Y != zero_zero_complex )
% 11.11/6.16       => ( ( Z != zero_zero_complex )
% 11.11/6.16         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 11.11/6.16            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3404_add__divide__eq__if__simps_I1_J,axiom,
% 11.11/6.16      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ( Z = zero_zero_rat )
% 11.11/6.16         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 11.11/6.16            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3405_add__divide__eq__if__simps_I1_J,axiom,
% 11.11/6.16      ! [Z: real,A: real,B: real] :
% 11.11/6.16        ( ( ( Z = zero_zero_real )
% 11.11/6.16         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 11.11/6.16            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3406_add__divide__eq__if__simps_I1_J,axiom,
% 11.11/6.16      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.16        ( ( ( Z = zero_zero_complex )
% 11.11/6.16         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_complex )
% 11.11/6.16         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 11.11/6.16            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3407_add__divide__eq__if__simps_I2_J,axiom,
% 11.11/6.16      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ( Z = zero_zero_rat )
% 11.11/6.16         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 11.11/6.16            = B ) )
% 11.11/6.16        & ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 11.11/6.16            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3408_add__divide__eq__if__simps_I2_J,axiom,
% 11.11/6.16      ! [Z: real,A: real,B: real] :
% 11.11/6.16        ( ( ( Z = zero_zero_real )
% 11.11/6.16         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 11.11/6.16            = B ) )
% 11.11/6.16        & ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 11.11/6.16            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3409_add__divide__eq__if__simps_I2_J,axiom,
% 11.11/6.16      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.16        ( ( ( Z = zero_zero_complex )
% 11.11/6.16         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 11.11/6.16            = B ) )
% 11.11/6.16        & ( ( Z != zero_zero_complex )
% 11.11/6.16         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 11.11/6.16            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3410_power__less__power__Suc,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.16       => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3411_power__less__power__Suc,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.16       => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3412_power__less__power__Suc,axiom,
% 11.11/6.16      ! [A: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.16       => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3413_power__less__power__Suc,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.16       => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3414_power__gt1__lemma,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.16       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3415_power__gt1__lemma,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_rat @ one_one_rat @ A )
% 11.11/6.16       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3416_power__gt1__lemma,axiom,
% 11.11/6.16      ! [A: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ one_one_nat @ A )
% 11.11/6.16       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3417_power__gt1__lemma,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_int @ one_one_int @ A )
% 11.11/6.16       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3418_dvd__imp__le,axiom,
% 11.11/6.16      ! [K: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ K @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16         => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3419_mult__div__mod__eq,axiom,
% 11.11/6.16      ! [B: nat,A: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3420_mult__div__mod__eq,axiom,
% 11.11/6.16      ! [B: int,A: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3421_mult__div__mod__eq,axiom,
% 11.11/6.16      ! [B: code_integer,A: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3422_mod__mult__div__eq,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3423_mod__mult__div__eq,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3424_mod__mult__div__eq,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3425_mod__div__mult__eq,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3426_mod__div__mult__eq,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3427_mod__div__mult__eq,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3428_div__mult__mod__eq,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3429_div__mult__mod__eq,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3430_div__mult__mod__eq,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3431_mod__div__decomp,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( A
% 11.11/6.16        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3432_mod__div__decomp,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( A
% 11.11/6.16        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3433_mod__div__decomp,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( A
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3434_cancel__div__mod__rules_I1_J,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_plus_nat @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3435_cancel__div__mod__rules_I1_J,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_plus_int @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3436_cancel__div__mod__rules_I1_J,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3437_cancel__div__mod__rules_I2_J,axiom,
% 11.11/6.16      ! [B: nat,A: nat,C: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_plus_nat @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3438_cancel__div__mod__rules_I2_J,axiom,
% 11.11/6.16      ! [B: int,A: int,C: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_plus_int @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3439_cancel__div__mod__rules_I2_J,axiom,
% 11.11/6.16      ! [B: code_integer,A: code_integer,C: code_integer] :
% 11.11/6.16        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3440_div__mult1__eq,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 11.11/6.16        = ( 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 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3441_div__mult1__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 11.11/6.16        = ( 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 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3442_div__mult1__eq,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.16        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3443_pos__zmod__mult__2,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.16       => ( ( 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 ) )
% 11.11/6.16          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3444_one__less__mult,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 11.11/6.16         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3445_n__less__m__mult__n,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 11.11/6.16         => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3446_n__less__n__mult__m,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 11.11/6.16         => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3447_mod__greater__zero__iff__not__dvd,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.16        = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3448_nat__mult__le__cancel1,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.16       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3449_div__less__iff__less__mult,axiom,
% 11.11/6.16      ! [Q3: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 11.11/6.16       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N2 )
% 11.11/6.16          = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3450_nat__mult__div__cancel1,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.16       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 11.11/6.16          = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3451_mod__eq__nat1E,axiom,
% 11.11/6.16      ! [M: nat,Q3: nat,N2: nat] :
% 11.11/6.16        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 11.11/6.16          = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 11.11/6.16       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16         => ~ ! [S3: nat] :
% 11.11/6.16                ( M
% 11.11/6.16               != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3452_mod__eq__nat2E,axiom,
% 11.11/6.16      ! [M: nat,Q3: nat,N2: nat] :
% 11.11/6.16        ( ( ( modulo_modulo_nat @ M @ Q3 )
% 11.11/6.16          = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 11.11/6.16       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16         => ~ ! [S3: nat] :
% 11.11/6.16                ( N2
% 11.11/6.16               != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3453_nat__mod__eq__lemma,axiom,
% 11.11/6.16      ! [X4: nat,N2: nat,Y: nat] :
% 11.11/6.16        ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 11.11/6.16          = ( modulo_modulo_nat @ Y @ N2 ) )
% 11.11/6.16       => ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.16         => ? [Q2: nat] :
% 11.11/6.16              ( X4
% 11.11/6.16              = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3454_div__mod__decomp,axiom,
% 11.11/6.16      ! [A2: nat,N2: nat] :
% 11.11/6.16        ( A2
% 11.11/6.16        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3455_mod__mult2__eq,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.16        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 11.11/6.16        = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3456_even__zero,axiom,
% 11.11/6.16      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3457_even__zero,axiom,
% 11.11/6.16      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3458_even__zero,axiom,
% 11.11/6.16      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3459_odd__one,axiom,
% 11.11/6.16      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3460_odd__one,axiom,
% 11.11/6.16      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3461_odd__one,axiom,
% 11.11/6.16      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3462_odd__even__add,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 11.11/6.16         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3463_odd__even__add,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.16         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3464_odd__even__add,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 11.11/6.16         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3465_bit__eq__rec,axiom,
% 11.11/6.16      ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: nat,B2: nat] :
% 11.11/6.16            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 11.11/6.16              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 11.11/6.16            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16              = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3466_bit__eq__rec,axiom,
% 11.11/6.16      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: int,B2: int] :
% 11.11/6.16            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 11.11/6.16              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 11.11/6.16            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16              = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3467_bit__eq__rec,axiom,
% 11.11/6.16      ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: code_integer,B2: code_integer] :
% 11.11/6.16            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 11.11/6.16              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 11.11/6.16            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16              = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3468_dvd__power__iff,axiom,
% 11.11/6.16      ! [X4: code_integer,M: nat,N2: nat] :
% 11.11/6.16        ( ( X4 != zero_z3403309356797280102nteger )
% 11.11/6.16       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ M ) @ ( power_8256067586552552935nteger @ X4 @ N2 ) )
% 11.11/6.16          = ( ( dvd_dvd_Code_integer @ X4 @ one_one_Code_integer )
% 11.11/6.16            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3469_dvd__power__iff,axiom,
% 11.11/6.16      ! [X4: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( X4 != zero_zero_nat )
% 11.11/6.16       => ( ( dvd_dvd_nat @ ( power_power_nat @ X4 @ M ) @ ( power_power_nat @ X4 @ N2 ) )
% 11.11/6.16          = ( ( dvd_dvd_nat @ X4 @ one_one_nat )
% 11.11/6.16            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3470_dvd__power__iff,axiom,
% 11.11/6.16      ! [X4: int,M: nat,N2: nat] :
% 11.11/6.16        ( ( X4 != zero_zero_int )
% 11.11/6.16       => ( ( dvd_dvd_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ N2 ) )
% 11.11/6.16          = ( ( dvd_dvd_int @ X4 @ one_one_int )
% 11.11/6.16            | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3471_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: code_integer] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_Code_integer ) )
% 11.11/6.16       => ( dvd_dvd_Code_integer @ X4 @ ( power_8256067586552552935nteger @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3472_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: rat] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_rat ) )
% 11.11/6.16       => ( dvd_dvd_rat @ X4 @ ( power_power_rat @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3473_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: nat] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_nat ) )
% 11.11/6.16       => ( dvd_dvd_nat @ X4 @ ( power_power_nat @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3474_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: real] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_real ) )
% 11.11/6.16       => ( dvd_dvd_real @ X4 @ ( power_power_real @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3475_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: int] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_int ) )
% 11.11/6.16       => ( dvd_dvd_int @ X4 @ ( power_power_int @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3476_dvd__power,axiom,
% 11.11/6.16      ! [N2: nat,X4: complex] :
% 11.11/6.16        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          | ( X4 = one_one_complex ) )
% 11.11/6.16       => ( dvd_dvd_complex @ X4 @ ( power_power_complex @ X4 @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3477_field__le__mult__one__interval,axiom,
% 11.11/6.16      ! [X4: real,Y: real] :
% 11.11/6.16        ( ! [Z2: real] :
% 11.11/6.16            ( ( ord_less_real @ zero_zero_real @ Z2 )
% 11.11/6.16           => ( ( ord_less_real @ Z2 @ one_one_real )
% 11.11/6.16             => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X4 ) @ Y ) ) )
% 11.11/6.16       => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3478_field__le__mult__one__interval,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat] :
% 11.11/6.16        ( ! [Z2: rat] :
% 11.11/6.16            ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 11.11/6.16           => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 11.11/6.16             => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X4 ) @ Y ) ) )
% 11.11/6.16       => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3479_mult__less__cancel__right2,axiom,
% 11.11/6.16      ! [A: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ A @ one_one_real ) )
% 11.11/6.16          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3480_mult__less__cancel__right2,axiom,
% 11.11/6.16      ! [A: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ A @ one_one_rat ) )
% 11.11/6.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3481_mult__less__cancel__right2,axiom,
% 11.11/6.16      ! [A: int,C: int] :
% 11.11/6.16        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_int @ A @ one_one_int ) )
% 11.11/6.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3482_mult__less__cancel__right1,axiom,
% 11.11/6.16      ! [C: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ one_one_real @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3483_mult__less__cancel__right1,axiom,
% 11.11/6.16      ! [C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ one_one_rat @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3484_mult__less__cancel__right1,axiom,
% 11.11/6.16      ! [C: int,B: int] :
% 11.11/6.16        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_int @ one_one_int @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3485_mult__less__cancel__left2,axiom,
% 11.11/6.16      ! [C: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ A @ one_one_real ) )
% 11.11/6.16          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3486_mult__less__cancel__left2,axiom,
% 11.11/6.16      ! [C: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ A @ one_one_rat ) )
% 11.11/6.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3487_mult__less__cancel__left2,axiom,
% 11.11/6.16      ! [C: int,A: int] :
% 11.11/6.16        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_int @ A @ one_one_int ) )
% 11.11/6.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3488_mult__less__cancel__left1,axiom,
% 11.11/6.16      ! [C: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ one_one_real @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3489_mult__less__cancel__left1,axiom,
% 11.11/6.16      ! [C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ one_one_rat @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3490_mult__less__cancel__left1,axiom,
% 11.11/6.16      ! [C: int,B: int] :
% 11.11/6.16        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_int @ one_one_int @ B ) )
% 11.11/6.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3491_mult__le__cancel__right2,axiom,
% 11.11/6.16      ! [A: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ A @ one_one_real ) )
% 11.11/6.16          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3492_mult__le__cancel__right2,axiom,
% 11.11/6.16      ! [A: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 11.11/6.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3493_mult__le__cancel__right2,axiom,
% 11.11/6.16      ! [A: int,C: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 11.11/6.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_eq_int @ A @ one_one_int ) )
% 11.11/6.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3494_mult__le__cancel__right1,axiom,
% 11.11/6.16      ! [C: real,B: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ one_one_real @ B ) )
% 11.11/6.16          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3495_mult__le__cancel__right1,axiom,
% 11.11/6.16      ! [C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 11.11/6.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3496_mult__le__cancel__right1,axiom,
% 11.11/6.16      ! [C: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_eq_int @ one_one_int @ B ) )
% 11.11/6.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3497_mult__le__cancel__left2,axiom,
% 11.11/6.16      ! [C: real,A: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ A @ one_one_real ) )
% 11.11/6.16          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3498_mult__le__cancel__left2,axiom,
% 11.11/6.16      ! [C: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 11.11/6.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3499_mult__le__cancel__left2,axiom,
% 11.11/6.16      ! [C: int,A: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 11.11/6.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_eq_int @ A @ one_one_int ) )
% 11.11/6.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3500_mult__le__cancel__left1,axiom,
% 11.11/6.16      ! [C: real,B: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ one_one_real @ B ) )
% 11.11/6.16          & ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3501_mult__le__cancel__left1,axiom,
% 11.11/6.16      ! [C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 11.11/6.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3502_mult__le__cancel__left1,axiom,
% 11.11/6.16      ! [C: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 11.11/6.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 11.11/6.16           => ( ord_less_eq_int @ one_one_int @ B ) )
% 11.11/6.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 11.11/6.16           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3503_divide__left__mono__neg,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.16         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.16           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3504_divide__left__mono__neg,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 11.11/6.16         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.16           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3505_mult__imp__le__div__pos,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.16       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 11.11/6.16         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3506_mult__imp__le__div__pos,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.16       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 11.11/6.16         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3507_mult__imp__div__pos__le,axiom,
% 11.11/6.16      ! [Y: real,X4: real,Z: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.16       => ( ( ord_less_eq_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 11.11/6.16         => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3508_mult__imp__div__pos__le,axiom,
% 11.11/6.16      ! [Y: rat,X4: rat,Z: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.16       => ( ( ord_less_eq_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 11.11/6.16         => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3509_pos__le__divide__eq,axiom,
% 11.11/6.16      ! [C: real,A: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3510_pos__le__divide__eq,axiom,
% 11.11/6.16      ! [C: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3511_pos__divide__le__eq,axiom,
% 11.11/6.16      ! [C: real,B: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3512_pos__divide__le__eq,axiom,
% 11.11/6.16      ! [C: rat,B: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3513_neg__le__divide__eq,axiom,
% 11.11/6.16      ! [C: real,A: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3514_neg__le__divide__eq,axiom,
% 11.11/6.16      ! [C: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3515_neg__divide__le__eq,axiom,
% 11.11/6.16      ! [C: real,B: real,A: real] :
% 11.11/6.16        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3516_neg__divide__le__eq,axiom,
% 11.11/6.16      ! [C: rat,B: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3517_divide__left__mono,axiom,
% 11.11/6.16      ! [B: real,A: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.16       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.16         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.16           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3518_divide__left__mono,axiom,
% 11.11/6.16      ! [B: rat,A: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.16       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 11.11/6.16         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.16           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3519_le__divide__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3520_le__divide__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3521_divide__le__eq,axiom,
% 11.11/6.16      ! [B: real,C: real,A: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3522_divide__le__eq,axiom,
% 11.11/6.16      ! [B: rat,C: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3523_convex__bound__le,axiom,
% 11.11/6.16      ! [X4: real,A: real,Y: real,U: real,V: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_eq_real @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 11.11/6.16           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 11.11/6.16             => ( ( ( plus_plus_real @ U @ V )
% 11.11/6.16                  = one_one_real )
% 11.11/6.16               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3524_convex__bound__le,axiom,
% 11.11/6.16      ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_eq_rat @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 11.11/6.16           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 11.11/6.16             => ( ( ( plus_plus_rat @ U @ V )
% 11.11/6.16                  = one_one_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3525_convex__bound__le,axiom,
% 11.11/6.16      ! [X4: int,A: int,Y: int,U: int,V: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_eq_int @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 11.11/6.16           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 11.11/6.16             => ( ( ( plus_plus_int @ U @ V )
% 11.11/6.16                  = one_one_int )
% 11.11/6.16               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3526_less__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3527_less__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3528_divide__less__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: rat,C: rat,W: num] :
% 11.11/6.16        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3529_divide__less__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: real,C: real,W: num] :
% 11.11/6.16        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3530_power__Suc__less,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.16       => ( ( ord_less_real @ A @ one_one_real )
% 11.11/6.16         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3531_power__Suc__less,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.16       => ( ( ord_less_rat @ A @ one_one_rat )
% 11.11/6.16         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3532_power__Suc__less,axiom,
% 11.11/6.16      ! [A: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ A )
% 11.11/6.16       => ( ( ord_less_nat @ A @ one_one_nat )
% 11.11/6.16         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3533_power__Suc__less,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.16       => ( ( ord_less_int @ A @ one_one_int )
% 11.11/6.16         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3534_left__add__twice,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.16        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3535_left__add__twice,axiom,
% 11.11/6.16      ! [A: extended_enat,B: extended_enat] :
% 11.11/6.16        ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 11.11/6.16        = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3536_left__add__twice,axiom,
% 11.11/6.16      ! [A: complex,B: complex] :
% 11.11/6.16        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 11.11/6.16        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3537_left__add__twice,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 11.11/6.16        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3538_left__add__twice,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.16        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3539_left__add__twice,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 11.11/6.16        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3540_mult__2__right,axiom,
% 11.11/6.16      ! [Z: rat] :
% 11.11/6.16        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_rat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3541_mult__2__right,axiom,
% 11.11/6.16      ! [Z: extended_enat] :
% 11.11/6.16        ( ( times_7803423173614009249d_enat @ Z @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3542_mult__2__right,axiom,
% 11.11/6.16      ! [Z: complex] :
% 11.11/6.16        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_complex @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3543_mult__2__right,axiom,
% 11.11/6.16      ! [Z: real] :
% 11.11/6.16        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_real @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3544_mult__2__right,axiom,
% 11.11/6.16      ! [Z: nat] :
% 11.11/6.16        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_nat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3545_mult__2__right,axiom,
% 11.11/6.16      ! [Z: int] :
% 11.11/6.16        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_int @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3546_mult__2,axiom,
% 11.11/6.16      ! [Z: rat] :
% 11.11/6.16        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_plus_rat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3547_mult__2,axiom,
% 11.11/6.16      ! [Z: extended_enat] :
% 11.11/6.16        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3548_mult__2,axiom,
% 11.11/6.16      ! [Z: complex] :
% 11.11/6.16        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_plus_complex @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3549_mult__2,axiom,
% 11.11/6.16      ! [Z: real] :
% 11.11/6.16        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_plus_real @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3550_mult__2,axiom,
% 11.11/6.16      ! [Z: nat] :
% 11.11/6.16        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_plus_nat @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3551_mult__2,axiom,
% 11.11/6.16      ! [Z: int] :
% 11.11/6.16        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 11.11/6.16        = ( plus_plus_int @ Z @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3552_power2__eq__square,axiom,
% 11.11/6.16      ! [A: complex] :
% 11.11/6.16        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( times_times_complex @ A @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3553_power2__eq__square,axiom,
% 11.11/6.16      ! [A: real] :
% 11.11/6.16        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( times_times_real @ A @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3554_power2__eq__square,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( times_times_nat @ A @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3555_power2__eq__square,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( times_times_int @ A @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3556_power4__eq__xxxx,axiom,
% 11.11/6.16      ! [X4: complex] :
% 11.11/6.16        ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.16        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3557_power4__eq__xxxx,axiom,
% 11.11/6.16      ! [X4: real] :
% 11.11/6.16        ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.16        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3558_power4__eq__xxxx,axiom,
% 11.11/6.16      ! [X4: nat] :
% 11.11/6.16        ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.16        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3559_power4__eq__xxxx,axiom,
% 11.11/6.16      ! [X4: int] :
% 11.11/6.16        ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.16        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3560_double__not__eq__Suc__double,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 11.11/6.16       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3561_Suc__double__not__eq__double,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3562_power__even__eq,axiom,
% 11.11/6.16      ! [A: nat,N2: nat] :
% 11.11/6.16        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.16        = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3563_power__even__eq,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.16        = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3564_power__even__eq,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.16        = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3565_power__even__eq,axiom,
% 11.11/6.16      ! [A: complex,N2: nat] :
% 11.11/6.16        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.16        = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3566_power__dvd__imp__le,axiom,
% 11.11/6.16      ! [I2: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 11.11/6.16       => ( ( ord_less_nat @ one_one_nat @ I2 )
% 11.11/6.16         => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3567_neg__zdiv__mult__2,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.16       => ( ( 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 ) )
% 11.11/6.16          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3568_pos__zdiv__mult__2,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.16       => ( ( 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 ) )
% 11.11/6.16          = ( divide_divide_int @ B @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3569_div__nat__eqI,axiom,
% 11.11/6.16      ! [N2: nat,Q3: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q3 ) @ M )
% 11.11/6.16       => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q3 ) ) )
% 11.11/6.16         => ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.16            = Q3 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3570_less__eq__div__iff__mult__less__eq,axiom,
% 11.11/6.16      ! [Q3: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 11.11/6.16       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q3 ) )
% 11.11/6.16          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3571_dividend__less__times__div,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3572_dividend__less__div__times,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3573_split__div,axiom,
% 11.11/6.16      ! [P: nat > $o,M: nat,N2: nat] :
% 11.11/6.16        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.16        = ( ( ( N2 = zero_zero_nat )
% 11.11/6.16           => ( P @ zero_zero_nat ) )
% 11.11/6.16          & ( ( N2 != zero_zero_nat )
% 11.11/6.16           => ! [I3: nat,J3: nat] :
% 11.11/6.16                ( ( ord_less_nat @ J3 @ N2 )
% 11.11/6.16               => ( ( M
% 11.11/6.16                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 11.11/6.16                 => ( P @ I3 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3574_split__mod,axiom,
% 11.11/6.16      ! [P: nat > $o,M: nat,N2: nat] :
% 11.11/6.16        ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.16        = ( ( ( N2 = zero_zero_nat )
% 11.11/6.16           => ( P @ M ) )
% 11.11/6.16          & ( ( N2 != zero_zero_nat )
% 11.11/6.16           => ! [I3: nat,J3: nat] :
% 11.11/6.16                ( ( ord_less_nat @ J3 @ N2 )
% 11.11/6.16               => ( ( M
% 11.11/6.16                    = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 11.11/6.16                 => ( P @ J3 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3575_VEBT__internal_Onaive__member_Ocases,axiom,
% 11.11/6.16      ! [X4: produc9072475918466114483BT_nat] :
% 11.11/6.16        ( ! [A5: $o,B5: $o,X5: nat] :
% 11.11/6.16            ( X4
% 11.11/6.16           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 11.11/6.16       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 11.11/6.16              ( X4
% 11.11/6.16             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 11.11/6.16         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 11.11/6.16                ( X4
% 11.11/6.16               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X5 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3576_even__iff__mod__2__eq__zero,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16          = zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3577_even__iff__mod__2__eq__zero,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16          = zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3578_even__iff__mod__2__eq__zero,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3579_odd__iff__mod__2__eq__one,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.16        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16          = one_one_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3580_odd__iff__mod__2__eq__one,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.16        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16          = one_one_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3581_odd__iff__mod__2__eq__one,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.16        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16          = one_one_Code_integer ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3582_power__mono__odd,axiom,
% 11.11/6.16      ! [N2: nat,A: real,B: real] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.16         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3583_power__mono__odd,axiom,
% 11.11/6.16      ! [N2: nat,A: rat,B: rat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.16         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3584_power__mono__odd,axiom,
% 11.11/6.16      ! [N2: nat,A: int,B: int] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_int @ A @ B )
% 11.11/6.16         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3585_convex__bound__lt,axiom,
% 11.11/6.16      ! [X4: real,A: real,Y: real,U: real,V: real] :
% 11.11/6.16        ( ( ord_less_real @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_real @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 11.11/6.16           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 11.11/6.16             => ( ( ( plus_plus_real @ U @ V )
% 11.11/6.16                  = one_one_real )
% 11.11/6.16               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3586_convex__bound__lt,axiom,
% 11.11/6.16      ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_rat @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 11.11/6.16           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 11.11/6.16             => ( ( ( plus_plus_rat @ U @ V )
% 11.11/6.16                  = one_one_rat )
% 11.11/6.16               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3587_convex__bound__lt,axiom,
% 11.11/6.16      ! [X4: int,A: int,Y: int,U: int,V: int] :
% 11.11/6.16        ( ( ord_less_int @ X4 @ A )
% 11.11/6.16       => ( ( ord_less_int @ Y @ A )
% 11.11/6.16         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 11.11/6.16           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 11.11/6.16             => ( ( ( plus_plus_int @ U @ V )
% 11.11/6.16                  = one_one_int )
% 11.11/6.16               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3588_le__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3589_le__divide__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [W: num,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3590_divide__le__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: real,C: real,W: num] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 11.11/6.16        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.16           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.16               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3591_divide__le__eq__numeral_I1_J,axiom,
% 11.11/6.16      ! [B: rat,C: rat,W: num] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 11.11/6.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 11.11/6.16          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.16           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 11.11/6.16              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.16               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3592_odd__pos,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3593_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 11.11/6.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 11.11/6.16       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 11.11/6.16          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3594_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 11.11/6.16      ! [C: nat,A: nat,B: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 11.11/6.16       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 11.11/6.16          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3595_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 11.11/6.16      ! [C: int,A: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 11.11/6.16       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 11.11/6.16          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3596_dvd__power__iff__le,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 11.11/6.16       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3597_num_Osize__gen_I1_J,axiom,
% 11.11/6.16      ( ( size_num @ one )
% 11.11/6.16      = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3598_four__x__squared,axiom,
% 11.11/6.16      ! [X4: real] :
% 11.11/6.16        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.16        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3599_split__div_H,axiom,
% 11.11/6.16      ! [P: nat > $o,M: nat,N2: nat] :
% 11.11/6.16        ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.16        = ( ( ( N2 = zero_zero_nat )
% 11.11/6.16            & ( P @ zero_zero_nat ) )
% 11.11/6.16          | ? [Q5: nat] :
% 11.11/6.16              ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M )
% 11.11/6.16              & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 11.11/6.16              & ( P @ Q5 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3600_Suc__times__mod__eq,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 11.11/6.16       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 11.11/6.16          = one_one_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3601_parity__cases,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16           != zero_zero_nat ) )
% 11.11/6.16       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16             != one_one_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3602_parity__cases,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16           != zero_zero_int ) )
% 11.11/6.16       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16             != one_one_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3603_parity__cases,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16           != zero_z3403309356797280102nteger ) )
% 11.11/6.16       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16             != one_one_Code_integer ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3604_mod2__eq__if,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16            = zero_zero_nat ) )
% 11.11/6.16        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16            = one_one_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3605_mod2__eq__if,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16            = zero_zero_int ) )
% 11.11/6.16        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.16            = one_one_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3606_mod2__eq__if,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16            = zero_z3403309356797280102nteger ) )
% 11.11/6.16        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.16            = one_one_Code_integer ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3607_zero__le__even__power,axiom,
% 11.11/6.16      ! [N2: nat,A: real] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3608_zero__le__even__power,axiom,
% 11.11/6.16      ! [N2: nat,A: rat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3609_zero__le__even__power,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3610_zero__le__odd__power,axiom,
% 11.11/6.16      ! [N2: nat,A: real] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3611_zero__le__odd__power,axiom,
% 11.11/6.16      ! [N2: nat,A: rat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3612_zero__le__odd__power,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3613_zero__le__power__eq,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3614_zero__le__power__eq,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3615_zero__le__power__eq,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3616_divmod__digit__0_I2_J,axiom,
% 11.11/6.16      ! [B: nat,A: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.16       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 11.11/6.16            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3617_divmod__digit__0_I2_J,axiom,
% 11.11/6.16      ! [B: int,A: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.16       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 11.11/6.16            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3618_divmod__digit__0_I2_J,axiom,
% 11.11/6.16      ! [B: code_integer,A: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.16       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 11.11/6.16            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3619_power2__sum,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat] :
% 11.11/6.16        ( ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3620_power2__sum,axiom,
% 11.11/6.16      ! [X4: extended_enat,Y: extended_enat] :
% 11.11/6.16        ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3621_power2__sum,axiom,
% 11.11/6.16      ! [X4: complex,Y: complex] :
% 11.11/6.16        ( ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3622_power2__sum,axiom,
% 11.11/6.16      ! [X4: real,Y: real] :
% 11.11/6.16        ( ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3623_power2__sum,axiom,
% 11.11/6.16      ! [X4: nat,Y: nat] :
% 11.11/6.16        ( ( power_power_nat @ ( plus_plus_nat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3624_power2__sum,axiom,
% 11.11/6.16      ! [X4: int,Y: int] :
% 11.11/6.16        ( ( power_power_int @ ( plus_plus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3625_zero__le__even__power_H,axiom,
% 11.11/6.16      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3626_zero__le__even__power_H,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3627_zero__le__even__power_H,axiom,
% 11.11/6.16      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3628_nat__bit__induct,axiom,
% 11.11/6.16      ! [P: nat > $o,N2: nat] :
% 11.11/6.16        ( ( P @ zero_zero_nat )
% 11.11/6.16       => ( ! [N3: nat] :
% 11.11/6.16              ( ( P @ N3 )
% 11.11/6.16             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.16               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 11.11/6.16         => ( ! [N3: nat] :
% 11.11/6.16                ( ( P @ N3 )
% 11.11/6.16               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 11.11/6.16           => ( P @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3629_L2__set__mult__ineq__lemma,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real,D: 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 @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3630_zero__less__power__eq,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 11.11/6.16        = ( ( N2 = zero_zero_nat )
% 11.11/6.16          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( A != zero_zero_real ) )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3631_zero__less__power__eq,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.16        = ( ( N2 = zero_zero_nat )
% 11.11/6.16          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( A != zero_zero_rat ) )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3632_zero__less__power__eq,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 11.11/6.16        = ( ( N2 = zero_zero_nat )
% 11.11/6.16          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( A != zero_zero_int ) )
% 11.11/6.16          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3633_Euclid__induct,axiom,
% 11.11/6.16      ! [P: nat > nat > $o,A: nat,B: nat] :
% 11.11/6.16        ( ! [A5: nat,B5: nat] :
% 11.11/6.16            ( ( P @ A5 @ B5 )
% 11.11/6.16            = ( P @ B5 @ A5 ) )
% 11.11/6.16       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 11.11/6.16         => ( ! [A5: nat,B5: nat] :
% 11.11/6.16                ( ( P @ A5 @ B5 )
% 11.11/6.16               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 11.11/6.16           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3634_sum__squares__bound,axiom,
% 11.11/6.16      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3635_sum__squares__bound,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3636_divmod__digit__0_I1_J,axiom,
% 11.11/6.16      ! [B: nat,A: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.16       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.16            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3637_divmod__digit__0_I1_J,axiom,
% 11.11/6.16      ! [B: int,A: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.16       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.16            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3638_divmod__digit__0_I1_J,axiom,
% 11.11/6.16      ! [B: code_integer,A: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.16       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.16         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.16            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3639_odd__0__le__power__imp__0__le,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.16       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3640_odd__0__le__power__imp__0__le,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.16       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3641_odd__0__le__power__imp__0__le,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.16       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3642_odd__power__less__zero,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.16       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3643_odd__power__less__zero,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.16       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3644_odd__power__less__zero,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.16       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3645_VEBT__internal_Omembermima_Ocases,axiom,
% 11.11/6.16      ! [X4: produc9072475918466114483BT_nat] :
% 11.11/6.16        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 11.11/6.16            ( X4
% 11.11/6.16           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 11.11/6.16       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 11.11/6.16              ( X4
% 11.11/6.16             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 11.11/6.16         => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 11.11/6.16                ( X4
% 11.11/6.16               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 11.11/6.16           => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT,X5: nat] :
% 11.11/6.16                  ( X4
% 11.11/6.16                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ X5 ) )
% 11.11/6.16             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 11.11/6.16                    ( X4
% 11.11/6.16                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3646_power__le__zero__eq,axiom,
% 11.11/6.16      ! [A: real,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 11.11/6.16        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 11.11/6.16            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( A = zero_zero_real ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3647_power__le__zero__eq,axiom,
% 11.11/6.16      ! [A: rat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 11.11/6.16        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 11.11/6.16            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( A = zero_zero_rat ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3648_power__le__zero__eq,axiom,
% 11.11/6.16      ! [A: int,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 11.11/6.16        = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 11.11/6.16            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16              & ( A = zero_zero_int ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3649_mod__double__modulus,axiom,
% 11.11/6.16      ! [M: code_integer,X4: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 11.11/6.16       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 11.11/6.16         => ( ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( modulo364778990260209775nteger @ X4 @ M ) )
% 11.11/6.16            | ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X4 @ M ) @ M ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3650_mod__double__modulus,axiom,
% 11.11/6.16      ! [M: nat,X4: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.16       => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 11.11/6.16         => ( ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( modulo_modulo_nat @ X4 @ M ) )
% 11.11/6.16            | ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( plus_plus_nat @ ( modulo_modulo_nat @ X4 @ M ) @ M ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3651_mod__double__modulus,axiom,
% 11.11/6.16      ! [M: int,X4: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ M )
% 11.11/6.16       => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.16         => ( ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( modulo_modulo_int @ X4 @ M ) )
% 11.11/6.16            | ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 11.11/6.16              = ( plus_plus_int @ ( modulo_modulo_int @ X4 @ M ) @ M ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3652_option_Osize__gen_I1_J,axiom,
% 11.11/6.16      ! [X4: product_prod_nat_nat > nat] :
% 11.11/6.16        ( ( size_o8335143837870341156at_nat @ X4 @ none_P5556105721700978146at_nat )
% 11.11/6.16        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3653_option_Osize__gen_I1_J,axiom,
% 11.11/6.16      ! [X4: num > nat] :
% 11.11/6.16        ( ( size_option_num @ X4 @ none_num )
% 11.11/6.16        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3654_flip__bit__0,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3655_flip__bit__0,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 11.11/6.16        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3656_flip__bit__0,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 11.11/6.16        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3657_set__bit__0,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3658_set__bit__0,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 11.11/6.16        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3659_set__bit__0,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 11.11/6.16        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3660_even__even__mod__4__iff,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3661_div2__even__ext__nat,axiom,
% 11.11/6.16      ! [X4: nat,Y: nat] :
% 11.11/6.16        ( ( ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16          = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.16       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.16            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 11.11/6.16         => ( X4 = Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3662_unset__bit__0,axiom,
% 11.11/6.16      ! [A: code_integer] :
% 11.11/6.16        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 11.11/6.16        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3663_unset__bit__0,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 11.11/6.16        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3664_unset__bit__0,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 11.11/6.16        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3665_incr__mult__lemma,axiom,
% 11.11/6.16      ! [D: int,P: int > $o,K: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.16       => ( ! [X5: int] :
% 11.11/6.16              ( ( P @ X5 )
% 11.11/6.16             => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 11.11/6.16         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.16           => ! [X2: int] :
% 11.11/6.16                ( ( P @ X2 )
% 11.11/6.16               => ( P @ ( plus_plus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3666_unset__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: code_integer] :
% 11.11/6.16        ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3667_unset__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3668_unset__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: nat] :
% 11.11/6.16        ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3669_flip__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: code_integer] :
% 11.11/6.16        ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3670_flip__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3671_flip__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: nat] :
% 11.11/6.16        ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3672_set__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: code_integer] :
% 11.11/6.16        ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3673_set__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3674_set__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: nat] :
% 11.11/6.16        ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3675_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: code_integer > $o,L: code_integer] :
% 11.11/6.16        ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: code_integer] :
% 11.11/6.16              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3676_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: rat > $o,L: rat] :
% 11.11/6.16        ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: rat] :
% 11.11/6.16              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3677_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: complex > $o,L: complex] :
% 11.11/6.16        ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: complex] :
% 11.11/6.16              ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3678_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: real > $o,L: real] :
% 11.11/6.16        ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: real] :
% 11.11/6.16              ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3679_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: nat > $o,L: nat] :
% 11.11/6.16        ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: nat] :
% 11.11/6.16              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3680_unity__coeff__ex,axiom,
% 11.11/6.16      ! [P: int > $o,L: int] :
% 11.11/6.16        ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 11.11/6.16        = ( ? [X: int] :
% 11.11/6.16              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 11.11/6.16              & ( P @ X ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3681_unset__bit__nonnegative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 11.11/6.16        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3682_set__bit__nonnegative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 11.11/6.16        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3683_flip__bit__nonnegative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 11.11/6.16        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3684_unset__bit__negative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.16        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3685_set__bit__negative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.16        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3686_flip__bit__negative__int__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.16        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3687_unset__bit__less__eq,axiom,
% 11.11/6.16      ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3688_set__bit__greater__eq,axiom,
% 11.11/6.16      ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3689_minf_I7_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_real @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3690_minf_I7_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_rat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3691_minf_I7_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_num @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3692_minf_I7_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_nat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3693_minf_I7_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_int @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3694_minf_I5_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_real @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3695_minf_I5_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_rat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3696_minf_I5_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_num @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3697_minf_I5_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_nat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3698_minf_I5_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_int @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3699_minf_I4_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3700_minf_I4_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3701_minf_I4_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3702_minf_I4_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3703_minf_I4_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3704_minf_I3_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3705_minf_I3_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3706_minf_I3_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3707_minf_I3_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3708_minf_I3_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3709_minf_I2_J,axiom,
% 11.11/6.16      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 11.11/6.16        ( ? [Z3: real] :
% 11.11/6.16          ! [X5: real] :
% 11.11/6.16            ( ( ord_less_real @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: real] :
% 11.11/6.16            ! [X5: real] :
% 11.11/6.16              ( ( ord_less_real @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: real] :
% 11.11/6.16            ! [X2: real] :
% 11.11/6.16              ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3710_minf_I2_J,axiom,
% 11.11/6.16      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 11.11/6.16        ( ? [Z3: rat] :
% 11.11/6.16          ! [X5: rat] :
% 11.11/6.16            ( ( ord_less_rat @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: rat] :
% 11.11/6.16            ! [X5: rat] :
% 11.11/6.16              ( ( ord_less_rat @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: rat] :
% 11.11/6.16            ! [X2: rat] :
% 11.11/6.16              ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3711_minf_I2_J,axiom,
% 11.11/6.16      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 11.11/6.16        ( ? [Z3: num] :
% 11.11/6.16          ! [X5: num] :
% 11.11/6.16            ( ( ord_less_num @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: num] :
% 11.11/6.16            ! [X5: num] :
% 11.11/6.16              ( ( ord_less_num @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: num] :
% 11.11/6.16            ! [X2: num] :
% 11.11/6.16              ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3712_minf_I2_J,axiom,
% 11.11/6.16      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 11.11/6.16        ( ? [Z3: nat] :
% 11.11/6.16          ! [X5: nat] :
% 11.11/6.16            ( ( ord_less_nat @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: nat] :
% 11.11/6.16            ! [X5: nat] :
% 11.11/6.16              ( ( ord_less_nat @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: nat] :
% 11.11/6.16            ! [X2: nat] :
% 11.11/6.16              ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3713_minf_I2_J,axiom,
% 11.11/6.16      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 11.11/6.16        ( ? [Z3: int] :
% 11.11/6.16          ! [X5: int] :
% 11.11/6.16            ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: int] :
% 11.11/6.16            ! [X5: int] :
% 11.11/6.16              ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: int] :
% 11.11/6.16            ! [X2: int] :
% 11.11/6.16              ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3714_minf_I1_J,axiom,
% 11.11/6.16      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 11.11/6.16        ( ? [Z3: real] :
% 11.11/6.16          ! [X5: real] :
% 11.11/6.16            ( ( ord_less_real @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: real] :
% 11.11/6.16            ! [X5: real] :
% 11.11/6.16              ( ( ord_less_real @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: real] :
% 11.11/6.16            ! [X2: real] :
% 11.11/6.16              ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3715_minf_I1_J,axiom,
% 11.11/6.16      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 11.11/6.16        ( ? [Z3: rat] :
% 11.11/6.16          ! [X5: rat] :
% 11.11/6.16            ( ( ord_less_rat @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: rat] :
% 11.11/6.16            ! [X5: rat] :
% 11.11/6.16              ( ( ord_less_rat @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: rat] :
% 11.11/6.16            ! [X2: rat] :
% 11.11/6.16              ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3716_minf_I1_J,axiom,
% 11.11/6.16      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 11.11/6.16        ( ? [Z3: num] :
% 11.11/6.16          ! [X5: num] :
% 11.11/6.16            ( ( ord_less_num @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: num] :
% 11.11/6.16            ! [X5: num] :
% 11.11/6.16              ( ( ord_less_num @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: num] :
% 11.11/6.16            ! [X2: num] :
% 11.11/6.16              ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3717_minf_I1_J,axiom,
% 11.11/6.16      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 11.11/6.16        ( ? [Z3: nat] :
% 11.11/6.16          ! [X5: nat] :
% 11.11/6.16            ( ( ord_less_nat @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: nat] :
% 11.11/6.16            ! [X5: nat] :
% 11.11/6.16              ( ( ord_less_nat @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: nat] :
% 11.11/6.16            ! [X2: nat] :
% 11.11/6.16              ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3718_minf_I1_J,axiom,
% 11.11/6.16      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 11.11/6.16        ( ? [Z3: int] :
% 11.11/6.16          ! [X5: int] :
% 11.11/6.16            ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: int] :
% 11.11/6.16            ! [X5: int] :
% 11.11/6.16              ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: int] :
% 11.11/6.16            ! [X2: int] :
% 11.11/6.16              ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3719_pinf_I7_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_real @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3720_pinf_I7_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_rat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3721_pinf_I7_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_num @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3722_pinf_I7_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_nat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3723_pinf_I7_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_int @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3724_pinf_I5_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_real @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3725_pinf_I5_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_rat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3726_pinf_I5_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_num @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3727_pinf_I5_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_nat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3728_pinf_I5_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_int @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3729_pinf_I4_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3730_pinf_I4_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3731_pinf_I4_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3732_pinf_I4_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3733_pinf_I4_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3734_pinf_I3_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3735_pinf_I3_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3736_pinf_I3_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3737_pinf_I3_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3738_pinf_I3_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( X2 != T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3739_pinf_I2_J,axiom,
% 11.11/6.16      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 11.11/6.16        ( ? [Z3: real] :
% 11.11/6.16          ! [X5: real] :
% 11.11/6.16            ( ( ord_less_real @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: real] :
% 11.11/6.16            ! [X5: real] :
% 11.11/6.16              ( ( ord_less_real @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: real] :
% 11.11/6.16            ! [X2: real] :
% 11.11/6.16              ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3740_pinf_I2_J,axiom,
% 11.11/6.16      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 11.11/6.16        ( ? [Z3: rat] :
% 11.11/6.16          ! [X5: rat] :
% 11.11/6.16            ( ( ord_less_rat @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: rat] :
% 11.11/6.16            ! [X5: rat] :
% 11.11/6.16              ( ( ord_less_rat @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: rat] :
% 11.11/6.16            ! [X2: rat] :
% 11.11/6.16              ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3741_pinf_I2_J,axiom,
% 11.11/6.16      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 11.11/6.16        ( ? [Z3: num] :
% 11.11/6.16          ! [X5: num] :
% 11.11/6.16            ( ( ord_less_num @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: num] :
% 11.11/6.16            ! [X5: num] :
% 11.11/6.16              ( ( ord_less_num @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: num] :
% 11.11/6.16            ! [X2: num] :
% 11.11/6.16              ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3742_pinf_I2_J,axiom,
% 11.11/6.16      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 11.11/6.16        ( ? [Z3: nat] :
% 11.11/6.16          ! [X5: nat] :
% 11.11/6.16            ( ( ord_less_nat @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: nat] :
% 11.11/6.16            ! [X5: nat] :
% 11.11/6.16              ( ( ord_less_nat @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: nat] :
% 11.11/6.16            ! [X2: nat] :
% 11.11/6.16              ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3743_pinf_I2_J,axiom,
% 11.11/6.16      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 11.11/6.16        ( ? [Z3: int] :
% 11.11/6.16          ! [X5: int] :
% 11.11/6.16            ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: int] :
% 11.11/6.16            ! [X5: int] :
% 11.11/6.16              ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: int] :
% 11.11/6.16            ! [X2: int] :
% 11.11/6.16              ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  | ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  | ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3744_pinf_I1_J,axiom,
% 11.11/6.16      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 11.11/6.16        ( ? [Z3: real] :
% 11.11/6.16          ! [X5: real] :
% 11.11/6.16            ( ( ord_less_real @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: real] :
% 11.11/6.16            ! [X5: real] :
% 11.11/6.16              ( ( ord_less_real @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: real] :
% 11.11/6.16            ! [X2: real] :
% 11.11/6.16              ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3745_pinf_I1_J,axiom,
% 11.11/6.16      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 11.11/6.16        ( ? [Z3: rat] :
% 11.11/6.16          ! [X5: rat] :
% 11.11/6.16            ( ( ord_less_rat @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: rat] :
% 11.11/6.16            ! [X5: rat] :
% 11.11/6.16              ( ( ord_less_rat @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: rat] :
% 11.11/6.16            ! [X2: rat] :
% 11.11/6.16              ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3746_pinf_I1_J,axiom,
% 11.11/6.16      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 11.11/6.16        ( ? [Z3: num] :
% 11.11/6.16          ! [X5: num] :
% 11.11/6.16            ( ( ord_less_num @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: num] :
% 11.11/6.16            ! [X5: num] :
% 11.11/6.16              ( ( ord_less_num @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: num] :
% 11.11/6.16            ! [X2: num] :
% 11.11/6.16              ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3747_pinf_I1_J,axiom,
% 11.11/6.16      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 11.11/6.16        ( ? [Z3: nat] :
% 11.11/6.16          ! [X5: nat] :
% 11.11/6.16            ( ( ord_less_nat @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: nat] :
% 11.11/6.16            ! [X5: nat] :
% 11.11/6.16              ( ( ord_less_nat @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: nat] :
% 11.11/6.16            ! [X2: nat] :
% 11.11/6.16              ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3748_pinf_I1_J,axiom,
% 11.11/6.16      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 11.11/6.16        ( ? [Z3: int] :
% 11.11/6.16          ! [X5: int] :
% 11.11/6.16            ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.16           => ( ( P @ X5 )
% 11.11/6.16              = ( P6 @ X5 ) ) )
% 11.11/6.16       => ( ? [Z3: int] :
% 11.11/6.16            ! [X5: int] :
% 11.11/6.16              ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.16             => ( ( Q @ X5 )
% 11.11/6.16                = ( Q6 @ X5 ) ) )
% 11.11/6.16         => ? [Z2: int] :
% 11.11/6.16            ! [X2: int] :
% 11.11/6.16              ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16             => ( ( ( P @ X2 )
% 11.11/6.16                  & ( Q @ X2 ) )
% 11.11/6.16                = ( ( P6 @ X2 )
% 11.11/6.16                  & ( Q6 @ X2 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3749_minf_I8_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3750_minf_I8_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3751_minf_I8_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3752_minf_I8_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3753_minf_I8_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ~ ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3754_minf_I6_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3755_minf_I6_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3756_minf_I6_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3757_minf_I6_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3758_minf_I6_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3759_pinf_I8_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3760_pinf_I8_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3761_pinf_I8_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3762_pinf_I8_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3763_pinf_I8_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3764_pinf_I6_J,axiom,
% 11.11/6.16      ! [T2: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3765_pinf_I6_J,axiom,
% 11.11/6.16      ! [T2: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3766_pinf_I6_J,axiom,
% 11.11/6.16      ! [T2: num] :
% 11.11/6.16      ? [Z2: num] :
% 11.11/6.16      ! [X2: num] :
% 11.11/6.16        ( ( ord_less_num @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3767_pinf_I6_J,axiom,
% 11.11/6.16      ! [T2: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3768_pinf_I6_J,axiom,
% 11.11/6.16      ! [T2: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ~ ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3769_list__decode_Ocases,axiom,
% 11.11/6.16      ! [X4: nat] :
% 11.11/6.16        ( ( X4 != zero_zero_nat )
% 11.11/6.16       => ~ ! [N3: nat] :
% 11.11/6.16              ( X4
% 11.11/6.16             != ( suc @ N3 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3770_imp__le__cong,axiom,
% 11.11/6.16      ! [X4: int,X7: int,P: $o,P6: $o] :
% 11.11/6.16        ( ( X4 = X7 )
% 11.11/6.16       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 11.11/6.16           => ( P = P6 ) )
% 11.11/6.16         => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.16             => P )
% 11.11/6.16            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 11.11/6.16             => P6 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3771_conj__le__cong,axiom,
% 11.11/6.16      ! [X4: int,X7: int,P: $o,P6: $o] :
% 11.11/6.16        ( ( X4 = X7 )
% 11.11/6.16       => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 11.11/6.16           => ( P = P6 ) )
% 11.11/6.16         => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.16              & P )
% 11.11/6.16            = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 11.11/6.16              & P6 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3772_even__set__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          & ( M != zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3773_even__set__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          & ( M != zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3774_even__set__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          & ( M != zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3775_even__flip__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         != ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3776_even__flip__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         != ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3777_even__flip__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16         != ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3778_even__unset__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          | ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3779_even__unset__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          | ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3780_even__unset__bit__iff,axiom,
% 11.11/6.16      ! [M: nat,A: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 11.11/6.16        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.16          | ( M = zero_zero_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3781_minf_I10_J,axiom,
% 11.11/6.16      ! [D: code_integer,S: code_integer] :
% 11.11/6.16      ? [Z2: code_integer] :
% 11.11/6.16      ! [X2: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3782_minf_I10_J,axiom,
% 11.11/6.16      ! [D: real,S: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3783_minf_I10_J,axiom,
% 11.11/6.16      ! [D: rat,S: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3784_minf_I10_J,axiom,
% 11.11/6.16      ! [D: nat,S: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3785_minf_I10_J,axiom,
% 11.11/6.16      ! [D: int,S: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3786_minf_I9_J,axiom,
% 11.11/6.16      ! [D: code_integer,S: code_integer] :
% 11.11/6.16      ? [Z2: code_integer] :
% 11.11/6.16      ! [X2: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 11.11/6.16       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3787_minf_I9_J,axiom,
% 11.11/6.16      ! [D: real,S: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ X2 @ Z2 )
% 11.11/6.16       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3788_minf_I9_J,axiom,
% 11.11/6.16      ! [D: rat,S: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ X2 @ Z2 )
% 11.11/6.16       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3789_minf_I9_J,axiom,
% 11.11/6.16      ! [D: nat,S: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ X2 @ Z2 )
% 11.11/6.16       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3790_minf_I9_J,axiom,
% 11.11/6.16      ! [D: int,S: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ X2 @ Z2 )
% 11.11/6.16       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3791_pinf_I10_J,axiom,
% 11.11/6.16      ! [D: code_integer,S: code_integer] :
% 11.11/6.16      ? [Z2: code_integer] :
% 11.11/6.16      ! [X2: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3792_pinf_I10_J,axiom,
% 11.11/6.16      ! [D: real,S: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3793_pinf_I10_J,axiom,
% 11.11/6.16      ! [D: rat,S: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3794_pinf_I10_J,axiom,
% 11.11/6.16      ! [D: nat,S: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3795_pinf_I10_J,axiom,
% 11.11/6.16      ! [D: int,S: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 11.11/6.16          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3796_pinf_I9_J,axiom,
% 11.11/6.16      ! [D: code_integer,S: code_integer] :
% 11.11/6.16      ? [Z2: code_integer] :
% 11.11/6.16      ! [X2: code_integer] :
% 11.11/6.16        ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 11.11/6.16       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3797_pinf_I9_J,axiom,
% 11.11/6.16      ! [D: real,S: real] :
% 11.11/6.16      ? [Z2: real] :
% 11.11/6.16      ! [X2: real] :
% 11.11/6.16        ( ( ord_less_real @ Z2 @ X2 )
% 11.11/6.16       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3798_pinf_I9_J,axiom,
% 11.11/6.16      ! [D: rat,S: rat] :
% 11.11/6.16      ? [Z2: rat] :
% 11.11/6.16      ! [X2: rat] :
% 11.11/6.16        ( ( ord_less_rat @ Z2 @ X2 )
% 11.11/6.16       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3799_pinf_I9_J,axiom,
% 11.11/6.16      ! [D: nat,S: nat] :
% 11.11/6.16      ? [Z2: nat] :
% 11.11/6.16      ! [X2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ Z2 @ X2 )
% 11.11/6.16       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3800_pinf_I9_J,axiom,
% 11.11/6.16      ! [D: int,S: int] :
% 11.11/6.16      ? [Z2: int] :
% 11.11/6.16      ! [X2: int] :
% 11.11/6.16        ( ( ord_less_int @ Z2 @ X2 )
% 11.11/6.16       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 11.11/6.16          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3801_length__mul__elem,axiom,
% 11.11/6.16      ! [Xs: list_list_VEBT_VEBT,N2: nat] :
% 11.11/6.16        ( ! [X5: list_VEBT_VEBT] :
% 11.11/6.16            ( ( member2936631157270082147T_VEBT @ X5 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 11.11/6.16           => ( ( size_s6755466524823107622T_VEBT @ X5 )
% 11.11/6.16              = N2 ) )
% 11.11/6.16       => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 11.11/6.16          = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3802_length__mul__elem,axiom,
% 11.11/6.16      ! [Xs: list_list_o,N2: nat] :
% 11.11/6.16        ( ! [X5: list_o] :
% 11.11/6.16            ( ( member_list_o @ X5 @ ( set_list_o2 @ Xs ) )
% 11.11/6.16           => ( ( size_size_list_o @ X5 )
% 11.11/6.16              = N2 ) )
% 11.11/6.16       => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 11.11/6.16          = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3803_length__mul__elem,axiom,
% 11.11/6.16      ! [Xs: list_list_nat,N2: nat] :
% 11.11/6.16        ( ! [X5: list_nat] :
% 11.11/6.16            ( ( member_list_nat @ X5 @ ( set_list_nat2 @ Xs ) )
% 11.11/6.16           => ( ( size_size_list_nat @ X5 )
% 11.11/6.16              = N2 ) )
% 11.11/6.16       => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 11.11/6.16          = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3804_length__mul__elem,axiom,
% 11.11/6.16      ! [Xs: list_list_int,N2: nat] :
% 11.11/6.16        ( ! [X5: list_int] :
% 11.11/6.16            ( ( member_list_int @ X5 @ ( set_list_int2 @ Xs ) )
% 11.11/6.16           => ( ( size_size_list_int @ X5 )
% 11.11/6.16              = N2 ) )
% 11.11/6.16       => ( ( size_size_list_int @ ( concat_int @ Xs ) )
% 11.11/6.16          = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3805_mult__le__cancel__iff2,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ Z )
% 11.11/6.16       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X4 ) @ ( times_times_real @ Z @ Y ) )
% 11.11/6.16          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3806_mult__le__cancel__iff2,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 11.11/6.16       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X4 ) @ ( times_times_rat @ Z @ Y ) )
% 11.11/6.16          = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3807_mult__le__cancel__iff2,axiom,
% 11.11/6.16      ! [Z: int,X4: int,Y: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.16       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X4 ) @ ( times_times_int @ Z @ Y ) )
% 11.11/6.16          = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3808_mult__le__cancel__iff1,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ Z )
% 11.11/6.16       => ( ( ord_less_eq_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3809_mult__le__cancel__iff1,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 11.11/6.16       => ( ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3810_mult__le__cancel__iff1,axiom,
% 11.11/6.16      ! [Z: int,X4: int,Y: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.16       => ( ( ord_less_eq_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3811_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_num,Ys: list_num] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3812_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3813_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3814_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3815_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3816_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3817_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3818_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_o,Ys: list_o] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3819_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3820_product__nth,axiom,
% 11.11/6.16      ! [N2: nat,Xs: list_o,Ys: list_int] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 11.11/6.16       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 11.11/6.16          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3821_triangle__def,axiom,
% 11.11/6.16      ( nat_triangle
% 11.11/6.16      = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3822_pos__eucl__rel__int__mult__2,axiom,
% 11.11/6.16      ! [B: int,A: int,Q3: int,R3: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.16       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16         => ( 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 @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3823_length__product,axiom,
% 11.11/6.16      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 11.11/6.16        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3824_length__product,axiom,
% 11.11/6.16      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 11.11/6.16        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3825_length__product,axiom,
% 11.11/6.16      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 11.11/6.16        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3826_length__product,axiom,
% 11.11/6.16      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 11.11/6.16        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3827_length__product,axiom,
% 11.11/6.16      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 11.11/6.16        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3828_length__product,axiom,
% 11.11/6.16      ! [Xs: list_o,Ys: list_o] :
% 11.11/6.16        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3829_length__product,axiom,
% 11.11/6.16      ! [Xs: list_o,Ys: list_nat] :
% 11.11/6.16        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3830_length__product,axiom,
% 11.11/6.16      ! [Xs: list_o,Ys: list_int] :
% 11.11/6.16        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3831_length__product,axiom,
% 11.11/6.16      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 11.11/6.16        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3832_length__product,axiom,
% 11.11/6.16      ! [Xs: list_nat,Ys: list_o] :
% 11.11/6.16        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 11.11/6.16        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3833_triangle__Suc,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( nat_triangle @ ( suc @ N2 ) )
% 11.11/6.16        = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3834_unique__remainder,axiom,
% 11.11/6.16      ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 11.11/6.16        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 11.11/6.16         => ( R3 = R4 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3835_unique__quotient,axiom,
% 11.11/6.16      ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 11.11/6.16        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 11.11/6.16         => ( Q3 = Q4 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3836_eucl__rel__int__by0,axiom,
% 11.11/6.16      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3837_div__int__unique,axiom,
% 11.11/6.16      ! [K: int,L: int,Q3: int,R3: int] :
% 11.11/6.16        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16       => ( ( divide_divide_int @ K @ L )
% 11.11/6.16          = Q3 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3838_mod__int__unique,axiom,
% 11.11/6.16      ! [K: int,L: int,Q3: int,R3: int] :
% 11.11/6.16        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16       => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.16          = R3 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3839_eucl__rel__int__dividesI,axiom,
% 11.11/6.16      ! [L: int,K: int,Q3: int] :
% 11.11/6.16        ( ( L != zero_zero_int )
% 11.11/6.16       => ( ( K
% 11.11/6.16            = ( times_times_int @ Q3 @ L ) )
% 11.11/6.16         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3840_eucl__rel__int,axiom,
% 11.11/6.16      ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3841_eucl__rel__int__iff,axiom,
% 11.11/6.16      ! [K: int,L: int,Q3: int,R3: int] :
% 11.11/6.16        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16        = ( ( K
% 11.11/6.16            = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R3 ) )
% 11.11/6.16          & ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.16           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 11.11/6.16              & ( ord_less_int @ R3 @ L ) ) )
% 11.11/6.16          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.16           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 11.11/6.16               => ( ( ord_less_int @ L @ R3 )
% 11.11/6.16                  & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 11.11/6.16              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 11.11/6.16               => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3842_mult__less__iff1,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ Z )
% 11.11/6.16       => ( ( ord_less_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_real @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3843_mult__less__iff1,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 11.11/6.16       => ( ( ord_less_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_rat @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3844_mult__less__iff1,axiom,
% 11.11/6.16      ! [Z: int,X4: int,Y: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.16       => ( ( ord_less_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 11.11/6.16          = ( ord_less_int @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3845_Divides_Oadjust__div__eq,axiom,
% 11.11/6.16      ! [Q3: int,R3: int] :
% 11.11/6.16        ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16        = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3846_concat__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 11.11/6.16        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3847_neg__eucl__rel__int__mult__2,axiom,
% 11.11/6.16      ! [B: int,A: int,Q3: int,R3: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 11.11/6.16       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.16         => ( 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 @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3848_signed__take__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: code_integer] :
% 11.11/6.16        ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3849_signed__take__bit__Suc,axiom,
% 11.11/6.16      ! [N2: nat,A: int] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 11.11/6.16        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3850_set__decode__Suc,axiom,
% 11.11/6.16      ! [N2: nat,X4: nat] :
% 11.11/6.16        ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X4 ) )
% 11.11/6.16        = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3851_set__decode__0,axiom,
% 11.11/6.16      ! [X4: nat] :
% 11.11/6.16        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X4 ) )
% 11.11/6.16        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3852_add__scale__eq__noteq,axiom,
% 11.11/6.16      ! [R3: rat,A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.16        ( ( R3 != zero_zero_rat )
% 11.11/6.16       => ( ( ( A = B )
% 11.11/6.16            & ( C != D ) )
% 11.11/6.16         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 11.11/6.16           != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3853_add__scale__eq__noteq,axiom,
% 11.11/6.16      ! [R3: complex,A: complex,B: complex,C: complex,D: complex] :
% 11.11/6.16        ( ( R3 != zero_zero_complex )
% 11.11/6.16       => ( ( ( A = B )
% 11.11/6.16            & ( C != D ) )
% 11.11/6.16         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C ) )
% 11.11/6.16           != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3854_add__scale__eq__noteq,axiom,
% 11.11/6.16      ! [R3: real,A: real,B: real,C: real,D: real] :
% 11.11/6.16        ( ( R3 != zero_zero_real )
% 11.11/6.16       => ( ( ( A = B )
% 11.11/6.16            & ( C != D ) )
% 11.11/6.16         => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C ) )
% 11.11/6.16           != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3855_add__scale__eq__noteq,axiom,
% 11.11/6.16      ! [R3: nat,A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.16        ( ( R3 != zero_zero_nat )
% 11.11/6.16       => ( ( ( A = B )
% 11.11/6.16            & ( C != D ) )
% 11.11/6.16         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 11.11/6.16           != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3856_add__scale__eq__noteq,axiom,
% 11.11/6.16      ! [R3: int,A: int,B: int,C: int,D: int] :
% 11.11/6.16        ( ( R3 != zero_zero_int )
% 11.11/6.16       => ( ( ( A = B )
% 11.11/6.16            & ( C != D ) )
% 11.11/6.16         => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 11.11/6.16           != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3857_even__mult__exp__div__exp__iff,axiom,
% 11.11/6.16      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.16        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.16          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            = zero_zero_nat )
% 11.11/6.16          | ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3858_even__mult__exp__div__exp__iff,axiom,
% 11.11/6.16      ! [A: int,M: nat,N2: nat] :
% 11.11/6.16        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.16        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.16          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            = zero_zero_int )
% 11.11/6.16          | ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3859_even__mult__exp__div__exp__iff,axiom,
% 11.11/6.16      ! [A: code_integer,M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.16        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.16          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16            = zero_z3403309356797280102nteger )
% 11.11/6.16          | ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3860_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 11.11/6.16      ! [A: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ A @ A )
% 11.11/6.16        = zero_zero_complex ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3861_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 11.11/6.16      ! [A: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ A )
% 11.11/6.16        = zero_zero_real ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3862_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 11.11/6.16      ! [A: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ A )
% 11.11/6.16        = zero_zero_rat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3863_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ A )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3864_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ A )
% 11.11/6.16        = zero_zero_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3865_diff__zero,axiom,
% 11.11/6.16      ! [A: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3866_diff__zero,axiom,
% 11.11/6.16      ! [A: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ zero_zero_real )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3867_diff__zero,axiom,
% 11.11/6.16      ! [A: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3868_diff__zero,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3869_diff__zero,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ zero_zero_int )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3870_zero__diff,axiom,
% 11.11/6.16      ! [A: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3871_diff__0__right,axiom,
% 11.11/6.16      ! [A: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3872_diff__0__right,axiom,
% 11.11/6.16      ! [A: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ zero_zero_real )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3873_diff__0__right,axiom,
% 11.11/6.16      ! [A: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3874_diff__0__right,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ zero_zero_int )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3875_diff__self,axiom,
% 11.11/6.16      ! [A: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ A @ A )
% 11.11/6.16        = zero_zero_complex ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3876_diff__self,axiom,
% 11.11/6.16      ! [A: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ A )
% 11.11/6.16        = zero_zero_real ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3877_diff__self,axiom,
% 11.11/6.16      ! [A: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ A )
% 11.11/6.16        = zero_zero_rat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3878_diff__self,axiom,
% 11.11/6.16      ! [A: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ A )
% 11.11/6.16        = zero_zero_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3879_add__diff__cancel,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3880_add__diff__cancel,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3881_add__diff__cancel,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3882_diff__add__cancel,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3883_diff__add__cancel,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3884_diff__add__cancel,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3885_add__diff__cancel__left,axiom,
% 11.11/6.16      ! [C: real,A: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 11.11/6.16        = ( minus_minus_real @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3886_add__diff__cancel__left,axiom,
% 11.11/6.16      ! [C: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 11.11/6.16        = ( minus_minus_rat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3887_add__diff__cancel__left,axiom,
% 11.11/6.16      ! [C: nat,A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 11.11/6.16        = ( minus_minus_nat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3888_add__diff__cancel__left,axiom,
% 11.11/6.16      ! [C: int,A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 11.11/6.16        = ( minus_minus_int @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3889_add__diff__cancel__left_H,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 11.11/6.16        = B ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3890_add__diff__cancel__left_H,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 11.11/6.16        = B ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3891_add__diff__cancel__left_H,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 11.11/6.16        = B ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3892_add__diff__cancel__left_H,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 11.11/6.16        = B ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3893_add__diff__cancel__right,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3894_add__diff__cancel__right,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3895_add__diff__cancel__right,axiom,
% 11.11/6.16      ! [A: nat,C: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_nat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3896_add__diff__cancel__right,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3897_add__diff__cancel__right_H,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3898_add__diff__cancel__right_H,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3899_add__diff__cancel__right_H,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3900_add__diff__cancel__right_H,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 11.11/6.16        = A ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3901_minus__mod__self2,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 11.11/6.16        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3902_minus__mod__self2,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 11.11/6.16        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3903_diff__Suc__Suc,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 11.11/6.16        = ( minus_minus_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3904_Suc__diff__diff,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 11.11/6.16        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3905_diff__self__eq__0,axiom,
% 11.11/6.16      ! [M: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ M @ M )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3906_diff__0__eq__0,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3907_diff__diff__cancel,axiom,
% 11.11/6.16      ! [I2: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ I2 @ N2 )
% 11.11/6.16       => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 11.11/6.16          = I2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3908_diff__diff__left,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 11.11/6.16        = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3909_signed__take__bit__of__0,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 11.11/6.16        = zero_zero_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3910_concat__bit__0,axiom,
% 11.11/6.16      ! [K: int,L: int] :
% 11.11/6.16        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 11.11/6.16        = L ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3911_diff__ge__0__iff__ge,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 11.11/6.16        = ( ord_less_eq_real @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3912_diff__ge__0__iff__ge,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.16        = ( ord_less_eq_rat @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3913_diff__ge__0__iff__ge,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 11.11/6.16        = ( ord_less_eq_int @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3914_diff__gt__0__iff__gt,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 11.11/6.16        = ( ord_less_real @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3915_diff__gt__0__iff__gt,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.16        = ( ord_less_rat @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3916_diff__gt__0__iff__gt,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 11.11/6.16        = ( ord_less_int @ B @ A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3917_le__add__diff__inverse2,axiom,
% 11.11/6.16      ! [B: real,A: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.16       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3918_le__add__diff__inverse2,axiom,
% 11.11/6.16      ! [B: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.16       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3919_le__add__diff__inverse2,axiom,
% 11.11/6.16      ! [B: nat,A: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.16       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3920_le__add__diff__inverse2,axiom,
% 11.11/6.16      ! [B: int,A: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.16       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3921_le__add__diff__inverse,axiom,
% 11.11/6.16      ! [B: real,A: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.16       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3922_le__add__diff__inverse,axiom,
% 11.11/6.16      ! [B: rat,A: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.16       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3923_le__add__diff__inverse,axiom,
% 11.11/6.16      ! [B: nat,A: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ B @ A )
% 11.11/6.16       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3924_le__add__diff__inverse,axiom,
% 11.11/6.16      ! [B: int,A: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.16       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3925_diff__numeral__special_I9_J,axiom,
% 11.11/6.16      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 11.11/6.16      = zero_zero_complex ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3926_diff__numeral__special_I9_J,axiom,
% 11.11/6.16      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 11.11/6.16      = zero_zero_real ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3927_diff__numeral__special_I9_J,axiom,
% 11.11/6.16      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 11.11/6.16      = zero_zero_rat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3928_diff__numeral__special_I9_J,axiom,
% 11.11/6.16      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 11.11/6.16      = zero_zero_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3929_diff__add__zero,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3930_right__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [V: num,B: rat,C: rat] :
% 11.11/6.16        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3931_right__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [V: num,B: complex,C: complex] :
% 11.11/6.16        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3932_right__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [V: num,B: real,C: real] :
% 11.11/6.16        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3933_right__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [V: num,B: int,C: int] :
% 11.11/6.16        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3934_left__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [A: rat,B: rat,V: num] :
% 11.11/6.16        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3935_left__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [A: complex,B: complex,V: num] :
% 11.11/6.16        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3936_left__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [A: real,B: real,V: num] :
% 11.11/6.16        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3937_left__diff__distrib__numeral,axiom,
% 11.11/6.16      ! [A: int,B: int,V: num] :
% 11.11/6.16        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3938_div__diff,axiom,
% 11.11/6.16      ! [C: int,A: int,B: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ C @ A )
% 11.11/6.16       => ( ( dvd_dvd_int @ C @ B )
% 11.11/6.16         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3939_div__diff,axiom,
% 11.11/6.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ C @ A )
% 11.11/6.16       => ( ( dvd_dvd_Code_integer @ C @ B )
% 11.11/6.16         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 11.11/6.16            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3940_zero__less__diff,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.16        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3941_diff__is__0__eq_H,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16       => ( ( minus_minus_nat @ M @ N2 )
% 11.11/6.16          = zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3942_diff__is__0__eq,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ( minus_minus_nat @ M @ N2 )
% 11.11/6.16          = zero_zero_nat )
% 11.11/6.16        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3943_of__bool__not__iff,axiom,
% 11.11/6.16      ! [P: $o] :
% 11.11/6.16        ( ( zero_n1201886186963655149omplex @ ~ P )
% 11.11/6.16        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3944_of__bool__not__iff,axiom,
% 11.11/6.16      ! [P: $o] :
% 11.11/6.16        ( ( zero_n3304061248610475627l_real @ ~ P )
% 11.11/6.16        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3945_of__bool__not__iff,axiom,
% 11.11/6.16      ! [P: $o] :
% 11.11/6.16        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 11.11/6.16        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3946_of__bool__not__iff,axiom,
% 11.11/6.16      ! [P: $o] :
% 11.11/6.16        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 11.11/6.16        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3947_of__bool__not__iff,axiom,
% 11.11/6.16      ! [P: $o] :
% 11.11/6.16        ( ( zero_n356916108424825756nteger @ ~ P )
% 11.11/6.16        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3948_Nat_Odiff__diff__right,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3949_Nat_Oadd__diff__assoc2,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3950_Nat_Oadd__diff__assoc,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3951_diff__Suc__1,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 11.11/6.16        = N2 ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3952_signed__take__bit__Suc__1,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 11.11/6.16        = one_one_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3953_signed__take__bit__numeral__of__1,axiom,
% 11.11/6.16      ! [K: num] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 11.11/6.16        = one_one_int ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3954_concat__bit__nonnegative__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 11.11/6.16        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3955_concat__bit__negative__iff,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 11.11/6.16        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3956_Suc__pred,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 11.11/6.16          = N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3957_diff__Suc__diff__eq2,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 11.11/6.16          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3958_diff__Suc__diff__eq1,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3959_zle__diff1__eq,axiom,
% 11.11/6.16      ! [W: int,Z: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 11.11/6.16        = ( ord_less_int @ W @ Z ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3960_signed__take__bit__Suc__bit0,axiom,
% 11.11/6.16      ! [N2: nat,K: num] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 11.11/6.16        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3961_Suc__diff__1,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 11.11/6.16          = N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3962_even__diff,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 11.11/6.16        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3963_even__diff,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 11.11/6.16        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3964_odd__Suc__minus__one,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 11.11/6.16          = N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3965_even__diff__nat,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16        = ( ( ord_less_nat @ M @ N2 )
% 11.11/6.16          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3966_semiring__parity__class_Oeven__mask__iff,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 11.11/6.16        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3967_semiring__parity__class_Oeven__mask__iff,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 11.11/6.16        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3968_semiring__parity__class_Oeven__mask__iff,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 11.11/6.16        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3969_odd__two__times__div__two__nat,axiom,
% 11.11/6.16      ! [N2: nat] :
% 11.11/6.16        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.16       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.16          = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3970_diff__right__commute,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 11.11/6.16        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3971_diff__right__commute,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 11.11/6.16        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3972_diff__right__commute,axiom,
% 11.11/6.16      ! [A: nat,C: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 11.11/6.16        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3973_diff__right__commute,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 11.11/6.16        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3974_diff__eq__diff__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.16        ( ( ( minus_minus_real @ A @ B )
% 11.11/6.16          = ( minus_minus_real @ C @ D ) )
% 11.11/6.16       => ( ( A = B )
% 11.11/6.16          = ( C = D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3975_diff__eq__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.16        ( ( ( minus_minus_rat @ A @ B )
% 11.11/6.16          = ( minus_minus_rat @ C @ D ) )
% 11.11/6.16       => ( ( A = B )
% 11.11/6.16          = ( C = D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3976_diff__eq__diff__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.16        ( ( ( minus_minus_int @ A @ B )
% 11.11/6.16          = ( minus_minus_int @ C @ D ) )
% 11.11/6.16       => ( ( A = B )
% 11.11/6.16          = ( C = D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3977_signed__take__bit__diff,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 11.11/6.16        = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3978_diff__commute,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 11.11/6.16        = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3979_diff__mono,axiom,
% 11.11/6.16      ! [A: real,B: real,D: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_real @ D @ C )
% 11.11/6.16         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3980_diff__mono,axiom,
% 11.11/6.16      ! [A: rat,B: rat,D: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_rat @ D @ C )
% 11.11/6.16         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3981_diff__mono,axiom,
% 11.11/6.16      ! [A: int,B: int,D: int,C: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_int @ D @ C )
% 11.11/6.16         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3982_diff__left__mono,axiom,
% 11.11/6.16      ! [B: real,A: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.16       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3983_diff__left__mono,axiom,
% 11.11/6.16      ! [B: rat,A: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ B @ A )
% 11.11/6.16       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3984_diff__left__mono,axiom,
% 11.11/6.16      ! [B: int,A: int,C: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ B @ A )
% 11.11/6.16       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3985_diff__right__mono,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.16       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3986_diff__right__mono,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.16       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3987_diff__right__mono,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.16       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3988_diff__eq__diff__less__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.16        ( ( ( minus_minus_real @ A @ B )
% 11.11/6.16          = ( minus_minus_real @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.16          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3989_diff__eq__diff__less__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.16        ( ( ( minus_minus_rat @ A @ B )
% 11.11/6.16          = ( minus_minus_rat @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.16          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3990_diff__eq__diff__less__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.16        ( ( ( minus_minus_int @ A @ B )
% 11.11/6.16          = ( minus_minus_int @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_eq_int @ A @ B )
% 11.11/6.16          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3991_eq__iff__diff__eq__0,axiom,
% 11.11/6.16      ( ( ^ [Y6: complex,Z4: complex] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: complex,B2: complex] :
% 11.11/6.16            ( ( minus_minus_complex @ A3 @ B2 )
% 11.11/6.16            = zero_zero_complex ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3992_eq__iff__diff__eq__0,axiom,
% 11.11/6.16      ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: real,B2: real] :
% 11.11/6.16            ( ( minus_minus_real @ A3 @ B2 )
% 11.11/6.16            = zero_zero_real ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3993_eq__iff__diff__eq__0,axiom,
% 11.11/6.16      ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: rat,B2: rat] :
% 11.11/6.16            ( ( minus_minus_rat @ A3 @ B2 )
% 11.11/6.16            = zero_zero_rat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3994_eq__iff__diff__eq__0,axiom,
% 11.11/6.16      ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 11.11/6.16      = ( ^ [A3: int,B2: int] :
% 11.11/6.16            ( ( minus_minus_int @ A3 @ B2 )
% 11.11/6.16            = zero_zero_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3995_diff__strict__mono,axiom,
% 11.11/6.16      ! [A: real,B: real,D: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ A @ B )
% 11.11/6.16       => ( ( ord_less_real @ D @ C )
% 11.11/6.16         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3996_diff__strict__mono,axiom,
% 11.11/6.16      ! [A: rat,B: rat,D: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ A @ B )
% 11.11/6.16       => ( ( ord_less_rat @ D @ C )
% 11.11/6.16         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3997_diff__strict__mono,axiom,
% 11.11/6.16      ! [A: int,B: int,D: int,C: int] :
% 11.11/6.16        ( ( ord_less_int @ A @ B )
% 11.11/6.16       => ( ( ord_less_int @ D @ C )
% 11.11/6.16         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3998_diff__eq__diff__less,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.16        ( ( ( minus_minus_real @ A @ B )
% 11.11/6.16          = ( minus_minus_real @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_real @ A @ B )
% 11.11/6.16          = ( ord_less_real @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_3999_diff__eq__diff__less,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.16        ( ( ( minus_minus_rat @ A @ B )
% 11.11/6.16          = ( minus_minus_rat @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_rat @ A @ B )
% 11.11/6.16          = ( ord_less_rat @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4000_diff__eq__diff__less,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.16        ( ( ( minus_minus_int @ A @ B )
% 11.11/6.16          = ( minus_minus_int @ C @ D ) )
% 11.11/6.16       => ( ( ord_less_int @ A @ B )
% 11.11/6.16          = ( ord_less_int @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4001_diff__strict__left__mono,axiom,
% 11.11/6.16      ! [B: real,A: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ B @ A )
% 11.11/6.16       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4002_diff__strict__left__mono,axiom,
% 11.11/6.16      ! [B: rat,A: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ B @ A )
% 11.11/6.16       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4003_diff__strict__left__mono,axiom,
% 11.11/6.16      ! [B: int,A: int,C: int] :
% 11.11/6.16        ( ( ord_less_int @ B @ A )
% 11.11/6.16       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4004_diff__strict__right__mono,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ A @ B )
% 11.11/6.16       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4005_diff__strict__right__mono,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ A @ B )
% 11.11/6.16       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4006_diff__strict__right__mono,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( ord_less_int @ A @ B )
% 11.11/6.16       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4007_right__diff__distrib_H,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4008_right__diff__distrib_H,axiom,
% 11.11/6.16      ! [A: complex,B: complex,C: complex] :
% 11.11/6.16        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4009_right__diff__distrib_H,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4010_right__diff__distrib_H,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4011_right__diff__distrib_H,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4012_left__diff__distrib_H,axiom,
% 11.11/6.16      ! [B: rat,C: rat,A: rat] :
% 11.11/6.16        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4013_left__diff__distrib_H,axiom,
% 11.11/6.16      ! [B: complex,C: complex,A: complex] :
% 11.11/6.16        ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4014_left__diff__distrib_H,axiom,
% 11.11/6.16      ! [B: real,C: real,A: real] :
% 11.11/6.16        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4015_left__diff__distrib_H,axiom,
% 11.11/6.16      ! [B: nat,C: nat,A: nat] :
% 11.11/6.16        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 11.11/6.16        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4016_left__diff__distrib_H,axiom,
% 11.11/6.16      ! [B: int,C: int,A: int] :
% 11.11/6.16        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4017_right__diff__distrib,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4018_right__diff__distrib,axiom,
% 11.11/6.16      ! [A: complex,B: complex,C: complex] :
% 11.11/6.16        ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4019_right__diff__distrib,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4020_right__diff__distrib,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4021_left__diff__distrib,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4022_left__diff__distrib,axiom,
% 11.11/6.16      ! [A: complex,B: complex,C: complex] :
% 11.11/6.16        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4023_left__diff__distrib,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4024_left__diff__distrib,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4025_add__diff__add,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 11.11/6.16        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4026_add__diff__add,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 11.11/6.16        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4027_add__diff__add,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 11.11/6.16        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4028_group__cancel_Osub1,axiom,
% 11.11/6.16      ! [A2: real,K: real,A: real,B: real] :
% 11.11/6.16        ( ( A2
% 11.11/6.16          = ( plus_plus_real @ K @ A ) )
% 11.11/6.16       => ( ( minus_minus_real @ A2 @ B )
% 11.11/6.16          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4029_group__cancel_Osub1,axiom,
% 11.11/6.16      ! [A2: rat,K: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( A2
% 11.11/6.16          = ( plus_plus_rat @ K @ A ) )
% 11.11/6.16       => ( ( minus_minus_rat @ A2 @ B )
% 11.11/6.16          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4030_group__cancel_Osub1,axiom,
% 11.11/6.16      ! [A2: int,K: int,A: int,B: int] :
% 11.11/6.16        ( ( A2
% 11.11/6.16          = ( plus_plus_int @ K @ A ) )
% 11.11/6.16       => ( ( minus_minus_int @ A2 @ B )
% 11.11/6.16          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4031_diff__eq__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ( minus_minus_real @ A @ B )
% 11.11/6.16          = C )
% 11.11/6.16        = ( A
% 11.11/6.16          = ( plus_plus_real @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4032_diff__eq__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ( minus_minus_rat @ A @ B )
% 11.11/6.16          = C )
% 11.11/6.16        = ( A
% 11.11/6.16          = ( plus_plus_rat @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4033_diff__eq__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( ( minus_minus_int @ A @ B )
% 11.11/6.16          = C )
% 11.11/6.16        = ( A
% 11.11/6.16          = ( plus_plus_int @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4034_eq__diff__eq,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real] :
% 11.11/6.16        ( ( A
% 11.11/6.16          = ( minus_minus_real @ C @ B ) )
% 11.11/6.16        = ( ( plus_plus_real @ A @ B )
% 11.11/6.16          = C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4035_eq__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat] :
% 11.11/6.16        ( ( A
% 11.11/6.16          = ( minus_minus_rat @ C @ B ) )
% 11.11/6.16        = ( ( plus_plus_rat @ A @ B )
% 11.11/6.16          = C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4036_eq__diff__eq,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( A
% 11.11/6.16          = ( minus_minus_int @ C @ B ) )
% 11.11/6.16        = ( ( plus_plus_int @ A @ B )
% 11.11/6.16          = C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4037_add__diff__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4038_add__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4039_add__diff__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4040_diff__diff__eq2,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4041_diff__diff__eq2,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4042_diff__diff__eq2,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4043_diff__add__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4044_diff__add__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4045_diff__add__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4046_diff__add__eq__diff__diff__swap,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 11.11/6.16        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4047_diff__add__eq__diff__diff__swap,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 11.11/6.16        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4048_diff__add__eq__diff__diff__swap,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 11.11/6.16        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4049_add__implies__diff,axiom,
% 11.11/6.16      ! [C: real,B: real,A: real] :
% 11.11/6.16        ( ( ( plus_plus_real @ C @ B )
% 11.11/6.16          = A )
% 11.11/6.16       => ( C
% 11.11/6.16          = ( minus_minus_real @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4050_add__implies__diff,axiom,
% 11.11/6.16      ! [C: rat,B: rat,A: rat] :
% 11.11/6.16        ( ( ( plus_plus_rat @ C @ B )
% 11.11/6.16          = A )
% 11.11/6.16       => ( C
% 11.11/6.16          = ( minus_minus_rat @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4051_add__implies__diff,axiom,
% 11.11/6.16      ! [C: nat,B: nat,A: nat] :
% 11.11/6.16        ( ( ( plus_plus_nat @ C @ B )
% 11.11/6.16          = A )
% 11.11/6.16       => ( C
% 11.11/6.16          = ( minus_minus_nat @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4052_add__implies__diff,axiom,
% 11.11/6.16      ! [C: int,B: int,A: int] :
% 11.11/6.16        ( ( ( plus_plus_int @ C @ B )
% 11.11/6.16          = A )
% 11.11/6.16       => ( C
% 11.11/6.16          = ( minus_minus_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4053_diff__diff__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4054_diff__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4055_diff__diff__eq,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4056_diff__diff__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4057_diff__divide__distrib,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4058_diff__divide__distrib,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4059_diff__divide__distrib,axiom,
% 11.11/6.16      ! [A: complex,B: complex,C: complex] :
% 11.11/6.16        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 11.11/6.16        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4060_dvd__diff,axiom,
% 11.11/6.16      ! [X4: code_integer,Y: code_integer,Z: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 11.11/6.16       => ( ( dvd_dvd_Code_integer @ X4 @ Z )
% 11.11/6.16         => ( dvd_dvd_Code_integer @ X4 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4061_dvd__diff,axiom,
% 11.11/6.16      ! [X4: real,Y: real,Z: real] :
% 11.11/6.16        ( ( dvd_dvd_real @ X4 @ Y )
% 11.11/6.16       => ( ( dvd_dvd_real @ X4 @ Z )
% 11.11/6.16         => ( dvd_dvd_real @ X4 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4062_dvd__diff,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat,Z: rat] :
% 11.11/6.16        ( ( dvd_dvd_rat @ X4 @ Y )
% 11.11/6.16       => ( ( dvd_dvd_rat @ X4 @ Z )
% 11.11/6.16         => ( dvd_dvd_rat @ X4 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4063_dvd__diff,axiom,
% 11.11/6.16      ! [X4: int,Y: int,Z: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ X4 @ Y )
% 11.11/6.16       => ( ( dvd_dvd_int @ X4 @ Z )
% 11.11/6.16         => ( dvd_dvd_int @ X4 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4064_dvd__diff__commute,axiom,
% 11.11/6.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 11.11/6.16        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4065_dvd__diff__commute,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 11.11/6.16        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4066_zero__induct__lemma,axiom,
% 11.11/6.16      ! [P: nat > $o,K: nat,I2: nat] :
% 11.11/6.16        ( ( P @ K )
% 11.11/6.16       => ( ! [N3: nat] :
% 11.11/6.16              ( ( P @ ( suc @ N3 ) )
% 11.11/6.16             => ( P @ N3 ) )
% 11.11/6.16         => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4067_diffs0__imp__equal,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ( minus_minus_nat @ M @ N2 )
% 11.11/6.16          = zero_zero_nat )
% 11.11/6.16       => ( ( ( minus_minus_nat @ N2 @ M )
% 11.11/6.16            = zero_zero_nat )
% 11.11/6.16         => ( M = N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4068_minus__nat_Odiff__0,axiom,
% 11.11/6.16      ! [M: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 11.11/6.16        = M ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4069_mod__diff__right__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.16        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4070_mod__diff__right__eq,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer,C: code_integer] :
% 11.11/6.16        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.16        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4071_mod__diff__left__eq,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 11.11/6.16        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4072_mod__diff__left__eq,axiom,
% 11.11/6.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.16        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 11.11/6.16        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4073_mod__diff__cong,axiom,
% 11.11/6.16      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 11.11/6.16        ( ( ( modulo_modulo_int @ A @ C )
% 11.11/6.16          = ( modulo_modulo_int @ A4 @ C ) )
% 11.11/6.16       => ( ( ( modulo_modulo_int @ B @ C )
% 11.11/6.16            = ( modulo_modulo_int @ B4 @ C ) )
% 11.11/6.16         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16            = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4074_mod__diff__cong,axiom,
% 11.11/6.16      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 11.11/6.16        ( ( ( modulo364778990260209775nteger @ A @ C )
% 11.11/6.16          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 11.11/6.16       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 11.11/6.16            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 11.11/6.16         => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 11.11/6.16            = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4075_mod__diff__eq,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 11.11/6.16        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4076_mod__diff__eq,axiom,
% 11.11/6.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.16        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 11.11/6.16        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4077_diff__less__mono2,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,L: nat] :
% 11.11/6.16        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ M @ L )
% 11.11/6.16         => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4078_less__imp__diff__less,axiom,
% 11.11/6.16      ! [J: nat,K: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ J @ K )
% 11.11/6.16       => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4079_signed__take__bit__mult,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 11.11/6.16        = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4080_eq__diff__iff,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.16       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.16         => ( ( ( minus_minus_nat @ M @ K )
% 11.11/6.16              = ( minus_minus_nat @ N2 @ K ) )
% 11.11/6.16            = ( M = N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4081_le__diff__iff,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.16       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.16         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 11.11/6.16            = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4082_Nat_Odiff__diff__eq,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.16       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.16         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 11.11/6.16            = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4083_diff__le__mono,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,L: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4084_diff__le__self,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4085_le__diff__iff_H,axiom,
% 11.11/6.16      ! [A: nat,C: nat,B: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ C )
% 11.11/6.16       => ( ( ord_less_eq_nat @ B @ C )
% 11.11/6.16         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 11.11/6.16            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4086_diff__le__mono2,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,L: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4087_signed__take__bit__add,axiom,
% 11.11/6.16      ! [N2: nat,K: int,L: int] :
% 11.11/6.16        ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 11.11/6.16        = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4088_Nat_Odiff__cancel,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 11.11/6.16        = ( minus_minus_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4089_diff__cancel2,axiom,
% 11.11/6.16      ! [M: nat,K: nat,N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.16        = ( minus_minus_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4090_diff__add__inverse,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 11.11/6.16        = M ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4091_diff__add__inverse2,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 11.11/6.16        = M ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4092_diff__mult__distrib,axiom,
% 11.11/6.16      ! [M: nat,N2: nat,K: nat] :
% 11.11/6.16        ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 11.11/6.16        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4093_diff__mult__distrib2,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4094_dvd__diff__nat,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ K @ M )
% 11.11/6.16       => ( ( dvd_dvd_nat @ K @ N2 )
% 11.11/6.16         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4095_concat__bit__assoc,axiom,
% 11.11/6.16      ! [N2: nat,K: int,M: nat,L: int,R3: int] :
% 11.11/6.16        ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L @ R3 ) )
% 11.11/6.16        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4096_subset__decode__imp__le,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 11.11/6.16       => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4097_le__iff__diff__le__0,axiom,
% 11.11/6.16      ( ord_less_eq_real
% 11.11/6.16      = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4098_le__iff__diff__le__0,axiom,
% 11.11/6.16      ( ord_less_eq_rat
% 11.11/6.16      = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4099_le__iff__diff__le__0,axiom,
% 11.11/6.16      ( ord_less_eq_int
% 11.11/6.16      = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4100_less__iff__diff__less__0,axiom,
% 11.11/6.16      ( ord_less_real
% 11.11/6.16      = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4101_less__iff__diff__less__0,axiom,
% 11.11/6.16      ( ord_less_rat
% 11.11/6.16      = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4102_less__iff__diff__less__0,axiom,
% 11.11/6.16      ( ord_less_int
% 11.11/6.16      = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4103_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16         => ( ( ( minus_minus_nat @ B @ A )
% 11.11/6.16              = C )
% 11.11/6.16            = ( B
% 11.11/6.16              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4104_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 11.11/6.16          = B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4105_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4106_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 11.11/6.16          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4107_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4108_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 11.11/6.16          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4109_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4110_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 11.11/6.16          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4111_le__add__diff,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4112_add__le__add__imp__diff__le,axiom,
% 11.11/6.16      ! [I2: real,K: real,N2: real,J: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 11.11/6.16         => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 11.11/6.16           => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 11.11/6.16             => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4113_add__le__add__imp__diff__le,axiom,
% 11.11/6.16      ! [I2: rat,K: rat,N2: rat,J: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 11.11/6.16         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 11.11/6.16           => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 11.11/6.16             => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4114_add__le__add__imp__diff__le,axiom,
% 11.11/6.16      ! [I2: nat,K: nat,N2: nat,J: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 11.11/6.16         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 11.11/6.16           => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 11.11/6.16             => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4115_add__le__add__imp__diff__le,axiom,
% 11.11/6.16      ! [I2: int,K: int,N2: int,J: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 11.11/6.16         => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 11.11/6.16           => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 11.11/6.16             => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4116_diff__add,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 11.11/6.16          = B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4117_add__le__imp__le__diff,axiom,
% 11.11/6.16      ! [I2: real,K: real,N2: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4118_add__le__imp__le__diff,axiom,
% 11.11/6.16      ! [I2: rat,K: rat,N2: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4119_add__le__imp__le__diff,axiom,
% 11.11/6.16      ! [I2: nat,K: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4120_add__le__imp__le__diff,axiom,
% 11.11/6.16      ! [I2: int,K: int,N2: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 11.11/6.16       => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4121_le__diff__eq,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 11.11/6.16        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4122_le__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 11.11/6.16        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4123_le__diff__eq,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 11.11/6.16        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4124_diff__le__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4125_diff__le__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4126_diff__le__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4127_diff__less__eq,axiom,
% 11.11/6.16      ! [A: real,B: real,C: real] :
% 11.11/6.16        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4128_diff__less__eq,axiom,
% 11.11/6.16      ! [A: rat,B: rat,C: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4129_diff__less__eq,axiom,
% 11.11/6.16      ! [A: int,B: int,C: int] :
% 11.11/6.16        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 11.11/6.16        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4130_less__diff__eq,axiom,
% 11.11/6.16      ! [A: real,C: real,B: real] :
% 11.11/6.16        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 11.11/6.16        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4131_less__diff__eq,axiom,
% 11.11/6.16      ! [A: rat,C: rat,B: rat] :
% 11.11/6.16        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 11.11/6.16        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4132_less__diff__eq,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 11.11/6.16        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4133_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 11.11/6.16      ! [A: real,B: real] :
% 11.11/6.16        ( ~ ( ord_less_real @ A @ B )
% 11.11/6.16       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4134_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 11.11/6.16      ! [A: rat,B: rat] :
% 11.11/6.16        ( ~ ( ord_less_rat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4135_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ~ ( ord_less_nat @ A @ B )
% 11.11/6.16       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4136_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ~ ( ord_less_int @ A @ B )
% 11.11/6.16       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 11.11/6.16          = A ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4137_square__diff__square__factored,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 11.11/6.16        = ( times_times_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_rat @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4138_square__diff__square__factored,axiom,
% 11.11/6.16      ! [X4: complex,Y: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ ( times_times_complex @ Y @ Y ) )
% 11.11/6.16        = ( times_times_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_complex @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4139_square__diff__square__factored,axiom,
% 11.11/6.16      ! [X4: real,Y: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 11.11/6.16        = ( times_times_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4140_square__diff__square__factored,axiom,
% 11.11/6.16      ! [X4: int,Y: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 11.11/6.16        = ( times_times_int @ ( plus_plus_int @ X4 @ Y ) @ ( minus_minus_int @ X4 @ Y ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4141_eq__add__iff2,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( C
% 11.11/6.16          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4142_eq__add__iff2,axiom,
% 11.11/6.16      ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 11.11/6.16        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( C
% 11.11/6.16          = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4143_eq__add__iff2,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( C
% 11.11/6.16          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4144_eq__add__iff2,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( C
% 11.11/6.16          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4145_eq__add__iff1,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 11.11/6.16          = D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4146_eq__add__iff1,axiom,
% 11.11/6.16      ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 11.11/6.16        ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E2 ) @ C )
% 11.11/6.16          = D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4147_eq__add__iff1,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 11.11/6.16          = D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4148_eq__add__iff1,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 11.11/6.16          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 11.11/6.16          = D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4149_mult__diff__mult,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ Y ) @ ( times_times_rat @ A @ B ) )
% 11.11/6.16        = ( plus_plus_rat @ ( times_times_rat @ X4 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X4 @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4150_mult__diff__mult,axiom,
% 11.11/6.16      ! [X4: complex,Y: complex,A: complex,B: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ Y ) @ ( times_times_complex @ A @ B ) )
% 11.11/6.16        = ( plus_plus_complex @ ( times_times_complex @ X4 @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X4 @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4151_mult__diff__mult,axiom,
% 11.11/6.16      ! [X4: real,Y: real,A: real,B: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( times_times_real @ X4 @ Y ) @ ( times_times_real @ A @ B ) )
% 11.11/6.16        = ( plus_plus_real @ ( times_times_real @ X4 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X4 @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4152_mult__diff__mult,axiom,
% 11.11/6.16      ! [X4: int,Y: int,A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( times_times_int @ X4 @ Y ) @ ( times_times_int @ A @ B ) )
% 11.11/6.16        = ( plus_plus_int @ ( times_times_int @ X4 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X4 @ A ) @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4153_mod__eq__dvd__iff,axiom,
% 11.11/6.16      ! [A: int,C: int,B: int] :
% 11.11/6.16        ( ( ( modulo_modulo_int @ A @ C )
% 11.11/6.16          = ( modulo_modulo_int @ B @ C ) )
% 11.11/6.16        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4154_mod__eq__dvd__iff,axiom,
% 11.11/6.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 11.11/6.16        ( ( ( modulo364778990260209775nteger @ A @ C )
% 11.11/6.16          = ( modulo364778990260209775nteger @ B @ C ) )
% 11.11/6.16        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4155_dvd__minus__mod,axiom,
% 11.11/6.16      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4156_dvd__minus__mod,axiom,
% 11.11/6.16      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4157_dvd__minus__mod,axiom,
% 11.11/6.16      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4158_diff__less__Suc,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4159_Suc__diff__Suc,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ N2 @ M )
% 11.11/6.16       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.16          = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4160_diff__less,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.16         => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4161_Suc__diff__le,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 11.11/6.16          = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4162_diff__less__mono,axiom,
% 11.11/6.16      ! [A: nat,B: nat,C: nat] :
% 11.11/6.16        ( ( ord_less_nat @ A @ B )
% 11.11/6.16       => ( ( ord_less_eq_nat @ C @ A )
% 11.11/6.16         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4163_less__diff__iff,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.16       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.16         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 11.11/6.16            = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4164_diff__add__0,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.16        = zero_zero_nat ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4165_less__diff__conv,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.16        ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 11.11/6.16        = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4166_add__diff__inverse__nat,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ~ ( ord_less_nat @ M @ N2 )
% 11.11/6.16       => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16          = M ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4167_Nat_Ole__imp__diff__is__add,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.16       => ( ( ( minus_minus_nat @ J @ I2 )
% 11.11/6.16            = K )
% 11.11/6.16          = ( J
% 11.11/6.16            = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4168_Nat_Odiff__add__assoc2,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 11.11/6.16          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4169_Nat_Odiff__add__assoc,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 11.11/6.16          = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4170_Nat_Ole__diff__conv2,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 11.11/6.16          = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4171_le__diff__conv,axiom,
% 11.11/6.16      ! [J: nat,K: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 11.11/6.16        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4172_diff__Suc__eq__diff__pred,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 11.11/6.16        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4173_int__le__induct,axiom,
% 11.11/6.16      ! [I2: int,K: int,P: int > $o] :
% 11.11/6.16        ( ( ord_less_eq_int @ I2 @ K )
% 11.11/6.16       => ( ( P @ K )
% 11.11/6.16         => ( ! [I4: int] :
% 11.11/6.16                ( ( ord_less_eq_int @ I4 @ K )
% 11.11/6.16               => ( ( P @ I4 )
% 11.11/6.16                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.16           => ( P @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4174_dvd__minus__self,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.16        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.16          | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4175_int__less__induct,axiom,
% 11.11/6.16      ! [I2: int,K: int,P: int > $o] :
% 11.11/6.16        ( ( ord_less_int @ I2 @ K )
% 11.11/6.16       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 11.11/6.16         => ( ! [I4: int] :
% 11.11/6.16                ( ( ord_less_int @ I4 @ K )
% 11.11/6.16               => ( ( P @ I4 )
% 11.11/6.16                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.16           => ( P @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4176_dvd__diffD,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16       => ( ( dvd_dvd_nat @ K @ N2 )
% 11.11/6.16         => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4177_dvd__diffD1,axiom,
% 11.11/6.16      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16       => ( ( dvd_dvd_nat @ K @ M )
% 11.11/6.16         => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16           => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4178_less__eq__dvd__minus,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.16       => ( ( dvd_dvd_nat @ M @ N2 )
% 11.11/6.16          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4179_mod__geq,axiom,
% 11.11/6.16      ! [M: nat,N2: nat] :
% 11.11/6.16        ( ~ ( ord_less_nat @ M @ N2 )
% 11.11/6.16       => ( ( modulo_modulo_nat @ M @ N2 )
% 11.11/6.16          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4180_mod__if,axiom,
% 11.11/6.16      ( modulo_modulo_nat
% 11.11/6.16      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4181_le__mod__geq,axiom,
% 11.11/6.16      ! [N2: nat,M: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16       => ( ( modulo_modulo_nat @ M @ N2 )
% 11.11/6.16          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4182_signed__take__bit__int__less__eq,axiom,
% 11.11/6.16      ! [N2: nat,K: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 11.11/6.16       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4183_ordered__ring__class_Ole__add__iff2,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4184_ordered__ring__class_Ole__add__iff2,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4185_ordered__ring__class_Ole__add__iff2,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4186_ordered__ring__class_Ole__add__iff1,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4187_ordered__ring__class_Ole__add__iff1,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4188_ordered__ring__class_Ole__add__iff1,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4189_less__add__iff1,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4190_less__add__iff1,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4191_less__add__iff1,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4192_less__add__iff2,axiom,
% 11.11/6.16      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.16        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4193_less__add__iff2,axiom,
% 11.11/6.16      ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 11.11/6.16        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4194_less__add__iff2,axiom,
% 11.11/6.16      ! [A: int,E2: int,C: int,B: int,D: int] :
% 11.11/6.16        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 11.11/6.16        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4195_divide__diff__eq__iff,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( Z != zero_zero_rat )
% 11.11/6.16       => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide_divide_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4196_divide__diff__eq__iff,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( Z != zero_zero_real )
% 11.11/6.16       => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4197_divide__diff__eq__iff,axiom,
% 11.11/6.16      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.16        ( ( Z != zero_zero_complex )
% 11.11/6.16       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4198_diff__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.16        ( ( Z != zero_zero_rat )
% 11.11/6.16       => ( ( minus_minus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 11.11/6.16          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4199_diff__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: real,X4: real,Y: real] :
% 11.11/6.16        ( ( Z != zero_zero_real )
% 11.11/6.16       => ( ( minus_minus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 11.11/6.16          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4200_diff__divide__eq__iff,axiom,
% 11.11/6.16      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.16        ( ( Z != zero_zero_complex )
% 11.11/6.16       => ( ( minus_minus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 11.11/6.16          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4201_diff__frac__eq,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 11.11/6.16            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4202_diff__frac__eq,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real,W: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 11.11/6.16            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4203_diff__frac__eq,axiom,
% 11.11/6.16      ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 11.11/6.16        ( ( Y != zero_zero_complex )
% 11.11/6.16       => ( ( Z != zero_zero_complex )
% 11.11/6.16         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 11.11/6.16            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4204_add__divide__eq__if__simps_I4_J,axiom,
% 11.11/6.16      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.16        ( ( ( Z = zero_zero_rat )
% 11.11/6.16         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 11.11/6.16            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4205_add__divide__eq__if__simps_I4_J,axiom,
% 11.11/6.16      ! [Z: real,A: real,B: real] :
% 11.11/6.16        ( ( ( Z = zero_zero_real )
% 11.11/6.16         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 11.11/6.16            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4206_add__divide__eq__if__simps_I4_J,axiom,
% 11.11/6.16      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.16        ( ( ( Z = zero_zero_complex )
% 11.11/6.16         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 11.11/6.16            = A ) )
% 11.11/6.16        & ( ( Z != zero_zero_complex )
% 11.11/6.16         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 11.11/6.16            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4207_square__diff__one__factored,axiom,
% 11.11/6.16      ! [X4: rat] :
% 11.11/6.16        ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ one_one_rat )
% 11.11/6.16        = ( times_times_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4208_square__diff__one__factored,axiom,
% 11.11/6.16      ! [X4: complex] :
% 11.11/6.16        ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ one_one_complex )
% 11.11/6.16        = ( times_times_complex @ ( plus_plus_complex @ X4 @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4209_square__diff__one__factored,axiom,
% 11.11/6.16      ! [X4: real] :
% 11.11/6.16        ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ one_one_real )
% 11.11/6.16        = ( times_times_real @ ( plus_plus_real @ X4 @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4210_square__diff__one__factored,axiom,
% 11.11/6.16      ! [X4: int] :
% 11.11/6.16        ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ one_one_int )
% 11.11/6.16        = ( times_times_int @ ( plus_plus_int @ X4 @ one_one_int ) @ ( minus_minus_int @ X4 @ one_one_int ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4211_inf__period_I4_J,axiom,
% 11.11/6.16      ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 11.11/6.16       => ! [X2: code_integer,K4: code_integer] :
% 11.11/6.16            ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) ) )
% 11.11/6.16            = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4212_inf__period_I4_J,axiom,
% 11.11/6.16      ! [D: rat,D4: rat,T2: rat] :
% 11.11/6.16        ( ( dvd_dvd_rat @ D @ D4 )
% 11.11/6.16       => ! [X2: rat,K4: rat] :
% 11.11/6.16            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) ) )
% 11.11/6.16            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4213_inf__period_I4_J,axiom,
% 11.11/6.16      ! [D: complex,D4: complex,T2: complex] :
% 11.11/6.16        ( ( dvd_dvd_complex @ D @ D4 )
% 11.11/6.16       => ! [X2: complex,K4: complex] :
% 11.11/6.16            ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) ) )
% 11.11/6.16            = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4214_inf__period_I4_J,axiom,
% 11.11/6.16      ! [D: real,D4: real,T2: real] :
% 11.11/6.16        ( ( dvd_dvd_real @ D @ D4 )
% 11.11/6.16       => ! [X2: real,K4: real] :
% 11.11/6.16            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) ) )
% 11.11/6.16            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4215_inf__period_I4_J,axiom,
% 11.11/6.16      ! [D: int,D4: int,T2: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ D @ D4 )
% 11.11/6.16       => ! [X2: int,K4: int] :
% 11.11/6.16            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) ) )
% 11.11/6.16            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4216_inf__period_I3_J,axiom,
% 11.11/6.16      ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 11.11/6.16        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 11.11/6.16       => ! [X2: code_integer,K4: code_integer] :
% 11.11/6.16            ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) )
% 11.11/6.16            = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4217_inf__period_I3_J,axiom,
% 11.11/6.16      ! [D: rat,D4: rat,T2: rat] :
% 11.11/6.16        ( ( dvd_dvd_rat @ D @ D4 )
% 11.11/6.16       => ! [X2: rat,K4: rat] :
% 11.11/6.16            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) )
% 11.11/6.16            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4218_inf__period_I3_J,axiom,
% 11.11/6.16      ! [D: complex,D4: complex,T2: complex] :
% 11.11/6.16        ( ( dvd_dvd_complex @ D @ D4 )
% 11.11/6.16       => ! [X2: complex,K4: complex] :
% 11.11/6.16            ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) )
% 11.11/6.16            = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4219_inf__period_I3_J,axiom,
% 11.11/6.16      ! [D: real,D4: real,T2: real] :
% 11.11/6.16        ( ( dvd_dvd_real @ D @ D4 )
% 11.11/6.16       => ! [X2: real,K4: real] :
% 11.11/6.16            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) )
% 11.11/6.16            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4220_inf__period_I3_J,axiom,
% 11.11/6.16      ! [D: int,D4: int,T2: int] :
% 11.11/6.16        ( ( dvd_dvd_int @ D @ D4 )
% 11.11/6.16       => ! [X2: int,K4: int] :
% 11.11/6.16            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) )
% 11.11/6.16            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4221_minus__mult__div__eq__mod,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 11.11/6.16        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4222_minus__mult__div__eq__mod,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 11.11/6.16        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4223_minus__mult__div__eq__mod,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 11.11/6.16        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4224_minus__mod__eq__mult__div,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.16        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4225_minus__mod__eq__mult__div,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.16        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4226_minus__mod__eq__mult__div,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.16        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4227_minus__mod__eq__div__mult,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.16        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4228_minus__mod__eq__div__mult,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 11.11/6.16        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4229_minus__mod__eq__div__mult,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 11.11/6.16        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4230_minus__div__mult__eq__mod,axiom,
% 11.11/6.16      ! [A: nat,B: nat] :
% 11.11/6.16        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 11.11/6.16        = ( modulo_modulo_nat @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4231_minus__div__mult__eq__mod,axiom,
% 11.11/6.16      ! [A: int,B: int] :
% 11.11/6.16        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 11.11/6.16        = ( modulo_modulo_int @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4232_minus__div__mult__eq__mod,axiom,
% 11.11/6.16      ! [A: code_integer,B: code_integer] :
% 11.11/6.16        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 11.11/6.16        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4233_diff__Suc__less,axiom,
% 11.11/6.16      ! [N2: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.16       => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4234_nat__diff__split,axiom,
% 11.11/6.16      ! [P: nat > $o,A: nat,B: nat] :
% 11.11/6.16        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.16        = ( ( ( ord_less_nat @ A @ B )
% 11.11/6.16           => ( P @ zero_zero_nat ) )
% 11.11/6.16          & ! [D5: nat] :
% 11.11/6.16              ( ( A
% 11.11/6.16                = ( plus_plus_nat @ B @ D5 ) )
% 11.11/6.16             => ( P @ D5 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4235_nat__diff__split__asm,axiom,
% 11.11/6.16      ! [P: nat > $o,A: nat,B: nat] :
% 11.11/6.16        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.16        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 11.11/6.16                & ~ ( P @ zero_zero_nat ) )
% 11.11/6.16              | ? [D5: nat] :
% 11.11/6.16                  ( ( A
% 11.11/6.16                    = ( plus_plus_nat @ B @ D5 ) )
% 11.11/6.16                  & ~ ( P @ D5 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4236_less__diff__conv2,axiom,
% 11.11/6.16      ! [K: nat,J: nat,I2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ K @ J )
% 11.11/6.16       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 11.11/6.16          = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4237_nat__diff__add__eq2,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4238_nat__diff__add__eq1,axiom,
% 11.11/6.16      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ J @ I2 )
% 11.11/6.16       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4239_nat__le__add__iff2,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.16       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4240_nat__le__add__iff1,axiom,
% 11.11/6.16      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ J @ I2 )
% 11.11/6.16       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4241_nat__eq__add__iff2,axiom,
% 11.11/6.16      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.16       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 11.11/6.16            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( M
% 11.11/6.16            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4242_nat__eq__add__iff1,axiom,
% 11.11/6.16      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ J @ I2 )
% 11.11/6.16       => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 11.11/6.16            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.16          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 11.11/6.16            = N2 ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4243_plusinfinity,axiom,
% 11.11/6.16      ! [D: int,P6: int > $o,P: int > $o] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.16       => ( ! [X5: int,K2: int] :
% 11.11/6.16              ( ( P6 @ X5 )
% 11.11/6.16              = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 11.11/6.16         => ( ? [Z3: int] :
% 11.11/6.16              ! [X5: int] :
% 11.11/6.16                ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.16               => ( ( P @ X5 )
% 11.11/6.16                  = ( P6 @ X5 ) ) )
% 11.11/6.16           => ( ? [X_1: int] : ( P6 @ X_1 )
% 11.11/6.16             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4244_minusinfinity,axiom,
% 11.11/6.16      ! [D: int,P1: int > $o,P: int > $o] :
% 11.11/6.16        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.16       => ( ! [X5: int,K2: int] :
% 11.11/6.16              ( ( P1 @ X5 )
% 11.11/6.16              = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 11.11/6.16         => ( ? [Z3: int] :
% 11.11/6.16              ! [X5: int] :
% 11.11/6.16                ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.16               => ( ( P @ X5 )
% 11.11/6.16                  = ( P1 @ X5 ) ) )
% 11.11/6.16           => ( ? [X_1: int] : ( P1 @ X_1 )
% 11.11/6.16             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4245_int__induct,axiom,
% 11.11/6.16      ! [P: int > $o,K: int,I2: int] :
% 11.11/6.16        ( ( P @ K )
% 11.11/6.16       => ( ! [I4: int] :
% 11.11/6.16              ( ( ord_less_eq_int @ K @ I4 )
% 11.11/6.16             => ( ( P @ I4 )
% 11.11/6.16               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.16         => ( ! [I4: int] :
% 11.11/6.16                ( ( ord_less_eq_int @ I4 @ K )
% 11.11/6.16               => ( ( P @ I4 )
% 11.11/6.16                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 11.11/6.16           => ( P @ I2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4246_mod__eq__dvd__iff__nat,axiom,
% 11.11/6.16      ! [N2: nat,M: nat,Q3: nat] :
% 11.11/6.16        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16       => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 11.11/6.16            = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 11.11/6.16          = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4247_modulo__nat__def,axiom,
% 11.11/6.16      ( modulo_modulo_nat
% 11.11/6.16      = ( ^ [M6: nat,N: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N ) @ N ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4248_frac__le__eq,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real,W: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 11.11/6.16            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4249_frac__le__eq,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 11.11/6.16            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4250_frac__less__eq,axiom,
% 11.11/6.16      ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 11.11/6.16        ( ( Y != zero_zero_rat )
% 11.11/6.16       => ( ( Z != zero_zero_rat )
% 11.11/6.16         => ( ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 11.11/6.16            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4251_frac__less__eq,axiom,
% 11.11/6.16      ! [Y: real,Z: real,X4: real,W: real] :
% 11.11/6.16        ( ( Y != zero_zero_real )
% 11.11/6.16       => ( ( Z != zero_zero_real )
% 11.11/6.16         => ( ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 11.11/6.16            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4252_power2__commute,axiom,
% 11.11/6.16      ! [X4: complex,Y: complex] :
% 11.11/6.16        ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( power_power_complex @ ( minus_minus_complex @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4253_power2__commute,axiom,
% 11.11/6.16      ! [X4: real,Y: real] :
% 11.11/6.16        ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( power_power_real @ ( minus_minus_real @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4254_power2__commute,axiom,
% 11.11/6.16      ! [X4: rat,Y: rat] :
% 11.11/6.16        ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( power_power_rat @ ( minus_minus_rat @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4255_power2__commute,axiom,
% 11.11/6.16      ! [X4: int,Y: int] :
% 11.11/6.16        ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.16        = ( power_power_int @ ( minus_minus_int @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4256_power__diff,axiom,
% 11.11/6.16      ! [A: rat,N2: nat,M: nat] :
% 11.11/6.16        ( ( A != zero_zero_rat )
% 11.11/6.16       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.16         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.16            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.16  
% 11.11/6.16  thf(fact_4257_power__diff,axiom,
% 11.11/6.16      ! [A: nat,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_nat )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4258_power__diff,axiom,
% 11.11/6.17      ! [A: int,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_int )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4259_power__diff,axiom,
% 11.11/6.17      ! [A: real,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_real )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4260_power__diff,axiom,
% 11.11/6.17      ! [A: complex,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_complex )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4261_power__diff,axiom,
% 11.11/6.17      ! [A: code_integer,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17            = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4262_Suc__pred_H,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( N2
% 11.11/6.17          = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4263_Suc__diff__eq__diff__pred,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 11.11/6.17          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4264_div__geq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ~ ( ord_less_nat @ M @ N2 )
% 11.11/6.17         => ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.17            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4265_div__if,axiom,
% 11.11/6.17      ( divide_divide_nat
% 11.11/6.17      = ( ^ [M6: nat,N: nat] :
% 11.11/6.17            ( if_nat
% 11.11/6.17            @ ( ( ord_less_nat @ M6 @ N )
% 11.11/6.17              | ( N = zero_zero_nat ) )
% 11.11/6.17            @ zero_zero_nat
% 11.11/6.17            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4266_add__eq__if,axiom,
% 11.11/6.17      ( plus_plus_nat
% 11.11/6.17      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4267_nat__less__add__iff1,axiom,
% 11.11/6.17      ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ J @ I2 )
% 11.11/6.17       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.17          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4268_nat__less__add__iff2,axiom,
% 11.11/6.17      ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.17       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 11.11/6.17          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4269_mult__eq__if,axiom,
% 11.11/6.17      ( times_times_nat
% 11.11/6.17      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4270_decr__mult__lemma,axiom,
% 11.11/6.17      ! [D: int,P: int > $o,K: int] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.17       => ( ! [X5: int] :
% 11.11/6.17              ( ( P @ X5 )
% 11.11/6.17             => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 11.11/6.17         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.17           => ! [X2: int] :
% 11.11/6.17                ( ( P @ X2 )
% 11.11/6.17               => ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4271_dvd__minus__add,axiom,
% 11.11/6.17      ! [Q3: nat,N2: nat,R3: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ Q3 @ N2 )
% 11.11/6.17       => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R3 @ M ) )
% 11.11/6.17         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q3 ) )
% 11.11/6.17            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M ) @ Q3 ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4272_mod__nat__eqI,axiom,
% 11.11/6.17      ! [R3: nat,N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_nat @ R3 @ N2 )
% 11.11/6.17       => ( ( ord_less_eq_nat @ R3 @ M )
% 11.11/6.17         => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R3 ) )
% 11.11/6.17           => ( ( modulo_modulo_nat @ M @ N2 )
% 11.11/6.17              = R3 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4273_mod__pos__geq,axiom,
% 11.11/6.17      ! [L: int,K: int] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.17       => ( ( ord_less_eq_int @ L @ K )
% 11.11/6.17         => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.17            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4274_scaling__mono,axiom,
% 11.11/6.17      ! [U: real,V: real,R3: real,S: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ U @ V )
% 11.11/6.17       => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 11.11/6.17         => ( ( ord_less_eq_real @ R3 @ S )
% 11.11/6.17           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4275_scaling__mono,axiom,
% 11.11/6.17      ! [U: rat,V: rat,R3: rat,S: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ U @ V )
% 11.11/6.17       => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 11.11/6.17         => ( ( ord_less_eq_rat @ R3 @ S )
% 11.11/6.17           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4276_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17         != zero_zero_nat )
% 11.11/6.17       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.17         != zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4277_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17         != zero_zero_int )
% 11.11/6.17       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.17         != zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4278_power__diff__power__eq,axiom,
% 11.11/6.17      ! [A: nat,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_nat )
% 11.11/6.17       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 11.11/6.17              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 11.11/6.17          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 11.11/6.17              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4279_power__diff__power__eq,axiom,
% 11.11/6.17      ! [A: int,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_zero_int )
% 11.11/6.17       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 11.11/6.17              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 11.11/6.17          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 11.11/6.17              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4280_power__diff__power__eq,axiom,
% 11.11/6.17      ! [A: code_integer,N2: nat,M: nat] :
% 11.11/6.17        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.17       => ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 11.11/6.17              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 11.11/6.17          & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 11.11/6.17              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4281_signed__take__bit__int__less__exp,axiom,
% 11.11/6.17      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4282_power__eq__if,axiom,
% 11.11/6.17      ( power_power_rat
% 11.11/6.17      = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4283_power__eq__if,axiom,
% 11.11/6.17      ( power_power_complex
% 11.11/6.17      = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4284_power__eq__if,axiom,
% 11.11/6.17      ( power_power_real
% 11.11/6.17      = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4285_power__eq__if,axiom,
% 11.11/6.17      ( power_power_nat
% 11.11/6.17      = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4286_power__eq__if,axiom,
% 11.11/6.17      ( power_power_int
% 11.11/6.17      = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4287_power__minus__mult,axiom,
% 11.11/6.17      ! [N2: nat,A: complex] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 11.11/6.17          = ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4288_power__minus__mult,axiom,
% 11.11/6.17      ! [N2: nat,A: real] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 11.11/6.17          = ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4289_power__minus__mult,axiom,
% 11.11/6.17      ! [N2: nat,A: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 11.11/6.17          = ( power_power_nat @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4290_power__minus__mult,axiom,
% 11.11/6.17      ! [N2: nat,A: int] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 11.11/6.17          = ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4291_diff__le__diff__pow,axiom,
% 11.11/6.17      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 11.11/6.17       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4292_le__div__geq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.17       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( divide_divide_nat @ M @ N2 )
% 11.11/6.17            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4293_even__diff__iff,axiom,
% 11.11/6.17      ! [K: int,L: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 11.11/6.17        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4294_even__signed__take__bit__iff,axiom,
% 11.11/6.17      ! [M: nat,A: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 11.11/6.17        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4295_even__signed__take__bit__iff,axiom,
% 11.11/6.17      ! [M: nat,A: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 11.11/6.17        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4296_signed__take__bit__int__greater__eq__self__iff,axiom,
% 11.11/6.17      ! [K: int,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 11.11/6.17        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4297_signed__take__bit__int__less__self__iff,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 11.11/6.17        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4298_div__pos__geq,axiom,
% 11.11/6.17      ! [L: int,K: int] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ L )
% 11.11/6.17       => ( ( ord_less_eq_int @ L @ K )
% 11.11/6.17         => ( ( divide_divide_int @ K @ L )
% 11.11/6.17            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4299_add__0__iff,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( B
% 11.11/6.17          = ( plus_plus_complex @ B @ A ) )
% 11.11/6.17        = ( A = zero_zero_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4300_add__0__iff,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( B
% 11.11/6.17          = ( plus_plus_real @ B @ A ) )
% 11.11/6.17        = ( A = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4301_add__0__iff,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( B
% 11.11/6.17          = ( plus_plus_rat @ B @ A ) )
% 11.11/6.17        = ( A = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4302_add__0__iff,axiom,
% 11.11/6.17      ! [B: nat,A: nat] :
% 11.11/6.17        ( ( B
% 11.11/6.17          = ( plus_plus_nat @ B @ A ) )
% 11.11/6.17        = ( A = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4303_add__0__iff,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( B
% 11.11/6.17          = ( plus_plus_int @ B @ A ) )
% 11.11/6.17        = ( A = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4304_crossproduct__eq,axiom,
% 11.11/6.17      ! [W: rat,Y: rat,X4: rat,Z: rat] :
% 11.11/6.17        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X4 @ Z ) )
% 11.11/6.17          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X4 @ Y ) ) )
% 11.11/6.17        = ( ( W = X4 )
% 11.11/6.17          | ( Y = Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4305_crossproduct__eq,axiom,
% 11.11/6.17      ! [W: complex,Y: complex,X4: complex,Z: complex] :
% 11.11/6.17        ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X4 @ Z ) )
% 11.11/6.17          = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X4 @ Y ) ) )
% 11.11/6.17        = ( ( W = X4 )
% 11.11/6.17          | ( Y = Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4306_crossproduct__eq,axiom,
% 11.11/6.17      ! [W: real,Y: real,X4: real,Z: real] :
% 11.11/6.17        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X4 @ Z ) )
% 11.11/6.17          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X4 @ Y ) ) )
% 11.11/6.17        = ( ( W = X4 )
% 11.11/6.17          | ( Y = Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4307_crossproduct__eq,axiom,
% 11.11/6.17      ! [W: nat,Y: nat,X4: nat,Z: nat] :
% 11.11/6.17        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X4 @ Z ) )
% 11.11/6.17          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X4 @ Y ) ) )
% 11.11/6.17        = ( ( W = X4 )
% 11.11/6.17          | ( Y = Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4308_crossproduct__eq,axiom,
% 11.11/6.17      ! [W: int,Y: int,X4: int,Z: int] :
% 11.11/6.17        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X4 @ Z ) )
% 11.11/6.17          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X4 @ Y ) ) )
% 11.11/6.17        = ( ( W = X4 )
% 11.11/6.17          | ( Y = Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4309_crossproduct__noteq,axiom,
% 11.11/6.17      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.17        ( ( ( A != B )
% 11.11/6.17          & ( C != D ) )
% 11.11/6.17        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 11.11/6.17         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4310_crossproduct__noteq,axiom,
% 11.11/6.17      ! [A: complex,B: complex,C: complex,D: complex] :
% 11.11/6.17        ( ( ( A != B )
% 11.11/6.17          & ( C != D ) )
% 11.11/6.17        = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 11.11/6.17         != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4311_crossproduct__noteq,axiom,
% 11.11/6.17      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.17        ( ( ( A != B )
% 11.11/6.17          & ( C != D ) )
% 11.11/6.17        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 11.11/6.17         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4312_crossproduct__noteq,axiom,
% 11.11/6.17      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.17        ( ( ( A != B )
% 11.11/6.17          & ( C != D ) )
% 11.11/6.17        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 11.11/6.17         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4313_crossproduct__noteq,axiom,
% 11.11/6.17      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.17        ( ( ( A != B )
% 11.11/6.17          & ( C != D ) )
% 11.11/6.17        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 11.11/6.17         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4314_power2__diff,axiom,
% 11.11/6.17      ! [X4: rat,Y: rat] :
% 11.11/6.17        ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4315_power2__diff,axiom,
% 11.11/6.17      ! [X4: complex,Y: complex] :
% 11.11/6.17        ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4316_power2__diff,axiom,
% 11.11/6.17      ! [X4: real,Y: real] :
% 11.11/6.17        ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4317_power2__diff,axiom,
% 11.11/6.17      ! [X4: int,Y: int] :
% 11.11/6.17        ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4318_mult__exp__mod__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,A: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4319_mult__exp__mod__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,A: int] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4320_mult__exp__mod__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,A: code_integer] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4321_int__power__div__base,axiom,
% 11.11/6.17      ! [M: nat,K: int] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.17       => ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.17         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 11.11/6.17            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4322_divmod__digit__1_I2_J,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.17       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.17         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.17           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.17              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4323_divmod__digit__1_I2_J,axiom,
% 11.11/6.17      ! [A: nat,B: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 11.11/6.17       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 11.11/6.17         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.17           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.17              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4324_divmod__digit__1_I2_J,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.17       => ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.17         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 11.11/6.17           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 11.11/6.17              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4325_even__mask__div__iff_H,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4326_even__mask__div__iff_H,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4327_even__mask__div__iff_H,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4328_even__mod__4__div__2,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.17          = ( suc @ zero_zero_nat ) )
% 11.11/6.17       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4329_even__mask__div__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17            = zero_zero_nat )
% 11.11/6.17          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4330_even__mask__div__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17            = zero_zero_int )
% 11.11/6.17          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4331_even__mask__div__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( 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 ) ) @ N2 ) ) )
% 11.11/6.17        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17            = zero_z3403309356797280102nteger )
% 11.11/6.17          | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4332_exp__div__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_times_nat
% 11.11/6.17          @ ( zero_n2687167440665602831ol_nat
% 11.11/6.17            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 11.11/6.17               != zero_zero_nat )
% 11.11/6.17              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 11.11/6.17          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4333_exp__div__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_times_int
% 11.11/6.17          @ ( zero_n2684676970156552555ol_int
% 11.11/6.17            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 11.11/6.17               != zero_zero_int )
% 11.11/6.17              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 11.11/6.17          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4334_exp__div__exp__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_3573771949741848930nteger
% 11.11/6.17          @ ( zero_n356916108424825756nteger
% 11.11/6.17            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 11.11/6.17               != zero_z3403309356797280102nteger )
% 11.11/6.17              & ( ord_less_eq_nat @ N2 @ M ) ) )
% 11.11/6.17          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4335_neg__zmod__mult__2,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.17       => ( ( 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 ) )
% 11.11/6.17          = ( 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 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4336_divmod__step__eq,axiom,
% 11.11/6.17      ! [L: num,R3: nat,Q3: nat] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 11.11/6.17         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 11.11/6.17            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 11.11/6.17         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 11.11/6.17            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4337_divmod__step__eq,axiom,
% 11.11/6.17      ! [L: num,R3: int,Q3: int] :
% 11.11/6.17        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 11.11/6.17         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.17            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 11.11/6.17         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.17            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4338_divmod__step__eq,axiom,
% 11.11/6.17      ! [L: num,R3: code_integer,Q3: code_integer] :
% 11.11/6.17        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 11.11/6.17         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 11.11/6.17            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 11.11/6.17        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 11.11/6.17         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 11.11/6.17            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4339_signed__take__bit__rec,axiom,
% 11.11/6.17      ( bit_ri6519982836138164636nteger
% 11.11/6.17      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = 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 @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4340_signed__take__bit__rec,axiom,
% 11.11/6.17      ( bit_ri631733984087533419it_int
% 11.11/6.17      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = 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 @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4341_take__bit__rec,axiom,
% 11.11/6.17      ( bit_se1745604003318907178nteger
% 11.11/6.17      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4342_take__bit__rec,axiom,
% 11.11/6.17      ( bit_se2923211474154528505it_int
% 11.11/6.17      = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ 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 ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4343_take__bit__rec,axiom,
% 11.11/6.17      ( bit_se2925701944663578781it_nat
% 11.11/6.17      = ( ^ [N: nat,A3: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ 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 ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4344_odd__mod__4__div__2,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.17          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 11.11/6.17       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4345_Bernoulli__inequality__even,axiom,
% 11.11/6.17      ! [N2: nat,X4: real] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4346_Suc__0__xor__eq,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.17        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.17          @ ( zero_n2687167440665602831ol_nat
% 11.11/6.17            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4347_add_Oinverse__inverse,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4348_add_Oinverse__inverse,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4349_add_Oinverse__inverse,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4350_add_Oinverse__inverse,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4351_add_Oinverse__inverse,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4352_neg__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ A )
% 11.11/6.17          = ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( A = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4353_neg__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ A )
% 11.11/6.17          = ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( A = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4354_neg__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( A = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4355_neg__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( A = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4356_neg__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( A = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4357_Compl__anti__mono,axiom,
% 11.11/6.17      ! [A2: set_int,B3: set_int] :
% 11.11/6.17        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.17       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4358_Compl__subset__Compl__iff,axiom,
% 11.11/6.17      ! [A2: set_int,B3: set_int] :
% 11.11/6.17        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 11.11/6.17        = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4359_of__nat__eq__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ( semiri5074537144036343181t_real @ M )
% 11.11/6.17          = ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4360_of__nat__eq__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ( semiri1314217659103216013at_int @ M )
% 11.11/6.17          = ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4361_of__nat__eq__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ( semiri1316708129612266289at_nat @ M )
% 11.11/6.17          = ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4362_semiring__norm_I90_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( bit1 @ M )
% 11.11/6.17          = ( bit1 @ N2 ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4363_bit_Oxor__left__self,axiom,
% 11.11/6.17      ! [X4: int,Y: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_se6526347334894502574or_int @ X4 @ Y ) )
% 11.11/6.17        = Y ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4364_idiff__0,axiom,
% 11.11/6.17      ! [N2: extended_enat] :
% 11.11/6.17        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 11.11/6.17        = zero_z5237406670263579293d_enat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4365_idiff__0__right,axiom,
% 11.11/6.17      ! [N2: extended_enat] :
% 11.11/6.17        ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 11.11/6.17        = N2 ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4366_neg__le__iff__le,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4367_neg__le__iff__le,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4368_neg__le__iff__le,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4369_neg__le__iff__le,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4370_add_Oinverse__neutral,axiom,
% 11.11/6.17      ( ( uminus_uminus_real @ zero_zero_real )
% 11.11/6.17      = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4371_add_Oinverse__neutral,axiom,
% 11.11/6.17      ( ( uminus_uminus_int @ zero_zero_int )
% 11.11/6.17      = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4372_add_Oinverse__neutral,axiom,
% 11.11/6.17      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 11.11/6.17      = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4373_add_Oinverse__neutral,axiom,
% 11.11/6.17      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 11.11/6.17      = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4374_add_Oinverse__neutral,axiom,
% 11.11/6.17      ( ( uminus_uminus_rat @ zero_zero_rat )
% 11.11/6.17      = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4375_neg__0__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( zero_zero_real
% 11.11/6.17          = ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( zero_zero_real = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4376_neg__0__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( zero_zero_int
% 11.11/6.17          = ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( zero_zero_int = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4377_neg__0__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( zero_zero_complex
% 11.11/6.17          = ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.17        = ( zero_zero_complex = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4378_neg__0__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( zero_z3403309356797280102nteger
% 11.11/6.17          = ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( zero_z3403309356797280102nteger = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4379_neg__0__equal__iff__equal,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( zero_zero_rat
% 11.11/6.17          = ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( zero_zero_rat = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4380_neg__equal__0__iff__equal,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ A )
% 11.11/6.17          = zero_zero_real )
% 11.11/6.17        = ( A = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4381_neg__equal__0__iff__equal,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ A )
% 11.11/6.17          = zero_zero_int )
% 11.11/6.17        = ( A = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4382_neg__equal__0__iff__equal,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.17          = zero_zero_complex )
% 11.11/6.17        = ( A = zero_zero_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4383_neg__equal__0__iff__equal,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = zero_z3403309356797280102nteger )
% 11.11/6.17        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4384_neg__equal__0__iff__equal,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = zero_zero_rat )
% 11.11/6.17        = ( A = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4385_equal__neg__zero,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( A = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4386_equal__neg__zero,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( A = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4387_equal__neg__zero,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4388_equal__neg__zero,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( A = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4389_neg__equal__zero,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ A )
% 11.11/6.17          = A )
% 11.11/6.17        = ( A = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4390_neg__equal__zero,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ A )
% 11.11/6.17          = A )
% 11.11/6.17        = ( A = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4391_neg__equal__zero,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = A )
% 11.11/6.17        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4392_neg__equal__zero,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = A )
% 11.11/6.17        = ( A = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4393_neg__less__iff__less,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_real @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4394_neg__less__iff__less,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_int @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4395_neg__less__iff__less,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4396_neg__less__iff__less,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4397_neg__numeral__eq__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 11.11/6.17          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4398_neg__numeral__eq__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 11.11/6.17          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4399_neg__numeral__eq__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4400_neg__numeral__eq__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4401_neg__numeral__eq__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 11.11/6.17          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( M = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4402_mult__minus__left,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4403_mult__minus__left,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4404_mult__minus__left,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4405_mult__minus__left,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4406_mult__minus__left,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4407_minus__mult__minus,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( times_times_real @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4408_minus__mult__minus,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( times_times_int @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4409_minus__mult__minus,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( times_times_complex @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4410_minus__mult__minus,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4411_minus__mult__minus,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( times_times_rat @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4412_mult__minus__right,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4413_mult__minus__right,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4414_mult__minus__right,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4415_mult__minus__right,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4416_mult__minus__right,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4417_minus__add__distrib,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 11.11/6.17        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4418_minus__add__distrib,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.17        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4419_minus__add__distrib,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 11.11/6.17        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4420_minus__add__distrib,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.17        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4421_minus__add__distrib,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.17        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4422_minus__add__cancel,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4423_minus__add__cancel,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4424_minus__add__cancel,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4425_minus__add__cancel,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4426_minus__add__cancel,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4427_add__minus__cancel,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4428_add__minus__cancel,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4429_add__minus__cancel,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4430_add__minus__cancel,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4431_add__minus__cancel,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 11.11/6.17        = B ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4432_minus__diff__eq,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 11.11/6.17        = ( minus_minus_real @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4433_minus__diff__eq,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 11.11/6.17        = ( minus_minus_int @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4434_minus__diff__eq,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 11.11/6.17        = ( minus_minus_complex @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4435_minus__diff__eq,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 11.11/6.17        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4436_minus__diff__eq,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.17        = ( minus_minus_rat @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4437_div__minus__minus,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( divide_divide_int @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4438_div__minus__minus,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4439_dvd__minus__iff,axiom,
% 11.11/6.17      ! [X4: real,Y: real] :
% 11.11/6.17        ( ( dvd_dvd_real @ X4 @ ( uminus_uminus_real @ Y ) )
% 11.11/6.17        = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4440_dvd__minus__iff,axiom,
% 11.11/6.17      ! [X4: int,Y: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ X4 @ ( uminus_uminus_int @ Y ) )
% 11.11/6.17        = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4441_dvd__minus__iff,axiom,
% 11.11/6.17      ! [X4: complex,Y: complex] :
% 11.11/6.17        ( ( dvd_dvd_complex @ X4 @ ( uminus1482373934393186551omplex @ Y ) )
% 11.11/6.17        = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4442_dvd__minus__iff,axiom,
% 11.11/6.17      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ X4 @ ( uminus1351360451143612070nteger @ Y ) )
% 11.11/6.17        = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4443_dvd__minus__iff,axiom,
% 11.11/6.17      ! [X4: rat,Y: rat] :
% 11.11/6.17        ( ( dvd_dvd_rat @ X4 @ ( uminus_uminus_rat @ Y ) )
% 11.11/6.17        = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4444_minus__dvd__iff,axiom,
% 11.11/6.17      ! [X4: real,Y: real] :
% 11.11/6.17        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X4 ) @ Y )
% 11.11/6.17        = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4445_minus__dvd__iff,axiom,
% 11.11/6.17      ! [X4: int,Y: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X4 ) @ Y )
% 11.11/6.17        = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4446_minus__dvd__iff,axiom,
% 11.11/6.17      ! [X4: complex,Y: complex] :
% 11.11/6.17        ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y )
% 11.11/6.17        = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4447_minus__dvd__iff,axiom,
% 11.11/6.17      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X4 ) @ Y )
% 11.11/6.17        = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4448_minus__dvd__iff,axiom,
% 11.11/6.17      ! [X4: rat,Y: rat] :
% 11.11/6.17        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X4 ) @ Y )
% 11.11/6.17        = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4449_semiring__norm_I88_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( bit0 @ M )
% 11.11/6.17       != ( bit1 @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4450_semiring__norm_I89_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( bit1 @ M )
% 11.11/6.17       != ( bit0 @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4451_semiring__norm_I84_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one
% 11.11/6.17       != ( bit1 @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4452_semiring__norm_I86_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( bit1 @ M )
% 11.11/6.17       != one ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4453_mod__minus__minus,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4454_mod__minus__minus,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4455_take__bit__of__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4456_take__bit__of__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 11.11/6.17        = zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4457_real__add__minus__iff,axiom,
% 11.11/6.17      ! [X4: real,A: real] :
% 11.11/6.17        ( ( ( plus_plus_real @ X4 @ ( uminus_uminus_real @ A ) )
% 11.11/6.17          = zero_zero_real )
% 11.11/6.17        = ( X4 = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4458_bit_Oxor__self,axiom,
% 11.11/6.17      ! [X4: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ X4 @ X4 )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4459_xor__self__eq,axiom,
% 11.11/6.17      ! [A: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ A @ A )
% 11.11/6.17        = zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4460_xor__self__eq,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ A @ A )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4461_xor_Oleft__neutral,axiom,
% 11.11/6.17      ! [A: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4462_xor_Oleft__neutral,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4463_xor_Oright__neutral,axiom,
% 11.11/6.17      ! [A: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4464_xor_Oright__neutral,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4465_take__bit__xor,axiom,
% 11.11/6.17      ! [N2: nat,A: int,B: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 11.11/6.17        = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4466_take__bit__xor,axiom,
% 11.11/6.17      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 11.11/6.17        = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4467_concat__bit__of__zero__2,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 11.11/6.17        = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4468_semiring__norm_I80_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4469_semiring__norm_I73_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4470_neg__less__eq__nonneg,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 11.11/6.17        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4471_neg__less__eq__nonneg,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4472_neg__less__eq__nonneg,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 11.11/6.17        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4473_neg__less__eq__nonneg,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 11.11/6.17        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4474_less__eq__neg__nonpos,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4475_less__eq__neg__nonpos,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4476_less__eq__neg__nonpos,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4477_less__eq__neg__nonpos,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4478_neg__le__0__iff__le,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 11.11/6.17        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4479_neg__le__0__iff__le,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4480_neg__le__0__iff__le,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 11.11/6.17        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4481_neg__le__0__iff__le,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 11.11/6.17        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4482_neg__0__le__iff__le,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4483_neg__0__le__iff__le,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4484_neg__0__le__iff__le,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4485_neg__0__le__iff__le,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4486_less__neg__neg,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4487_less__neg__neg,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4488_less__neg__neg,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4489_less__neg__neg,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4490_neg__less__pos,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 11.11/6.17        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4491_neg__less__pos,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 11.11/6.17        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4492_neg__less__pos,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4493_neg__less__pos,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 11.11/6.17        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4494_neg__0__less__iff__less,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4495_neg__0__less__iff__less,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4496_neg__0__less__iff__less,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4497_neg__0__less__iff__less,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4498_neg__less__0__iff__less,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 11.11/6.17        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4499_neg__less__0__iff__less,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 11.11/6.17        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4500_neg__less__0__iff__less,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4501_neg__less__0__iff__less,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 11.11/6.17        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4502_ab__left__minus,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 11.11/6.17        = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4503_ab__left__minus,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4504_ab__left__minus,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 11.11/6.17        = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4505_ab__left__minus,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 11.11/6.17        = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4506_ab__left__minus,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 11.11/6.17        = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4507_add_Oright__inverse,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 11.11/6.17        = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4508_add_Oright__inverse,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4509_add_Oright__inverse,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.17        = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4510_add_Oright__inverse,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.17        = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4511_add_Oright__inverse,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 11.11/6.17        = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4512_diff__0,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( minus_minus_real @ zero_zero_real @ A )
% 11.11/6.17        = ( uminus_uminus_real @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4513_diff__0,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( minus_minus_int @ zero_zero_int @ A )
% 11.11/6.17        = ( uminus_uminus_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4514_diff__0,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4515_diff__0,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4516_diff__0,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 11.11/6.17        = ( uminus_uminus_rat @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4517_add__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4518_add__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4519_add__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4520_add__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4521_add__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4522_mult__minus1,axiom,
% 11.11/6.17      ! [Z: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 11.11/6.17        = ( uminus_uminus_real @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4523_mult__minus1,axiom,
% 11.11/6.17      ! [Z: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 11.11/6.17        = ( uminus_uminus_int @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4524_mult__minus1,axiom,
% 11.11/6.17      ! [Z: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4525_mult__minus1,axiom,
% 11.11/6.17      ! [Z: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4526_mult__minus1,axiom,
% 11.11/6.17      ! [Z: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 11.11/6.17        = ( uminus_uminus_rat @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4527_mult__minus1__right,axiom,
% 11.11/6.17      ! [Z: real] :
% 11.11/6.17        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17        = ( uminus_uminus_real @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4528_mult__minus1__right,axiom,
% 11.11/6.17      ! [Z: int] :
% 11.11/6.17        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = ( uminus_uminus_int @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4529_mult__minus1__right,axiom,
% 11.11/6.17      ! [Z: complex] :
% 11.11/6.17        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4530_mult__minus1__right,axiom,
% 11.11/6.17      ! [Z: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4531_mult__minus1__right,axiom,
% 11.11/6.17      ! [Z: rat] :
% 11.11/6.17        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17        = ( uminus_uminus_rat @ Z ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4532_uminus__add__conv__diff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17        = ( minus_minus_real @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4533_uminus__add__conv__diff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17        = ( minus_minus_int @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4534_uminus__add__conv__diff,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 11.11/6.17        = ( minus_minus_complex @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4535_uminus__add__conv__diff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4536_uminus__add__conv__diff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17        = ( minus_minus_rat @ B @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4537_diff__minus__eq__add,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( plus_plus_real @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4538_diff__minus__eq__add,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( plus_plus_int @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4539_diff__minus__eq__add,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( plus_plus_complex @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4540_diff__minus__eq__add,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4541_diff__minus__eq__add,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( plus_plus_rat @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4542_divide__minus1,axiom,
% 11.11/6.17      ! [X4: real] :
% 11.11/6.17        ( ( divide_divide_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17        = ( uminus_uminus_real @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4543_divide__minus1,axiom,
% 11.11/6.17      ! [X4: complex] :
% 11.11/6.17        ( ( divide1717551699836669952omplex @ X4 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4544_divide__minus1,axiom,
% 11.11/6.17      ! [X4: rat] :
% 11.11/6.17        ( ( divide_divide_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17        = ( uminus_uminus_rat @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4545_div__minus1__right,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = ( uminus_uminus_int @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4546_div__minus1__right,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4547_of__nat__0,axiom,
% 11.11/6.17      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 11.11/6.17      = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4548_of__nat__0,axiom,
% 11.11/6.17      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 11.11/6.17      = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4549_of__nat__0,axiom,
% 11.11/6.17      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 11.11/6.17      = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4550_of__nat__0,axiom,
% 11.11/6.17      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 11.11/6.17      = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4551_of__nat__0,axiom,
% 11.11/6.17      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 11.11/6.17      = zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4552_of__nat__0__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( zero_zero_complex
% 11.11/6.17          = ( semiri8010041392384452111omplex @ N2 ) )
% 11.11/6.17        = ( zero_zero_nat = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4553_of__nat__0__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( zero_zero_rat
% 11.11/6.17          = ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17        = ( zero_zero_nat = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4554_of__nat__0__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( zero_zero_real
% 11.11/6.17          = ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( zero_zero_nat = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4555_of__nat__0__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( zero_zero_int
% 11.11/6.17          = ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( zero_zero_nat = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4556_of__nat__0__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( zero_zero_nat
% 11.11/6.17          = ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( zero_zero_nat = N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4557_of__nat__eq__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ( semiri8010041392384452111omplex @ M )
% 11.11/6.17          = zero_zero_complex )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4558_of__nat__eq__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ( semiri681578069525770553at_rat @ M )
% 11.11/6.17          = zero_zero_rat )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4559_of__nat__eq__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ( semiri5074537144036343181t_real @ M )
% 11.11/6.17          = zero_zero_real )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4560_of__nat__eq__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ( semiri1314217659103216013at_int @ M )
% 11.11/6.17          = zero_zero_int )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4561_of__nat__eq__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ( semiri1316708129612266289at_nat @ M )
% 11.11/6.17          = zero_zero_nat )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4562_of__nat__less__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4563_of__nat__less__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4564_of__nat__less__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4565_of__nat__less__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4566_of__nat__le__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4567_of__nat__le__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4568_of__nat__le__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4569_of__nat__le__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4570_of__nat__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.17        = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4571_of__nat__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.17        = ( numera6690914467698888265omplex @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4572_of__nat__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.17        = ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4573_of__nat__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.17        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4574_of__nat__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.17        = ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4575_minus__mod__self1,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 11.11/6.17        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4576_minus__mod__self1,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 11.11/6.17        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4577_of__nat__add,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.17        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4578_of__nat__add,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.17        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4579_of__nat__add,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.17        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4580_of__nat__add,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.17        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4581_of__nat__mult,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.17        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4582_of__nat__mult,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.17        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4583_of__nat__mult,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.17        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4584_of__nat__mult,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 11.11/6.17        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4585_take__bit__0,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4586_take__bit__0,axiom,
% 11.11/6.17      ! [A: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 11.11/6.17        = zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4587_of__nat__eq__1__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( semiri8010041392384452111omplex @ N2 )
% 11.11/6.17          = one_one_complex )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4588_of__nat__eq__1__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( semiri681578069525770553at_rat @ N2 )
% 11.11/6.17          = one_one_rat )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4589_of__nat__eq__1__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( semiri5074537144036343181t_real @ N2 )
% 11.11/6.17          = one_one_real )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4590_of__nat__eq__1__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( semiri1314217659103216013at_int @ N2 )
% 11.11/6.17          = one_one_int )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4591_of__nat__eq__1__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( semiri1316708129612266289at_nat @ N2 )
% 11.11/6.17          = one_one_nat )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4592_of__nat__1__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( one_one_complex
% 11.11/6.17          = ( semiri8010041392384452111omplex @ N2 ) )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4593_of__nat__1__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( one_one_rat
% 11.11/6.17          = ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4594_of__nat__1__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( one_one_real
% 11.11/6.17          = ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4595_of__nat__1__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( one_one_int
% 11.11/6.17          = ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4596_of__nat__1__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( one_one_nat
% 11.11/6.17          = ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( N2 = one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4597_of__nat__1,axiom,
% 11.11/6.17      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 11.11/6.17      = one_one_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4598_of__nat__1,axiom,
% 11.11/6.17      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 11.11/6.17      = one_one_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4599_of__nat__1,axiom,
% 11.11/6.17      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 11.11/6.17      = one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4600_of__nat__1,axiom,
% 11.11/6.17      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 11.11/6.17      = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4601_of__nat__1,axiom,
% 11.11/6.17      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 11.11/6.17      = one_one_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4602_take__bit__Suc__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 11.11/6.17        = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4603_take__bit__Suc__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 11.11/6.17        = one_one_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4604_take__bit__numeral__1,axiom,
% 11.11/6.17      ! [L: num] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 11.11/6.17        = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4605_take__bit__numeral__1,axiom,
% 11.11/6.17      ! [L: num] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 11.11/6.17        = one_one_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4606_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ( semiri8010041392384452111omplex @ X4 )
% 11.11/6.17          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 11.11/6.17        = ( X4
% 11.11/6.17          = ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4607_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ( semiri5074537144036343181t_real @ X4 )
% 11.11/6.17          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 11.11/6.17        = ( X4
% 11.11/6.17          = ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4608_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ( semiri1314217659103216013at_int @ X4 )
% 11.11/6.17          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 11.11/6.17        = ( X4
% 11.11/6.17          = ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4609_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ( semiri1316708129612266289at_nat @ X4 )
% 11.11/6.17          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 11.11/6.17        = ( X4
% 11.11/6.17          = ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4610_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 11.11/6.17          = ( semiri8010041392384452111omplex @ X4 ) )
% 11.11/6.17        = ( ( power_power_nat @ B @ W )
% 11.11/6.17          = X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4611_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 11.11/6.17          = ( semiri5074537144036343181t_real @ X4 ) )
% 11.11/6.17        = ( ( power_power_nat @ B @ W )
% 11.11/6.17          = X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4612_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 11.11/6.17          = ( semiri1314217659103216013at_int @ X4 ) )
% 11.11/6.17        = ( ( power_power_nat @ B @ W )
% 11.11/6.17          = X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4613_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 11.11/6.17          = ( semiri1316708129612266289at_nat @ X4 ) )
% 11.11/6.17        = ( ( power_power_nat @ B @ W )
% 11.11/6.17          = X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4614_of__nat__power,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 11.11/6.17        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4615_of__nat__power,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 11.11/6.17        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4616_of__nat__power,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 11.11/6.17        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4617_of__nat__power,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 11.11/6.17        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4618_signed__take__bit__of__minus__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4619_signed__take__bit__of__minus__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4620_semiring__norm_I9_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.17        = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4621_semiring__norm_I7_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4622_semiring__norm_I15_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.17        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4623_semiring__norm_I14_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4624_semiring__norm_I81_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.17        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4625_semiring__norm_I72_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4626_semiring__norm_I77_J,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4627_semiring__norm_I70_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4628_dbl__simps_I1_J,axiom,
% 11.11/6.17      ! [K: num] :
% 11.11/6.17        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4629_dbl__simps_I1_J,axiom,
% 11.11/6.17      ! [K: num] :
% 11.11/6.17        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4630_dbl__simps_I1_J,axiom,
% 11.11/6.17      ! [K: num] :
% 11.11/6.17        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4631_dbl__simps_I1_J,axiom,
% 11.11/6.17      ! [K: num] :
% 11.11/6.17        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4632_dbl__simps_I1_J,axiom,
% 11.11/6.17      ! [K: num] :
% 11.11/6.17        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4633_of__nat__of__bool,axiom,
% 11.11/6.17      ! [P: $o] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 11.11/6.17        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4634_of__nat__of__bool,axiom,
% 11.11/6.17      ! [P: $o] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 11.11/6.17        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4635_of__nat__of__bool,axiom,
% 11.11/6.17      ! [P: $o] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 11.11/6.17        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4636_of__nat__of__bool,axiom,
% 11.11/6.17      ! [P: $o] :
% 11.11/6.17        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 11.11/6.17        = ( zero_n356916108424825756nteger @ P ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4637_add__neg__numeral__special_I7_J,axiom,
% 11.11/6.17      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17      = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4638_add__neg__numeral__special_I7_J,axiom,
% 11.11/6.17      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17      = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4639_add__neg__numeral__special_I7_J,axiom,
% 11.11/6.17      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17      = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4640_add__neg__numeral__special_I7_J,axiom,
% 11.11/6.17      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17      = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4641_add__neg__numeral__special_I7_J,axiom,
% 11.11/6.17      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17      = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4642_add__neg__numeral__special_I8_J,axiom,
% 11.11/6.17      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 11.11/6.17      = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4643_add__neg__numeral__special_I8_J,axiom,
% 11.11/6.17      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 11.11/6.17      = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4644_add__neg__numeral__special_I8_J,axiom,
% 11.11/6.17      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 11.11/6.17      = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4645_add__neg__numeral__special_I8_J,axiom,
% 11.11/6.17      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 11.11/6.17      = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4646_add__neg__numeral__special_I8_J,axiom,
% 11.11/6.17      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 11.11/6.17      = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4647_diff__numeral__special_I12_J,axiom,
% 11.11/6.17      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17      = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4648_diff__numeral__special_I12_J,axiom,
% 11.11/6.17      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17      = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4649_diff__numeral__special_I12_J,axiom,
% 11.11/6.17      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17      = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4650_diff__numeral__special_I12_J,axiom,
% 11.11/6.17      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17      = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4651_diff__numeral__special_I12_J,axiom,
% 11.11/6.17      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17      = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4652_numeral__eq__neg__one__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.17          = ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4653_numeral__eq__neg__one__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.17          = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4654_numeral__eq__neg__one__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4655_numeral__eq__neg__one__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4656_numeral__eq__neg__one__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.17          = ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4657_neg__one__eq__numeral__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ one_one_real )
% 11.11/6.17          = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4658_neg__one__eq__numeral__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ one_one_int )
% 11.11/6.17          = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4659_neg__one__eq__numeral__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4660_neg__one__eq__numeral__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4661_neg__one__eq__numeral__iff,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ one_one_rat )
% 11.11/6.17          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( N2 = one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4662_of__nat__le__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4663_of__nat__le__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4664_of__nat__le__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4665_of__nat__le__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 11.11/6.17        = ( M = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4666_left__minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat,A: real] :
% 11.11/6.17        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4667_left__minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat,A: int] :
% 11.11/6.17        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4668_left__minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat,A: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4669_left__minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat,A: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4670_left__minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat,A: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 11.11/6.17        = A ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4671_minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 11.11/6.17        = one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4672_minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 11.11/6.17        = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4673_minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 11.11/6.17        = one_one_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4674_minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 11.11/6.17        = one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4675_minus__one__mult__self,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 11.11/6.17        = one_one_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4676_mod__minus1__right,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4677_mod__minus1__right,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4678_of__nat__Suc,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 11.11/6.17        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4679_of__nat__Suc,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 11.11/6.17        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4680_of__nat__Suc,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 11.11/6.17        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4681_of__nat__Suc,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 11.11/6.17        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4682_of__nat__Suc,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 11.11/6.17        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4683_take__bit__of__1__eq__0__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 11.11/6.17          = zero_zero_int )
% 11.11/6.17        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4684_take__bit__of__1__eq__0__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 11.11/6.17          = zero_zero_nat )
% 11.11/6.17        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4685_semiring__norm_I168_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: real] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 11.11/6.17        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4686_semiring__norm_I168_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: int] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 11.11/6.17        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4687_semiring__norm_I168_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 11.11/6.17        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4688_semiring__norm_I168_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 11.11/6.17        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4689_semiring__norm_I168_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 11.11/6.17        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4690_diff__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4691_diff__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4692_diff__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4693_diff__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4694_diff__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4695_diff__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4696_diff__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4697_diff__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4698_diff__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4699_diff__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4700_zdiv__numeral__Bit1,axiom,
% 11.11/6.17      ! [V: num,W: num] :
% 11.11/6.17        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 11.11/6.17        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4701_semiring__norm_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 11.11/6.17        = ( bit1 @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4702_semiring__norm_I4_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4703_semiring__norm_I5_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 11.11/6.17        = ( bit1 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4704_semiring__norm_I8_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 11.11/6.17        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4705_semiring__norm_I10_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4706_semiring__norm_I172_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4707_semiring__norm_I172_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4708_semiring__norm_I172_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4709_semiring__norm_I172_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4710_semiring__norm_I172_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4711_semiring__norm_I171_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: real] :
% 11.11/6.17        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4712_semiring__norm_I171_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: int] :
% 11.11/6.17        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4713_semiring__norm_I171_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4714_semiring__norm_I171_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4715_semiring__norm_I171_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 11.11/6.17        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4716_semiring__norm_I170_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 11.11/6.17        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4717_semiring__norm_I170_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 11.11/6.17        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4718_semiring__norm_I170_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 11.11/6.17        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4719_semiring__norm_I170_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4720_semiring__norm_I170_J,axiom,
% 11.11/6.17      ! [V: num,W: num,Y: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 11.11/6.17        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4721_mult__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4722_mult__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4723_mult__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4724_mult__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4725_mult__neg__numeral__simps_I3_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4726_mult__neg__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4727_mult__neg__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4728_mult__neg__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4729_mult__neg__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4730_mult__neg__numeral__simps_I2_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4731_mult__neg__numeral__simps_I1_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4732_mult__neg__numeral__simps_I1_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4733_mult__neg__numeral__simps_I1_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4734_mult__neg__numeral__simps_I1_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4735_mult__neg__numeral__simps_I1_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4736_neg__numeral__le__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4737_neg__numeral__le__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4738_neg__numeral__le__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4739_neg__numeral__le__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( ord_less_eq_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4740_neg__numeral__less__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( ord_less_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4741_neg__numeral__less__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( ord_less_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4742_neg__numeral__less__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( ord_less_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4743_neg__numeral__less__iff,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( ord_less_num @ N2 @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4744_take__bit__of__Suc__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.17        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4745_semiring__norm_I16_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4746_semiring__norm_I79_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4747_semiring__norm_I74_J,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.17        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4748_not__neg__one__le__neg__numeral__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4749_not__neg__one__le__neg__numeral__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4750_not__neg__one__le__neg__numeral__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4751_not__neg__one__le__neg__numeral__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4752_le__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: real,B: real,W: num] :
% 11.11/6.17        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 11.11/6.17        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4753_le__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: rat,B: rat,W: num] :
% 11.11/6.17        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 11.11/6.17        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4754_divide__le__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: real,W: num,A: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 11.11/6.17        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4755_divide__le__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: rat,W: num,A: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 11.11/6.17        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4756_eq__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: real,B: real,W: num] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 11.11/6.17        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.17             != zero_zero_real )
% 11.11/6.17           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.17              = B ) )
% 11.11/6.17          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.17              = zero_zero_real )
% 11.11/6.17           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4757_eq__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: complex,B: complex,W: num] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 11.11/6.17        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.17             != zero_zero_complex )
% 11.11/6.17           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.17              = B ) )
% 11.11/6.17          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.17              = zero_zero_complex )
% 11.11/6.17           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4758_eq__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: rat,B: rat,W: num] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 11.11/6.17        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.17             != zero_zero_rat )
% 11.11/6.17           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.17              = B ) )
% 11.11/6.17          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.17              = zero_zero_rat )
% 11.11/6.17           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4759_divide__eq__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: real,W: num,A: real] :
% 11.11/6.17        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.17          = A )
% 11.11/6.17        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.17             != zero_zero_real )
% 11.11/6.17           => ( B
% 11.11/6.17              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 11.11/6.17          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.17              = zero_zero_real )
% 11.11/6.17           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4760_divide__eq__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: complex,W: num,A: complex] :
% 11.11/6.17        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.17          = A )
% 11.11/6.17        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.17             != zero_zero_complex )
% 11.11/6.17           => ( B
% 11.11/6.17              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 11.11/6.17          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.17              = zero_zero_complex )
% 11.11/6.17           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4761_divide__eq__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: rat,W: num,A: rat] :
% 11.11/6.17        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.17          = A )
% 11.11/6.17        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.17             != zero_zero_rat )
% 11.11/6.17           => ( B
% 11.11/6.17              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 11.11/6.17          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.17              = zero_zero_rat )
% 11.11/6.17           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4762_neg__numeral__less__neg__one__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4763_neg__numeral__less__neg__one__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4764_neg__numeral__less__neg__one__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4765_neg__numeral__less__neg__one__iff,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17        = ( M != one ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4766_less__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: real,B: real,W: num] :
% 11.11/6.17        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 11.11/6.17        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4767_less__divide__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [A: rat,B: rat,W: num] :
% 11.11/6.17        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 11.11/6.17        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4768_divide__less__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: real,W: num,A: real] :
% 11.11/6.17        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 11.11/6.17        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4769_divide__less__eq__numeral1_I2_J,axiom,
% 11.11/6.17      ! [B: rat,W: num,A: rat] :
% 11.11/6.17        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 11.11/6.17        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4770_of__nat__0__less__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4771_of__nat__0__less__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4772_of__nat__0__less__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4773_of__nat__0__less__iff,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4774_power2__minus,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4775_power2__minus,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4776_power2__minus,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4777_power2__minus,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4778_power2__minus,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4779_xor__numerals_I3_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4780_xor__numerals_I3_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4781_of__nat__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4782_of__nat__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4783_of__nat__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4784_of__nat__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4785_of__nat__less__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4786_of__nat__less__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4787_of__nat__less__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4788_of__nat__less__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4789_xor__numerals_I1_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4790_xor__numerals_I1_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4791_xor__numerals_I2_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4792_xor__numerals_I2_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4793_xor__numerals_I5_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4794_xor__numerals_I5_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 11.11/6.17        = ( numeral_numeral_int @ ( bit1 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4795_xor__numerals_I8_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4796_xor__numerals_I8_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 11.11/6.17        = ( numeral_numeral_int @ ( bit0 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4797_of__nat__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4798_of__nat__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4799_of__nat__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4800_of__nat__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,B: nat,W: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4801_of__nat__le__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4802_of__nat__le__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4803_of__nat__le__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4804_of__nat__le__of__nat__power__cancel__iff,axiom,
% 11.11/6.17      ! [B: nat,W: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4805_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [Y: nat,X4: num,N2: nat] :
% 11.11/6.17        ( ( ( semiri4216267220026989637d_enat @ Y )
% 11.11/6.17          = ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 ) )
% 11.11/6.17        = ( Y
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4806_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [Y: nat,X4: num,N2: nat] :
% 11.11/6.17        ( ( ( semiri8010041392384452111omplex @ Y )
% 11.11/6.17          = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 11.11/6.17        = ( Y
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4807_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [Y: nat,X4: num,N2: nat] :
% 11.11/6.17        ( ( ( semiri5074537144036343181t_real @ Y )
% 11.11/6.17          = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.17        = ( Y
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4808_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [Y: nat,X4: num,N2: nat] :
% 11.11/6.17        ( ( ( semiri1314217659103216013at_int @ Y )
% 11.11/6.17          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 11.11/6.17        = ( Y
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4809_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [Y: nat,X4: num,N2: nat] :
% 11.11/6.17        ( ( ( semiri1316708129612266289at_nat @ Y )
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 11.11/6.17        = ( Y
% 11.11/6.17          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4810_numeral__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: num,N2: nat,Y: nat] :
% 11.11/6.17        ( ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 )
% 11.11/6.17          = ( semiri4216267220026989637d_enat @ Y ) )
% 11.11/6.17        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4811_numeral__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: num,N2: nat,Y: nat] :
% 11.11/6.17        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 11.11/6.17          = ( semiri8010041392384452111omplex @ Y ) )
% 11.11/6.17        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4812_numeral__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: num,N2: nat,Y: nat] :
% 11.11/6.17        ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 11.11/6.17          = ( semiri5074537144036343181t_real @ Y ) )
% 11.11/6.17        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4813_numeral__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: num,N2: nat,Y: nat] :
% 11.11/6.17        ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.17          = ( semiri1314217659103216013at_int @ Y ) )
% 11.11/6.17        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4814_numeral__power__eq__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [X4: num,N2: nat,Y: nat] :
% 11.11/6.17        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = ( semiri1316708129612266289at_nat @ Y ) )
% 11.11/6.17        = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.17          = Y ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4815_real__of__nat__less__numeral__iff,axiom,
% 11.11/6.17      ! [N2: nat,W: num] :
% 11.11/6.17        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 11.11/6.17        = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4816_numeral__less__real__of__nat__iff,axiom,
% 11.11/6.17      ! [W: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4817_numeral__le__real__of__nat__iff,axiom,
% 11.11/6.17      ! [N2: num,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4818_take__bit__of__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 11.11/6.17        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4819_take__bit__of__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 11.11/6.17        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4820_take__bit__of__1,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 11.11/6.17        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4821_add__neg__numeral__special_I9_J,axiom,
% 11.11/6.17      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4822_add__neg__numeral__special_I9_J,axiom,
% 11.11/6.17      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4823_add__neg__numeral__special_I9_J,axiom,
% 11.11/6.17      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4824_add__neg__numeral__special_I9_J,axiom,
% 11.11/6.17      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4825_add__neg__numeral__special_I9_J,axiom,
% 11.11/6.17      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4826_diff__numeral__special_I10_J,axiom,
% 11.11/6.17      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 11.11/6.17      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4827_diff__numeral__special_I10_J,axiom,
% 11.11/6.17      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 11.11/6.17      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4828_diff__numeral__special_I10_J,axiom,
% 11.11/6.17      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 11.11/6.17      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4829_diff__numeral__special_I10_J,axiom,
% 11.11/6.17      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 11.11/6.17      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4830_diff__numeral__special_I10_J,axiom,
% 11.11/6.17      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 11.11/6.17      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4831_diff__numeral__special_I11_J,axiom,
% 11.11/6.17      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4832_diff__numeral__special_I11_J,axiom,
% 11.11/6.17      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4833_diff__numeral__special_I11_J,axiom,
% 11.11/6.17      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4834_diff__numeral__special_I11_J,axiom,
% 11.11/6.17      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4835_diff__numeral__special_I11_J,axiom,
% 11.11/6.17      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4836_minus__1__div__2__eq,axiom,
% 11.11/6.17      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.17      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4837_minus__1__div__2__eq,axiom,
% 11.11/6.17      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.17      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4838_bits__minus__1__mod__2__eq,axiom,
% 11.11/6.17      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.17      = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4839_bits__minus__1__mod__2__eq,axiom,
% 11.11/6.17      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.17      = one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4840_minus__1__mod__2__eq,axiom,
% 11.11/6.17      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.17      = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4841_minus__1__mod__2__eq,axiom,
% 11.11/6.17      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.17      = one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4842_of__nat__zero__less__power__iff,axiom,
% 11.11/6.17      ! [X4: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X4 ) @ N2 ) )
% 11.11/6.17        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.17          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4843_of__nat__zero__less__power__iff,axiom,
% 11.11/6.17      ! [X4: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X4 ) @ N2 ) )
% 11.11/6.17        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.17          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4844_of__nat__zero__less__power__iff,axiom,
% 11.11/6.17      ! [X4: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X4 ) @ N2 ) )
% 11.11/6.17        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.17          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4845_of__nat__zero__less__power__iff,axiom,
% 11.11/6.17      ! [X4: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ N2 ) )
% 11.11/6.17        = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.17          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4846_Power_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [A: real,N2: nat] :
% 11.11/6.17        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4847_Power_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [A: int,N2: nat] :
% 11.11/6.17        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4848_Power_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [A: complex,N2: nat] :
% 11.11/6.17        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4849_Power_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [A: code_integer,N2: nat] :
% 11.11/6.17        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4850_Power_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [A: rat,N2: nat] :
% 11.11/6.17        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4851_Parity_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [N2: nat,A: real] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 11.11/6.17          = ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4852_Parity_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [N2: nat,A: int] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 11.11/6.17          = ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4853_Parity_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [N2: nat,A: complex] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 11.11/6.17          = ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4854_Parity_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [N2: nat,A: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 11.11/6.17          = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4855_Parity_Oring__1__class_Opower__minus__even,axiom,
% 11.11/6.17      ! [N2: nat,A: rat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 11.11/6.17          = ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4856_power__minus__odd,axiom,
% 11.11/6.17      ! [N2: nat,A: real] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4857_power__minus__odd,axiom,
% 11.11/6.17      ! [N2: nat,A: int] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4858_power__minus__odd,axiom,
% 11.11/6.17      ! [N2: nat,A: complex] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4859_power__minus__odd,axiom,
% 11.11/6.17      ! [N2: nat,A: code_integer] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4860_power__minus__odd,axiom,
% 11.11/6.17      ! [N2: nat,A: rat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4861_even__take__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,A: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 11.11/6.17        = ( ( N2 = zero_zero_nat )
% 11.11/6.17          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4862_even__take__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,A: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 11.11/6.17        = ( ( N2 = zero_zero_nat )
% 11.11/6.17          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4863_even__take__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,A: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 11.11/6.17        = ( ( N2 = zero_zero_nat )
% 11.11/6.17          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4864_xor__numerals_I7_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4865_xor__numerals_I7_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4866_diff__numeral__special_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4867_diff__numeral__special_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4868_diff__numeral__special_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.17        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4869_diff__numeral__special_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.17        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4870_diff__numeral__special_I3_J,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.17        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4871_diff__numeral__special_I4_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 11.11/6.17        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4872_diff__numeral__special_I4_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 11.11/6.17        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4873_diff__numeral__special_I4_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4874_diff__numeral__special_I4_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4875_diff__numeral__special_I4_J,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 11.11/6.17        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4876_Suc__div__eq__add3__div__numeral,axiom,
% 11.11/6.17      ! [M: nat,V: num] :
% 11.11/6.17        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 11.11/6.17        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4877_div__Suc__eq__div__add3,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 11.11/6.17        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4878_Suc__mod__eq__add3__mod__numeral,axiom,
% 11.11/6.17      ! [M: nat,V: num] :
% 11.11/6.17        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 11.11/6.17        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4879_mod__Suc__eq__mod__add3,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 11.11/6.17        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4880_signed__take__bit__Suc__minus__bit0,axiom,
% 11.11/6.17      ! [N2: nat,K: num] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.17        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4881_xor__nat__numerals_I4_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4882_xor__nat__numerals_I3_J,axiom,
% 11.11/6.17      ! [X4: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4883_xor__nat__numerals_I2_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4884_xor__nat__numerals_I1_J,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4885_dbl__simps_I4_J,axiom,
% 11.11/6.17      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.17      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4886_dbl__simps_I4_J,axiom,
% 11.11/6.17      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.17      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4887_dbl__simps_I4_J,axiom,
% 11.11/6.17      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.17      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4888_dbl__simps_I4_J,axiom,
% 11.11/6.17      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.17      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4889_dbl__simps_I4_J,axiom,
% 11.11/6.17      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.17      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4890_power__minus1__even,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4891_power__minus1__even,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4892_power__minus1__even,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = one_one_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4893_power__minus1__even,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4894_power__minus1__even,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = one_one_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4895_neg__one__even__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 11.11/6.17          = one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4896_neg__one__even__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 11.11/6.17          = one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4897_neg__one__even__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 11.11/6.17          = one_one_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4898_neg__one__even__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 11.11/6.17          = one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4899_neg__one__even__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 11.11/6.17          = one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4900_neg__one__odd__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4901_neg__one__odd__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4902_neg__one__odd__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4903_neg__one__odd__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4904_neg__one__odd__power,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.17       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 11.11/6.17          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4905_even__of__nat,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4906_even__of__nat,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4907_even__of__nat,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4908_take__bit__Suc__0,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 11.11/6.17        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4909_take__bit__Suc__0,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 11.11/6.17        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4910_take__bit__Suc__0,axiom,
% 11.11/6.17      ! [A: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 11.11/6.17        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4911_of__nat__less__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4912_of__nat__less__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4913_of__nat__less__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4914_of__nat__less__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4915_numeral__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4916_numeral__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4917_numeral__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4918_numeral__power__less__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 11.11/6.17        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4919_of__nat__le__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4920_of__nat__le__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4921_of__nat__le__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4922_of__nat__le__numeral__power__cancel__iff,axiom,
% 11.11/6.17      ! [X4: nat,I2: num,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4923_numeral__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4924_numeral__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4925_numeral__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4926_numeral__power__le__of__nat__cancel__iff,axiom,
% 11.11/6.17      ! [I2: num,N2: nat,X4: nat] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 11.11/6.17        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4927_signed__take__bit__0,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4928_signed__take__bit__0,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 11.11/6.17        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4929_xor__numerals_I4_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4930_xor__numerals_I4_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.17        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4931_xor__numerals_I6_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4932_xor__numerals_I6_J,axiom,
% 11.11/6.17      ! [X4: num,Y: num] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.17        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4933_take__bit__of__exp,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4934_take__bit__of__exp,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4935_take__bit__of__exp,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.17        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4936_take__bit__of__2,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4937_take__bit__of__2,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4938_take__bit__of__2,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.17        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4939_zmod__numeral__Bit1,axiom,
% 11.11/6.17      ! [V: num,W: num] :
% 11.11/6.17        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 11.11/6.17        = ( 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 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4940_signed__take__bit__Suc__bit1,axiom,
% 11.11/6.17      ! [N2: nat,K: num] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4941_signed__take__bit__Suc__minus__bit1,axiom,
% 11.11/6.17      ! [N2: nat,K: num] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.17        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4942_signed__take__bit__minus,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 11.11/6.17        = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4943_minus__real__def,axiom,
% 11.11/6.17      ( minus_minus_real
% 11.11/6.17      = ( ^ [X: real,Y5: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y5 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4944_xor_Oassoc,axiom,
% 11.11/6.17      ! [A: nat,B: nat,C: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 11.11/6.17        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4945_xor_Oassoc,axiom,
% 11.11/6.17      ! [A: int,B: int,C: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 11.11/6.17        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4946_xor_Ocommute,axiom,
% 11.11/6.17      ( bit_se6528837805403552850or_nat
% 11.11/6.17      = ( ^ [A3: nat,B2: nat] : ( bit_se6528837805403552850or_nat @ B2 @ A3 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4947_xor_Ocommute,axiom,
% 11.11/6.17      ( bit_se6526347334894502574or_int
% 11.11/6.17      = ( ^ [A3: int,B2: int] : ( bit_se6526347334894502574or_int @ B2 @ A3 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4948_of__nat__xor__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 11.11/6.17        = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4949_of__nat__xor__eq,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 11.11/6.17        = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4950_take__bit__of__nat,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 11.11/6.17        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4951_take__bit__of__nat,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 11.11/6.17        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4952_xor_Oleft__commute,axiom,
% 11.11/6.17      ! [B: nat,A: nat,C: nat] :
% 11.11/6.17        ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 11.11/6.17        = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4953_xor_Oleft__commute,axiom,
% 11.11/6.17      ! [B: int,A: int,C: int] :
% 11.11/6.17        ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 11.11/6.17        = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4954_equation__minus__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4955_equation__minus__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4956_equation__minus__iff,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4957_equation__minus__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4958_equation__minus__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4959_minus__equation__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( uminus_uminus_real @ B )
% 11.11/6.17          = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4960_minus__equation__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( uminus_uminus_int @ B )
% 11.11/6.17          = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4961_minus__equation__iff,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( uminus1482373934393186551omplex @ B )
% 11.11/6.17          = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4962_minus__equation__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( uminus1351360451143612070nteger @ B )
% 11.11/6.17          = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4963_minus__equation__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( uminus_uminus_rat @ B )
% 11.11/6.17          = A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4964_power__minus__Bit1,axiom,
% 11.11/6.17      ! [X4: real,K: num] :
% 11.11/6.17        ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4965_power__minus__Bit1,axiom,
% 11.11/6.17      ! [X4: int,K: num] :
% 11.11/6.17        ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4966_power__minus__Bit1,axiom,
% 11.11/6.17      ! [X4: complex,K: num] :
% 11.11/6.17        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4967_power__minus__Bit1,axiom,
% 11.11/6.17      ! [X4: code_integer,K: num] :
% 11.11/6.17        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4968_power__minus__Bit1,axiom,
% 11.11/6.17      ! [X4: rat,K: num] :
% 11.11/6.17        ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4969_take__bit__add,axiom,
% 11.11/6.17      ! [N2: nat,A: int,B: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 11.11/6.17        = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4970_take__bit__add,axiom,
% 11.11/6.17      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.17        ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 11.11/6.17        = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4971_take__bit__tightened,axiom,
% 11.11/6.17      ! [N2: nat,A: int,B: int,M: nat] :
% 11.11/6.17        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 11.11/6.17          = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 11.11/6.17       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 11.11/6.17            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4972_take__bit__tightened,axiom,
% 11.11/6.17      ! [N2: nat,A: nat,B: nat,M: nat] :
% 11.11/6.17        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 11.11/6.17          = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 11.11/6.17       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 11.11/6.17            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4973_take__bit__tightened__less__eq__nat,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q3 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4974_take__bit__nat__less__eq__self,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4975_mult__of__nat__commute,axiom,
% 11.11/6.17      ! [X4: nat,Y: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X4 ) @ Y )
% 11.11/6.17        = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4976_mult__of__nat__commute,axiom,
% 11.11/6.17      ! [X4: nat,Y: real] :
% 11.11/6.17        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ Y )
% 11.11/6.17        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4977_mult__of__nat__commute,axiom,
% 11.11/6.17      ! [X4: nat,Y: int] :
% 11.11/6.17        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X4 ) @ Y )
% 11.11/6.17        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4978_mult__of__nat__commute,axiom,
% 11.11/6.17      ! [X4: nat,Y: nat] :
% 11.11/6.17        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ Y )
% 11.11/6.17        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4979_take__bit__mult,axiom,
% 11.11/6.17      ! [N2: nat,K: int,L: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 11.11/6.17        = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4980_le__imp__neg__le,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.17       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4981_le__imp__neg__le,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ A @ B )
% 11.11/6.17       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4982_le__imp__neg__le,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.17       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4983_le__imp__neg__le,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.17       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4984_minus__le__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4985_minus__le__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4986_minus__le__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4987_minus__le__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4988_le__minus__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4989_le__minus__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4990_le__minus__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4991_le__minus__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4992_verit__negate__coefficient_I2_J,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_real @ A @ B )
% 11.11/6.17       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4993_verit__negate__coefficient_I2_J,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_int @ A @ B )
% 11.11/6.17       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4994_verit__negate__coefficient_I2_J,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ A @ B )
% 11.11/6.17       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4995_verit__negate__coefficient_I2_J,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_rat @ A @ B )
% 11.11/6.17       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4996_minus__less__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4997_minus__less__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4998_minus__less__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_4999_minus__less__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5000_less__minus__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5001_less__minus__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5002_less__minus__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5003_less__minus__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5004_verit__eq__simplify_I14_J,axiom,
% 11.11/6.17      ! [X22: num,X32: num] :
% 11.11/6.17        ( ( bit0 @ X22 )
% 11.11/6.17       != ( bit1 @ X32 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5005_verit__eq__simplify_I12_J,axiom,
% 11.11/6.17      ! [X32: num] :
% 11.11/6.17        ( one
% 11.11/6.17       != ( bit1 @ X32 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5006_numeral__neq__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( numeral_numeral_real @ M )
% 11.11/6.17       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5007_numeral__neq__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( numeral_numeral_int @ M )
% 11.11/6.17       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5008_numeral__neq__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( numera6690914467698888265omplex @ M )
% 11.11/6.17       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5009_numeral__neq__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( numera6620942414471956472nteger @ M )
% 11.11/6.17       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5010_numeral__neq__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( numeral_numeral_rat @ M )
% 11.11/6.17       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5011_neg__numeral__neq__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 11.11/6.17       != ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5012_neg__numeral__neq__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 11.11/6.17       != ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5013_neg__numeral__neq__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 11.11/6.17       != ( numera6690914467698888265omplex @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5014_neg__numeral__neq__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 11.11/6.17       != ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5015_neg__numeral__neq__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 11.11/6.17       != ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5016_square__eq__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( times_times_real @ A @ A )
% 11.11/6.17          = ( times_times_real @ B @ B ) )
% 11.11/6.17        = ( ( A = B )
% 11.11/6.17          | ( A
% 11.11/6.17            = ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5017_square__eq__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( times_times_int @ A @ A )
% 11.11/6.17          = ( times_times_int @ B @ B ) )
% 11.11/6.17        = ( ( A = B )
% 11.11/6.17          | ( A
% 11.11/6.17            = ( uminus_uminus_int @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5018_square__eq__iff,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( times_times_complex @ A @ A )
% 11.11/6.17          = ( times_times_complex @ B @ B ) )
% 11.11/6.17        = ( ( A = B )
% 11.11/6.17          | ( A
% 11.11/6.17            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5019_square__eq__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( times_3573771949741848930nteger @ A @ A )
% 11.11/6.17          = ( times_3573771949741848930nteger @ B @ B ) )
% 11.11/6.17        = ( ( A = B )
% 11.11/6.17          | ( A
% 11.11/6.17            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5020_square__eq__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( times_times_rat @ A @ A )
% 11.11/6.17          = ( times_times_rat @ B @ B ) )
% 11.11/6.17        = ( ( A = B )
% 11.11/6.17          | ( A
% 11.11/6.17            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5021_minus__mult__commute,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5022_minus__mult__commute,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5023_minus__mult__commute,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 11.11/6.17        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5024_minus__mult__commute,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5025_minus__mult__commute,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5026_one__neq__neg__one,axiom,
% 11.11/6.17      ( one_one_real
% 11.11/6.17     != ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5027_one__neq__neg__one,axiom,
% 11.11/6.17      ( one_one_int
% 11.11/6.17     != ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5028_one__neq__neg__one,axiom,
% 11.11/6.17      ( one_one_complex
% 11.11/6.17     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5029_one__neq__neg__one,axiom,
% 11.11/6.17      ( one_one_Code_integer
% 11.11/6.17     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5030_one__neq__neg__one,axiom,
% 11.11/6.17      ( one_one_rat
% 11.11/6.17     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5031_add_Oinverse__distrib__swap,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 11.11/6.17        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5032_add_Oinverse__distrib__swap,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.17        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5033_add_Oinverse__distrib__swap,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 11.11/6.17        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5034_add_Oinverse__distrib__swap,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.17        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5035_add_Oinverse__distrib__swap,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.17        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5036_group__cancel_Oneg1,axiom,
% 11.11/6.17      ! [A2: real,K: real,A: real] :
% 11.11/6.17        ( ( A2
% 11.11/6.17          = ( plus_plus_real @ K @ A ) )
% 11.11/6.17       => ( ( uminus_uminus_real @ A2 )
% 11.11/6.17          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5037_group__cancel_Oneg1,axiom,
% 11.11/6.17      ! [A2: int,K: int,A: int] :
% 11.11/6.17        ( ( A2
% 11.11/6.17          = ( plus_plus_int @ K @ A ) )
% 11.11/6.17       => ( ( uminus_uminus_int @ A2 )
% 11.11/6.17          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5038_group__cancel_Oneg1,axiom,
% 11.11/6.17      ! [A2: complex,K: complex,A: complex] :
% 11.11/6.17        ( ( A2
% 11.11/6.17          = ( plus_plus_complex @ K @ A ) )
% 11.11/6.17       => ( ( uminus1482373934393186551omplex @ A2 )
% 11.11/6.17          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5039_group__cancel_Oneg1,axiom,
% 11.11/6.17      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 11.11/6.17        ( ( A2
% 11.11/6.17          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 11.11/6.17       => ( ( uminus1351360451143612070nteger @ A2 )
% 11.11/6.17          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5040_group__cancel_Oneg1,axiom,
% 11.11/6.17      ! [A2: rat,K: rat,A: rat] :
% 11.11/6.17        ( ( A2
% 11.11/6.17          = ( plus_plus_rat @ K @ A ) )
% 11.11/6.17       => ( ( uminus_uminus_rat @ A2 )
% 11.11/6.17          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5041_is__num__normalize_I8_J,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 11.11/6.17        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5042_is__num__normalize_I8_J,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.17        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5043_is__num__normalize_I8_J,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 11.11/6.17        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5044_is__num__normalize_I8_J,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.17        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5045_is__num__normalize_I8_J,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.17        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5046_take__bit__diff,axiom,
% 11.11/6.17      ! [N2: nat,K: int,L: int] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 11.11/6.17        = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5047_minus__diff__minus,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5048_minus__diff__minus,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5049_minus__diff__minus,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5050_minus__diff__minus,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5051_minus__diff__minus,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5052_minus__diff__commute,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 11.11/6.17        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5053_minus__diff__commute,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 11.11/6.17        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5054_minus__diff__commute,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 11.11/6.17        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5055_minus__diff__commute,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 11.11/6.17        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5056_minus__diff__commute,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 11.11/6.17        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5057_minus__divide__left,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.17        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5058_minus__divide__left,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.17        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5059_minus__divide__left,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.17        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5060_minus__divide__divide,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( divide_divide_real @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5061_minus__divide__divide,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5062_minus__divide__divide,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( divide_divide_rat @ A @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5063_minus__divide__right,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.17        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5064_minus__divide__right,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.17        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5065_minus__divide__right,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.17        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5066_div__minus__right,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5067_div__minus__right,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5068_Diff__mono,axiom,
% 11.11/6.17      ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 11.11/6.17        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 11.11/6.17       => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 11.11/6.17         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5069_Diff__mono,axiom,
% 11.11/6.17      ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 11.11/6.17        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 11.11/6.17       => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 11.11/6.17         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5070_Diff__subset,axiom,
% 11.11/6.17      ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5071_Diff__subset,axiom,
% 11.11/6.17      ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5072_double__diff,axiom,
% 11.11/6.17      ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 11.11/6.17        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 11.11/6.17       => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 11.11/6.17         => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 11.11/6.17            = A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5073_double__diff,axiom,
% 11.11/6.17      ! [A2: set_int,B3: set_int,C4: set_int] :
% 11.11/6.17        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 11.11/6.17       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 11.11/6.17         => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 11.11/6.17            = A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5074_mod__minus__eq,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 11.11/6.17        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5075_mod__minus__eq,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 11.11/6.17        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5076_mod__minus__cong,axiom,
% 11.11/6.17      ! [A: int,B: int,A4: int] :
% 11.11/6.17        ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.17          = ( modulo_modulo_int @ A4 @ B ) )
% 11.11/6.17       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17          = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5077_mod__minus__cong,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer,A4: code_integer] :
% 11.11/6.17        ( ( ( modulo364778990260209775nteger @ A @ B )
% 11.11/6.17          = ( modulo364778990260209775nteger @ A4 @ B ) )
% 11.11/6.17       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5078_mod__minus__right,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5079_mod__minus__right,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5080_psubset__imp__ex__mem,axiom,
% 11.11/6.17      ! [A2: set_real,B3: set_real] :
% 11.11/6.17        ( ( ord_less_set_real @ A2 @ B3 )
% 11.11/6.17       => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5081_psubset__imp__ex__mem,axiom,
% 11.11/6.17      ! [A2: set_complex,B3: set_complex] :
% 11.11/6.17        ( ( ord_less_set_complex @ A2 @ B3 )
% 11.11/6.17       => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5082_psubset__imp__ex__mem,axiom,
% 11.11/6.17      ! [A2: set_int,B3: set_int] :
% 11.11/6.17        ( ( ord_less_set_int @ A2 @ B3 )
% 11.11/6.17       => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5083_psubset__imp__ex__mem,axiom,
% 11.11/6.17      ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 11.11/6.17        ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 11.11/6.17       => ? [B5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B5 @ ( minus_1356011639430497352at_nat @ B3 @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5084_psubset__imp__ex__mem,axiom,
% 11.11/6.17      ! [A2: set_nat,B3: set_nat] :
% 11.11/6.17        ( ( ord_less_set_nat @ A2 @ B3 )
% 11.11/6.17       => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5085_concat__bit__eq__iff,axiom,
% 11.11/6.17      ! [N2: nat,K: int,L: int,R3: int,S: int] :
% 11.11/6.17        ( ( ( bit_concat_bit @ N2 @ K @ L )
% 11.11/6.17          = ( bit_concat_bit @ N2 @ R3 @ S ) )
% 11.11/6.17        = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.17            = ( bit_se2923211474154528505it_int @ N2 @ R3 ) )
% 11.11/6.17          & ( L = S ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5086_concat__bit__take__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,B: int] :
% 11.11/6.17        ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 11.11/6.17        = ( bit_concat_bit @ N2 @ B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5087_real__of__nat__div2,axiom,
% 11.11/6.17      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5088_real__of__nat__div3,axiom,
% 11.11/6.17      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5089_of__nat__0__le__iff,axiom,
% 11.11/6.17      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5090_of__nat__0__le__iff,axiom,
% 11.11/6.17      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5091_of__nat__0__le__iff,axiom,
% 11.11/6.17      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5092_of__nat__0__le__iff,axiom,
% 11.11/6.17      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5093_of__nat__less__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5094_of__nat__less__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5095_of__nat__less__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5096_of__nat__less__0__iff,axiom,
% 11.11/6.17      ! [M: nat] :
% 11.11/6.17        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5097_of__nat__neq__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 11.11/6.17       != zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5098_of__nat__neq__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 11.11/6.17       != zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5099_of__nat__neq__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 11.11/6.17       != zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5100_of__nat__neq__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 11.11/6.17       != zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5101_of__nat__neq__0,axiom,
% 11.11/6.17      ! [N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 11.11/6.17       != zero_zero_nat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5102_div__mult2__eq_H,axiom,
% 11.11/6.17      ! [A: code_integer,M: nat,N2: nat] :
% 11.11/6.17        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 11.11/6.17        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5103_div__mult2__eq_H,axiom,
% 11.11/6.17      ! [A: int,M: nat,N2: nat] :
% 11.11/6.17        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.17        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5104_div__mult2__eq_H,axiom,
% 11.11/6.17      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.17        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 11.11/6.17        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5105_of__nat__less__imp__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.17       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5106_of__nat__less__imp__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.17       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5107_of__nat__less__imp__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5108_of__nat__less__imp__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17       => ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5109_less__imp__of__nat__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5110_less__imp__of__nat__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5111_less__imp__of__nat__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5112_less__imp__of__nat__less,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( ord_less_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5113_take__bit__tightened__less__eq__int,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,K: int] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.17       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5114_of__nat__mono,axiom,
% 11.11/6.17      ! [I2: nat,J: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.17       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5115_of__nat__mono,axiom,
% 11.11/6.17      ! [I2: nat,J: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.17       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5116_of__nat__mono,axiom,
% 11.11/6.17      ! [I2: nat,J: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.17       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5117_of__nat__mono,axiom,
% 11.11/6.17      ! [I2: nat,J: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.17       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5118_take__bit__int__less__eq__self__iff,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 11.11/6.17        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5119_take__bit__nonnegative,axiom,
% 11.11/6.17      ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5120_take__bit__int__greater__self__iff,axiom,
% 11.11/6.17      ! [K: int,N2: nat] :
% 11.11/6.17        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 11.11/6.17        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5121_not__take__bit__negative,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5122_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,A: int,B: int] :
% 11.11/6.17        ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 11.11/6.17          = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 11.11/6.17        = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 11.11/6.17          = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5123_signed__take__bit__take__bit,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,A: int] :
% 11.11/6.17        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 11.11/6.17        = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5124_neg__numeral__le__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5125_neg__numeral__le__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5126_neg__numeral__le__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5127_neg__numeral__le__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5128_not__numeral__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5129_not__numeral__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5130_not__numeral__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5131_not__numeral__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5132_zero__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( zero_zero_real
% 11.11/6.17       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5133_zero__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( zero_zero_int
% 11.11/6.17       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5134_zero__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( zero_zero_complex
% 11.11/6.17       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5135_zero__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( zero_z3403309356797280102nteger
% 11.11/6.17       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5136_zero__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( zero_zero_rat
% 11.11/6.17       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5137_not__numeral__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5138_not__numeral__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5139_not__numeral__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5140_not__numeral__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] :
% 11.11/6.17        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5141_neg__numeral__less__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5142_neg__numeral__less__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5143_neg__numeral__less__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5144_neg__numeral__less__numeral,axiom,
% 11.11/6.17      ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5145_le__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5146_le__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5147_le__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5148_le__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5149_le__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5150_le__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5151_le__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5152_le__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5153_zero__neq__neg__one,axiom,
% 11.11/6.17      ( zero_zero_real
% 11.11/6.17     != ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5154_zero__neq__neg__one,axiom,
% 11.11/6.17      ( zero_zero_int
% 11.11/6.17     != ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5155_zero__neq__neg__one,axiom,
% 11.11/6.17      ( zero_zero_complex
% 11.11/6.17     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5156_zero__neq__neg__one,axiom,
% 11.11/6.17      ( zero_z3403309356797280102nteger
% 11.11/6.17     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5157_zero__neq__neg__one,axiom,
% 11.11/6.17      ( zero_zero_rat
% 11.11/6.17     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5158_neg__eq__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( plus_plus_real @ A @ B )
% 11.11/6.17          = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5159_neg__eq__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( uminus_uminus_int @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( plus_plus_int @ A @ B )
% 11.11/6.17          = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5160_neg__eq__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( plus_plus_complex @ A @ B )
% 11.11/6.17          = zero_zero_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5161_neg__eq__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 11.11/6.17          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5162_neg__eq__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = B )
% 11.11/6.17        = ( ( plus_plus_rat @ A @ B )
% 11.11/6.17          = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5163_eq__neg__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_real @ B ) )
% 11.11/6.17        = ( ( plus_plus_real @ A @ B )
% 11.11/6.17          = zero_zero_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5164_eq__neg__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_int @ B ) )
% 11.11/6.17        = ( ( plus_plus_int @ A @ B )
% 11.11/6.17          = zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5165_eq__neg__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17        = ( ( plus_plus_complex @ A @ B )
% 11.11/6.17          = zero_zero_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5166_eq__neg__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 11.11/6.17          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5167_eq__neg__iff__add__eq__0,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_rat @ B ) )
% 11.11/6.17        = ( ( plus_plus_rat @ A @ B )
% 11.11/6.17          = zero_zero_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5168_add_Oinverse__unique,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.17          = zero_zero_real )
% 11.11/6.17       => ( ( uminus_uminus_real @ A )
% 11.11/6.17          = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5169_add_Oinverse__unique,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.17          = zero_zero_int )
% 11.11/6.17       => ( ( uminus_uminus_int @ A )
% 11.11/6.17          = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5170_add_Oinverse__unique,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( plus_plus_complex @ A @ B )
% 11.11/6.17          = zero_zero_complex )
% 11.11/6.17       => ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.17          = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5171_add_Oinverse__unique,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 11.11/6.17          = zero_z3403309356797280102nteger )
% 11.11/6.17       => ( ( uminus1351360451143612070nteger @ A )
% 11.11/6.17          = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5172_add_Oinverse__unique,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.17          = zero_zero_rat )
% 11.11/6.17       => ( ( uminus_uminus_rat @ A )
% 11.11/6.17          = B ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5173_ab__group__add__class_Oab__left__minus,axiom,
% 11.11/6.17      ! [A: real] :
% 11.11/6.17        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 11.11/6.17        = zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5174_ab__group__add__class_Oab__left__minus,axiom,
% 11.11/6.17      ! [A: int] :
% 11.11/6.17        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 11.11/6.17        = zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5175_ab__group__add__class_Oab__left__minus,axiom,
% 11.11/6.17      ! [A: complex] :
% 11.11/6.17        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 11.11/6.17        = zero_zero_complex ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5176_ab__group__add__class_Oab__left__minus,axiom,
% 11.11/6.17      ! [A: code_integer] :
% 11.11/6.17        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 11.11/6.17        = zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5177_ab__group__add__class_Oab__left__minus,axiom,
% 11.11/6.17      ! [A: rat] :
% 11.11/6.17        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 11.11/6.17        = zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5178_add__eq__0__iff,axiom,
% 11.11/6.17      ! [A: real,B: real] :
% 11.11/6.17        ( ( ( plus_plus_real @ A @ B )
% 11.11/6.17          = zero_zero_real )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5179_add__eq__0__iff,axiom,
% 11.11/6.17      ! [A: int,B: int] :
% 11.11/6.17        ( ( ( plus_plus_int @ A @ B )
% 11.11/6.17          = zero_zero_int )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5180_add__eq__0__iff,axiom,
% 11.11/6.17      ! [A: complex,B: complex] :
% 11.11/6.17        ( ( ( plus_plus_complex @ A @ B )
% 11.11/6.17          = zero_zero_complex )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5181_add__eq__0__iff,axiom,
% 11.11/6.17      ! [A: code_integer,B: code_integer] :
% 11.11/6.17        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 11.11/6.17          = zero_z3403309356797280102nteger )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5182_add__eq__0__iff,axiom,
% 11.11/6.17      ! [A: rat,B: rat] :
% 11.11/6.17        ( ( ( plus_plus_rat @ A @ B )
% 11.11/6.17          = zero_zero_rat )
% 11.11/6.17        = ( B
% 11.11/6.17          = ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5183_xor__num_Ocases,axiom,
% 11.11/6.17      ! [X4: product_prod_num_num] :
% 11.11/6.17        ( ( X4
% 11.11/6.17         != ( product_Pair_num_num @ one @ one ) )
% 11.11/6.17       => ( ! [N3: num] :
% 11.11/6.17              ( X4
% 11.11/6.17             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 11.11/6.17         => ( ! [N3: num] :
% 11.11/6.17                ( X4
% 11.11/6.17               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 11.11/6.17           => ( ! [M5: num] :
% 11.11/6.17                  ( X4
% 11.11/6.17                 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 11.11/6.17             => ( ! [M5: num,N3: num] :
% 11.11/6.17                    ( X4
% 11.11/6.17                   != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 11.11/6.17               => ( ! [M5: num,N3: num] :
% 11.11/6.17                      ( X4
% 11.11/6.17                     != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 11.11/6.17                 => ( ! [M5: num] :
% 11.11/6.17                        ( X4
% 11.11/6.17                       != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 11.11/6.17                   => ( ! [M5: num,N3: num] :
% 11.11/6.17                          ( X4
% 11.11/6.17                         != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 11.11/6.17                     => ~ ! [M5: num,N3: num] :
% 11.11/6.17                            ( X4
% 11.11/6.17                           != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5184_num_Oexhaust,axiom,
% 11.11/6.17      ! [Y: num] :
% 11.11/6.17        ( ( Y != one )
% 11.11/6.17       => ( ! [X23: num] :
% 11.11/6.17              ( Y
% 11.11/6.17             != ( bit0 @ X23 ) )
% 11.11/6.17         => ~ ! [X33: num] :
% 11.11/6.17                ( Y
% 11.11/6.17               != ( bit1 @ X33 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5185_less__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5186_less__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5187_less__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5188_less__minus__one__simps_I2_J,axiom,
% 11.11/6.17      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5189_less__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5190_less__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5191_less__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5192_less__minus__one__simps_I4_J,axiom,
% 11.11/6.17      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5193_numeral__times__minus__swap,axiom,
% 11.11/6.17      ! [W: num,X4: real] :
% 11.11/6.17        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.17        = ( times_times_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5194_numeral__times__minus__swap,axiom,
% 11.11/6.17      ! [W: num,X4: int] :
% 11.11/6.17        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X4 ) )
% 11.11/6.17        = ( times_times_int @ X4 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5195_numeral__times__minus__swap,axiom,
% 11.11/6.17      ! [W: num,X4: complex] :
% 11.11/6.17        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X4 ) )
% 11.11/6.17        = ( times_times_complex @ X4 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5196_numeral__times__minus__swap,axiom,
% 11.11/6.17      ! [W: num,X4: code_integer] :
% 11.11/6.17        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X4 ) )
% 11.11/6.17        = ( times_3573771949741848930nteger @ X4 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5197_numeral__times__minus__swap,axiom,
% 11.11/6.17      ! [W: num,X4: rat] :
% 11.11/6.17        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X4 ) )
% 11.11/6.17        = ( times_times_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5198_nonzero__minus__divide__divide,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( B != zero_zero_real )
% 11.11/6.17       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 11.11/6.17          = ( divide_divide_real @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5199_nonzero__minus__divide__divide,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( B != zero_zero_complex )
% 11.11/6.17       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5200_nonzero__minus__divide__divide,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( B != zero_zero_rat )
% 11.11/6.17       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17          = ( divide_divide_rat @ A @ B ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5201_nonzero__minus__divide__right,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( B != zero_zero_real )
% 11.11/6.17       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.17          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5202_nonzero__minus__divide__right,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( B != zero_zero_complex )
% 11.11/6.17       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.17          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5203_nonzero__minus__divide__right,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( B != zero_zero_rat )
% 11.11/6.17       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.17          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5204_one__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one_one_real
% 11.11/6.17       != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5205_one__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one_one_int
% 11.11/6.17       != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5206_one__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one_one_complex
% 11.11/6.17       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5207_one__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one_one_Code_integer
% 11.11/6.17       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5208_one__neq__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( one_one_rat
% 11.11/6.17       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5209_numeral__neq__neg__one,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_real @ N2 )
% 11.11/6.17       != ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5210_numeral__neq__neg__one,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_int @ N2 )
% 11.11/6.17       != ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5211_numeral__neq__neg__one,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numera6690914467698888265omplex @ N2 )
% 11.11/6.17       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5212_numeral__neq__neg__one,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numera6620942414471956472nteger @ N2 )
% 11.11/6.17       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5213_numeral__neq__neg__one,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_rat @ N2 )
% 11.11/6.17       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5214_square__eq__1__iff,axiom,
% 11.11/6.17      ! [X4: real] :
% 11.11/6.17        ( ( ( times_times_real @ X4 @ X4 )
% 11.11/6.17          = one_one_real )
% 11.11/6.17        = ( ( X4 = one_one_real )
% 11.11/6.17          | ( X4
% 11.11/6.17            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5215_square__eq__1__iff,axiom,
% 11.11/6.17      ! [X4: int] :
% 11.11/6.17        ( ( ( times_times_int @ X4 @ X4 )
% 11.11/6.17          = one_one_int )
% 11.11/6.17        = ( ( X4 = one_one_int )
% 11.11/6.17          | ( X4
% 11.11/6.17            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5216_square__eq__1__iff,axiom,
% 11.11/6.17      ! [X4: complex] :
% 11.11/6.17        ( ( ( times_times_complex @ X4 @ X4 )
% 11.11/6.17          = one_one_complex )
% 11.11/6.17        = ( ( X4 = one_one_complex )
% 11.11/6.17          | ( X4
% 11.11/6.17            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5217_square__eq__1__iff,axiom,
% 11.11/6.17      ! [X4: code_integer] :
% 11.11/6.17        ( ( ( times_3573771949741848930nteger @ X4 @ X4 )
% 11.11/6.17          = one_one_Code_integer )
% 11.11/6.17        = ( ( X4 = one_one_Code_integer )
% 11.11/6.17          | ( X4
% 11.11/6.17            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5218_square__eq__1__iff,axiom,
% 11.11/6.17      ! [X4: rat] :
% 11.11/6.17        ( ( ( times_times_rat @ X4 @ X4 )
% 11.11/6.17          = one_one_rat )
% 11.11/6.17        = ( ( X4 = one_one_rat )
% 11.11/6.17          | ( X4
% 11.11/6.17            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5219_group__cancel_Osub2,axiom,
% 11.11/6.17      ! [B3: real,K: real,B: real,A: real] :
% 11.11/6.17        ( ( B3
% 11.11/6.17          = ( plus_plus_real @ K @ B ) )
% 11.11/6.17       => ( ( minus_minus_real @ A @ B3 )
% 11.11/6.17          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5220_group__cancel_Osub2,axiom,
% 11.11/6.17      ! [B3: int,K: int,B: int,A: int] :
% 11.11/6.17        ( ( B3
% 11.11/6.17          = ( plus_plus_int @ K @ B ) )
% 11.11/6.17       => ( ( minus_minus_int @ A @ B3 )
% 11.11/6.17          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5221_group__cancel_Osub2,axiom,
% 11.11/6.17      ! [B3: complex,K: complex,B: complex,A: complex] :
% 11.11/6.17        ( ( B3
% 11.11/6.17          = ( plus_plus_complex @ K @ B ) )
% 11.11/6.17       => ( ( minus_minus_complex @ A @ B3 )
% 11.11/6.17          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5222_group__cancel_Osub2,axiom,
% 11.11/6.17      ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( B3
% 11.11/6.17          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 11.11/6.17       => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 11.11/6.17          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5223_group__cancel_Osub2,axiom,
% 11.11/6.17      ! [B3: rat,K: rat,B: rat,A: rat] :
% 11.11/6.17        ( ( B3
% 11.11/6.17          = ( plus_plus_rat @ K @ B ) )
% 11.11/6.17       => ( ( minus_minus_rat @ A @ B3 )
% 11.11/6.17          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5224_diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_real
% 11.11/6.17      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5225_diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_int
% 11.11/6.17      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5226_diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_complex
% 11.11/6.17      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5227_diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_8373710615458151222nteger
% 11.11/6.17      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5228_diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_rat
% 11.11/6.17      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5229_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_real
% 11.11/6.17      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5230_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_int
% 11.11/6.17      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5231_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_complex
% 11.11/6.17      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5232_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_8373710615458151222nteger
% 11.11/6.17      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5233_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 11.11/6.17      ( minus_minus_rat
% 11.11/6.17      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5234_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.17        = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5235_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.17        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5236_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.17        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5237_of__nat__dvd__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5238_of__nat__dvd__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5239_of__nat__dvd__iff,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 11.11/6.17        = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5240_take__bit__unset__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: int] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5241_take__bit__unset__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: nat] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5242_take__bit__set__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: int] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5243_take__bit__set__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: nat] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5244_take__bit__flip__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: int] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 11.11/6.17            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5245_take__bit__flip__bit__eq,axiom,
% 11.11/6.17      ! [N2: nat,M: nat,A: nat] :
% 11.11/6.17        ( ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 11.11/6.17        & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17         => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 11.11/6.17            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5246_dvd__div__neg,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( dvd_dvd_real @ B @ A )
% 11.11/6.17       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 11.11/6.17          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5247_dvd__div__neg,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.17       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.17          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5248_dvd__div__neg,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( dvd_dvd_complex @ B @ A )
% 11.11/6.17       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5249_dvd__div__neg,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.17       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5250_dvd__div__neg,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( dvd_dvd_rat @ B @ A )
% 11.11/6.17       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 11.11/6.17          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5251_dvd__neg__div,axiom,
% 11.11/6.17      ! [B: real,A: real] :
% 11.11/6.17        ( ( dvd_dvd_real @ B @ A )
% 11.11/6.17       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.17          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5252_dvd__neg__div,axiom,
% 11.11/6.17      ! [B: int,A: int] :
% 11.11/6.17        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.17       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.17          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5253_dvd__neg__div,axiom,
% 11.11/6.17      ! [B: complex,A: complex] :
% 11.11/6.17        ( ( dvd_dvd_complex @ B @ A )
% 11.11/6.17       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5254_dvd__neg__div,axiom,
% 11.11/6.17      ! [B: code_integer,A: code_integer] :
% 11.11/6.17        ( ( dvd_dvd_Code_integer @ B @ A )
% 11.11/6.17       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.17          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5255_dvd__neg__div,axiom,
% 11.11/6.17      ! [B: rat,A: rat] :
% 11.11/6.17        ( ( dvd_dvd_rat @ B @ A )
% 11.11/6.17       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.17          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5256_real__of__nat__div4,axiom,
% 11.11/6.17      ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5257_of__nat__mod,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.17        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5258_of__nat__mod,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.17        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5259_of__nat__mod,axiom,
% 11.11/6.17      ! [M: nat,N2: nat] :
% 11.11/6.17        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 11.11/6.17        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5260_real__minus__mult__self__le,axiom,
% 11.11/6.17      ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X4 @ X4 ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5261_real__of__nat__div,axiom,
% 11.11/6.17      ! [D: nat,N2: nat] :
% 11.11/6.17        ( ( dvd_dvd_nat @ D @ N2 )
% 11.11/6.17       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 11.11/6.17          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5262_zmod__zminus1__not__zero,axiom,
% 11.11/6.17      ! [K: int,L: int] :
% 11.11/6.17        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 11.11/6.17         != zero_zero_int )
% 11.11/6.17       => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.17         != zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5263_zmod__zminus2__not__zero,axiom,
% 11.11/6.17      ! [K: int,L: int] :
% 11.11/6.17        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 11.11/6.17         != zero_zero_int )
% 11.11/6.17       => ( ( modulo_modulo_int @ K @ L )
% 11.11/6.17         != zero_zero_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5264_take__bit__Suc__minus__bit0,axiom,
% 11.11/6.17      ! [N2: nat,K: num] :
% 11.11/6.17        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.17        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5265_Bernoulli__inequality,axiom,
% 11.11/6.17      ! [X4: real,N2: nat] :
% 11.11/6.17        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.17       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5266_add__diff__assoc__enat,axiom,
% 11.11/6.17      ! [Z: extended_enat,Y: extended_enat,X4: extended_enat] :
% 11.11/6.17        ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 11.11/6.17       => ( ( plus_p3455044024723400733d_enat @ X4 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 11.11/6.17          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5267_take__bit__signed__take__bit,axiom,
% 11.11/6.17      ! [M: nat,N2: nat,A: int] :
% 11.11/6.17        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.17       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 11.11/6.17          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5268_neg__numeral__le__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5269_neg__numeral__le__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5270_neg__numeral__le__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5271_neg__numeral__le__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5272_not__zero__le__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5273_not__zero__le__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5274_not__zero__le__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5275_not__zero__le__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5276_not__zero__less__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5277_not__zero__less__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5278_not__zero__less__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5279_not__zero__less__neg__numeral,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5280_neg__numeral__less__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5281_neg__numeral__less__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5282_neg__numeral__less__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5283_neg__numeral__less__zero,axiom,
% 11.11/6.17      ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5284_le__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5285_le__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5286_le__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5287_le__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5288_le__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5289_le__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5290_le__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5291_le__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5292_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5293_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5294_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5295_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5296_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5297_numeral__Bit1,axiom,
% 11.11/6.17      ! [N2: num] :
% 11.11/6.17        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 11.11/6.17        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5298_take__bit__decr__eq,axiom,
% 11.11/6.17      ! [N2: nat,K: int] :
% 11.11/6.17        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.17         != zero_zero_int )
% 11.11/6.17       => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 11.11/6.17          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5299_less__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5300_less__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5301_less__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5302_less__minus__one__simps_I1_J,axiom,
% 11.11/6.17      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5303_less__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5304_less__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5305_less__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5306_less__minus__one__simps_I3_J,axiom,
% 11.11/6.17      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5307_of__nat__diff,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5308_of__nat__diff,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5309_of__nat__diff,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5310_of__nat__diff,axiom,
% 11.11/6.17      ! [N2: nat,M: nat] :
% 11.11/6.17        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.17       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 11.11/6.17          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5311_not__one__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5312_not__one__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5313_not__one__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5314_not__one__le__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5315_not__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5316_not__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5317_not__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5318_not__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5319_neg__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5320_neg__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5321_neg__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5322_neg__numeral__le__neg__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5323_neg__one__le__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5324_neg__one__le__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5325_neg__one__le__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5326_neg__one__le__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5327_neg__numeral__le__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5328_neg__numeral__le__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5329_neg__numeral__le__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5330_neg__numeral__le__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5331_not__neg__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5332_not__neg__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5333_not__neg__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5334_not__neg__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5335_not__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5336_not__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5337_not__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5338_not__one__less__neg__numeral,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5339_not__numeral__less__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5340_not__numeral__less__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5341_not__numeral__less__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5342_not__numeral__less__neg__one,axiom,
% 11.11/6.17      ! [M: num] :
% 11.11/6.17        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5343_neg__one__less__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5344_neg__one__less__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5345_neg__one__less__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5346_neg__one__less__numeral,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5347_neg__numeral__less__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5348_neg__numeral__less__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5349_neg__numeral__less__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5350_neg__numeral__less__one,axiom,
% 11.11/6.17      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5351_eq__minus__divide__eq,axiom,
% 11.11/6.17      ! [A: real,B: real,C: real] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.17        = ( ( ( C != zero_zero_real )
% 11.11/6.17           => ( ( times_times_real @ A @ C )
% 11.11/6.17              = ( uminus_uminus_real @ B ) ) )
% 11.11/6.17          & ( ( C = zero_zero_real )
% 11.11/6.17           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5352_eq__minus__divide__eq,axiom,
% 11.11/6.17      ! [A: complex,B: complex,C: complex] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 11.11/6.17        = ( ( ( C != zero_zero_complex )
% 11.11/6.17           => ( ( times_times_complex @ A @ C )
% 11.11/6.17              = ( uminus1482373934393186551omplex @ B ) ) )
% 11.11/6.17          & ( ( C = zero_zero_complex )
% 11.11/6.17           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5353_eq__minus__divide__eq,axiom,
% 11.11/6.17      ! [A: rat,B: rat,C: rat] :
% 11.11/6.17        ( ( A
% 11.11/6.17          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.17        = ( ( ( C != zero_zero_rat )
% 11.11/6.17           => ( ( times_times_rat @ A @ C )
% 11.11/6.17              = ( uminus_uminus_rat @ B ) ) )
% 11.11/6.17          & ( ( C = zero_zero_rat )
% 11.11/6.17           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5354_minus__divide__eq__eq,axiom,
% 11.11/6.17      ! [B: real,C: real,A: real] :
% 11.11/6.17        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 11.11/6.17          = A )
% 11.11/6.17        = ( ( ( C != zero_zero_real )
% 11.11/6.17           => ( ( uminus_uminus_real @ B )
% 11.11/6.17              = ( times_times_real @ A @ C ) ) )
% 11.11/6.17          & ( ( C = zero_zero_real )
% 11.11/6.17           => ( A = zero_zero_real ) ) ) ) ).
% 11.11/6.17  
% 11.11/6.17  thf(fact_5355_minus__divide__eq__eq,axiom,
% 11.11/6.17      ! [B: complex,C: complex,A: complex] :
% 11.11/6.17        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.17          = A )
% 11.11/6.17        = ( ( ( C != zero_zero_complex )
% 11.11/6.18           => ( ( uminus1482373934393186551omplex @ B )
% 11.11/6.18              = ( times_times_complex @ A @ C ) ) )
% 11.11/6.18          & ( ( C = zero_zero_complex )
% 11.11/6.18           => ( A = zero_zero_complex ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5356_minus__divide__eq__eq,axiom,
% 11.11/6.18      ! [B: rat,C: rat,A: rat] :
% 11.11/6.18        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.18          = A )
% 11.11/6.18        = ( ( ( C != zero_zero_rat )
% 11.11/6.18           => ( ( uminus_uminus_rat @ B )
% 11.11/6.18              = ( times_times_rat @ A @ C ) ) )
% 11.11/6.18          & ( ( C = zero_zero_rat )
% 11.11/6.18           => ( A = zero_zero_rat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5357_nonzero__neg__divide__eq__eq,axiom,
% 11.11/6.18      ! [B: real,A: real,C: real] :
% 11.11/6.18        ( ( B != zero_zero_real )
% 11.11/6.18       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.18            = C )
% 11.11/6.18          = ( ( uminus_uminus_real @ A )
% 11.11/6.18            = ( times_times_real @ C @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5358_nonzero__neg__divide__eq__eq,axiom,
% 11.11/6.18      ! [B: complex,A: complex,C: complex] :
% 11.11/6.18        ( ( B != zero_zero_complex )
% 11.11/6.18       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.18            = C )
% 11.11/6.18          = ( ( uminus1482373934393186551omplex @ A )
% 11.11/6.18            = ( times_times_complex @ C @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5359_nonzero__neg__divide__eq__eq,axiom,
% 11.11/6.18      ! [B: rat,A: rat,C: rat] :
% 11.11/6.18        ( ( B != zero_zero_rat )
% 11.11/6.18       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.18            = C )
% 11.11/6.18          = ( ( uminus_uminus_rat @ A )
% 11.11/6.18            = ( times_times_rat @ C @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5360_nonzero__neg__divide__eq__eq2,axiom,
% 11.11/6.18      ! [B: real,C: real,A: real] :
% 11.11/6.18        ( ( B != zero_zero_real )
% 11.11/6.18       => ( ( C
% 11.11/6.18            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 11.11/6.18          = ( ( times_times_real @ C @ B )
% 11.11/6.18            = ( uminus_uminus_real @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5361_nonzero__neg__divide__eq__eq2,axiom,
% 11.11/6.18      ! [B: complex,C: complex,A: complex] :
% 11.11/6.18        ( ( B != zero_zero_complex )
% 11.11/6.18       => ( ( C
% 11.11/6.18            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.18          = ( ( times_times_complex @ C @ B )
% 11.11/6.18            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5362_nonzero__neg__divide__eq__eq2,axiom,
% 11.11/6.18      ! [B: rat,C: rat,A: rat] :
% 11.11/6.18        ( ( B != zero_zero_rat )
% 11.11/6.18       => ( ( C
% 11.11/6.18            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 11.11/6.18          = ( ( times_times_rat @ C @ B )
% 11.11/6.18            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5363_divide__eq__minus__1__iff,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ( divide_divide_real @ A @ B )
% 11.11/6.18          = ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18        = ( ( B != zero_zero_real )
% 11.11/6.18          & ( A
% 11.11/6.18            = ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5364_divide__eq__minus__1__iff,axiom,
% 11.11/6.18      ! [A: complex,B: complex] :
% 11.11/6.18        ( ( ( divide1717551699836669952omplex @ A @ B )
% 11.11/6.18          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.18        = ( ( B != zero_zero_complex )
% 11.11/6.18          & ( A
% 11.11/6.18            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5365_divide__eq__minus__1__iff,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ( divide_divide_rat @ A @ B )
% 11.11/6.18          = ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18        = ( ( B != zero_zero_rat )
% 11.11/6.18          & ( A
% 11.11/6.18            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5366_mult__1s__ring__1_I1_J,axiom,
% 11.11/6.18      ! [B: real] :
% 11.11/6.18        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 11.11/6.18        = ( uminus_uminus_real @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5367_mult__1s__ring__1_I1_J,axiom,
% 11.11/6.18      ! [B: int] :
% 11.11/6.18        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 11.11/6.18        = ( uminus_uminus_int @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5368_mult__1s__ring__1_I1_J,axiom,
% 11.11/6.18      ! [B: complex] :
% 11.11/6.18        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5369_mult__1s__ring__1_I1_J,axiom,
% 11.11/6.18      ! [B: code_integer] :
% 11.11/6.18        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5370_mult__1s__ring__1_I1_J,axiom,
% 11.11/6.18      ! [B: rat] :
% 11.11/6.18        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 11.11/6.18        = ( uminus_uminus_rat @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5371_mult__1s__ring__1_I2_J,axiom,
% 11.11/6.18      ! [B: real] :
% 11.11/6.18        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 11.11/6.18        = ( uminus_uminus_real @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5372_mult__1s__ring__1_I2_J,axiom,
% 11.11/6.18      ! [B: int] :
% 11.11/6.18        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5373_mult__1s__ring__1_I2_J,axiom,
% 11.11/6.18      ! [B: complex] :
% 11.11/6.18        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5374_mult__1s__ring__1_I2_J,axiom,
% 11.11/6.18      ! [B: code_integer] :
% 11.11/6.18        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5375_mult__1s__ring__1_I2_J,axiom,
% 11.11/6.18      ! [B: rat] :
% 11.11/6.18        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 11.11/6.18        = ( uminus_uminus_rat @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5376_uminus__numeral__One,axiom,
% 11.11/6.18      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 11.11/6.18      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5377_uminus__numeral__One,axiom,
% 11.11/6.18      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 11.11/6.18      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5378_uminus__numeral__One,axiom,
% 11.11/6.18      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 11.11/6.18      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5379_uminus__numeral__One,axiom,
% 11.11/6.18      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 11.11/6.18      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5380_uminus__numeral__One,axiom,
% 11.11/6.18      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 11.11/6.18      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5381_power__minus,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 11.11/6.18        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5382_power__minus,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 11.11/6.18        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5383_power__minus,axiom,
% 11.11/6.18      ! [A: complex,N2: nat] :
% 11.11/6.18        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 11.11/6.18        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5384_power__minus,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 11.11/6.18        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5385_power__minus,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 11.11/6.18        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5386_eval__nat__numeral_I3_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 11.11/6.18        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5387_cong__exp__iff__simps_I10_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5388_cong__exp__iff__simps_I10_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5389_cong__exp__iff__simps_I10_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5390_cong__exp__iff__simps_I12_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5391_cong__exp__iff__simps_I12_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5392_cong__exp__iff__simps_I12_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5393_cong__exp__iff__simps_I13_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.18          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5394_cong__exp__iff__simps_I13_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 11.11/6.18          = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5395_cong__exp__iff__simps_I13_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 11.11/6.18          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5396_power__minus__Bit0,axiom,
% 11.11/6.18      ! [X4: real,K: num] :
% 11.11/6.18        ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5397_power__minus__Bit0,axiom,
% 11.11/6.18      ! [X4: int,K: num] :
% 11.11/6.18        ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5398_power__minus__Bit0,axiom,
% 11.11/6.18      ! [X4: complex,K: num] :
% 11.11/6.18        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5399_power__minus__Bit0,axiom,
% 11.11/6.18      ! [X4: code_integer,K: num] :
% 11.11/6.18        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5400_power__minus__Bit0,axiom,
% 11.11/6.18      ! [X4: rat,K: num] :
% 11.11/6.18        ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5401_reals__Archimedean3,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ! [Y4: real] :
% 11.11/6.18          ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5402_take__bit__Suc__bit1,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5403_take__bit__Suc__bit1,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.18        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5404_take__bit__Suc__minus__1__eq,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5405_take__bit__Suc__minus__1__eq,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5406_take__bit__numeral__minus__1__eq,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5407_take__bit__numeral__minus__1__eq,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5408_real__0__less__add__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.18        = ( ord_less_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5409_real__add__less__0__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 11.11/6.18        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5410_real__0__le__add__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.18        = ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5411_real__add__le__0__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 11.11/6.18        = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5412_real__of__nat__div__aux,axiom,
% 11.11/6.18      ! [X4: nat,D: nat] :
% 11.11/6.18        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( semiri5074537144036343181t_real @ D ) )
% 11.11/6.18        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X4 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X4 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5413_zmod__zminus1__eq__if,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18            = zero_zero_int )
% 11.11/6.18         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.18            = zero_zero_int ) )
% 11.11/6.18        & ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18           != zero_zero_int )
% 11.11/6.18         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.18            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5414_zmod__zminus2__eq__if,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18            = zero_zero_int )
% 11.11/6.18         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.18            = zero_zero_int ) )
% 11.11/6.18        & ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18           != zero_zero_int )
% 11.11/6.18         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.18            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5415_mod__mult2__eq_H,axiom,
% 11.11/6.18      ! [A: code_integer,M: nat,N2: nat] :
% 11.11/6.18        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 11.11/6.18        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5416_mod__mult2__eq_H,axiom,
% 11.11/6.18      ! [A: int,M: nat,N2: nat] :
% 11.11/6.18        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5417_mod__mult2__eq_H,axiom,
% 11.11/6.18      ! [A: nat,M: nat,N2: nat] :
% 11.11/6.18        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 11.11/6.18        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5418_take__bit__minus__small__eq,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.18       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18         => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 11.11/6.18            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5419_numeral__Bit1__div__2,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5420_numeral__Bit1__div__2,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5421_numeral__Bit1__div__2,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5422_pos__minus__divide__less__eq,axiom,
% 11.11/6.18      ! [C: real,B: real,A: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5423_pos__minus__divide__less__eq,axiom,
% 11.11/6.18      ! [C: rat,B: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5424_pos__less__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: real,A: real,B: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5425_pos__less__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5426_neg__minus__divide__less__eq,axiom,
% 11.11/6.18      ! [C: real,B: real,A: real] :
% 11.11/6.18        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5427_neg__minus__divide__less__eq,axiom,
% 11.11/6.18      ! [C: rat,B: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5428_neg__less__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: real,A: real,B: real] :
% 11.11/6.18        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5429_neg__less__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5430_minus__divide__less__eq,axiom,
% 11.11/6.18      ! [B: real,C: real,A: real] :
% 11.11/6.18        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5431_minus__divide__less__eq,axiom,
% 11.11/6.18      ! [B: rat,C: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5432_less__minus__divide__eq,axiom,
% 11.11/6.18      ! [A: real,B: real,C: real] :
% 11.11/6.18        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5433_less__minus__divide__eq,axiom,
% 11.11/6.18      ! [A: rat,B: rat,C: rat] :
% 11.11/6.18        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5434_eq__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: real,C: real] :
% 11.11/6.18        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.18          = ( divide_divide_real @ B @ C ) )
% 11.11/6.18        = ( ( ( C != zero_zero_real )
% 11.11/6.18           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 11.11/6.18              = B ) )
% 11.11/6.18          & ( ( C = zero_zero_real )
% 11.11/6.18           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.18              = zero_zero_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5435_eq__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: complex,C: complex] :
% 11.11/6.18        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.18          = ( divide1717551699836669952omplex @ B @ C ) )
% 11.11/6.18        = ( ( ( C != zero_zero_complex )
% 11.11/6.18           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 11.11/6.18              = B ) )
% 11.11/6.18          & ( ( C = zero_zero_complex )
% 11.11/6.18           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.18              = zero_zero_complex ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5436_eq__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: rat,C: rat] :
% 11.11/6.18        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.18          = ( divide_divide_rat @ B @ C ) )
% 11.11/6.18        = ( ( ( C != zero_zero_rat )
% 11.11/6.18           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 11.11/6.18              = B ) )
% 11.11/6.18          & ( ( C = zero_zero_rat )
% 11.11/6.18           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.18              = zero_zero_rat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5437_divide__eq__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: real,C: real,W: num] :
% 11.11/6.18        ( ( ( divide_divide_real @ B @ C )
% 11.11/6.18          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( ( ( C != zero_zero_real )
% 11.11/6.18           => ( B
% 11.11/6.18              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ( C = zero_zero_real )
% 11.11/6.18           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.18              = zero_zero_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5438_divide__eq__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: complex,C: complex,W: num] :
% 11.11/6.18        ( ( ( divide1717551699836669952omplex @ B @ C )
% 11.11/6.18          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.18        = ( ( ( C != zero_zero_complex )
% 11.11/6.18           => ( B
% 11.11/6.18              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ( C = zero_zero_complex )
% 11.11/6.18           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.18              = zero_zero_complex ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5439_divide__eq__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: rat,C: rat,W: num] :
% 11.11/6.18        ( ( ( divide_divide_rat @ B @ C )
% 11.11/6.18          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.18        = ( ( ( C != zero_zero_rat )
% 11.11/6.18           => ( B
% 11.11/6.18              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ( C = zero_zero_rat )
% 11.11/6.18           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.18              = zero_zero_rat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5440_odd__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5441_odd__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5442_odd__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5443_minus__divide__add__eq__iff,axiom,
% 11.11/6.18      ! [Z: real,X4: real,Y: real] :
% 11.11/6.18        ( ( Z != zero_zero_real )
% 11.11/6.18       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5444_minus__divide__add__eq__iff,axiom,
% 11.11/6.18      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.18        ( ( Z != zero_zero_complex )
% 11.11/6.18       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5445_minus__divide__add__eq__iff,axiom,
% 11.11/6.18      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.18        ( ( Z != zero_zero_rat )
% 11.11/6.18       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5446_add__divide__eq__if__simps_I3_J,axiom,
% 11.11/6.18      ! [Z: real,A: real,B: real] :
% 11.11/6.18        ( ( ( Z = zero_zero_real )
% 11.11/6.18         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 11.11/6.18            = B ) )
% 11.11/6.18        & ( ( Z != zero_zero_real )
% 11.11/6.18         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5447_add__divide__eq__if__simps_I3_J,axiom,
% 11.11/6.18      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.18        ( ( ( Z = zero_zero_complex )
% 11.11/6.18         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 11.11/6.18            = B ) )
% 11.11/6.18        & ( ( Z != zero_zero_complex )
% 11.11/6.18         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5448_add__divide__eq__if__simps_I3_J,axiom,
% 11.11/6.18      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ( Z = zero_zero_rat )
% 11.11/6.18         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 11.11/6.18            = B ) )
% 11.11/6.18        & ( ( Z != zero_zero_rat )
% 11.11/6.18         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5449_cong__exp__iff__simps_I3_J,axiom,
% 11.11/6.18      ! [N2: num,Q3: num] :
% 11.11/6.18        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != zero_zero_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5450_cong__exp__iff__simps_I3_J,axiom,
% 11.11/6.18      ! [N2: num,Q3: num] :
% 11.11/6.18        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5451_cong__exp__iff__simps_I3_J,axiom,
% 11.11/6.18      ! [N2: num,Q3: num] :
% 11.11/6.18        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18       != zero_z3403309356797280102nteger ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5452_add__divide__eq__if__simps_I6_J,axiom,
% 11.11/6.18      ! [Z: real,A: real,B: real] :
% 11.11/6.18        ( ( ( Z = zero_zero_real )
% 11.11/6.18         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 11.11/6.18            = ( uminus_uminus_real @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_real )
% 11.11/6.18         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5453_add__divide__eq__if__simps_I6_J,axiom,
% 11.11/6.18      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.18        ( ( ( Z = zero_zero_complex )
% 11.11/6.18         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 11.11/6.18            = ( uminus1482373934393186551omplex @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_complex )
% 11.11/6.18         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5454_add__divide__eq__if__simps_I6_J,axiom,
% 11.11/6.18      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ( Z = zero_zero_rat )
% 11.11/6.18         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 11.11/6.18            = ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_rat )
% 11.11/6.18         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 11.11/6.18            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5455_add__divide__eq__if__simps_I5_J,axiom,
% 11.11/6.18      ! [Z: real,A: real,B: real] :
% 11.11/6.18        ( ( ( Z = zero_zero_real )
% 11.11/6.18         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 11.11/6.18            = ( uminus_uminus_real @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_real )
% 11.11/6.18         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 11.11/6.18            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5456_add__divide__eq__if__simps_I5_J,axiom,
% 11.11/6.18      ! [Z: complex,A: complex,B: complex] :
% 11.11/6.18        ( ( ( Z = zero_zero_complex )
% 11.11/6.18         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 11.11/6.18            = ( uminus1482373934393186551omplex @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_complex )
% 11.11/6.18         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 11.11/6.18            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5457_add__divide__eq__if__simps_I5_J,axiom,
% 11.11/6.18      ! [Z: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ( Z = zero_zero_rat )
% 11.11/6.18         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 11.11/6.18            = ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18        & ( ( Z != zero_zero_rat )
% 11.11/6.18         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 11.11/6.18            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5458_minus__divide__diff__eq__iff,axiom,
% 11.11/6.18      ! [Z: real,X4: real,Y: real] :
% 11.11/6.18        ( ( Z != zero_zero_real )
% 11.11/6.18       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5459_minus__divide__diff__eq__iff,axiom,
% 11.11/6.18      ! [Z: complex,X4: complex,Y: complex] :
% 11.11/6.18        ( ( Z != zero_zero_complex )
% 11.11/6.18       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5460_minus__divide__diff__eq__iff,axiom,
% 11.11/6.18      ! [Z: rat,X4: rat,Y: rat] :
% 11.11/6.18        ( ( Z != zero_zero_rat )
% 11.11/6.18       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 11.11/6.18          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5461_power3__eq__cube,axiom,
% 11.11/6.18      ! [A: complex] :
% 11.11/6.18        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 11.11/6.18        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5462_power3__eq__cube,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 11.11/6.18        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5463_power3__eq__cube,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 11.11/6.18        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5464_power3__eq__cube,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 11.11/6.18        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5465_even__minus,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 11.11/6.18        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5466_even__minus,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.18        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5467_numeral__3__eq__3,axiom,
% 11.11/6.18      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 11.11/6.18      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5468_even__xor__iff,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 11.11/6.18        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.18          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5469_even__xor__iff,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 11.11/6.18        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.18          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5470_even__xor__iff,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 11.11/6.18        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.18          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5471_power2__eq__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5472_power2__eq__iff,axiom,
% 11.11/6.18      ! [X4: int,Y: int] :
% 11.11/6.18        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5473_power2__eq__iff,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex] :
% 11.11/6.18        ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5474_power2__eq__iff,axiom,
% 11.11/6.18      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.18        ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5475_power2__eq__iff,axiom,
% 11.11/6.18      ! [X4: rat,Y: rat] :
% 11.11/6.18        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5476_Suc3__eq__add__3,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 11.11/6.18        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5477_field__char__0__class_Oof__nat__div,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.18        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5478_field__char__0__class_Oof__nat__div,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.18        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5479_field__char__0__class_Oof__nat__div,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 11.11/6.18        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5480_nat__less__real__le,axiom,
% 11.11/6.18      ( ord_less_nat
% 11.11/6.18      = ( ^ [N: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5481_nat__le__real__less,axiom,
% 11.11/6.18      ( ord_less_eq_nat
% 11.11/6.18      = ( ^ [N: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5482_verit__less__mono__div__int2,axiom,
% 11.11/6.18      ! [A2: int,B3: int,N2: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ A2 @ B3 )
% 11.11/6.18       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 11.11/6.18         => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5483_div__eq__minus1,axiom,
% 11.11/6.18      ! [B: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.18       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 11.11/6.18          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5484_take__bit__Suc__bit0,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5485_take__bit__Suc__bit0,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5486_take__bit__eq__mod,axiom,
% 11.11/6.18      ( bit_se1745604003318907178nteger
% 11.11/6.18      = ( ^ [N: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5487_take__bit__eq__mod,axiom,
% 11.11/6.18      ( bit_se2923211474154528505it_int
% 11.11/6.18      = ( ^ [N: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5488_take__bit__eq__mod,axiom,
% 11.11/6.18      ( bit_se2925701944663578781it_nat
% 11.11/6.18      = ( ^ [N: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5489_take__bit__nat__eq__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 11.11/6.18          = M )
% 11.11/6.18        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5490_take__bit__nat__less__exp,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5491_take__bit__nat__eq__self,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18       => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 11.11/6.18          = M ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5492_num_Osize__gen_I3_J,axiom,
% 11.11/6.18      ! [X32: num] :
% 11.11/6.18        ( ( size_num @ ( bit1 @ X32 ) )
% 11.11/6.18        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5493_num_Osize_I6_J,axiom,
% 11.11/6.18      ! [X32: num] :
% 11.11/6.18        ( ( size_size_num @ ( bit1 @ X32 ) )
% 11.11/6.18        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5494_take__bit__nat__def,axiom,
% 11.11/6.18      ( bit_se2925701944663578781it_nat
% 11.11/6.18      = ( ^ [N: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5495_of__nat__less__two__power,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5496_of__nat__less__two__power,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5497_of__nat__less__two__power,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5498_inverse__of__nat__le,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5499_inverse__of__nat__le,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5500_take__bit__int__less__exp,axiom,
% 11.11/6.18      ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5501_le__minus__divide__eq,axiom,
% 11.11/6.18      ! [A: real,B: real,C: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5502_le__minus__divide__eq,axiom,
% 11.11/6.18      ! [A: rat,B: rat,C: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5503_minus__divide__le__eq,axiom,
% 11.11/6.18      ! [B: real,C: real,A: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5504_minus__divide__le__eq,axiom,
% 11.11/6.18      ! [B: rat,C: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5505_neg__le__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: real,A: real,B: real] :
% 11.11/6.18        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5506_neg__le__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5507_neg__minus__divide__le__eq,axiom,
% 11.11/6.18      ! [C: real,B: real,A: real] :
% 11.11/6.18        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5508_neg__minus__divide__le__eq,axiom,
% 11.11/6.18      ! [C: rat,B: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5509_pos__le__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: real,A: real,B: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5510_pos__le__minus__divide__eq,axiom,
% 11.11/6.18      ! [C: rat,A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 11.11/6.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5511_pos__minus__divide__le__eq,axiom,
% 11.11/6.18      ! [C: real,B: real,A: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5512_pos__minus__divide__le__eq,axiom,
% 11.11/6.18      ! [C: rat,B: rat,A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 11.11/6.18          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5513_less__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: real,C: real] :
% 11.11/6.18        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5514_less__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: rat,C: rat] :
% 11.11/6.18        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5515_divide__less__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: real,C: real,W: num] :
% 11.11/6.18        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5516_divide__less__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: rat,C: rat,W: num] :
% 11.11/6.18        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5517_take__bit__int__def,axiom,
% 11.11/6.18      ( bit_se2923211474154528505it_int
% 11.11/6.18      = ( ^ [N: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5518_cong__exp__iff__simps_I7_J,axiom,
% 11.11/6.18      ! [Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.18          = zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5519_cong__exp__iff__simps_I7_J,axiom,
% 11.11/6.18      ! [Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 11.11/6.18          = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5520_cong__exp__iff__simps_I7_J,axiom,
% 11.11/6.18      ! [Q3: num,N2: num] :
% 11.11/6.18        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 11.11/6.18          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5521_cong__exp__iff__simps_I11_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num] :
% 11.11/6.18        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.18          = zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5522_cong__exp__iff__simps_I11_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num] :
% 11.11/6.18        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 11.11/6.18          = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5523_cong__exp__iff__simps_I11_J,axiom,
% 11.11/6.18      ! [M: num,Q3: num] :
% 11.11/6.18        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 11.11/6.18          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 11.11/6.18        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 11.11/6.18          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5524_power2__eq__1__iff,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_real )
% 11.11/6.18        = ( ( A = one_one_real )
% 11.11/6.18          | ( A
% 11.11/6.18            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5525_power2__eq__1__iff,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_int )
% 11.11/6.18        = ( ( A = one_one_int )
% 11.11/6.18          | ( A
% 11.11/6.18            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5526_power2__eq__1__iff,axiom,
% 11.11/6.18      ! [A: complex] :
% 11.11/6.18        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_complex )
% 11.11/6.18        = ( ( A = one_one_complex )
% 11.11/6.18          | ( A
% 11.11/6.18            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5527_power2__eq__1__iff,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_Code_integer )
% 11.11/6.18        = ( ( A = one_one_Code_integer )
% 11.11/6.18          | ( A
% 11.11/6.18            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5528_power2__eq__1__iff,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_rat )
% 11.11/6.18        = ( ( A = one_one_rat )
% 11.11/6.18          | ( A
% 11.11/6.18            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5529_real__archimedian__rdiv__eq__0,axiom,
% 11.11/6.18      ! [X4: real,C: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.18         => ( ! [M5: nat] :
% 11.11/6.18                ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 11.11/6.18               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X4 ) @ C ) )
% 11.11/6.18           => ( X4 = zero_zero_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5530_uminus__power__if,axiom,
% 11.11/6.18      ! [N2: nat,A: real] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 11.11/6.18            = ( power_power_real @ A @ N2 ) ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5531_uminus__power__if,axiom,
% 11.11/6.18      ! [N2: nat,A: int] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 11.11/6.18            = ( power_power_int @ A @ N2 ) ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5532_uminus__power__if,axiom,
% 11.11/6.18      ! [N2: nat,A: complex] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 11.11/6.18            = ( power_power_complex @ A @ N2 ) ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 11.11/6.18            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5533_uminus__power__if,axiom,
% 11.11/6.18      ! [N2: nat,A: code_integer] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 11.11/6.18            = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 11.11/6.18            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5534_uminus__power__if,axiom,
% 11.11/6.18      ! [N2: nat,A: rat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 11.11/6.18            = ( power_power_rat @ A @ N2 ) ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5535_Suc__div__eq__add3__div,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 11.11/6.18        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5536_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.18          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5537_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.18          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5538_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.18          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5539_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.18          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5540_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 11.11/6.18          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5541_Suc__mod__eq__add3__mod,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 11.11/6.18        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5542_realpow__square__minus__le,axiom,
% 11.11/6.18      ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5543_signed__take__bit__int__less__eq__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 11.11/6.18        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5544_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 11.11/6.18      ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5545_signed__take__bit__int__greater__self__iff,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 11.11/6.18        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5546_take__bit__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,A: code_integer] :
% 11.11/6.18        ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 11.11/6.18          = zero_z3403309356797280102nteger )
% 11.11/6.18        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5547_take__bit__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,A: int] :
% 11.11/6.18        ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 11.11/6.18          = zero_zero_int )
% 11.11/6.18        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5548_take__bit__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,A: nat] :
% 11.11/6.18        ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 11.11/6.18          = zero_zero_nat )
% 11.11/6.18        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5549_minus__mod__int__eq,axiom,
% 11.11/6.18      ! [L: int,K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 11.11/6.18       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 11.11/6.18          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5550_zmod__minus1,axiom,
% 11.11/6.18      ! [B: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.18       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 11.11/6.18          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5551_zdiv__zminus1__eq__if,axiom,
% 11.11/6.18      ! [B: int,A: int] :
% 11.11/6.18        ( ( B != zero_zero_int )
% 11.11/6.18       => ( ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18              = zero_zero_int )
% 11.11/6.18           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.18              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 11.11/6.18          & ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18             != zero_zero_int )
% 11.11/6.18           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.18              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5552_zdiv__zminus2__eq__if,axiom,
% 11.11/6.18      ! [B: int,A: int] :
% 11.11/6.18        ( ( B != zero_zero_int )
% 11.11/6.18       => ( ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18              = zero_zero_int )
% 11.11/6.18           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.18              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 11.11/6.18          & ( ( ( modulo_modulo_int @ A @ B )
% 11.11/6.18             != zero_zero_int )
% 11.11/6.18           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 11.11/6.18              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5553_take__bit__nat__less__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 11.11/6.18        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5554_zminus1__lemma,axiom,
% 11.11/6.18      ! [A: int,B: int,Q3: int,R3: int] :
% 11.11/6.18        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 11.11/6.18       => ( ( B != zero_zero_int )
% 11.11/6.18         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5555_take__bit__int__less__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 11.11/6.18        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5556_take__bit__int__greater__eq__self__iff,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 11.11/6.18        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5557_le__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: real,C: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5558_le__divide__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [W: num,B: rat,C: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5559_divide__le__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: real,C: real,W: num] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.18           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 11.11/6.18              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.18               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5560_divide__le__eq__numeral_I2_J,axiom,
% 11.11/6.18      ! [B: rat,C: rat,W: num] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 11.11/6.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 11.11/6.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 11.11/6.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 11.11/6.18               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5561_square__le__1,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.18         => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5562_square__le__1,axiom,
% 11.11/6.18      ! [X4: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 11.11/6.18       => ( ( ord_le3102999989581377725nteger @ X4 @ one_one_Code_integer )
% 11.11/6.18         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5563_square__le__1,axiom,
% 11.11/6.18      ! [X4: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_rat @ X4 @ one_one_rat )
% 11.11/6.18         => ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5564_square__le__1,axiom,
% 11.11/6.18      ! [X4: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_int @ X4 @ one_one_int )
% 11.11/6.18         => ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5565_minus__power__mult__self,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 11.11/6.18        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5566_minus__power__mult__self,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 11.11/6.18        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5567_minus__power__mult__self,axiom,
% 11.11/6.18      ! [A: complex,N2: nat] :
% 11.11/6.18        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 11.11/6.18        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5568_minus__power__mult__self,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 11.11/6.18        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5569_minus__power__mult__self,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 11.11/6.18        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5570_minus__one__power__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 11.11/6.18            = one_one_real ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5571_minus__one__power__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 11.11/6.18            = one_one_int ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5572_minus__one__power__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 11.11/6.18            = one_one_complex ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 11.11/6.18            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5573_minus__one__power__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 11.11/6.18            = one_one_Code_integer ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 11.11/6.18            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5574_minus__one__power__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 11.11/6.18            = one_one_rat ) )
% 11.11/6.18        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 11.11/6.18            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5575_signed__take__bit__int__eq__self,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 11.11/6.18       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18         => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 11.11/6.18            = K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5576_signed__take__bit__int__eq__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 11.11/6.18          = K )
% 11.11/6.18        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 11.11/6.18          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5577_minus__1__div__exp__eq__int,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5578_div__pos__neg__trivial,axiom,
% 11.11/6.18      ! [K: int,L: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.18       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 11.11/6.18         => ( ( divide_divide_int @ K @ L )
% 11.11/6.18            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5579_take__bit__int__eq__self,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.18       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18         => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.18            = K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5580_take__bit__int__eq__self__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.18          = K )
% 11.11/6.18        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.18          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5581_signed__take__bit__eq__take__bit__shift,axiom,
% 11.11/6.18      ( bit_ri631733984087533419it_int
% 11.11/6.18      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5582_take__bit__incr__eq,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.18         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 11.11/6.18       => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 11.11/6.18          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5583_power__minus1__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5584_power__minus1__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5585_power__minus1__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5586_power__minus1__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5587_power__minus1__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5588_take__bit__Suc,axiom,
% 11.11/6.18      ! [N2: nat,A: code_integer] :
% 11.11/6.18        ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 11.11/6.18        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5589_take__bit__Suc,axiom,
% 11.11/6.18      ! [N2: nat,A: int] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5590_take__bit__Suc,axiom,
% 11.11/6.18      ! [N2: nat,A: nat] :
% 11.11/6.18        ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 11.11/6.18        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5591_int__bit__induct,axiom,
% 11.11/6.18      ! [P: int > $o,K: int] :
% 11.11/6.18        ( ( P @ zero_zero_int )
% 11.11/6.18       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18         => ( ! [K2: int] :
% 11.11/6.18                ( ( P @ K2 )
% 11.11/6.18               => ( ( K2 != zero_zero_int )
% 11.11/6.18                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.18           => ( ! [K2: int] :
% 11.11/6.18                  ( ( P @ K2 )
% 11.11/6.18                 => ( ( K2
% 11.11/6.18                     != ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 11.11/6.18             => ( P @ K ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5592_take__bit__int__less__eq,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 11.11/6.18       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5593_xor__nat__unfold,axiom,
% 11.11/6.18      ( bit_se6528837805403552850or_nat
% 11.11/6.18      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = 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 @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5594_take__bit__int__greater__eq,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.18       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5595_xor__nat__rec,axiom,
% 11.11/6.18      ( bit_se6528837805403552850or_nat
% 11.11/6.18      = ( ^ [M6: nat,N: nat] :
% 11.11/6.18            ( plus_plus_nat
% 11.11/6.18            @ ( zero_n2687167440665602831ol_nat
% 11.11/6.18              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 11.11/6.18               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 11.11/6.18            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5596_stable__imp__take__bit__eq,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.18          = A )
% 11.11/6.18       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 11.11/6.18              = zero_z3403309356797280102nteger ) )
% 11.11/6.18          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 11.11/6.18              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5597_stable__imp__take__bit__eq,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.18          = A )
% 11.11/6.18       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 11.11/6.18              = zero_zero_int ) )
% 11.11/6.18          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 11.11/6.18              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5598_stable__imp__take__bit__eq,axiom,
% 11.11/6.18      ! [A: nat,N2: nat] :
% 11.11/6.18        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = A )
% 11.11/6.18       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 11.11/6.18              = zero_zero_nat ) )
% 11.11/6.18          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.18           => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 11.11/6.18              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5599_xor__one__eq,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 11.11/6.18        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n356916108424825756nteger
% 11.11/6.18            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5600_xor__one__eq,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 11.11/6.18        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n2687167440665602831ol_nat
% 11.11/6.18            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5601_xor__one__eq,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 11.11/6.18        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n2684676970156552555ol_int
% 11.11/6.18            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5602_one__xor__eq,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 11.11/6.18        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n356916108424825756nteger
% 11.11/6.18            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5603_one__xor__eq,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 11.11/6.18        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n2687167440665602831ol_nat
% 11.11/6.18            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5604_one__xor__eq,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 11.11/6.18        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.18          @ ( zero_n2684676970156552555ol_int
% 11.11/6.18            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5605_signed__take__bit__int__greater__eq,axiom,
% 11.11/6.18      ! [K: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5606_xor__Suc__0__eq,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.18        = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.18          @ ( zero_n2687167440665602831ol_nat
% 11.11/6.18            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5607_real__average__minus__first,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 11.11/6.18        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5608_real__average__minus__second,axiom,
% 11.11/6.18      ! [B: real,A: real] :
% 11.11/6.18        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 11.11/6.18        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5609_linear__plus__1__le__power,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X4 @ one_one_real ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5610_mod__exhaust__less__4,axiom,
% 11.11/6.18      ! [M: nat] :
% 11.11/6.18        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.18          = zero_zero_nat )
% 11.11/6.18        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.18          = one_one_nat )
% 11.11/6.18        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.18          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.18          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5611_nat__approx__posE,axiom,
% 11.11/6.18      ! [E2: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5612_nat__approx__posE,axiom,
% 11.11/6.18      ! [E2: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5613_compl__le__compl__iff,axiom,
% 11.11/6.18      ! [X4: set_int,Y: set_int] :
% 11.11/6.18        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 11.11/6.18        = ( ord_less_eq_set_int @ Y @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5614_dbl__dec__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5615_dbl__dec__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5616_dbl__dec__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.18      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5617_dbl__dec__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5618_dbl__dec__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5619_int__eq__iff__numeral,axiom,
% 11.11/6.18      ! [M: nat,V: num] :
% 11.11/6.18        ( ( ( semiri1314217659103216013at_int @ M )
% 11.11/6.18          = ( numeral_numeral_int @ V ) )
% 11.11/6.18        = ( M
% 11.11/6.18          = ( numeral_numeral_nat @ V ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5620_xor__nonnegative__int__iff,axiom,
% 11.11/6.18      ! [K: int,L: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 11.11/6.18        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.18          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5621_xor__negative__int__iff,axiom,
% 11.11/6.18      ! [K: int,L: int] :
% 11.11/6.18        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 11.11/6.18        = ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.18         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5622_negative__zle,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5623_dbl__dec__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5624_dbl__dec__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5625_dbl__dec__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5626_dbl__dec__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5627_negative__zless,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5628_dbl__dec__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 11.11/6.18      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5629_dbl__dec__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 11.11/6.18      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5630_dbl__dec__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 11.11/6.18      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5631_dbl__dec__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 11.11/6.18      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5632_dbl__dec__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 11.11/6.18      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5633_take__bit__minus,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 11.11/6.18        = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5634_int__cases,axiom,
% 11.11/6.18      ! [Z: int] :
% 11.11/6.18        ( ! [N3: nat] :
% 11.11/6.18            ( Z
% 11.11/6.18           != ( semiri1314217659103216013at_int @ N3 ) )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( Z
% 11.11/6.18             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5635_int__of__nat__induct,axiom,
% 11.11/6.18      ! [P: int > $o,Z: int] :
% 11.11/6.18        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 11.11/6.18       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 11.11/6.18         => ( P @ Z ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5636_not__int__zless__negative,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5637_XOR__lower,axiom,
% 11.11/6.18      ! [X4: int,Y: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.18         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5638_int__cases4,axiom,
% 11.11/6.18      ! [M: int] :
% 11.11/6.18        ( ! [N3: nat] :
% 11.11/6.18            ( M
% 11.11/6.18           != ( semiri1314217659103216013at_int @ N3 ) )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.18             => ( M
% 11.11/6.18               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5639_int__ops_I3_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5640_int__zle__neg,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 11.11/6.18        = ( ( N2 = zero_zero_nat )
% 11.11/6.18          & ( M = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5641_nat__int__comparison_I2_J,axiom,
% 11.11/6.18      ( ord_less_nat
% 11.11/6.18      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5642_zle__int,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.18        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5643_nat__int__comparison_I3_J,axiom,
% 11.11/6.18      ( ord_less_eq_nat
% 11.11/6.18      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5644_nonneg__int__cases,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( K
% 11.11/6.18             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5645_zero__le__imp__eq__int,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.18       => ? [N3: nat] :
% 11.11/6.18            ( K
% 11.11/6.18            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5646_negative__zle__0,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5647_nonpos__int__cases,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( K
% 11.11/6.18             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5648_zadd__int__left,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: int] :
% 11.11/6.18        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 11.11/6.18        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5649_int__plus,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5650_int__ops_I5_J,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.18        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5651_int__ops_I2_J,axiom,
% 11.11/6.18      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5652_zle__iff__zadd,axiom,
% 11.11/6.18      ( ord_less_eq_int
% 11.11/6.18      = ( ^ [W3: int,Z5: int] :
% 11.11/6.18          ? [N: nat] :
% 11.11/6.18            ( Z5
% 11.11/6.18            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5653_zdiv__int,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 11.11/6.18        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5654_zmod__int,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 11.11/6.18        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5655_int__cases3,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( K != zero_zero_int )
% 11.11/6.18       => ( ! [N3: nat] :
% 11.11/6.18              ( ( K
% 11.11/6.18                = ( semiri1314217659103216013at_int @ N3 ) )
% 11.11/6.18             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 11.11/6.18         => ~ ! [N3: nat] :
% 11.11/6.18                ( ( K
% 11.11/6.18                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 11.11/6.18               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5656_not__zle__0__negative,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5657_negD,axiom,
% 11.11/6.18      ! [X4: int] :
% 11.11/6.18        ( ( ord_less_int @ X4 @ zero_zero_int )
% 11.11/6.18       => ? [N3: nat] :
% 11.11/6.18            ( X4
% 11.11/6.18            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5658_negative__zless__0,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5659_int__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 11.11/6.18        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5660_int__ops_I4_J,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 11.11/6.18        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5661_zless__iff__Suc__zadd,axiom,
% 11.11/6.18      ( ord_less_int
% 11.11/6.18      = ( ^ [W3: int,Z5: int] :
% 11.11/6.18          ? [N: nat] :
% 11.11/6.18            ( Z5
% 11.11/6.18            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5662_pos__int__cases,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( ( K
% 11.11/6.18                = ( semiri1314217659103216013at_int @ N3 ) )
% 11.11/6.18             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5663_zero__less__imp__eq__int,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ K )
% 11.11/6.18       => ? [N3: nat] :
% 11.11/6.18            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.18            & ( K
% 11.11/6.18              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5664_neg__int__cases,axiom,
% 11.11/6.18      ! [K: int] :
% 11.11/6.18        ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.18       => ~ ! [N3: nat] :
% 11.11/6.18              ( ( K
% 11.11/6.18                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 11.11/6.18             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5665_zmult__zless__mono2__lemma,axiom,
% 11.11/6.18      ! [I2: int,J: int,K: nat] :
% 11.11/6.18        ( ( ord_less_int @ I2 @ J )
% 11.11/6.18       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.18         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5666_int__ops_I6_J,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 11.11/6.18         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.18            = zero_zero_int ) )
% 11.11/6.18        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 11.11/6.18         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 11.11/6.18            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5667_zdiff__int__split,axiom,
% 11.11/6.18      ! [P: int > $o,X4: nat,Y: nat] :
% 11.11/6.18        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X4 @ Y ) ) )
% 11.11/6.18        = ( ( ( ord_less_eq_nat @ Y @ X4 )
% 11.11/6.18           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 11.11/6.18          & ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.18           => ( P @ zero_zero_int ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5668_dbl__dec__def,axiom,
% 11.11/6.18      ( neg_nu6511756317524482435omplex
% 11.11/6.18      = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5669_dbl__dec__def,axiom,
% 11.11/6.18      ( neg_nu6075765906172075777c_real
% 11.11/6.18      = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5670_dbl__dec__def,axiom,
% 11.11/6.18      ( neg_nu3179335615603231917ec_rat
% 11.11/6.18      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5671_dbl__dec__def,axiom,
% 11.11/6.18      ( neg_nu3811975205180677377ec_int
% 11.11/6.18      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5672_compl__le__swap2,axiom,
% 11.11/6.18      ! [Y: set_int,X4: set_int] :
% 11.11/6.18        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X4 )
% 11.11/6.18       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ Y ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5673_compl__le__swap1,axiom,
% 11.11/6.18      ! [Y: set_int,X4: set_int] :
% 11.11/6.18        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X4 ) )
% 11.11/6.18       => ( ord_less_eq_set_int @ X4 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5674_compl__mono,axiom,
% 11.11/6.18      ! [X4: set_int,Y: set_int] :
% 11.11/6.18        ( ( ord_less_eq_set_int @ X4 @ Y )
% 11.11/6.18       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5675_XOR__upper,axiom,
% 11.11/6.18      ! [X4: int,N2: nat,Y: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.18       => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5676_real__arch__simple,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18      ? [N3: nat] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5677_real__arch__simple,axiom,
% 11.11/6.18      ! [X4: rat] :
% 11.11/6.18      ? [N3: nat] : ( ord_less_eq_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5678_reals__Archimedean2,axiom,
% 11.11/6.18      ! [X4: rat] :
% 11.11/6.18      ? [N3: nat] : ( ord_less_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5679_reals__Archimedean2,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18      ? [N3: nat] : ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5680_exists__least__lemma,axiom,
% 11.11/6.18      ! [P: nat > $o] :
% 11.11/6.18        ( ~ ( P @ zero_zero_nat )
% 11.11/6.18       => ( ? [X_1: nat] : ( P @ X_1 )
% 11.11/6.18         => ? [N3: nat] :
% 11.11/6.18              ( ~ ( P @ N3 )
% 11.11/6.18              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5681_xor__int__rec,axiom,
% 11.11/6.18      ( bit_se6526347334894502574or_int
% 11.11/6.18      = ( ^ [K3: int,L2: int] :
% 11.11/6.18            ( plus_plus_int
% 11.11/6.18            @ ( zero_n2684676970156552555ol_int
% 11.11/6.18              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 11.11/6.18               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 11.11/6.18            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5682_Bolzano,axiom,
% 11.11/6.18      ! [A: real,B: real,P: real > real > $o] :
% 11.11/6.18        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.18       => ( ! [A5: real,B5: real,C3: real] :
% 11.11/6.18              ( ( P @ A5 @ B5 )
% 11.11/6.18             => ( ( P @ B5 @ C3 )
% 11.11/6.18               => ( ( ord_less_eq_real @ A5 @ B5 )
% 11.11/6.18                 => ( ( ord_less_eq_real @ B5 @ C3 )
% 11.11/6.18                   => ( P @ A5 @ C3 ) ) ) ) )
% 11.11/6.18         => ( ! [X5: real] :
% 11.11/6.18                ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.18               => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.18                 => ? [D6: real] :
% 11.11/6.18                      ( ( ord_less_real @ zero_zero_real @ D6 )
% 11.11/6.18                      & ! [A5: real,B5: real] :
% 11.11/6.18                          ( ( ( ord_less_eq_real @ A5 @ X5 )
% 11.11/6.18                            & ( ord_less_eq_real @ X5 @ B5 )
% 11.11/6.18                            & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D6 ) )
% 11.11/6.18                         => ( P @ A5 @ B5 ) ) ) ) )
% 11.11/6.18           => ( P @ A @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5683_ex__less__of__nat__mult,axiom,
% 11.11/6.18      ! [X4: rat,Y: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.18       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5684_ex__less__of__nat__mult,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5685_signed__take__bit__numeral__minus__bit1,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5686_divmod__algorithm__code_I7_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5687_divmod__algorithm__code_I7_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5688_divmod__algorithm__code_I7_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_eq_num @ M @ N2 )
% 11.11/6.18         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5689_divmod__algorithm__code_I8_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5690_divmod__algorithm__code_I8_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5691_divmod__algorithm__code_I8_J,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 11.11/6.18        & ( ~ ( ord_less_num @ M @ N2 )
% 11.11/6.18         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.18            = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5692_take__bit__Suc__minus__bit1,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5693_lemma__termdiff3,axiom,
% 11.11/6.18      ! [H: real,Z: real,K5: real,N2: nat] :
% 11.11/6.18        ( ( H != zero_zero_real )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 11.11/6.18         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K5 )
% 11.11/6.18           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5694_lemma__termdiff3,axiom,
% 11.11/6.18      ! [H: complex,Z: complex,K5: real,N2: nat] :
% 11.11/6.18        ( ( H != zero_zero_complex )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 11.11/6.18         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K5 )
% 11.11/6.18           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5695_signed__take__bit__numeral__bit1,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5696_dbl__inc__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 11.11/6.18      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5697_dbl__inc__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 11.11/6.18      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5698_dbl__inc__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 11.11/6.18      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5699_dbl__inc__simps_I3_J,axiom,
% 11.11/6.18      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 11.11/6.18      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5700_pred__numeral__simps_I1_J,axiom,
% 11.11/6.18      ( ( pred_numeral @ one )
% 11.11/6.18      = zero_zero_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5701_Suc__eq__numeral,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( ( suc @ N2 )
% 11.11/6.18          = ( numeral_numeral_nat @ K ) )
% 11.11/6.18        = ( N2
% 11.11/6.18          = ( pred_numeral @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5702_eq__numeral__Suc,axiom,
% 11.11/6.18      ! [K: num,N2: nat] :
% 11.11/6.18        ( ( ( numeral_numeral_nat @ K )
% 11.11/6.18          = ( suc @ N2 ) )
% 11.11/6.18        = ( ( pred_numeral @ K )
% 11.11/6.18          = N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5703_dbl__inc__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5704_dbl__inc__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5705_dbl__inc__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5706_dbl__inc__simps_I2_J,axiom,
% 11.11/6.18      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5707_pred__numeral__inc,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( pred_numeral @ ( inc @ K ) )
% 11.11/6.18        = ( numeral_numeral_nat @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5708_dbl__inc__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5709_dbl__inc__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5710_dbl__inc__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.18      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5711_dbl__inc__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5712_dbl__inc__simps_I4_J,axiom,
% 11.11/6.18      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5713_dbl__inc__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 11.11/6.18        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5714_dbl__inc__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 11.11/6.18        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5715_dbl__inc__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 11.11/6.18        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5716_pred__numeral__simps_I3_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( pred_numeral @ ( bit1 @ K ) )
% 11.11/6.18        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5717_less__numeral__Suc,axiom,
% 11.11/6.18      ! [K: num,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5718_less__Suc__numeral,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.18        = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5719_le__Suc__numeral,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.18        = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5720_le__numeral__Suc,axiom,
% 11.11/6.18      ! [K: num,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5721_diff__Suc__numeral,axiom,
% 11.11/6.18      ! [N2: nat,K: num] :
% 11.11/6.18        ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.18        = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5722_diff__numeral__Suc,axiom,
% 11.11/6.18      ! [K: num,N2: nat] :
% 11.11/6.18        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5723_minus__numeral__div__numeral,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5724_numeral__div__minus__numeral,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5725_dbl__inc__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5726_dbl__inc__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5727_dbl__inc__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5728_dbl__inc__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5729_dbl__inc__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5730_dbl__dec__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5731_dbl__dec__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5732_dbl__dec__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5733_dbl__dec__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5734_dbl__dec__simps_I1_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 11.11/6.18        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5735_dvd__numeral__simp,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.18        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5736_dvd__numeral__simp,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5737_dvd__numeral__simp,axiom,
% 11.11/6.18      ! [M: num,N2: num] :
% 11.11/6.18        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.18        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5738_divmod__algorithm__code_I2_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( unique5052692396658037445od_int @ M @ one )
% 11.11/6.18        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5739_divmod__algorithm__code_I2_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( unique5055182867167087721od_nat @ M @ one )
% 11.11/6.18        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5740_divmod__algorithm__code_I2_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( unique3479559517661332726nteger @ M @ one )
% 11.11/6.18        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5741_add__neg__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5742_add__neg__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5743_add__neg__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5744_add__neg__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5745_add__neg__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5746_add__neg__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5747_add__neg__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5748_add__neg__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5749_add__neg__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5750_add__neg__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5751_diff__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5752_diff__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5753_diff__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.18        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5754_diff__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5755_diff__numeral__special_I6_J,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5756_diff__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5757_diff__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5758_diff__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.18        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5759_diff__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.18        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5760_diff__numeral__special_I5_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5761_divmod__algorithm__code_I3_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 11.11/6.18        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5762_divmod__algorithm__code_I3_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 11.11/6.18        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5763_divmod__algorithm__code_I3_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 11.11/6.18        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5764_divmod__algorithm__code_I4_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 11.11/6.18        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5765_divmod__algorithm__code_I4_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 11.11/6.18        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5766_divmod__algorithm__code_I4_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 11.11/6.18        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5767_one__div__minus__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5768_minus__one__div__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.18        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5769_signed__take__bit__numeral__bit0,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5770_signed__take__bit__numeral__minus__bit0,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.18        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5771_num__induct,axiom,
% 11.11/6.18      ! [P: num > $o,X4: num] :
% 11.11/6.18        ( ( P @ one )
% 11.11/6.18       => ( ! [X5: num] :
% 11.11/6.18              ( ( P @ X5 )
% 11.11/6.18             => ( P @ ( inc @ X5 ) ) )
% 11.11/6.18         => ( P @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5772_add__inc,axiom,
% 11.11/6.18      ! [X4: num,Y: num] :
% 11.11/6.18        ( ( plus_plus_num @ X4 @ ( inc @ Y ) )
% 11.11/6.18        = ( inc @ ( plus_plus_num @ X4 @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5773_numeral__eq__Suc,axiom,
% 11.11/6.18      ( numeral_numeral_nat
% 11.11/6.18      = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5774_inc_Osimps_I1_J,axiom,
% 11.11/6.18      ( ( inc @ one )
% 11.11/6.18      = ( bit0 @ one ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5775_inc_Osimps_I2_J,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( inc @ ( bit0 @ X4 ) )
% 11.11/6.18        = ( bit1 @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5776_inc_Osimps_I3_J,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( inc @ ( bit1 @ X4 ) )
% 11.11/6.18        = ( bit0 @ ( inc @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5777_add__One,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( plus_plus_num @ X4 @ one )
% 11.11/6.18        = ( inc @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5778_mult__inc,axiom,
% 11.11/6.18      ! [X4: num,Y: num] :
% 11.11/6.18        ( ( times_times_num @ X4 @ ( inc @ Y ) )
% 11.11/6.18        = ( plus_plus_num @ ( times_times_num @ X4 @ Y ) @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5779_pred__numeral__def,axiom,
% 11.11/6.18      ( pred_numeral
% 11.11/6.18      = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5780_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numeral_numeral_rat @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5781_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numera1916890842035813515d_enat @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5782_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numera6690914467698888265omplex @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5783_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numeral_numeral_real @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5784_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numeral_numeral_nat @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5785_numeral__inc,axiom,
% 11.11/6.18      ! [X4: num] :
% 11.11/6.18        ( ( numeral_numeral_int @ ( inc @ X4 ) )
% 11.11/6.18        = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5786_dbl__inc__def,axiom,
% 11.11/6.18      ( neg_nu8557863876264182079omplex
% 11.11/6.18      = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5787_dbl__inc__def,axiom,
% 11.11/6.18      ( neg_nu8295874005876285629c_real
% 11.11/6.18      = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5788_dbl__inc__def,axiom,
% 11.11/6.18      ( neg_nu5219082963157363817nc_rat
% 11.11/6.18      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5789_dbl__inc__def,axiom,
% 11.11/6.18      ( neg_nu5851722552734809277nc_int
% 11.11/6.18      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5790_divmod__int__def,axiom,
% 11.11/6.18      ( unique5052692396658037445od_int
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5791_divmod__def,axiom,
% 11.11/6.18      ( unique5052692396658037445od_int
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5792_divmod__def,axiom,
% 11.11/6.18      ( unique5055182867167087721od_nat
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5793_divmod__def,axiom,
% 11.11/6.18      ( unique3479559517661332726nteger
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5794_divmod_H__nat__def,axiom,
% 11.11/6.18      ( unique5055182867167087721od_nat
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5795_take__bit__numeral__minus__bit1,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5796_take__bit__numeral__bit0,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5797_take__bit__numeral__bit0,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 11.11/6.18        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5798_take__bit__numeral__minus__bit0,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.18        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5799_divmod__divmod__step,axiom,
% 11.11/6.18      ( unique5055182867167087721od_nat
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5800_divmod__divmod__step,axiom,
% 11.11/6.18      ( unique5052692396658037445od_int
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5801_divmod__divmod__step,axiom,
% 11.11/6.18      ( unique3479559517661332726nteger
% 11.11/6.18      = ( ^ [M6: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5802_take__bit__numeral__bit1,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5803_take__bit__numeral__bit1,axiom,
% 11.11/6.18      ! [L: num,K: num] :
% 11.11/6.18        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 11.11/6.18        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5804_norm__divide__numeral,axiom,
% 11.11/6.18      ! [A: real,W: num] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5805_norm__divide__numeral,axiom,
% 11.11/6.18      ! [A: complex,W: num] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.18        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5806_norm__mult__numeral2,axiom,
% 11.11/6.18      ! [A: real,W: num] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5807_norm__mult__numeral2,axiom,
% 11.11/6.18      ! [A: complex,W: num] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.18        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5808_norm__mult__numeral1,axiom,
% 11.11/6.18      ! [W: num,A: real] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 11.11/6.18        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5809_norm__mult__numeral1,axiom,
% 11.11/6.18      ! [W: num,A: complex] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 11.11/6.18        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5810_norm__neg__numeral,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.18        = ( numeral_numeral_real @ W ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5811_norm__neg__numeral,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.18        = ( numeral_numeral_real @ W ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5812_norm__le__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ zero_zero_real )
% 11.11/6.18        = ( X4 = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5813_norm__le__zero__iff,axiom,
% 11.11/6.18      ! [X4: complex] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real )
% 11.11/6.18        = ( X4 = zero_zero_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5814_zero__less__norm__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X4 ) )
% 11.11/6.18        = ( X4 != zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5815_zero__less__norm__iff,axiom,
% 11.11/6.18      ! [X4: complex] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) )
% 11.11/6.18        = ( X4 != zero_zero_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5816_norm__numeral,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.18        = ( numeral_numeral_real @ W ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5817_norm__numeral,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.18        = ( numeral_numeral_real @ W ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5818_norm__one,axiom,
% 11.11/6.18      ( ( real_V7735802525324610683m_real @ one_one_real )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5819_norm__one,axiom,
% 11.11/6.18      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5820_norm__not__less__zero,axiom,
% 11.11/6.18      ! [X4: complex] :
% 11.11/6.18        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5821_norm__ge__zero,axiom,
% 11.11/6.18      ! [X4: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5822_norm__divide,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.18        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5823_norm__divide,axiom,
% 11.11/6.18      ! [A: complex,B: complex] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.18        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5824_norm__power,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.18        = ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5825_norm__power,axiom,
% 11.11/6.18      ! [X4: complex,N2: nat] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) )
% 11.11/6.18        = ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5826_norm__uminus__minus,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ Y ) )
% 11.11/6.18        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5827_norm__uminus__minus,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex] :
% 11.11/6.18        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y ) )
% 11.11/6.18        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5828_nonzero__norm__divide,axiom,
% 11.11/6.18      ! [B: real,A: real] :
% 11.11/6.18        ( ( B != zero_zero_real )
% 11.11/6.18       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.18          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5829_nonzero__norm__divide,axiom,
% 11.11/6.18      ! [B: complex,A: complex] :
% 11.11/6.18        ( ( B != zero_zero_complex )
% 11.11/6.18       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.18          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5830_power__eq__imp__eq__norm,axiom,
% 11.11/6.18      ! [W: real,N2: nat,Z: real] :
% 11.11/6.18        ( ( ( power_power_real @ W @ N2 )
% 11.11/6.18          = ( power_power_real @ Z @ N2 ) )
% 11.11/6.18       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18         => ( ( real_V7735802525324610683m_real @ W )
% 11.11/6.18            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5831_power__eq__imp__eq__norm,axiom,
% 11.11/6.18      ! [W: complex,N2: nat,Z: complex] :
% 11.11/6.18        ( ( ( power_power_complex @ W @ N2 )
% 11.11/6.18          = ( power_power_complex @ Z @ N2 ) )
% 11.11/6.18       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18         => ( ( real_V1022390504157884413omplex @ W )
% 11.11/6.18            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5832_norm__mult__less,axiom,
% 11.11/6.18      ! [X4: real,R3: real,Y: real,S: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 11.11/6.18         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5833_norm__mult__less,axiom,
% 11.11/6.18      ! [X4: complex,R3: real,Y: complex,S: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 11.11/6.18         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5834_norm__mult__ineq,axiom,
% 11.11/6.18      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5835_norm__mult__ineq,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5836_norm__triangle__lt,axiom,
% 11.11/6.18      ! [X4: real,Y: real,E2: real] :
% 11.11/6.18        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5837_norm__triangle__lt,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex,E2: real] :
% 11.11/6.18        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5838_norm__add__less,axiom,
% 11.11/6.18      ! [X4: real,R3: real,Y: real,S: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 11.11/6.18         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5839_norm__add__less,axiom,
% 11.11/6.18      ! [X4: complex,R3: real,Y: complex,S: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 11.11/6.18         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5840_norm__add__leD,axiom,
% 11.11/6.18      ! [A: real,B: real,C: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5841_norm__add__leD,axiom,
% 11.11/6.18      ! [A: complex,B: complex,C: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5842_norm__triangle__le,axiom,
% 11.11/6.18      ! [X4: real,Y: real,E2: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5843_norm__triangle__le,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex,E2: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5844_norm__triangle__ineq,axiom,
% 11.11/6.18      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5845_norm__triangle__ineq,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5846_norm__triangle__mono,axiom,
% 11.11/6.18      ! [A: real,R3: real,B: real,S: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R3 )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 11.11/6.18         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5847_norm__triangle__mono,axiom,
% 11.11/6.18      ! [A: complex,R3: real,B: complex,S: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R3 )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 11.11/6.18         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5848_norm__diff__triangle__less,axiom,
% 11.11/6.18      ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 11.11/6.18         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5849_norm__diff__triangle__less,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 11.11/6.18        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 11.11/6.18       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 11.11/6.18         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5850_norm__power__ineq,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5851_norm__power__ineq,axiom,
% 11.11/6.18      ! [X4: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5852_norm__triangle__sub,axiom,
% 11.11/6.18      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5853_norm__triangle__sub,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5854_norm__triangle__ineq4,axiom,
% 11.11/6.18      ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5855_norm__triangle__ineq4,axiom,
% 11.11/6.18      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5856_norm__diff__triangle__le,axiom,
% 11.11/6.18      ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 11.11/6.18         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5857_norm__diff__triangle__le,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 11.11/6.18         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5858_norm__triangle__le__diff,axiom,
% 11.11/6.18      ! [X4: real,Y: real,E2: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5859_norm__triangle__le__diff,axiom,
% 11.11/6.18      ! [X4: complex,Y: complex,E2: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5860_norm__diff__ineq,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5861_norm__diff__ineq,axiom,
% 11.11/6.18      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5862_norm__triangle__ineq2,axiom,
% 11.11/6.18      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5863_norm__triangle__ineq2,axiom,
% 11.11/6.18      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5864_power__eq__1__iff,axiom,
% 11.11/6.18      ! [W: real,N2: nat] :
% 11.11/6.18        ( ( ( power_power_real @ W @ N2 )
% 11.11/6.18          = one_one_real )
% 11.11/6.18       => ( ( ( real_V7735802525324610683m_real @ W )
% 11.11/6.18            = one_one_real )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5865_power__eq__1__iff,axiom,
% 11.11/6.18      ! [W: complex,N2: nat] :
% 11.11/6.18        ( ( ( power_power_complex @ W @ N2 )
% 11.11/6.18          = one_one_complex )
% 11.11/6.18       => ( ( ( real_V1022390504157884413omplex @ W )
% 11.11/6.18            = one_one_real )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5866_norm__diff__triangle__ineq,axiom,
% 11.11/6.18      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5867_norm__diff__triangle__ineq,axiom,
% 11.11/6.18      ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5868_square__norm__one,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_real )
% 11.11/6.18       => ( ( real_V7735802525324610683m_real @ X4 )
% 11.11/6.18          = one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5869_square__norm__one,axiom,
% 11.11/6.18      ! [X4: complex] :
% 11.11/6.18        ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18          = one_one_complex )
% 11.11/6.18       => ( ( real_V1022390504157884413omplex @ X4 )
% 11.11/6.18          = one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5870_norm__power__diff,axiom,
% 11.11/6.18      ! [Z: real,W: real,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 11.11/6.18         => ( 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 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5871_norm__power__diff,axiom,
% 11.11/6.18      ! [Z: complex,W: complex,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 11.11/6.18         => ( 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 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5872_arcosh__1,axiom,
% 11.11/6.18      ( ( arcosh_real @ one_one_real )
% 11.11/6.18      = zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5873_pochhammer__double,axiom,
% 11.11/6.18      ! [Z: rat,N2: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5874_pochhammer__double,axiom,
% 11.11/6.18      ! [Z: complex,N2: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5875_pochhammer__double,axiom,
% 11.11/6.18      ! [Z: real,N2: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5876_ln__one__minus__pos__lower__bound,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.18         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5877_central__binomial__lower__bound,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5878_divmod__BitM__2__eq,axiom,
% 11.11/6.18      ! [M: num] :
% 11.11/6.18        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 11.11/6.18        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5879_ln__one,axiom,
% 11.11/6.18      ( ( ln_ln_real @ one_one_real )
% 11.11/6.18      = zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5880_ln__inj__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ( ( ln_ln_real @ X4 )
% 11.11/6.18              = ( ln_ln_real @ Y ) )
% 11.11/6.18            = ( X4 = Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5881_ln__less__cancel__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 11.11/6.18            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5882_pochhammer__0,axiom,
% 11.11/6.18      ! [A: complex] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 11.11/6.18        = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5883_pochhammer__0,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 11.11/6.18        = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5884_pochhammer__0,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 11.11/6.18        = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5885_pochhammer__0,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 11.11/6.18        = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5886_pochhammer__0,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 11.11/6.18        = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5887_dbl__dec__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 11.11/6.18        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5888_dbl__dec__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 11.11/6.18        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5889_dbl__dec__simps_I5_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 11.11/6.18        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5890_ln__le__cancel__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 11.11/6.18            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5891_ln__less__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 11.11/6.18          = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5892_ln__gt__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.18          = ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5893_ln__eq__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ( ln_ln_real @ X4 )
% 11.11/6.18            = zero_zero_real )
% 11.11/6.18          = ( X4 = one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5894_pred__numeral__simps_I2_J,axiom,
% 11.11/6.18      ! [K: num] :
% 11.11/6.18        ( ( pred_numeral @ ( bit0 @ K ) )
% 11.11/6.18        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5895_ln__ge__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.18          = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5896_ln__le__zero__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 11.11/6.18          = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5897_semiring__norm_I26_J,axiom,
% 11.11/6.18      ( ( bitM @ one )
% 11.11/6.18      = one ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5898_ln__less__self,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5899_pochhammer__pos,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5900_pochhammer__pos,axiom,
% 11.11/6.18      ! [X4: rat,N2: nat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.18       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5901_pochhammer__pos,axiom,
% 11.11/6.18      ! [X4: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.18       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5902_pochhammer__pos,axiom,
% 11.11/6.18      ! [X4: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ X4 )
% 11.11/6.18       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5903_pochhammer__neq__0__mono,axiom,
% 11.11/6.18      ! [A: complex,M: nat,N2: nat] :
% 11.11/6.18        ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 11.11/6.18         != zero_zero_complex )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 11.11/6.18           != zero_zero_complex ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5904_pochhammer__neq__0__mono,axiom,
% 11.11/6.18      ! [A: real,M: nat,N2: nat] :
% 11.11/6.18        ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 11.11/6.18         != zero_zero_real )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 11.11/6.18           != zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5905_pochhammer__neq__0__mono,axiom,
% 11.11/6.18      ! [A: rat,M: nat,N2: nat] :
% 11.11/6.18        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 11.11/6.18         != zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 11.11/6.18           != zero_zero_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5906_pochhammer__eq__0__mono,axiom,
% 11.11/6.18      ! [A: complex,N2: nat,M: nat] :
% 11.11/6.18        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 11.11/6.18          = zero_zero_complex )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s2602460028002588243omplex @ A @ M )
% 11.11/6.18            = zero_zero_complex ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5907_pochhammer__eq__0__mono,axiom,
% 11.11/6.18      ! [A: real,N2: nat,M: nat] :
% 11.11/6.18        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 11.11/6.18          = zero_zero_real )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s7457072308508201937r_real @ A @ M )
% 11.11/6.18            = zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5908_pochhammer__eq__0__mono,axiom,
% 11.11/6.18      ! [A: rat,N2: nat,M: nat] :
% 11.11/6.18        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 11.11/6.18          = zero_zero_rat )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 11.11/6.18            = zero_zero_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5909_semiring__norm_I27_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( bitM @ ( bit0 @ N2 ) )
% 11.11/6.18        = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5910_semiring__norm_I28_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( bitM @ ( bit1 @ N2 ) )
% 11.11/6.18        = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5911_inc__BitM__eq,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( inc @ ( bitM @ N2 ) )
% 11.11/6.18        = ( bit0 @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5912_BitM__inc__eq,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( bitM @ ( inc @ N2 ) )
% 11.11/6.18        = ( bit1 @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5913_ln__bound,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5914_ln__gt__zero__imp__gt__one,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18         => ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5915_ln__less__zero,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.18         => ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5916_ln__gt__zero,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.18       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5917_ln__ge__zero,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5918_pochhammer__nonneg,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5919_pochhammer__nonneg,axiom,
% 11.11/6.18      ! [X4: rat,N2: nat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.18       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5920_pochhammer__nonneg,axiom,
% 11.11/6.18      ! [X4: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 11.11/6.18       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5921_pochhammer__nonneg,axiom,
% 11.11/6.18      ! [X4: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ X4 )
% 11.11/6.18       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5922_pochhammer__0__left,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( N2 = zero_zero_nat )
% 11.11/6.18         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 11.11/6.18            = one_one_complex ) )
% 11.11/6.18        & ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 11.11/6.18            = zero_zero_complex ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5923_pochhammer__0__left,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( N2 = zero_zero_nat )
% 11.11/6.18         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 11.11/6.18            = one_one_real ) )
% 11.11/6.18        & ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 11.11/6.18            = zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5924_pochhammer__0__left,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( N2 = zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 11.11/6.18            = one_one_rat ) )
% 11.11/6.18        & ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 11.11/6.18            = zero_zero_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5925_pochhammer__0__left,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( N2 = zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 11.11/6.18            = one_one_nat ) )
% 11.11/6.18        & ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 11.11/6.18            = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5926_pochhammer__0__left,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( ( N2 = zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 11.11/6.18            = one_one_int ) )
% 11.11/6.18        & ( ( N2 != zero_zero_nat )
% 11.11/6.18         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 11.11/6.18            = zero_zero_int ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5927_eval__nat__numeral_I2_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 11.11/6.18        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5928_ln__ge__zero__imp__ge__one,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18         => ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5929_one__plus__BitM,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 11.11/6.18        = ( bit0 @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5930_BitM__plus__one,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 11.11/6.18        = ( bit0 @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5931_ln__add__one__self__le__self,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5932_ln__mult,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ( ln_ln_real @ ( times_times_real @ X4 @ Y ) )
% 11.11/6.18            = ( plus_plus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5933_ln__eq__minus__one,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ( ln_ln_real @ X4 )
% 11.11/6.18            = ( minus_minus_real @ X4 @ one_one_real ) )
% 11.11/6.18         => ( X4 = one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5934_ln__div,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ( ln_ln_real @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.18            = ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5935_pochhammer__rec,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5936_pochhammer__rec,axiom,
% 11.11/6.18      ! [A: complex,N2: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5937_pochhammer__rec,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5938_pochhammer__rec,axiom,
% 11.11/6.18      ! [A: nat,N2: nat] :
% 11.11/6.18        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5939_pochhammer__rec,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5940_pochhammer__rec_H,axiom,
% 11.11/6.18      ! [Z: rat,N2: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5941_pochhammer__rec_H,axiom,
% 11.11/6.18      ! [Z: complex,N2: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5942_pochhammer__rec_H,axiom,
% 11.11/6.18      ! [Z: real,N2: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5943_pochhammer__rec_H,axiom,
% 11.11/6.18      ! [Z: int,N2: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5944_pochhammer__rec_H,axiom,
% 11.11/6.18      ! [Z: nat,N2: nat] :
% 11.11/6.18        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5945_pochhammer__Suc,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5946_pochhammer__Suc,axiom,
% 11.11/6.18      ! [A: complex,N2: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5947_pochhammer__Suc,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5948_pochhammer__Suc,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5949_pochhammer__Suc,axiom,
% 11.11/6.18      ! [A: nat,N2: nat] :
% 11.11/6.18        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5950_pochhammer__of__nat__eq__0__lemma,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5951_pochhammer__of__nat__eq__0__lemma,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 11.11/6.18          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5952_pochhammer__of__nat__eq__0__lemma,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5953_pochhammer__of__nat__eq__0__lemma,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5954_pochhammer__of__nat__eq__0__lemma,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5955_pochhammer__of__nat__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_complex )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5956_pochhammer__of__nat__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 11.11/6.18          = zero_z3403309356797280102nteger )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5957_pochhammer__of__nat__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_rat )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5958_pochhammer__of__nat__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_real )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5959_pochhammer__of__nat__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 11.11/6.18          = zero_zero_int )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5960_pochhammer__eq__0__iff,axiom,
% 11.11/6.18      ! [A: complex,N2: nat] :
% 11.11/6.18        ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 11.11/6.18          = zero_zero_complex )
% 11.11/6.18        = ( ? [K3: nat] :
% 11.11/6.18              ( ( ord_less_nat @ K3 @ N2 )
% 11.11/6.18              & ( A
% 11.11/6.18                = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5961_pochhammer__eq__0__iff,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 11.11/6.18          = zero_zero_rat )
% 11.11/6.18        = ( ? [K3: nat] :
% 11.11/6.18              ( ( ord_less_nat @ K3 @ N2 )
% 11.11/6.18              & ( A
% 11.11/6.18                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5962_pochhammer__eq__0__iff,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 11.11/6.18          = zero_zero_real )
% 11.11/6.18        = ( ? [K3: nat] :
% 11.11/6.18              ( ( ord_less_nat @ K3 @ N2 )
% 11.11/6.18              & ( A
% 11.11/6.18                = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5963_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 11.11/6.18         != zero_zero_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5964_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 11.11/6.18         != zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5965_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 11.11/6.18         != zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5966_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 11.11/6.18         != zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5967_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 11.11/6.18         != zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5968_pochhammer__product_H,axiom,
% 11.11/6.18      ! [Z: rat,N2: nat,M: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5969_pochhammer__product_H,axiom,
% 11.11/6.18      ! [Z: complex,N2: nat,M: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5970_pochhammer__product_H,axiom,
% 11.11/6.18      ! [Z: real,N2: nat,M: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5971_pochhammer__product_H,axiom,
% 11.11/6.18      ! [Z: int,N2: nat,M: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5972_pochhammer__product_H,axiom,
% 11.11/6.18      ! [Z: nat,N2: nat,M: nat] :
% 11.11/6.18        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 11.11/6.18        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5973_binomial__maximum_H,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5974_binomial__mono,axiom,
% 11.11/6.18      ! [K: nat,K6: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ K6 )
% 11.11/6.18       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 11.11/6.18         => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5975_ln__2__less__1,axiom,
% 11.11/6.18      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5976_numeral__BitM,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 11.11/6.18        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5977_numeral__BitM,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 11.11/6.18        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5978_numeral__BitM,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 11.11/6.18        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5979_numeral__BitM,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 11.11/6.18        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5980_binomial__antimono,axiom,
% 11.11/6.18      ! [K: nat,K6: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ K6 )
% 11.11/6.18       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 11.11/6.18         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 11.11/6.18           => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5981_binomial__maximum,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5982_odd__numeral__BitM,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5983_odd__numeral__BitM,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5984_odd__numeral__BitM,axiom,
% 11.11/6.18      ! [W: num] :
% 11.11/6.18        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5985_ln__le__minus__one,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5986_ln__diff__le,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.18         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X4 @ Y ) @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5987_ln__add__one__self__le__self2,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.18       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5988_ln__realpow,axiom,
% 11.11/6.18      ! [X4: real,N2: nat] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ln_ln_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.18          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5989_pochhammer__product,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: rat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 11.11/6.18          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5990_pochhammer__product,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: complex] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ( comm_s2602460028002588243omplex @ Z @ N2 )
% 11.11/6.18          = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5991_pochhammer__product,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: real] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 11.11/6.18          = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5992_pochhammer__product,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: int] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 11.11/6.18          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5993_pochhammer__product,axiom,
% 11.11/6.18      ! [M: nat,N2: nat,Z: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 11.11/6.18          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5994_binomial__strict__antimono,axiom,
% 11.11/6.18      ! [K: nat,K6: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ K @ K6 )
% 11.11/6.18       => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 11.11/6.18         => ( ( ord_less_eq_nat @ K6 @ N2 )
% 11.11/6.18           => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5995_binomial__strict__mono,axiom,
% 11.11/6.18      ! [K: nat,K6: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ K @ K6 )
% 11.11/6.18       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 11.11/6.18         => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5996_binomial__less__binomial__Suc,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18       => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5997_central__binomial__odd,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.18       => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.18          = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5998_ln__one__minus__pos__upper__bound,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.18         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_5999_pochhammer__absorb__comp,axiom,
% 11.11/6.18      ! [R3: complex,K: nat] :
% 11.11/6.18        ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K ) )
% 11.11/6.18        = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6000_pochhammer__absorb__comp,axiom,
% 11.11/6.18      ! [R3: code_integer,K: nat] :
% 11.11/6.18        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 11.11/6.18        = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6001_pochhammer__absorb__comp,axiom,
% 11.11/6.18      ! [R3: rat,K: nat] :
% 11.11/6.18        ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 11.11/6.18        = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6002_pochhammer__absorb__comp,axiom,
% 11.11/6.18      ! [R3: real,K: nat] :
% 11.11/6.18        ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K ) )
% 11.11/6.18        = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6003_pochhammer__absorb__comp,axiom,
% 11.11/6.18      ! [R3: int,K: nat] :
% 11.11/6.18        ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 11.11/6.18        = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6004_pochhammer__minus,axiom,
% 11.11/6.18      ! [B: complex,K: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 11.11/6.18        = ( 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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6005_pochhammer__minus,axiom,
% 11.11/6.18      ! [B: code_integer,K: nat] :
% 11.11/6.18        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 11.11/6.18        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6006_pochhammer__minus,axiom,
% 11.11/6.18      ! [B: rat,K: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 11.11/6.18        = ( 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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6007_pochhammer__minus,axiom,
% 11.11/6.18      ! [B: real,K: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 11.11/6.18        = ( 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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6008_pochhammer__minus,axiom,
% 11.11/6.18      ! [B: int,K: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 11.11/6.18        = ( 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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6009_pochhammer__minus_H,axiom,
% 11.11/6.18      ! [B: complex,K: nat] :
% 11.11/6.18        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 11.11/6.18        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6010_pochhammer__minus_H,axiom,
% 11.11/6.18      ! [B: code_integer,K: nat] :
% 11.11/6.18        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 11.11/6.18        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6011_pochhammer__minus_H,axiom,
% 11.11/6.18      ! [B: rat,K: nat] :
% 11.11/6.18        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 11.11/6.18        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6012_pochhammer__minus_H,axiom,
% 11.11/6.18      ! [B: real,K: nat] :
% 11.11/6.18        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 11.11/6.18        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6013_pochhammer__minus_H,axiom,
% 11.11/6.18      ! [B: int,K: nat] :
% 11.11/6.18        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 11.11/6.18        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6014_ln__one__plus__pos__lower__bound,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.18         => ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6015_zero__less__binomial__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 11.11/6.18        = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6016_artanh__def,axiom,
% 11.11/6.18      ( artanh_real
% 11.11/6.18      = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6017_choose__two,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6018_binomial__n__0,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ N2 @ zero_zero_nat )
% 11.11/6.18        = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6019_binomial__Suc__Suc,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 11.11/6.18        = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6020_binomial__eq__0__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ( binomial @ N2 @ K )
% 11.11/6.18          = zero_zero_nat )
% 11.11/6.18        = ( ord_less_nat @ N2 @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6021_binomial__Suc__n,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ ( suc @ N2 ) @ N2 )
% 11.11/6.18        = ( suc @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6022_binomial__n__n,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ N2 @ N2 )
% 11.11/6.18        = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6023_binomial__0__Suc,axiom,
% 11.11/6.18      ! [K: nat] :
% 11.11/6.18        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 11.11/6.18        = zero_zero_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6024_binomial__1,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.18        = N2 ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6025_choose__one,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( binomial @ N2 @ one_one_nat )
% 11.11/6.18        = N2 ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6026_binomial__eq__0,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ N2 @ K )
% 11.11/6.18       => ( ( binomial @ N2 @ K )
% 11.11/6.18          = zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6027_Suc__times__binomial,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 11.11/6.18        = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6028_Suc__times__binomial__eq,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 11.11/6.18        = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6029_binomial__symmetric,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ( binomial @ N2 @ K )
% 11.11/6.18          = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6030_choose__mult__lemma,axiom,
% 11.11/6.18      ! [M: nat,R3: nat,K: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 11.11/6.18        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R3 ) @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6031_binomial__le__pow,axiom,
% 11.11/6.18      ! [R3: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ R3 @ N2 )
% 11.11/6.18       => ( ord_less_eq_nat @ ( binomial @ N2 @ R3 ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6032_zero__less__binomial,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6033_Suc__times__binomial__add,axiom,
% 11.11/6.18      ! [A: nat,B: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 11.11/6.18        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6034_choose__mult,axiom,
% 11.11/6.18      ! [K: nat,M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.18       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18         => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 11.11/6.18            = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6035_binomial__Suc__Suc__eq__times,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 11.11/6.18        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6036_binomial__absorb__comp,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 11.11/6.18        = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6037_binomial__absorption,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 11.11/6.18        = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6038_binomial__ge__n__over__k__pow__k,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6039_binomial__ge__n__over__k__pow__k,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.18       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6040_binomial__le__pow2,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6041_choose__reduce__nat,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.18         => ( ( binomial @ N2 @ K )
% 11.11/6.18            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6042_times__binomial__minus1__eq,axiom,
% 11.11/6.18      ! [K: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.18       => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 11.11/6.18          = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6043_binomial__addition__formula,axiom,
% 11.11/6.18      ! [N2: nat,K: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.18       => ( ( binomial @ N2 @ ( suc @ K ) )
% 11.11/6.18          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6044_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.18         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6045_tanh__ln__real,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( tanh_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.18          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6046_abs__ln__one__plus__x__minus__x__bound,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.18       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6047_signed__take__bit__eq__take__bit__minus,axiom,
% 11.11/6.18      ( bit_ri631733984087533419it_int
% 11.11/6.18      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6048_fact__double,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6049_fact__double,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6050_fact__double,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.18        = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6051_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.18         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6052_abs__abs,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 11.11/6.18        = ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6053_abs__abs,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 11.11/6.18        = ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6054_abs__abs,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6055_abs__abs,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 11.11/6.18        = ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6056_abs__idempotent,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 11.11/6.18        = ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6057_abs__idempotent,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 11.11/6.18        = ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6058_abs__idempotent,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6059_abs__idempotent,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 11.11/6.18        = ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6060_abs__0,axiom,
% 11.11/6.18      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 11.11/6.18      = zero_z3403309356797280102nteger ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6061_abs__0,axiom,
% 11.11/6.18      ( ( abs_abs_complex @ zero_zero_complex )
% 11.11/6.18      = zero_zero_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6062_abs__0,axiom,
% 11.11/6.18      ( ( abs_abs_real @ zero_zero_real )
% 11.11/6.18      = zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6063_abs__0,axiom,
% 11.11/6.18      ( ( abs_abs_rat @ zero_zero_rat )
% 11.11/6.18      = zero_zero_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6064_abs__0,axiom,
% 11.11/6.18      ( ( abs_abs_int @ zero_zero_int )
% 11.11/6.18      = zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6065_abs__0__eq,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( zero_z3403309356797280102nteger
% 11.11/6.18          = ( abs_abs_Code_integer @ A ) )
% 11.11/6.18        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6066_abs__0__eq,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( zero_zero_real
% 11.11/6.18          = ( abs_abs_real @ A ) )
% 11.11/6.18        = ( A = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6067_abs__0__eq,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( zero_zero_rat
% 11.11/6.18          = ( abs_abs_rat @ A ) )
% 11.11/6.18        = ( A = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6068_abs__0__eq,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( zero_zero_int
% 11.11/6.18          = ( abs_abs_int @ A ) )
% 11.11/6.18        = ( A = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6069_abs__eq__0,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ( abs_abs_Code_integer @ A )
% 11.11/6.18          = zero_z3403309356797280102nteger )
% 11.11/6.18        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6070_abs__eq__0,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ( abs_abs_real @ A )
% 11.11/6.18          = zero_zero_real )
% 11.11/6.18        = ( A = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6071_abs__eq__0,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ( abs_abs_rat @ A )
% 11.11/6.18          = zero_zero_rat )
% 11.11/6.18        = ( A = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6072_abs__eq__0,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ( abs_abs_int @ A )
% 11.11/6.18          = zero_zero_int )
% 11.11/6.18        = ( A = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6073_abs__zero,axiom,
% 11.11/6.18      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 11.11/6.18      = zero_z3403309356797280102nteger ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6074_abs__zero,axiom,
% 11.11/6.18      ( ( abs_abs_real @ zero_zero_real )
% 11.11/6.18      = zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6075_abs__zero,axiom,
% 11.11/6.18      ( ( abs_abs_rat @ zero_zero_rat )
% 11.11/6.18      = zero_zero_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6076_abs__zero,axiom,
% 11.11/6.18      ( ( abs_abs_int @ zero_zero_int )
% 11.11/6.18      = zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6077_abs__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 11.11/6.18        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6078_abs__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.18        = ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6079_abs__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.18        = ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6080_abs__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.18        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6081_abs__mult__self__eq,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.18        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6082_abs__mult__self__eq,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 11.11/6.18        = ( times_times_rat @ A @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6083_abs__mult__self__eq,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 11.11/6.18        = ( times_times_real @ A @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6084_abs__mult__self__eq,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 11.11/6.18        = ( times_times_int @ A @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6085_abs__1,axiom,
% 11.11/6.18      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 11.11/6.18      = one_one_Code_integer ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6086_abs__1,axiom,
% 11.11/6.18      ( ( abs_abs_complex @ one_one_complex )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6087_abs__1,axiom,
% 11.11/6.18      ( ( abs_abs_real @ one_one_real )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6088_abs__1,axiom,
% 11.11/6.18      ( ( abs_abs_rat @ one_one_rat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6089_abs__1,axiom,
% 11.11/6.18      ( ( abs_abs_int @ one_one_int )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6090_abs__add__abs,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 11.11/6.18        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6091_abs__add__abs,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 11.11/6.18        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6092_abs__add__abs,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 11.11/6.18        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6093_abs__add__abs,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 11.11/6.18        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6094_abs__divide,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.18        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6095_abs__divide,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.18        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6096_abs__divide,axiom,
% 11.11/6.18      ! [A: complex,B: complex] :
% 11.11/6.18        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.18        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6097_abs__minus,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.18        = ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6098_abs__minus,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.18        = ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6099_abs__minus,axiom,
% 11.11/6.18      ! [A: complex] :
% 11.11/6.18        ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.18        = ( abs_abs_complex @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6100_abs__minus,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6101_abs__minus,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.18        = ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6102_abs__minus__cancel,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.18        = ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6103_abs__minus__cancel,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.18        = ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6104_abs__minus__cancel,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6105_abs__minus__cancel,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.18        = ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6106_abs__dvd__iff,axiom,
% 11.11/6.18      ! [M: real,K: real] :
% 11.11/6.18        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 11.11/6.18        = ( dvd_dvd_real @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6107_abs__dvd__iff,axiom,
% 11.11/6.18      ! [M: int,K: int] :
% 11.11/6.18        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 11.11/6.18        = ( dvd_dvd_int @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6108_abs__dvd__iff,axiom,
% 11.11/6.18      ! [M: code_integer,K: code_integer] :
% 11.11/6.18        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 11.11/6.18        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6109_abs__dvd__iff,axiom,
% 11.11/6.18      ! [M: rat,K: rat] :
% 11.11/6.18        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 11.11/6.18        = ( dvd_dvd_rat @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6110_dvd__abs__iff,axiom,
% 11.11/6.18      ! [M: real,K: real] :
% 11.11/6.18        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 11.11/6.18        = ( dvd_dvd_real @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6111_dvd__abs__iff,axiom,
% 11.11/6.18      ! [M: int,K: int] :
% 11.11/6.18        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 11.11/6.18        = ( dvd_dvd_int @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6112_dvd__abs__iff,axiom,
% 11.11/6.18      ! [M: code_integer,K: code_integer] :
% 11.11/6.18        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 11.11/6.18        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6113_dvd__abs__iff,axiom,
% 11.11/6.18      ! [M: rat,K: rat] :
% 11.11/6.18        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 11.11/6.18        = ( dvd_dvd_rat @ M @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6114_abs__of__nat,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 11.11/6.18        = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6115_abs__of__nat,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.18        = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6116_abs__of__nat,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.18        = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6117_abs__of__nat,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.18        = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6118_abs__bool__eq,axiom,
% 11.11/6.18      ! [P: $o] :
% 11.11/6.18        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 11.11/6.18        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6119_abs__bool__eq,axiom,
% 11.11/6.18      ! [P: $o] :
% 11.11/6.18        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 11.11/6.18        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6120_abs__bool__eq,axiom,
% 11.11/6.18      ! [P: $o] :
% 11.11/6.18        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 11.11/6.18        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6121_abs__bool__eq,axiom,
% 11.11/6.18      ! [P: $o] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 11.11/6.18        = ( zero_n356916108424825756nteger @ P ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6122_tanh__real__less__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 11.11/6.18        = ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6123_tanh__real__le__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 11.11/6.18        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6124_abs__le__zero__iff,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 11.11/6.18        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6125_abs__le__zero__iff,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 11.11/6.18        = ( A = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6126_abs__le__zero__iff,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 11.11/6.18        = ( A = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6127_abs__le__zero__iff,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 11.11/6.18        = ( A = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6128_abs__le__self__iff,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 11.11/6.18        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6129_abs__le__self__iff,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 11.11/6.18        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6130_abs__le__self__iff,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 11.11/6.18        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6131_abs__le__self__iff,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 11.11/6.18        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6132_abs__of__nonneg,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.18       => ( ( abs_abs_Code_integer @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6133_abs__of__nonneg,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.18       => ( ( abs_abs_real @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6134_abs__of__nonneg,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.18       => ( ( abs_abs_rat @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6135_abs__of__nonneg,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.18       => ( ( abs_abs_int @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6136_zero__less__abs__iff,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.18        = ( A != zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6137_zero__less__abs__iff,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 11.11/6.18        = ( A != zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6138_zero__less__abs__iff,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 11.11/6.18        = ( A != zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6139_zero__less__abs__iff,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 11.11/6.18        = ( A != zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6140_abs__neg__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.18        = ( numeral_numeral_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6141_abs__neg__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.18        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6142_abs__neg__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.18        = ( numera6620942414471956472nteger @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6143_abs__neg__numeral,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.18        = ( numeral_numeral_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6144_abs__neg__one,axiom,
% 11.11/6.18      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6145_abs__neg__one,axiom,
% 11.11/6.18      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6146_abs__neg__one,axiom,
% 11.11/6.18      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.18      = one_one_Code_integer ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6147_abs__neg__one,axiom,
% 11.11/6.18      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6148_abs__power__minus,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 11.11/6.18        = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6149_abs__power__minus,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 11.11/6.18        = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6150_abs__power__minus,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6151_abs__power__minus,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 11.11/6.18        = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6152_fact__0,axiom,
% 11.11/6.18      ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6153_fact__0,axiom,
% 11.11/6.18      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6154_fact__0,axiom,
% 11.11/6.18      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6155_fact__0,axiom,
% 11.11/6.18      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 11.11/6.18      = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6156_fact__0,axiom,
% 11.11/6.18      ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6157_fact__1,axiom,
% 11.11/6.18      ( ( semiri5044797733671781792omplex @ one_one_nat )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6158_fact__1,axiom,
% 11.11/6.18      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6159_fact__1,axiom,
% 11.11/6.18      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6160_fact__1,axiom,
% 11.11/6.18      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 11.11/6.18      = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6161_fact__1,axiom,
% 11.11/6.18      ( ( semiri2265585572941072030t_real @ one_one_nat )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6162_tanh__real__neg__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 11.11/6.18        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6163_tanh__real__pos__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 11.11/6.18        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6164_tanh__real__nonneg__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 11.11/6.18        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6165_tanh__real__nonpos__iff,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 11.11/6.18        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6166_divide__le__0__abs__iff,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 11.11/6.18        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.18          | ( B = zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6167_divide__le__0__abs__iff,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 11.11/6.18        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.18          | ( B = zero_zero_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6168_zero__le__divide__abs__iff,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 11.11/6.18        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.18          | ( B = zero_zero_real ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6169_zero__le__divide__abs__iff,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 11.11/6.18        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.18          | ( B = zero_zero_rat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6170_abs__of__nonpos,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.18       => ( ( abs_abs_real @ A )
% 11.11/6.18          = ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6171_abs__of__nonpos,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.18       => ( ( abs_abs_Code_integer @ A )
% 11.11/6.18          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6172_abs__of__nonpos,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 11.11/6.18       => ( ( abs_abs_rat @ A )
% 11.11/6.18          = ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6173_abs__of__nonpos,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 11.11/6.18       => ( ( abs_abs_int @ A )
% 11.11/6.18          = ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6174_bit__numeral__Bit0__Suc__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6175_bit__numeral__Bit0__Suc__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6176_fact__Suc__0,axiom,
% 11.11/6.18      ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 11.11/6.18      = one_one_complex ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6177_fact__Suc__0,axiom,
% 11.11/6.18      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6178_fact__Suc__0,axiom,
% 11.11/6.18      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6179_fact__Suc__0,axiom,
% 11.11/6.18      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 11.11/6.18      = one_one_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6180_fact__Suc__0,axiom,
% 11.11/6.18      ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6181_bit__numeral__Bit1__Suc__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6182_bit__numeral__Bit1__Suc__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6183_fact__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6184_fact__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6185_fact__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6186_fact__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 11.11/6.18        = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6187_artanh__minus__real,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.18       => ( ( artanh_real @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.18          = ( uminus_uminus_real @ ( artanh_real @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6188_signed__take__bit__nonnegative__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 11.11/6.18        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6189_signed__take__bit__negative__iff,axiom,
% 11.11/6.18      ! [N2: nat,K: int] :
% 11.11/6.18        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6190_zero__less__power__abs__iff,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 11.11/6.18        = ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6191_zero__less__power__abs__iff,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 11.11/6.18        = ( ( A != zero_zero_real )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6192_zero__less__power__abs__iff,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 11.11/6.18        = ( ( A != zero_zero_rat )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6193_zero__less__power__abs__iff,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 11.11/6.18        = ( ( A != zero_zero_int )
% 11.11/6.18          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6194_power2__abs,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6195_power2__abs,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6196_power2__abs,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6197_power2__abs,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6198_abs__power2,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6199_abs__power2,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6200_abs__power2,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6201_abs__power2,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.18        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6202_fact__2,axiom,
% 11.11/6.18      ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18      = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6203_fact__2,axiom,
% 11.11/6.18      ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6204_fact__2,axiom,
% 11.11/6.18      ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6205_fact__2,axiom,
% 11.11/6.18      ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6206_fact__2,axiom,
% 11.11/6.18      ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.18      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6207_bit__numeral__simps_I2_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6208_bit__numeral__simps_I2_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6209_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 11.11/6.18      ! [W: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6210_bit__numeral__simps_I3_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6211_bit__numeral__simps_I3_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6212_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 11.11/6.18      ! [W: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 11.11/6.18        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6213_bit__0,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 11.11/6.18        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6214_bit__0,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 11.11/6.18        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6215_bit__0,axiom,
% 11.11/6.18      ! [A: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 11.11/6.18        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6216_power__even__abs__numeral,axiom,
% 11.11/6.18      ! [W: num,A: code_integer] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6217_power__even__abs__numeral,axiom,
% 11.11/6.18      ! [W: num,A: rat] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6218_power__even__abs__numeral,axiom,
% 11.11/6.18      ! [W: num,A: real] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6219_power__even__abs__numeral,axiom,
% 11.11/6.18      ! [W: num,A: int] :
% 11.11/6.18        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 11.11/6.18          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6220_bit__minus__numeral__int_I1_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6221_bit__minus__numeral__int_I2_J,axiom,
% 11.11/6.18      ! [W: num,N2: num] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.18        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6222_bit__mod__2__iff,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 )
% 11.11/6.18        = ( ( N2 = zero_zero_nat )
% 11.11/6.18          & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6223_bit__mod__2__iff,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 11.11/6.18        = ( ( N2 = zero_zero_nat )
% 11.11/6.18          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6224_bit__mod__2__iff,axiom,
% 11.11/6.18      ! [A: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 11.11/6.18        = ( ( N2 = zero_zero_nat )
% 11.11/6.18          & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6225_bit__numeral__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6226_bit__numeral__iff,axiom,
% 11.11/6.18      ! [M: num,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6227_bit__of__nat__iff__bit,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N2 )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6228_bit__of__nat__iff__bit,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 )
% 11.11/6.18        = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6229_bit__disjunctive__add__iff,axiom,
% 11.11/6.18      ! [A: int,B: int,N2: nat] :
% 11.11/6.18        ( ! [N3: nat] :
% 11.11/6.18            ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 11.11/6.18            | ~ ( bit_se1146084159140164899it_int @ B @ N3 ) )
% 11.11/6.18       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 11.11/6.18          = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.18            | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6230_bit__disjunctive__add__iff,axiom,
% 11.11/6.18      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.18        ( ! [N3: nat] :
% 11.11/6.18            ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 11.11/6.18            | ~ ( bit_se1148574629649215175it_nat @ B @ N3 ) )
% 11.11/6.18       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 11.11/6.18          = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.18            | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6231_abs__ge__self,axiom,
% 11.11/6.18      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6232_abs__ge__self,axiom,
% 11.11/6.18      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6233_abs__ge__self,axiom,
% 11.11/6.18      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6234_abs__ge__self,axiom,
% 11.11/6.18      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6235_abs__le__D1,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_real @ A @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6236_abs__le__D1,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 11.11/6.18       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6237_abs__le__D1,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_rat @ A @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6238_abs__le__D1,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_int @ A @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6239_abs__eq__0__iff,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ( abs_abs_Code_integer @ A )
% 11.11/6.18          = zero_z3403309356797280102nteger )
% 11.11/6.18        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6240_abs__eq__0__iff,axiom,
% 11.11/6.18      ! [A: complex] :
% 11.11/6.18        ( ( ( abs_abs_complex @ A )
% 11.11/6.18          = zero_zero_complex )
% 11.11/6.18        = ( A = zero_zero_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6241_abs__eq__0__iff,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ( abs_abs_real @ A )
% 11.11/6.18          = zero_zero_real )
% 11.11/6.18        = ( A = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6242_abs__eq__0__iff,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ( abs_abs_rat @ A )
% 11.11/6.18          = zero_zero_rat )
% 11.11/6.18        = ( A = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6243_abs__eq__0__iff,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ( abs_abs_int @ A )
% 11.11/6.18          = zero_zero_int )
% 11.11/6.18        = ( A = zero_zero_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6244_abs__mult,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 11.11/6.18        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6245_abs__mult,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.18        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6246_abs__mult,axiom,
% 11.11/6.18      ! [A: complex,B: complex] :
% 11.11/6.18        ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 11.11/6.18        = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6247_abs__mult,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 11.11/6.18        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6248_abs__mult,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 11.11/6.18        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6249_abs__one,axiom,
% 11.11/6.18      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 11.11/6.18      = one_one_Code_integer ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6250_abs__one,axiom,
% 11.11/6.18      ( ( abs_abs_real @ one_one_real )
% 11.11/6.18      = one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6251_abs__one,axiom,
% 11.11/6.18      ( ( abs_abs_rat @ one_one_rat )
% 11.11/6.18      = one_one_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6252_abs__one,axiom,
% 11.11/6.18      ( ( abs_abs_int @ one_one_int )
% 11.11/6.18      = one_one_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6253_abs__minus__commute,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 11.11/6.18        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6254_abs__minus__commute,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 11.11/6.18        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6255_abs__minus__commute,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 11.11/6.18        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6256_abs__minus__commute,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 11.11/6.18        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6257_abs__eq__iff,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ( abs_abs_real @ X4 )
% 11.11/6.18          = ( abs_abs_real @ Y ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6258_abs__eq__iff,axiom,
% 11.11/6.18      ! [X4: int,Y: int] :
% 11.11/6.18        ( ( ( abs_abs_int @ X4 )
% 11.11/6.18          = ( abs_abs_int @ Y ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6259_abs__eq__iff,axiom,
% 11.11/6.18      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.18        ( ( ( abs_abs_Code_integer @ X4 )
% 11.11/6.18          = ( abs_abs_Code_integer @ Y ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6260_abs__eq__iff,axiom,
% 11.11/6.18      ! [X4: rat,Y: rat] :
% 11.11/6.18        ( ( ( abs_abs_rat @ X4 )
% 11.11/6.18          = ( abs_abs_rat @ Y ) )
% 11.11/6.18        = ( ( X4 = Y )
% 11.11/6.18          | ( X4
% 11.11/6.18            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6261_fact__ge__self,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6262_fact__mono__nat,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6263_power__abs,axiom,
% 11.11/6.18      ! [A: code_integer,N2: nat] :
% 11.11/6.18        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 11.11/6.18        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6264_power__abs,axiom,
% 11.11/6.18      ! [A: rat,N2: nat] :
% 11.11/6.18        ( ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.18        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6265_power__abs,axiom,
% 11.11/6.18      ! [A: real,N2: nat] :
% 11.11/6.18        ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 11.11/6.18        = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6266_power__abs,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 11.11/6.18        = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6267_dvd__if__abs__eq,axiom,
% 11.11/6.18      ! [L: real,K: real] :
% 11.11/6.18        ( ( ( abs_abs_real @ L )
% 11.11/6.18          = ( abs_abs_real @ K ) )
% 11.11/6.18       => ( dvd_dvd_real @ L @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6268_dvd__if__abs__eq,axiom,
% 11.11/6.18      ! [L: int,K: int] :
% 11.11/6.18        ( ( ( abs_abs_int @ L )
% 11.11/6.18          = ( abs_abs_int @ K ) )
% 11.11/6.18       => ( dvd_dvd_int @ L @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6269_dvd__if__abs__eq,axiom,
% 11.11/6.18      ! [L: code_integer,K: code_integer] :
% 11.11/6.18        ( ( ( abs_abs_Code_integer @ L )
% 11.11/6.18          = ( abs_abs_Code_integer @ K ) )
% 11.11/6.18       => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6270_dvd__if__abs__eq,axiom,
% 11.11/6.18      ! [L: rat,K: rat] :
% 11.11/6.18        ( ( ( abs_abs_rat @ L )
% 11.11/6.18          = ( abs_abs_rat @ K ) )
% 11.11/6.18       => ( dvd_dvd_rat @ L @ K ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6271_bit__xor__iff,axiom,
% 11.11/6.18      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ N2 )
% 11.11/6.18        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.18         != ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6272_bit__xor__iff,axiom,
% 11.11/6.18      ! [A: int,B: int,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ N2 )
% 11.11/6.18        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.18         != ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6273_bit__unset__bit__iff,axiom,
% 11.11/6.18      ! [M: nat,A: int,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N2 )
% 11.11/6.18        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.18          & ( M != N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6274_bit__unset__bit__iff,axiom,
% 11.11/6.18      ! [M: nat,A: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N2 )
% 11.11/6.18        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.18          & ( M != N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6275_bit__xor__int__iff,axiom,
% 11.11/6.18      ! [K: int,L: int,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N2 )
% 11.11/6.18        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 11.11/6.18         != ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6276_not__bit__1__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6277_not__bit__1__Suc,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6278_bit__1__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 11.11/6.18        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6279_bit__1__iff,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 11.11/6.18        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6280_abs__ge__zero,axiom,
% 11.11/6.18      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6281_abs__ge__zero,axiom,
% 11.11/6.18      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6282_abs__ge__zero,axiom,
% 11.11/6.18      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6283_abs__ge__zero,axiom,
% 11.11/6.18      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6284_bit__numeral__simps_I1_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6285_bit__numeral__simps_I1_J,axiom,
% 11.11/6.18      ! [N2: num] :
% 11.11/6.18        ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6286_abs__of__pos,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.18       => ( ( abs_abs_Code_integer @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6287_abs__of__pos,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.18       => ( ( abs_abs_real @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6288_abs__of__pos,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.18       => ( ( abs_abs_rat @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6289_abs__of__pos,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.18       => ( ( abs_abs_int @ A )
% 11.11/6.18          = A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6290_abs__not__less__zero,axiom,
% 11.11/6.18      ! [A: code_integer] :
% 11.11/6.18        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6291_abs__not__less__zero,axiom,
% 11.11/6.18      ! [A: real] :
% 11.11/6.18        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6292_abs__not__less__zero,axiom,
% 11.11/6.18      ! [A: rat] :
% 11.11/6.18        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6293_abs__not__less__zero,axiom,
% 11.11/6.18      ! [A: int] :
% 11.11/6.18        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6294_abs__triangle__ineq,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6295_abs__triangle__ineq,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6296_abs__triangle__ineq,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6297_abs__triangle__ineq,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6298_abs__mult__less,axiom,
% 11.11/6.18      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 11.11/6.18        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 11.11/6.18       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 11.11/6.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6299_abs__mult__less,axiom,
% 11.11/6.18      ! [A: real,C: real,B: real,D: real] :
% 11.11/6.18        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 11.11/6.18       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 11.11/6.18         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6300_abs__mult__less,axiom,
% 11.11/6.18      ! [A: rat,C: rat,B: rat,D: rat] :
% 11.11/6.18        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 11.11/6.18       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 11.11/6.18         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6301_abs__mult__less,axiom,
% 11.11/6.18      ! [A: int,C: int,B: int,D: int] :
% 11.11/6.18        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 11.11/6.18       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 11.11/6.18         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6302_abs__triangle__ineq2__sym,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6303_abs__triangle__ineq2__sym,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6304_abs__triangle__ineq2__sym,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6305_abs__triangle__ineq2__sym,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6306_abs__triangle__ineq3,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6307_abs__triangle__ineq3,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6308_abs__triangle__ineq3,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6309_abs__triangle__ineq3,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6310_abs__triangle__ineq2,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6311_abs__triangle__ineq2,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6312_abs__triangle__ineq2,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6313_abs__triangle__ineq2,axiom,
% 11.11/6.18      ! [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 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6314_abs__ge__minus__self,axiom,
% 11.11/6.18      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6315_abs__ge__minus__self,axiom,
% 11.11/6.18      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6316_abs__ge__minus__self,axiom,
% 11.11/6.18      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6317_abs__ge__minus__self,axiom,
% 11.11/6.18      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6318_abs__le__iff,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_eq_real @ A @ B )
% 11.11/6.18          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6319_abs__le__iff,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 11.11/6.18        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 11.11/6.18          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6320_abs__le__iff,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.18          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6321_abs__le__iff,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_eq_int @ A @ B )
% 11.11/6.18          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6322_abs__le__D2,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6323_abs__le__D2,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 11.11/6.18       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6324_abs__le__D2,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6325_abs__le__D2,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 11.11/6.18       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6326_abs__leI,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.18       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 11.11/6.18         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6327_abs__leI,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 11.11/6.18       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 11.11/6.18         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6328_abs__leI,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.18       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 11.11/6.18         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6329_abs__leI,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ A @ B )
% 11.11/6.18       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 11.11/6.18         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6330_nonzero__abs__divide,axiom,
% 11.11/6.18      ! [B: rat,A: rat] :
% 11.11/6.18        ( ( B != zero_zero_rat )
% 11.11/6.18       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.18          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6331_nonzero__abs__divide,axiom,
% 11.11/6.18      ! [B: real,A: real] :
% 11.11/6.18        ( ( B != zero_zero_real )
% 11.11/6.18       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.18          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6332_abs__less__iff,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_real @ A @ B )
% 11.11/6.18          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6333_abs__less__iff,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_int @ A @ B )
% 11.11/6.18          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6334_abs__less__iff,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 11.11/6.18        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 11.11/6.18          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6335_abs__less__iff,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 11.11/6.18        = ( ( ord_less_rat @ A @ B )
% 11.11/6.18          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6336_fact__less__mono__nat,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.18       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.18         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6337_bit__take__bit__iff,axiom,
% 11.11/6.18      ! [M: nat,A: int,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 11.11/6.18        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.18          & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6338_bit__take__bit__iff,axiom,
% 11.11/6.18      ! [M: nat,A: nat,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 11.11/6.18        = ( ( ord_less_nat @ N2 @ M )
% 11.11/6.18          & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6339_bit__of__bool__iff,axiom,
% 11.11/6.18      ! [B: $o,N2: nat] :
% 11.11/6.18        ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N2 )
% 11.11/6.18        = ( B
% 11.11/6.18          & ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6340_bit__of__bool__iff,axiom,
% 11.11/6.18      ! [B: $o,N2: nat] :
% 11.11/6.18        ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N2 )
% 11.11/6.18        = ( B
% 11.11/6.18          & ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6341_bit__of__bool__iff,axiom,
% 11.11/6.18      ! [B: $o,N2: nat] :
% 11.11/6.18        ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N2 )
% 11.11/6.18        = ( B
% 11.11/6.18          & ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6342_fact__ge__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6343_fact__ge__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6344_fact__ge__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6345_fact__ge__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6346_fact__not__neg,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6347_fact__not__neg,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6348_fact__not__neg,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6349_fact__not__neg,axiom,
% 11.11/6.18      ! [N2: nat] :
% 11.11/6.18        ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6350_fact__gt__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6351_fact__gt__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6352_fact__gt__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6353_fact__gt__zero,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6354_fact__ge__1,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6355_fact__ge__1,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6356_fact__ge__1,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6357_fact__ge__1,axiom,
% 11.11/6.18      ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6358_fact__mono,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6359_fact__mono,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6360_fact__mono,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6361_fact__mono,axiom,
% 11.11/6.18      ! [M: nat,N2: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.18       => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6362_signed__take__bit__eq__if__positive,axiom,
% 11.11/6.18      ! [A: int,N2: nat] :
% 11.11/6.18        ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.18       => ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 11.11/6.18          = ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6363_fact__dvd,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6364_fact__dvd,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6365_fact__dvd,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6366_fact__dvd,axiom,
% 11.11/6.18      ! [N2: nat,M: nat] :
% 11.11/6.18        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.18       => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6367_pochhammer__fact,axiom,
% 11.11/6.18      ( semiri5044797733671781792omplex
% 11.11/6.18      = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6368_pochhammer__fact,axiom,
% 11.11/6.18      ( semiri773545260158071498ct_rat
% 11.11/6.18      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6369_pochhammer__fact,axiom,
% 11.11/6.18      ( semiri1406184849735516958ct_int
% 11.11/6.18      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6370_pochhammer__fact,axiom,
% 11.11/6.18      ( semiri1408675320244567234ct_nat
% 11.11/6.18      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6371_pochhammer__fact,axiom,
% 11.11/6.18      ( semiri2265585572941072030t_real
% 11.11/6.18      = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6372_tanh__real__lt__1,axiom,
% 11.11/6.18      ! [X4: real] : ( ord_less_real @ ( tanh_real @ X4 ) @ one_one_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6373_dense__eq0__I,axiom,
% 11.11/6.18      ! [X4: real] :
% 11.11/6.18        ( ! [E: real] :
% 11.11/6.18            ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.18           => ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ E ) )
% 11.11/6.18       => ( X4 = zero_zero_real ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6374_dense__eq0__I,axiom,
% 11.11/6.18      ! [X4: rat] :
% 11.11/6.18        ( ! [E: rat] :
% 11.11/6.18            ( ( ord_less_rat @ zero_zero_rat @ E )
% 11.11/6.18           => ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ E ) )
% 11.11/6.18       => ( X4 = zero_zero_rat ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6375_abs__eq__mult,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.18            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 11.11/6.18          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.18            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 11.11/6.18       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 11.11/6.18          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6376_abs__eq__mult,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.18            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 11.11/6.18          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.18            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 11.11/6.18       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 11.11/6.18          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6377_abs__eq__mult,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.18            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 11.11/6.18          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.18            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 11.11/6.18       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.18          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6378_abs__eq__mult,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.18            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 11.11/6.18          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.18            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 11.11/6.18       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 11.11/6.18          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6379_abs__mult__pos,axiom,
% 11.11/6.18      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 11.11/6.18       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X4 )
% 11.11/6.18          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6380_abs__mult__pos,axiom,
% 11.11/6.18      ! [X4: real,Y: real] :
% 11.11/6.18        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.18       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X4 )
% 11.11/6.18          = ( abs_abs_real @ ( times_times_real @ Y @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6381_abs__mult__pos,axiom,
% 11.11/6.18      ! [X4: rat,Y: rat] :
% 11.11/6.18        ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.18       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X4 )
% 11.11/6.18          = ( abs_abs_rat @ ( times_times_rat @ Y @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6382_abs__mult__pos,axiom,
% 11.11/6.18      ! [X4: int,Y: int] :
% 11.11/6.18        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.18       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X4 )
% 11.11/6.18          = ( abs_abs_int @ ( times_times_int @ Y @ X4 ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6383_abs__minus__le__zero,axiom,
% 11.11/6.18      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6384_abs__minus__le__zero,axiom,
% 11.11/6.18      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6385_abs__minus__le__zero,axiom,
% 11.11/6.18      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6386_abs__minus__le__zero,axiom,
% 11.11/6.18      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6387_eq__abs__iff_H,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( A
% 11.11/6.18          = ( abs_abs_real @ B ) )
% 11.11/6.18        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.18          & ( ( B = A )
% 11.11/6.18            | ( B
% 11.11/6.18              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6388_eq__abs__iff_H,axiom,
% 11.11/6.18      ! [A: code_integer,B: code_integer] :
% 11.11/6.18        ( ( A
% 11.11/6.18          = ( abs_abs_Code_integer @ B ) )
% 11.11/6.18        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.18          & ( ( B = A )
% 11.11/6.18            | ( B
% 11.11/6.18              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6389_eq__abs__iff_H,axiom,
% 11.11/6.18      ! [A: rat,B: rat] :
% 11.11/6.18        ( ( A
% 11.11/6.18          = ( abs_abs_rat @ B ) )
% 11.11/6.18        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.18          & ( ( B = A )
% 11.11/6.18            | ( B
% 11.11/6.18              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6390_eq__abs__iff_H,axiom,
% 11.11/6.18      ! [A: int,B: int] :
% 11.11/6.18        ( ( A
% 11.11/6.18          = ( abs_abs_int @ B ) )
% 11.11/6.18        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 11.11/6.18          & ( ( B = A )
% 11.11/6.18            | ( B
% 11.11/6.18              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 11.11/6.18  
% 11.11/6.18  thf(fact_6391_abs__eq__iff_H,axiom,
% 11.11/6.18      ! [A: real,B: real] :
% 11.11/6.18        ( ( ( abs_abs_real @ A )
% 11.11/6.18          = B )
% 11.11/6.18        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.18          & ( ( A = B )
% 11.11/6.18            | ( A
% 11.11/6.18              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6392_abs__eq__iff_H,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer] :
% 11.11/6.19        ( ( ( abs_abs_Code_integer @ A )
% 11.11/6.19          = B )
% 11.11/6.19        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 11.11/6.19          & ( ( A = B )
% 11.11/6.19            | ( A
% 11.11/6.19              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6393_abs__eq__iff_H,axiom,
% 11.11/6.19      ! [A: rat,B: rat] :
% 11.11/6.19        ( ( ( abs_abs_rat @ A )
% 11.11/6.19          = B )
% 11.11/6.19        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.19          & ( ( A = B )
% 11.11/6.19            | ( A
% 11.11/6.19              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6394_abs__eq__iff_H,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( ( abs_abs_int @ A )
% 11.11/6.19          = B )
% 11.11/6.19        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.19          & ( ( A = B )
% 11.11/6.19            | ( A
% 11.11/6.19              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6395_zero__le__power__abs,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6396_zero__le__power__abs,axiom,
% 11.11/6.19      ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6397_zero__le__power__abs,axiom,
% 11.11/6.19      ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6398_zero__le__power__abs,axiom,
% 11.11/6.19      ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6399_abs__div__pos,axiom,
% 11.11/6.19      ! [Y: rat,X4: rat] :
% 11.11/6.19        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 11.11/6.19       => ( ( divide_divide_rat @ ( abs_abs_rat @ X4 ) @ Y )
% 11.11/6.19          = ( abs_abs_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6400_abs__div__pos,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19       => ( ( divide_divide_real @ ( abs_abs_real @ X4 ) @ Y )
% 11.11/6.19          = ( abs_abs_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6401_abs__if,axiom,
% 11.11/6.19      ( abs_abs_real
% 11.11/6.19      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6402_abs__if,axiom,
% 11.11/6.19      ( abs_abs_int
% 11.11/6.19      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6403_abs__if,axiom,
% 11.11/6.19      ( abs_abs_Code_integer
% 11.11/6.19      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6404_abs__if,axiom,
% 11.11/6.19      ( abs_abs_rat
% 11.11/6.19      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6405_abs__of__neg,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.19       => ( ( abs_abs_real @ A )
% 11.11/6.19          = ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6406_abs__of__neg,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.19       => ( ( abs_abs_int @ A )
% 11.11/6.19          = ( uminus_uminus_int @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6407_abs__of__neg,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.19       => ( ( abs_abs_Code_integer @ A )
% 11.11/6.19          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6408_abs__of__neg,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.19       => ( ( abs_abs_rat @ A )
% 11.11/6.19          = ( uminus_uminus_rat @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6409_abs__if__raw,axiom,
% 11.11/6.19      ( abs_abs_real
% 11.11/6.19      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6410_abs__if__raw,axiom,
% 11.11/6.19      ( abs_abs_int
% 11.11/6.19      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6411_abs__if__raw,axiom,
% 11.11/6.19      ( abs_abs_Code_integer
% 11.11/6.19      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6412_abs__if__raw,axiom,
% 11.11/6.19      ( abs_abs_rat
% 11.11/6.19      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6413_abs__diff__le__iff,axiom,
% 11.11/6.19      ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 11.11/6.19        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_le3102999989581377725nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6414_abs__diff__le__iff,axiom,
% 11.11/6.19      ! [X4: real,A: real,R3: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_eq_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6415_abs__diff__le__iff,axiom,
% 11.11/6.19      ! [X4: rat,A: rat,R3: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6416_abs__diff__le__iff,axiom,
% 11.11/6.19      ! [X4: int,A: int,R3: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_eq_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6417_abs__triangle__ineq4,axiom,
% 11.11/6.19      ! [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 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6418_abs__triangle__ineq4,axiom,
% 11.11/6.19      ! [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 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6419_abs__triangle__ineq4,axiom,
% 11.11/6.19      ! [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 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6420_abs__triangle__ineq4,axiom,
% 11.11/6.19      ! [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 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6421_abs__diff__triangle__ineq,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6422_abs__diff__triangle__ineq,axiom,
% 11.11/6.19      ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6423_abs__diff__triangle__ineq,axiom,
% 11.11/6.19      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6424_abs__diff__triangle__ineq,axiom,
% 11.11/6.19      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6425_abs__diff__less__iff,axiom,
% 11.11/6.19      ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_le6747313008572928689nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6426_abs__diff__less__iff,axiom,
% 11.11/6.19      ! [X4: real,A: real,R3: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6427_abs__diff__less__iff,axiom,
% 11.11/6.19      ! [X4: rat,A: rat,R3: rat] :
% 11.11/6.19        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6428_abs__diff__less__iff,axiom,
% 11.11/6.19      ! [X4: int,A: int,R3: int] :
% 11.11/6.19        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 11.11/6.19        = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 11.11/6.19          & ( ord_less_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6429_fact__ge__Suc__0__nat,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6430_dvd__fact,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 11.11/6.19       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6431_bit__not__int__iff_H,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 11.11/6.19        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6432_abs__real__def,axiom,
% 11.11/6.19      ( abs_abs_real
% 11.11/6.19      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6433_fact__less__mono,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.19         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6434_fact__less__mono,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.19         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6435_fact__less__mono,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.19         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6436_fact__less__mono,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19       => ( ( ord_less_nat @ M @ N2 )
% 11.11/6.19         => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6437_lemma__interval__lt,axiom,
% 11.11/6.19      ! [A: real,X4: real,B: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ B )
% 11.11/6.19         => ? [D3: real] :
% 11.11/6.19              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.19              & ! [Y4: real] :
% 11.11/6.19                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 11.11/6.19                 => ( ( ord_less_real @ A @ Y4 )
% 11.11/6.19                    & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6438_fact__fact__dvd__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6439_fact__fact__dvd__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6440_fact__fact__dvd__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6441_fact__fact__dvd__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6442_fact__mod,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 11.11/6.19          = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6443_fact__mod,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19       => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 11.11/6.19          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6444_fact__mod,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 11.11/6.19          = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6445_fact__le__power,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6446_fact__le__power,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6447_fact__le__power,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6448_fact__le__power,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6449_sin__bound__lemma,axiom,
% 11.11/6.19      ! [X4: real,Y: real,U: real,V: real] :
% 11.11/6.19        ( ( X4 = Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 11.11/6.19         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X4 @ U ) @ Y ) ) @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6450_flip__bit__eq__if,axiom,
% 11.11/6.19      ( bit_se2159334234014336723it_int
% 11.11/6.19      = ( ^ [N: nat,A3: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A3 @ N ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6451_flip__bit__eq__if,axiom,
% 11.11/6.19      ( bit_se2161824704523386999it_nat
% 11.11/6.19      = ( ^ [N: nat,A3: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A3 @ N ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6452_tanh__real__gt__neg1,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6453_abs__add__one__gt__zero,axiom,
% 11.11/6.19      ! [X4: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6454_abs__add__one__gt__zero,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6455_abs__add__one__gt__zero,axiom,
% 11.11/6.19      ! [X4: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6456_abs__add__one__gt__zero,axiom,
% 11.11/6.19      ! [X4: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6457_fact__diff__Suc,axiom,
% 11.11/6.19      ! [N2: nat,M: nat] :
% 11.11/6.19        ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 11.11/6.19       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 11.11/6.19          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6458_fact__div__fact__le__pow,axiom,
% 11.11/6.19      ! [R3: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ R3 @ N2 )
% 11.11/6.19       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R3 ) ) ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6459_binomial__fact__lemma,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 11.11/6.19          = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6460_bit__imp__take__bit__positive,axiom,
% 11.11/6.19      ! [N2: nat,M: nat,K: int] :
% 11.11/6.19        ( ( ord_less_nat @ N2 @ M )
% 11.11/6.19       => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 11.11/6.19         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6461_lemma__interval,axiom,
% 11.11/6.19      ! [A: real,X4: real,B: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ B )
% 11.11/6.19         => ? [D3: real] :
% 11.11/6.19              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.19              & ! [Y4: real] :
% 11.11/6.19                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 11.11/6.19                 => ( ( ord_less_eq_real @ A @ Y4 )
% 11.11/6.19                    & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6462_norm__triangle__ineq3,axiom,
% 11.11/6.19      ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6463_norm__triangle__ineq3,axiom,
% 11.11/6.19      ! [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 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6464_bit__concat__bit__iff,axiom,
% 11.11/6.19      ! [M: nat,K: int,L: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 11.11/6.19        = ( ( ( ord_less_nat @ N2 @ M )
% 11.11/6.19            & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 11.11/6.19          | ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6465_choose__dvd,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6466_choose__dvd,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6467_choose__dvd,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6468_choose__dvd,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6469_fact__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.19        = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6470_fact__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 11.11/6.19        = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6471_fact__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6472_fact__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.19        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6473_fact__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 11.11/6.19        = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6474_signed__take__bit__eq__concat__bit,axiom,
% 11.11/6.19      ( bit_ri631733984087533419it_int
% 11.11/6.19      = ( ^ [N: nat,K3: int] : ( bit_concat_bit @ N @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6475_exp__eq__0__imp__not__bit,axiom,
% 11.11/6.19      ! [N2: nat,A: int] :
% 11.11/6.19        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19          = zero_zero_int )
% 11.11/6.19       => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6476_exp__eq__0__imp__not__bit,axiom,
% 11.11/6.19      ! [N2: nat,A: nat] :
% 11.11/6.19        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19          = zero_zero_nat )
% 11.11/6.19       => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6477_bit__Suc,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] :
% 11.11/6.19        ( ( bit_se9216721137139052372nteger @ A @ ( suc @ N2 ) )
% 11.11/6.19        = ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6478_bit__Suc,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 11.11/6.19        = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6479_bit__Suc,axiom,
% 11.11/6.19      ! [A: nat,N2: nat] :
% 11.11/6.19        ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 11.11/6.19        = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6480_stable__imp__bit__iff__odd,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] :
% 11.11/6.19        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.19          = A )
% 11.11/6.19       => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 11.11/6.19          = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6481_stable__imp__bit__iff__odd,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.19          = A )
% 11.11/6.19       => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.19          = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6482_stable__imp__bit__iff__odd,axiom,
% 11.11/6.19      ! [A: nat,N2: nat] :
% 11.11/6.19        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = A )
% 11.11/6.19       => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.19          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6483_bit__iff__idd__imp__stable,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ! [N3: nat] :
% 11.11/6.19            ( ( bit_se9216721137139052372nteger @ A @ N3 )
% 11.11/6.19            = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.19       => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.19          = A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6484_bit__iff__idd__imp__stable,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ! [N3: nat] :
% 11.11/6.19            ( ( bit_se1146084159140164899it_int @ A @ N3 )
% 11.11/6.19            = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.19       => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.19          = A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6485_bit__iff__idd__imp__stable,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ! [N3: nat] :
% 11.11/6.19            ( ( bit_se1148574629649215175it_nat @ A @ N3 )
% 11.11/6.19            = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 11.11/6.19       => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6486_abs__le__square__iff,axiom,
% 11.11/6.19      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.19        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ Y ) )
% 11.11/6.19        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6487_abs__le__square__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6488_abs__le__square__iff,axiom,
% 11.11/6.19      ! [X4: rat,Y: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ ( abs_abs_rat @ Y ) )
% 11.11/6.19        = ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6489_abs__le__square__iff,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) )
% 11.11/6.19        = ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6490_abs__square__eq__1,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = one_one_Code_integer )
% 11.11/6.19        = ( ( abs_abs_Code_integer @ X4 )
% 11.11/6.19          = one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6491_abs__square__eq__1,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = one_one_rat )
% 11.11/6.19        = ( ( abs_abs_rat @ X4 )
% 11.11/6.19          = one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6492_abs__square__eq__1,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = one_one_real )
% 11.11/6.19        = ( ( abs_abs_real @ X4 )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6493_abs__square__eq__1,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = one_one_int )
% 11.11/6.19        = ( ( abs_abs_int @ X4 )
% 11.11/6.19          = one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6494_power__even__abs,axiom,
% 11.11/6.19      ! [N2: nat,A: code_integer] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 11.11/6.19          = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6495_power__even__abs,axiom,
% 11.11/6.19      ! [N2: nat,A: rat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 )
% 11.11/6.19          = ( power_power_rat @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6496_power__even__abs,axiom,
% 11.11/6.19      ! [N2: nat,A: real] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 11.11/6.19          = ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6497_power__even__abs,axiom,
% 11.11/6.19      ! [N2: nat,A: int] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 11.11/6.19          = ( power_power_int @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6498_int__bit__bound,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ~ ! [N3: nat] :
% 11.11/6.19            ( ! [M2: nat] :
% 11.11/6.19                ( ( ord_less_eq_nat @ N3 @ M2 )
% 11.11/6.19               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 11.11/6.19                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 11.11/6.19           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.19               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 11.11/6.19                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6499_binomial__altdef__nat,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( binomial @ N2 @ K )
% 11.11/6.19          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6500_bit__iff__odd,axiom,
% 11.11/6.19      ( bit_se9216721137139052372nteger
% 11.11/6.19      = ( ^ [A3: code_integer,N: nat] :
% 11.11/6.19            ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6501_bit__iff__odd,axiom,
% 11.11/6.19      ( bit_se1146084159140164899it_int
% 11.11/6.19      = ( ^ [A3: int,N: nat] :
% 11.11/6.19            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6502_bit__iff__odd,axiom,
% 11.11/6.19      ( bit_se1148574629649215175it_nat
% 11.11/6.19      = ( ^ [A3: nat,N: nat] :
% 11.11/6.19            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6503_power2__le__iff__abs__le,axiom,
% 11.11/6.19      ! [Y: code_integer,X4: code_integer] :
% 11.11/6.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 11.11/6.19       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6504_power2__le__iff__abs__le,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6505_power2__le__iff__abs__le,axiom,
% 11.11/6.19      ! [Y: rat,X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 11.11/6.19       => ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6506_power2__le__iff__abs__le,axiom,
% 11.11/6.19      ! [Y: int,X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6507_abs__square__le__1,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 11.11/6.19        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6508_abs__square__le__1,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 11.11/6.19        = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6509_abs__square__le__1,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 11.11/6.19        = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6510_abs__square__le__1,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 11.11/6.19        = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6511_abs__square__less__1,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 11.11/6.19        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6512_abs__square__less__1,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 11.11/6.19        = ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6513_abs__square__less__1,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 11.11/6.19        = ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6514_abs__square__less__1,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 11.11/6.19        = ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6515_square__fact__le__2__fact,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6516_power__mono__even,axiom,
% 11.11/6.19      ! [N2: nat,A: code_integer,B: code_integer] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 11.11/6.19         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6517_power__mono__even,axiom,
% 11.11/6.19      ! [N2: nat,A: real,B: real] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 11.11/6.19         => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6518_power__mono__even,axiom,
% 11.11/6.19      ! [N2: nat,A: rat,B: rat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 11.11/6.19         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6519_power__mono__even,axiom,
% 11.11/6.19      ! [N2: nat,A: int,B: int] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 11.11/6.19         => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6520_bit__int__def,axiom,
% 11.11/6.19      ( bit_se1146084159140164899it_int
% 11.11/6.19      = ( ^ [K3: int,N: nat] :
% 11.11/6.19            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6521_fact__num__eq__if,axiom,
% 11.11/6.19      ( semiri773545260158071498ct_rat
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6522_fact__num__eq__if,axiom,
% 11.11/6.19      ( semiri5044797733671781792omplex
% 11.11/6.19      = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6523_fact__num__eq__if,axiom,
% 11.11/6.19      ( semiri1406184849735516958ct_int
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6524_fact__num__eq__if,axiom,
% 11.11/6.19      ( semiri1408675320244567234ct_nat
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6525_fact__num__eq__if,axiom,
% 11.11/6.19      ( semiri2265585572941072030t_real
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6526_fact__reduce,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( semiri5044797733671781792omplex @ N2 )
% 11.11/6.19          = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6527_fact__reduce,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( semiri1406184849735516958ct_int @ N2 )
% 11.11/6.19          = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6528_fact__reduce,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( semiri1408675320244567234ct_nat @ N2 )
% 11.11/6.19          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6529_fact__reduce,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( semiri2265585572941072030t_real @ N2 )
% 11.11/6.19          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6530_pochhammer__same,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 11.11/6.19        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6531_pochhammer__same,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 11.11/6.19        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6532_pochhammer__same,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 11.11/6.19        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6533_pochhammer__same,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 11.11/6.19        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6534_pochhammer__same,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 11.11/6.19        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6535_binomial__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 11.11/6.19          = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6536_binomial__fact,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 11.11/6.19          = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6537_fact__binomial,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 11.11/6.19          = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6538_fact__binomial,axiom,
% 11.11/6.19      ! [K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.19       => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 11.11/6.19          = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6539_even__bit__succ__iff,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 11.11/6.19          = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6540_even__bit__succ__iff,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 11.11/6.19          = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6541_even__bit__succ__iff,axiom,
% 11.11/6.19      ! [A: nat,N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 11.11/6.19          = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6542_odd__bit__iff__bit__pred,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] :
% 11.11/6.19        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 11.11/6.19          = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6543_odd__bit__iff__bit__pred,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.19          = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6544_odd__bit__iff__bit__pred,axiom,
% 11.11/6.19      ! [A: nat,N2: nat] :
% 11.11/6.19        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.19       => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.19          = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 11.11/6.19            | ( N2 = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6545_bit__sum__mult__2__cases,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer,N2: nat] :
% 11.11/6.19        ( ! [J2: nat] :
% 11.11/6.19            ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 11.11/6.19       => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 11.11/6.19          = ( ( ( N2 = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.19            & ( ( N2 != zero_zero_nat )
% 11.11/6.19             => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6546_bit__sum__mult__2__cases,axiom,
% 11.11/6.19      ! [A: int,B: int,N2: nat] :
% 11.11/6.19        ( ! [J2: nat] :
% 11.11/6.19            ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 11.11/6.19       => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 11.11/6.19          = ( ( ( N2 = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.19            & ( ( N2 != zero_zero_nat )
% 11.11/6.19             => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6547_bit__sum__mult__2__cases,axiom,
% 11.11/6.19      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.19        ( ! [J2: nat] :
% 11.11/6.19            ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 11.11/6.19       => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 11.11/6.19          = ( ( ( N2 = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 11.11/6.19            & ( ( N2 != zero_zero_nat )
% 11.11/6.19             => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6548_bit__rec,axiom,
% 11.11/6.19      ( bit_se9216721137139052372nteger
% 11.11/6.19      = ( ^ [A3: code_integer,N: nat] :
% 11.11/6.19            ( ( ( N = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 11.11/6.19            & ( ( N != zero_zero_nat )
% 11.11/6.19             => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6549_bit__rec,axiom,
% 11.11/6.19      ( bit_se1146084159140164899it_int
% 11.11/6.19      = ( ^ [A3: int,N: nat] :
% 11.11/6.19            ( ( ( N = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 11.11/6.19            & ( ( N != zero_zero_nat )
% 11.11/6.19             => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6550_bit__rec,axiom,
% 11.11/6.19      ( bit_se1148574629649215175it_nat
% 11.11/6.19      = ( ^ [A3: nat,N: nat] :
% 11.11/6.19            ( ( ( N = zero_zero_nat )
% 11.11/6.19             => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 11.11/6.19            & ( ( N != zero_zero_nat )
% 11.11/6.19             => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6551_set__bit__eq,axiom,
% 11.11/6.19      ( bit_se7879613467334960850it_int
% 11.11/6.19      = ( ^ [N: nat,K3: int] :
% 11.11/6.19            ( plus_plus_int @ K3
% 11.11/6.19            @ ( times_times_int
% 11.11/6.19              @ ( zero_n2684676970156552555ol_int
% 11.11/6.19                @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 11.11/6.19              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6552_unset__bit__eq,axiom,
% 11.11/6.19      ( bit_se4203085406695923979it_int
% 11.11/6.19      = ( ^ [N: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6553_take__bit__Suc__from__most,axiom,
% 11.11/6.19      ! [N2: nat,K: int] :
% 11.11/6.19        ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 11.11/6.19        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6554_abs__sqrt__wlog,axiom,
% 11.11/6.19      ! [P: code_integer > code_integer > $o,X4: code_integer] :
% 11.11/6.19        ( ! [X5: code_integer] :
% 11.11/6.19            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 11.11/6.19           => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19       => ( P @ ( abs_abs_Code_integer @ X4 ) @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6555_abs__sqrt__wlog,axiom,
% 11.11/6.19      ! [P: real > real > $o,X4: real] :
% 11.11/6.19        ( ! [X5: real] :
% 11.11/6.19            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 11.11/6.19           => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19       => ( P @ ( abs_abs_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6556_abs__sqrt__wlog,axiom,
% 11.11/6.19      ! [P: rat > rat > $o,X4: rat] :
% 11.11/6.19        ( ! [X5: rat] :
% 11.11/6.19            ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 11.11/6.19           => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19       => ( P @ ( abs_abs_rat @ X4 ) @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6557_abs__sqrt__wlog,axiom,
% 11.11/6.19      ! [P: int > int > $o,X4: int] :
% 11.11/6.19        ( ! [X5: int] :
% 11.11/6.19            ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 11.11/6.19           => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19       => ( P @ ( abs_abs_int @ X4 ) @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6558_sin__coeff__def,axiom,
% 11.11/6.19      ( sin_coeff
% 11.11/6.19      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6559_binomial__code,axiom,
% 11.11/6.19      ( binomial
% 11.11/6.19      = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6560_cos__coeff__def,axiom,
% 11.11/6.19      ( cos_coeff
% 11.11/6.19      = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6561_arctan__double,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.19       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X4 ) )
% 11.11/6.19          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6562_fact__code,axiom,
% 11.11/6.19      ( semiri1406184849735516958ct_int
% 11.11/6.19      = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6563_fact__code,axiom,
% 11.11/6.19      ( semiri1408675320244567234ct_nat
% 11.11/6.19      = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6564_fact__code,axiom,
% 11.11/6.19      ( semiri2265585572941072030t_real
% 11.11/6.19      = ( ^ [N: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6565_zabs__less__one__iff,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 11.11/6.19        = ( Z = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6566_zero__less__arctan__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6567_arctan__less__zero__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( arctan @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6568_zero__le__arctan__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X4 ) )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6569_arctan__le__zero__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( arctan @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6570_cos__coeff__0,axiom,
% 11.11/6.19      ( ( cos_coeff @ zero_zero_nat )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6571_arctan__less__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 11.11/6.19        = ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6572_arctan__monotone,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.19       => ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6573_arctan__le__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6574_arctan__monotone_H,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19       => ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6575_bit__Suc__0__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6576_not__bit__Suc__0__Suc,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6577_abs__div,axiom,
% 11.11/6.19      ! [Y: int,X4: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ Y @ X4 )
% 11.11/6.19       => ( ( abs_abs_int @ ( divide_divide_int @ X4 @ Y ) )
% 11.11/6.19          = ( divide_divide_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6578_sin__coeff__Suc,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sin_coeff @ ( suc @ N2 ) )
% 11.11/6.19        = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6579_not__bit__Suc__0__numeral,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6580_zabs__def,axiom,
% 11.11/6.19      ( abs_abs_int
% 11.11/6.19      = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6581_dvd__imp__le__int,axiom,
% 11.11/6.19      ! [I2: int,D: int] :
% 11.11/6.19        ( ( I2 != zero_zero_int )
% 11.11/6.19       => ( ( dvd_dvd_int @ D @ I2 )
% 11.11/6.19         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6582_abs__mod__less,axiom,
% 11.11/6.19      ! [L: int,K: int] :
% 11.11/6.19        ( ( L != zero_zero_int )
% 11.11/6.19       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6583_cos__coeff__Suc,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( cos_coeff @ ( suc @ N2 ) )
% 11.11/6.19        = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6584_fold__atLeastAtMost__nat_Oelims,axiom,
% 11.11/6.19      ! [X4: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 11.11/6.19        ( ( ( set_fo2584398358068434914at_nat @ X4 @ Xa @ Xb @ Xc )
% 11.11/6.19          = Y )
% 11.11/6.19       => ( ( ( ord_less_nat @ Xb @ Xa )
% 11.11/6.19           => ( Y = Xc ) )
% 11.11/6.19          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 11.11/6.19           => ( Y
% 11.11/6.19              = ( set_fo2584398358068434914at_nat @ X4 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X4 @ Xa @ Xc ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6585_fold__atLeastAtMost__nat_Osimps,axiom,
% 11.11/6.19      ( set_fo2584398358068434914at_nat
% 11.11/6.19      = ( ^ [F3: nat > nat > nat,A3: nat,B2: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6586_even__add__abs__iff,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 11.11/6.19        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6587_even__abs__add__iff,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 11.11/6.19        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6588_bit__nat__def,axiom,
% 11.11/6.19      ( bit_se1148574629649215175it_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] :
% 11.11/6.19            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6589_nat__intermed__int__val,axiom,
% 11.11/6.19      ! [M: nat,N2: nat,F: nat > int,K: int] :
% 11.11/6.19        ( ! [I4: nat] :
% 11.11/6.19            ( ( ( ord_less_eq_nat @ M @ I4 )
% 11.11/6.19              & ( ord_less_nat @ I4 @ N2 ) )
% 11.11/6.19           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 11.11/6.19       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 11.11/6.19           => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 11.11/6.19             => ? [I4: nat] :
% 11.11/6.19                  ( ( ord_less_eq_nat @ M @ I4 )
% 11.11/6.19                  & ( ord_less_eq_nat @ I4 @ N2 )
% 11.11/6.19                  & ( ( F @ I4 )
% 11.11/6.19                    = K ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6590_incr__lemma,axiom,
% 11.11/6.19      ! [D: int,Z: int,X4: int] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.19       => ( ord_less_int @ Z @ ( plus_plus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6591_decr__lemma,axiom,
% 11.11/6.19      ! [D: int,X4: int,Z: int] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.19       => ( ord_less_int @ ( minus_minus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6592_nat__ivt__aux,axiom,
% 11.11/6.19      ! [N2: nat,F: nat > int,K: int] :
% 11.11/6.19        ( ! [I4: nat] :
% 11.11/6.19            ( ( ord_less_nat @ I4 @ N2 )
% 11.11/6.19           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 11.11/6.19       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 11.11/6.19         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 11.11/6.19           => ? [I4: nat] :
% 11.11/6.19                ( ( ord_less_eq_nat @ I4 @ N2 )
% 11.11/6.19                & ( ( F @ I4 )
% 11.11/6.19                  = K ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6593_complex__mod__minus__le__complex__mod,axiom,
% 11.11/6.19      ! [X4: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6594_complex__mod__triangle__ineq2,axiom,
% 11.11/6.19      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6595_nat0__intermed__int__val,axiom,
% 11.11/6.19      ! [N2: nat,F: nat > int,K: int] :
% 11.11/6.19        ( ! [I4: nat] :
% 11.11/6.19            ( ( ord_less_nat @ I4 @ N2 )
% 11.11/6.19           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 11.11/6.19       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 11.11/6.19         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 11.11/6.19           => ? [I4: nat] :
% 11.11/6.19                ( ( ord_less_eq_nat @ I4 @ N2 )
% 11.11/6.19                & ( ( F @ I4 )
% 11.11/6.19                  = K ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6596_arctan__add,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.19       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.19         => ( ( plus_plus_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 11.11/6.19            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6597_xor__int__unfold,axiom,
% 11.11/6.19      ( bit_se6526347334894502574or_int
% 11.11/6.19      = ( ^ [K3: int,L2: int] :
% 11.11/6.19            ( if_int
% 11.11/6.19            @ ( K3
% 11.11/6.19              = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 11.11/6.19            @ ( if_int
% 11.11/6.19              @ ( L2
% 11.11/6.19                = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19              @ ( bit_ri7919022796975470100ot_int @ K3 )
% 11.11/6.19              @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = 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 @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6598_mask__numeral,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.19        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6599_mask__numeral,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.19        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6600_modulo__int__unfold,axiom,
% 11.11/6.19      ! [L: int,K: int,N2: nat,M: nat] :
% 11.11/6.19        ( ( ( ( ( sgn_sgn_int @ L )
% 11.11/6.19              = zero_zero_int )
% 11.11/6.19            | ( ( sgn_sgn_int @ K )
% 11.11/6.19              = zero_zero_int )
% 11.11/6.19            | ( N2 = zero_zero_nat ) )
% 11.11/6.19         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 11.11/6.19        & ( ~ ( ( ( sgn_sgn_int @ L )
% 11.11/6.19                = zero_zero_int )
% 11.11/6.19              | ( ( sgn_sgn_int @ K )
% 11.11/6.19                = zero_zero_int )
% 11.11/6.19              | ( N2 = zero_zero_nat ) )
% 11.11/6.19         => ( ( ( ( sgn_sgn_int @ K )
% 11.11/6.19                = ( sgn_sgn_int @ L ) )
% 11.11/6.19             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 11.11/6.19            & ( ( ( sgn_sgn_int @ K )
% 11.11/6.19               != ( sgn_sgn_int @ L ) )
% 11.11/6.19             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19                = ( times_times_int @ ( sgn_sgn_int @ L )
% 11.11/6.19                  @ ( minus_minus_int
% 11.11/6.19                    @ ( semiri1314217659103216013at_int
% 11.11/6.19                      @ ( times_times_nat @ N2
% 11.11/6.19                        @ ( zero_n2687167440665602831ol_nat
% 11.11/6.19                          @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 11.11/6.19                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6601_divide__int__unfold,axiom,
% 11.11/6.19      ! [L: int,K: int,N2: nat,M: nat] :
% 11.11/6.19        ( ( ( ( ( sgn_sgn_int @ L )
% 11.11/6.19              = zero_zero_int )
% 11.11/6.19            | ( ( sgn_sgn_int @ K )
% 11.11/6.19              = zero_zero_int )
% 11.11/6.19            | ( N2 = zero_zero_nat ) )
% 11.11/6.19         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19            = zero_zero_int ) )
% 11.11/6.19        & ( ~ ( ( ( sgn_sgn_int @ L )
% 11.11/6.19                = zero_zero_int )
% 11.11/6.19              | ( ( sgn_sgn_int @ K )
% 11.11/6.19                = zero_zero_int )
% 11.11/6.19              | ( N2 = zero_zero_nat ) )
% 11.11/6.19         => ( ( ( ( sgn_sgn_int @ K )
% 11.11/6.19                = ( sgn_sgn_int @ L ) )
% 11.11/6.19             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 11.11/6.19            & ( ( ( sgn_sgn_int @ K )
% 11.11/6.19               != ( sgn_sgn_int @ L ) )
% 11.11/6.19             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 11.11/6.19                = ( uminus_uminus_int
% 11.11/6.19                  @ ( semiri1314217659103216013at_int
% 11.11/6.19                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 11.11/6.19                      @ ( zero_n2687167440665602831ol_nat
% 11.11/6.19                        @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6602_tanh__real__altdef,axiom,
% 11.11/6.19      ( tanh_real
% 11.11/6.19      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6603_and__int__unfold,axiom,
% 11.11/6.19      ( bit_se725231765392027082nd_int
% 11.11/6.19      = ( ^ [K3: int,L2: int] :
% 11.11/6.19            ( if_int
% 11.11/6.19            @ ( ( K3 = zero_zero_int )
% 11.11/6.19              | ( L2 = zero_zero_int ) )
% 11.11/6.19            @ zero_zero_int
% 11.11/6.19            @ ( if_int
% 11.11/6.19              @ ( K3
% 11.11/6.19                = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19              @ L2
% 11.11/6.19              @ ( if_int
% 11.11/6.19                @ ( L2
% 11.11/6.19                  = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19                @ K3
% 11.11/6.19                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6604_and_Oidem,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ A @ A )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6605_and_Oidem,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6606_and_Oleft__idem,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6607_and_Oleft__idem,axiom,
% 11.11/6.19      ! [A: nat,B: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6608_and_Oright__idem,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6609_and_Oright__idem,axiom,
% 11.11/6.19      ! [A: nat,B: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6610_sgn__sgn,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19        = ( sgn_sgn_int @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6611_sgn__sgn,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19        = ( sgn_sgn_real @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6612_sgn__sgn,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 11.11/6.19        = ( sgn_sgn_complex @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6613_sgn__sgn,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19        = ( sgn_sgn_Code_integer @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6614_sgn__sgn,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19        = ( sgn_sgn_rat @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6615_bit_Odouble__compl,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6616_bit_Ocompl__eq__compl__iff,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ( bit_ri7919022796975470100ot_int @ X4 )
% 11.11/6.19          = ( bit_ri7919022796975470100ot_int @ Y ) )
% 11.11/6.19        = ( X4 = Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6617_mask__nat__positive__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 11.11/6.19        = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6618_and__zero__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6619_and__zero__eq,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6620_zero__and__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6621_zero__and__eq,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6622_bit_Oconj__zero__left,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X4 )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6623_bit_Oconj__zero__right,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ X4 @ zero_zero_int )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6624_sgn__0,axiom,
% 11.11/6.19      ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 11.11/6.19      = zero_z3403309356797280102nteger ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6625_sgn__0,axiom,
% 11.11/6.19      ( ( sgn_sgn_complex @ zero_zero_complex )
% 11.11/6.19      = zero_zero_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6626_sgn__0,axiom,
% 11.11/6.19      ( ( sgn_sgn_real @ zero_zero_real )
% 11.11/6.19      = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6627_sgn__0,axiom,
% 11.11/6.19      ( ( sgn_sgn_rat @ zero_zero_rat )
% 11.11/6.19      = zero_zero_rat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6628_sgn__0,axiom,
% 11.11/6.19      ( ( sgn_sgn_int @ zero_zero_int )
% 11.11/6.19      = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6629_sgn__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_int @ one_one_int )
% 11.11/6.19      = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6630_sgn__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_real @ one_one_real )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6631_sgn__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_complex @ one_one_complex )
% 11.11/6.19      = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6632_sgn__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 11.11/6.19      = one_one_Code_integer ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6633_sgn__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_rat @ one_one_rat )
% 11.11/6.19      = one_one_rat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6634_sgn__one,axiom,
% 11.11/6.19      ( ( sgn_sgn_real @ one_one_real )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6635_sgn__one,axiom,
% 11.11/6.19      ( ( sgn_sgn_complex @ one_one_complex )
% 11.11/6.19      = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6636_sgn__divide,axiom,
% 11.11/6.19      ! [A: rat,B: rat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 11.11/6.19        = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6637_sgn__divide,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.19        = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6638_sgn__divide,axiom,
% 11.11/6.19      ! [A: complex,B: complex] :
% 11.11/6.19        ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6639_idom__abs__sgn__class_Osgn__minus,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.19        = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6640_idom__abs__sgn__class_Osgn__minus,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6641_idom__abs__sgn__class_Osgn__minus,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.19        = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6642_idom__abs__sgn__class_Osgn__minus,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.19        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6643_idom__abs__sgn__class_Osgn__minus,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.19        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6644_power__sgn,axiom,
% 11.11/6.19      ! [A: code_integer,N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 11.11/6.19        = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6645_power__sgn,axiom,
% 11.11/6.19      ! [A: rat,N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N2 ) )
% 11.11/6.19        = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6646_power__sgn,axiom,
% 11.11/6.19      ! [A: real,N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( power_power_real @ A @ N2 ) )
% 11.11/6.19        = ( power_power_real @ ( sgn_sgn_real @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6647_power__sgn,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( power_power_int @ A @ N2 ) )
% 11.11/6.19        = ( power_power_int @ ( sgn_sgn_int @ A ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6648_exp__less__cancel__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 11.11/6.19        = ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6649_exp__less__mono,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.19       => ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6650_take__bit__and,axiom,
% 11.11/6.19      ! [N2: nat,A: int,B: int] :
% 11.11/6.19        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6651_take__bit__and,axiom,
% 11.11/6.19      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.19        ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6652_exp__le__cancel__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6653_bit_Oxor__compl__left,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ Y )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6654_bit_Oxor__compl__right,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ Y ) )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6655_sgn__less,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 11.11/6.19        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6656_sgn__less,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6657_sgn__less,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 11.11/6.19        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6658_sgn__less,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6659_sgn__greater,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6660_sgn__greater,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6661_sgn__greater,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6662_sgn__greater,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6663_exp__zero,axiom,
% 11.11/6.19      ( ( exp_complex @ zero_zero_complex )
% 11.11/6.19      = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6664_exp__zero,axiom,
% 11.11/6.19      ( ( exp_real @ zero_zero_real )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6665_bit_Oconj__one__right,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( bit_se3949692690581998587nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6666_bit_Oconj__one__right,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6667_and_Oright__neutral,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6668_and_Oright__neutral,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6669_and_Oleft__neutral,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6670_and_Oleft__neutral,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6671_divide__sgn,axiom,
% 11.11/6.19      ! [A: rat,B: rat] :
% 11.11/6.19        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 11.11/6.19        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6672_divide__sgn,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 11.11/6.19        = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6673_mask__0,axiom,
% 11.11/6.19      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 11.11/6.19      = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6674_mask__0,axiom,
% 11.11/6.19      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 11.11/6.19      = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6675_mask__eq__0__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 11.11/6.19          = zero_zero_nat )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6676_mask__eq__0__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 11.11/6.19          = zero_zero_int )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6677_bit_Oconj__cancel__left,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6678_bit_Oconj__cancel__right,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6679_exp__eq__one__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( exp_real @ X4 )
% 11.11/6.19          = one_one_real )
% 11.11/6.19        = ( X4 = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6680_and__nonnegative__int__iff,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 11.11/6.19        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6681_and__negative__int__iff,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 11.11/6.19        = ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.19          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6682_sgn__pos,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 11.11/6.19       => ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6683_sgn__pos,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( sgn_sgn_real @ A )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6684_sgn__pos,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.19       => ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6685_sgn__pos,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.19       => ( ( sgn_sgn_int @ A )
% 11.11/6.19          = one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6686_bit_Ocompl__one,axiom,
% 11.11/6.19      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19      = zero_z3403309356797280102nteger ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6687_bit_Ocompl__one,axiom,
% 11.11/6.19      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19      = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6688_bit_Ocompl__zero,axiom,
% 11.11/6.19      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 11.11/6.19      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6689_bit_Ocompl__zero,axiom,
% 11.11/6.19      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 11.11/6.19      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6690_and__numerals_I2_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.19        = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6691_and__numerals_I2_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.19        = one_one_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6692_and__numerals_I8_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 11.11/6.19        = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6693_and__numerals_I8_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 11.11/6.19        = one_one_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6694_abs__sgn__eq__1,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.19       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19          = one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6695_abs__sgn__eq__1,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( A != zero_zero_real )
% 11.11/6.19       => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6696_abs__sgn__eq__1,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( A != zero_zero_rat )
% 11.11/6.19       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19          = one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6697_abs__sgn__eq__1,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( A != zero_zero_int )
% 11.11/6.19       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19          = one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6698_sgn__mult__self__eq,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6699_sgn__mult__self__eq,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 11.11/6.19        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6700_sgn__mult__self__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 11.11/6.19        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6701_sgn__mult__self__eq,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6702_mask__Suc__0,axiom,
% 11.11/6.19      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 11.11/6.19      = one_one_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6703_mask__Suc__0,axiom,
% 11.11/6.19      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 11.11/6.19      = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6704_bit_Oxor__one__left,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 11.11/6.19        = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6705_bit_Oxor__one__left,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6706_bit_Oxor__one__right,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( bit_se3222712562003087583nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6707_bit_Oxor__one__right,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6708_bit_Oxor__cancel__left,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X4 ) @ X4 )
% 11.11/6.19        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6709_bit_Oxor__cancel__left,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 11.11/6.19        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6710_bit_Oxor__cancel__right,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( bit_se3222712562003087583nteger @ X4 @ ( bit_ri7632146776885996613nteger @ X4 ) )
% 11.11/6.19        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6711_bit_Oxor__cancel__right,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 11.11/6.19        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6712_idom__abs__sgn__class_Oabs__sgn,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 11.11/6.19        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6713_idom__abs__sgn__class_Oabs__sgn,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 11.11/6.19        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6714_idom__abs__sgn__class_Oabs__sgn,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 11.11/6.19        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6715_idom__abs__sgn__class_Oabs__sgn,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 11.11/6.19        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6716_idom__abs__sgn__class_Oabs__sgn,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.19        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6717_sgn__abs,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 11.11/6.19        = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6718_sgn__abs,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19        = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6719_sgn__abs,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6720_sgn__abs,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6721_sgn__abs,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6722_one__less__exp__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6723_exp__less__one__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( exp_real @ X4 ) @ one_one_real )
% 11.11/6.19        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6724_exp__le__one__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ one_one_real )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6725_one__le__exp__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X4 ) )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6726_take__bit__minus__one__eq__mask,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6727_take__bit__minus__one__eq__mask,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6728_not__negative__int__iff,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6729_not__nonnegative__int__iff,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 11.11/6.19        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6730_exp__ln,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.19          = X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6731_exp__ln__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.19          = X4 )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6732_minus__not__numeral__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 11.11/6.19        = ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6733_minus__not__numeral__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.19        = ( numeral_numeral_int @ ( inc @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6734_and__numerals_I1_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6735_and__numerals_I1_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6736_and__numerals_I5_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6737_and__numerals_I5_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6738_sgn__neg,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.19       => ( ( sgn_sgn_real @ A )
% 11.11/6.19          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6739_sgn__neg,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ord_less_int @ A @ zero_zero_int )
% 11.11/6.19       => ( ( sgn_sgn_int @ A )
% 11.11/6.19          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6740_sgn__neg,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 11.11/6.19       => ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6741_sgn__neg,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.19       => ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6742_and__numerals_I3_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6743_and__numerals_I3_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.19        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6744_even__not__iff,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 11.11/6.19        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6745_even__not__iff,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 11.11/6.19        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6746_sgn__of__nat,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 11.11/6.19        = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6747_sgn__of__nat,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.19        = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6748_sgn__of__nat,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.19        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6749_sgn__of__nat,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 11.11/6.19        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6750_and__minus__numerals_I2_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.19        = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6751_and__minus__numerals_I6_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 11.11/6.19        = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6752_not__one__eq,axiom,
% 11.11/6.19      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 11.11/6.19      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6753_not__one__eq,axiom,
% 11.11/6.19      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 11.11/6.19      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6754_and__numerals_I4_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6755_and__numerals_I4_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.19        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6756_and__numerals_I6_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6757_and__numerals_I6_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.19        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6758_and__minus__numerals_I1_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6759_and__minus__numerals_I5_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6760_and__numerals_I7_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 11.11/6.19        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6761_and__numerals_I7_J,axiom,
% 11.11/6.19      ! [X4: num,Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.19        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6762_disjunctive__diff,axiom,
% 11.11/6.19      ! [B: int,A: int] :
% 11.11/6.19        ( ! [N3: nat] :
% 11.11/6.19            ( ( bit_se1146084159140164899it_int @ B @ N3 )
% 11.11/6.19           => ( bit_se1146084159140164899it_int @ A @ N3 ) )
% 11.11/6.19       => ( ( minus_minus_int @ A @ B )
% 11.11/6.19          = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6763_norm__exp,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X4 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6764_norm__exp,axiom,
% 11.11/6.19      ! [X4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X4 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6765_and__not__numerals_I1_J,axiom,
% 11.11/6.19      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.19      = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6766_take__bit__eq__mask,axiom,
% 11.11/6.19      ( bit_se2923211474154528505it_int
% 11.11/6.19      = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6767_take__bit__eq__mask,axiom,
% 11.11/6.19      ( bit_se2925701944663578781it_nat
% 11.11/6.19      = ( ^ [N: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6768_and_Oassoc,axiom,
% 11.11/6.19      ! [A: int,B: int,C: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6769_and_Oassoc,axiom,
% 11.11/6.19      ! [A: nat,B: nat,C: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6770_and_Ocommute,axiom,
% 11.11/6.19      ( bit_se725231765392027082nd_int
% 11.11/6.19      = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6771_and_Ocommute,axiom,
% 11.11/6.19      ( bit_se727722235901077358nd_nat
% 11.11/6.19      = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6772_and_Oleft__commute,axiom,
% 11.11/6.19      ! [B: int,A: int,C: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6773_and_Oleft__commute,axiom,
% 11.11/6.19      ! [B: nat,A: nat,C: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6774_of__nat__mask__eq,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 11.11/6.19        = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6775_of__nat__mask__eq,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 11.11/6.19        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6776_of__nat__and__eq,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 11.11/6.19        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6777_of__nat__and__eq,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 11.11/6.19        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6778_exp__less__cancel,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 11.11/6.19       => ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6779_sgn__0__0,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = zero_z3403309356797280102nteger )
% 11.11/6.19        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6780_sgn__0__0,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ A )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19        = ( A = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6781_sgn__0__0,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = zero_zero_rat )
% 11.11/6.19        = ( A = zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6782_sgn__0__0,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ A )
% 11.11/6.19          = zero_zero_int )
% 11.11/6.19        = ( A = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6783_sgn__eq__0__iff,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = zero_z3403309356797280102nteger )
% 11.11/6.19        = ( A = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6784_sgn__eq__0__iff,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( ( sgn_sgn_complex @ A )
% 11.11/6.19          = zero_zero_complex )
% 11.11/6.19        = ( A = zero_zero_complex ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6785_sgn__eq__0__iff,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ A )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19        = ( A = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6786_sgn__eq__0__iff,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = zero_zero_rat )
% 11.11/6.19        = ( A = zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6787_sgn__eq__0__iff,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ A )
% 11.11/6.19          = zero_zero_int )
% 11.11/6.19        = ( A = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6788_sgn__mult,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer] :
% 11.11/6.19        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 11.11/6.19        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6789_sgn__mult,axiom,
% 11.11/6.19      ! [A: rat,B: rat] :
% 11.11/6.19        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.19        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6790_sgn__mult,axiom,
% 11.11/6.19      ! [A: complex,B: complex] :
% 11.11/6.19        ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 11.11/6.19        = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6791_sgn__mult,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 11.11/6.19        = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6792_sgn__mult,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 11.11/6.19        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6793_same__sgn__sgn__add,axiom,
% 11.11/6.19      ! [B: code_integer,A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ B )
% 11.11/6.19          = ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19       => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.19          = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6794_same__sgn__sgn__add,axiom,
% 11.11/6.19      ! [B: real,A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ B )
% 11.11/6.19          = ( sgn_sgn_real @ A ) )
% 11.11/6.19       => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 11.11/6.19          = ( sgn_sgn_real @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6795_same__sgn__sgn__add,axiom,
% 11.11/6.19      ! [B: rat,A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ B )
% 11.11/6.19          = ( sgn_sgn_rat @ A ) )
% 11.11/6.19       => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.19          = ( sgn_sgn_rat @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6796_same__sgn__sgn__add,axiom,
% 11.11/6.19      ! [B: int,A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ B )
% 11.11/6.19          = ( sgn_sgn_int @ A ) )
% 11.11/6.19       => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.19          = ( sgn_sgn_int @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6797_take__bit__not__eq__mask__diff,axiom,
% 11.11/6.19      ! [N2: nat,A: int] :
% 11.11/6.19        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 11.11/6.19        = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6798_bit__and__iff,axiom,
% 11.11/6.19      ! [A: int,B: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N2 )
% 11.11/6.19        = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 11.11/6.19          & ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6799_bit__and__iff,axiom,
% 11.11/6.19      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.19        ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N2 )
% 11.11/6.19        = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 11.11/6.19          & ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6800_bit_Oconj__xor__distrib,axiom,
% 11.11/6.19      ! [X4: int,Y: int,Z: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_se6526347334894502574or_int @ Y @ Z ) )
% 11.11/6.19        = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se725231765392027082nd_int @ X4 @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6801_bit_Oconj__xor__distrib2,axiom,
% 11.11/6.19      ! [Y: int,Z: int,X4: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y @ Z ) @ X4 )
% 11.11/6.19        = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y @ X4 ) @ ( bit_se725231765392027082nd_int @ Z @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6802_div__eq__sgn__abs,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ K )
% 11.11/6.19          = ( sgn_sgn_int @ L ) )
% 11.11/6.19       => ( ( divide_divide_int @ K @ L )
% 11.11/6.19          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6803_take__bit__not__iff,axiom,
% 11.11/6.19      ! [N2: nat,A: int,B: int] :
% 11.11/6.19        ( ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 11.11/6.19          = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 11.11/6.19        = ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 11.11/6.19          = ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6804_take__bit__not__take__bit,axiom,
% 11.11/6.19      ! [N2: nat,A: int] :
% 11.11/6.19        ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 11.11/6.19        = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6805_bit__not__int__iff,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 11.11/6.19        = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6806_bit__and__int__iff,axiom,
% 11.11/6.19      ! [K: int,L: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N2 )
% 11.11/6.19        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 11.11/6.19          & ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6807_less__eq__mask,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6808_and__not__numerals_I2_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.19        = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6809_and__not__numerals_I4_J,axiom,
% 11.11/6.19      ! [M: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.19        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6810_take__bit__not__mask__eq__0,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.19       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) )
% 11.11/6.19          = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6811_and__not__numerals_I5_J,axiom,
% 11.11/6.19      ! [M: num,N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6812_and__not__numerals_I7_J,axiom,
% 11.11/6.19      ! [M: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.19        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6813_and__not__numerals_I3_J,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.19        = zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6814_and__eq__minus__1__iff,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer] :
% 11.11/6.19        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 11.11/6.19          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = ( ( A
% 11.11/6.19            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19          & ( B
% 11.11/6.19            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6815_and__eq__minus__1__iff,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 11.11/6.19          = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = ( ( A
% 11.11/6.19            = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19          & ( B
% 11.11/6.19            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6816_exp__total,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19       => ? [X5: real] :
% 11.11/6.19            ( ( exp_real @ X5 )
% 11.11/6.19            = Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6817_exp__gt__zero,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6818_not__exp__less__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ~ ( ord_less_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6819_exp__ge__zero,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6820_not__exp__le__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ~ ( ord_less_eq_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6821_sgn__not__eq__imp,axiom,
% 11.11/6.19      ! [B: real,A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ B )
% 11.11/6.19         != ( sgn_sgn_real @ A ) )
% 11.11/6.19       => ( ( ( sgn_sgn_real @ A )
% 11.11/6.19           != zero_zero_real )
% 11.11/6.19         => ( ( ( sgn_sgn_real @ B )
% 11.11/6.19             != zero_zero_real )
% 11.11/6.19           => ( ( sgn_sgn_real @ A )
% 11.11/6.19              = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6822_sgn__not__eq__imp,axiom,
% 11.11/6.19      ! [B: int,A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ B )
% 11.11/6.19         != ( sgn_sgn_int @ A ) )
% 11.11/6.19       => ( ( ( sgn_sgn_int @ A )
% 11.11/6.19           != zero_zero_int )
% 11.11/6.19         => ( ( ( sgn_sgn_int @ B )
% 11.11/6.19             != zero_zero_int )
% 11.11/6.19           => ( ( sgn_sgn_int @ A )
% 11.11/6.19              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6823_sgn__not__eq__imp,axiom,
% 11.11/6.19      ! [B: code_integer,A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ B )
% 11.11/6.19         != ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19       => ( ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19           != zero_z3403309356797280102nteger )
% 11.11/6.19         => ( ( ( sgn_sgn_Code_integer @ B )
% 11.11/6.19             != zero_z3403309356797280102nteger )
% 11.11/6.19           => ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6824_sgn__not__eq__imp,axiom,
% 11.11/6.19      ! [B: rat,A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ B )
% 11.11/6.19         != ( sgn_sgn_rat @ A ) )
% 11.11/6.19       => ( ( ( sgn_sgn_rat @ A )
% 11.11/6.19           != zero_zero_rat )
% 11.11/6.19         => ( ( ( sgn_sgn_rat @ B )
% 11.11/6.19             != zero_zero_rat )
% 11.11/6.19           => ( ( sgn_sgn_rat @ A )
% 11.11/6.19              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6825_sgn__minus__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.19      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6826_sgn__minus__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19      = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6827_sgn__minus__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.19      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6828_sgn__minus__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6829_sgn__minus__1,axiom,
% 11.11/6.19      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.19      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6830_AND__upper2_H,axiom,
% 11.11/6.19      ! [Y: int,Z: int,X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( ord_less_eq_int @ Y @ Z )
% 11.11/6.19         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6831_AND__upper1_H,axiom,
% 11.11/6.19      ! [Y: int,Z: int,Ya: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( ord_less_eq_int @ Y @ Z )
% 11.11/6.19         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6832_AND__upper2,axiom,
% 11.11/6.19      ! [Y: int,X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6833_AND__upper1,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.19       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6834_AND__lower,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.19       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6835_not__diff__distrib,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 11.11/6.19        = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6836_not__add__distrib,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.19        = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6837_linordered__idom__class_Oabs__sgn,axiom,
% 11.11/6.19      ( abs_abs_Code_integer
% 11.11/6.19      = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6838_linordered__idom__class_Oabs__sgn,axiom,
% 11.11/6.19      ( abs_abs_rat
% 11.11/6.19      = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6839_linordered__idom__class_Oabs__sgn,axiom,
% 11.11/6.19      ( abs_abs_real
% 11.11/6.19      = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6840_linordered__idom__class_Oabs__sgn,axiom,
% 11.11/6.19      ( abs_abs_int
% 11.11/6.19      = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6841_abs__mult__sgn,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6842_abs__mult__sgn,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6843_abs__mult__sgn,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6844_abs__mult__sgn,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6845_abs__mult__sgn,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6846_sgn__mult__abs,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6847_sgn__mult__abs,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6848_sgn__mult__abs,axiom,
% 11.11/6.19      ! [A: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6849_sgn__mult__abs,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6850_sgn__mult__abs,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 11.11/6.19        = A ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6851_mult__sgn__abs,axiom,
% 11.11/6.19      ! [X4: code_integer] :
% 11.11/6.19        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ X4 ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6852_mult__sgn__abs,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( times_times_rat @ ( sgn_sgn_rat @ X4 ) @ ( abs_abs_rat @ X4 ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6853_mult__sgn__abs,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( times_times_real @ ( sgn_sgn_real @ X4 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6854_mult__sgn__abs,axiom,
% 11.11/6.19      ! [X4: int] :
% 11.11/6.19        ( ( times_times_int @ ( sgn_sgn_int @ X4 ) @ ( abs_abs_int @ X4 ) )
% 11.11/6.19        = X4 ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6855_same__sgn__abs__add,axiom,
% 11.11/6.19      ! [B: code_integer,A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ B )
% 11.11/6.19          = ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19       => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 11.11/6.19          = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6856_same__sgn__abs__add,axiom,
% 11.11/6.19      ! [B: real,A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ B )
% 11.11/6.19          = ( sgn_sgn_real @ A ) )
% 11.11/6.19       => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 11.11/6.19          = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6857_same__sgn__abs__add,axiom,
% 11.11/6.19      ! [B: rat,A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ B )
% 11.11/6.19          = ( sgn_sgn_rat @ A ) )
% 11.11/6.19       => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 11.11/6.19          = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6858_same__sgn__abs__add,axiom,
% 11.11/6.19      ! [B: int,A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ B )
% 11.11/6.19          = ( sgn_sgn_int @ A ) )
% 11.11/6.19       => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 11.11/6.19          = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6859_exp__add__commuting,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( ( times_times_complex @ X4 @ Y )
% 11.11/6.19          = ( times_times_complex @ Y @ X4 ) )
% 11.11/6.19       => ( ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.19          = ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6860_exp__add__commuting,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ( times_times_real @ X4 @ Y )
% 11.11/6.19          = ( times_times_real @ Y @ X4 ) )
% 11.11/6.19       => ( ( exp_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.19          = ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6861_mult__exp__exp,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) )
% 11.11/6.19        = ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6862_mult__exp__exp,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 11.11/6.19        = ( exp_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6863_exp__diff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( exp_real @ ( minus_minus_real @ X4 @ Y ) )
% 11.11/6.19        = ( divide_divide_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6864_exp__diff,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( exp_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6865_and__not__numerals_I6_J,axiom,
% 11.11/6.19      ! [M: num,N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6866_and__not__numerals_I9_J,axiom,
% 11.11/6.19      ! [M: num,N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.19        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6867_mask__nonnegative__int,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6868_not__mask__negative__int,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6869_minus__exp__eq__not__mask,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6870_minus__exp__eq__not__mask,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6871_exp__gt__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6872_sgn__1__pos,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = one_one_Code_integer )
% 11.11/6.19        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6873_sgn__1__pos,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ A )
% 11.11/6.19          = one_one_real )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6874_sgn__1__pos,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = one_one_rat )
% 11.11/6.19        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6875_sgn__1__pos,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ A )
% 11.11/6.19          = one_one_int )
% 11.11/6.19        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6876_exp__ge__add__one__self,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6877_abs__sgn__eq,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ( A = zero_z3403309356797280102nteger )
% 11.11/6.19         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19            = zero_z3403309356797280102nteger ) )
% 11.11/6.19        & ( ( A != zero_z3403309356797280102nteger )
% 11.11/6.19         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 11.11/6.19            = one_one_Code_integer ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6878_abs__sgn__eq,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ( A = zero_zero_real )
% 11.11/6.19         => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19            = zero_zero_real ) )
% 11.11/6.19        & ( ( A != zero_zero_real )
% 11.11/6.19         => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.19            = one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6879_abs__sgn__eq,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ( A = zero_zero_rat )
% 11.11/6.19         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19            = zero_zero_rat ) )
% 11.11/6.19        & ( ( A != zero_zero_rat )
% 11.11/6.19         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.19            = one_one_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6880_abs__sgn__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ( A = zero_zero_int )
% 11.11/6.19         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19            = zero_zero_int ) )
% 11.11/6.19        & ( ( A != zero_zero_int )
% 11.11/6.19         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 11.11/6.19            = one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6881_and__less__eq,axiom,
% 11.11/6.19      ! [L: int,K: int] :
% 11.11/6.19        ( ( ord_less_int @ L @ zero_zero_int )
% 11.11/6.19       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6882_AND__upper1_H_H,axiom,
% 11.11/6.19      ! [Y: int,Z: int,Ya: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( ord_less_int @ Y @ Z )
% 11.11/6.19         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6883_AND__upper2_H_H,axiom,
% 11.11/6.19      ! [Y: int,Z: int,X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( ord_less_int @ Y @ Z )
% 11.11/6.19         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6884_minus__eq__not__plus__1,axiom,
% 11.11/6.19      ( uminus1351360451143612070nteger
% 11.11/6.19      = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6885_minus__eq__not__plus__1,axiom,
% 11.11/6.19      ( uminus_uminus_int
% 11.11/6.19      = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6886_not__eq__complement,axiom,
% 11.11/6.19      ( bit_ri7632146776885996613nteger
% 11.11/6.19      = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6887_not__eq__complement,axiom,
% 11.11/6.19      ( bit_ri7919022796975470100ot_int
% 11.11/6.19      = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6888_minus__eq__not__minus__1,axiom,
% 11.11/6.19      ( uminus1351360451143612070nteger
% 11.11/6.19      = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6889_minus__eq__not__minus__1,axiom,
% 11.11/6.19      ( uminus_uminus_int
% 11.11/6.19      = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6890_div__sgn__abs__cancel,axiom,
% 11.11/6.19      ! [V: int,K: int,L: int] :
% 11.11/6.19        ( ( V != zero_zero_int )
% 11.11/6.19       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 11.11/6.19          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6891_not__int__def,axiom,
% 11.11/6.19      ( bit_ri7919022796975470100ot_int
% 11.11/6.19      = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6892_exp__minus__inverse,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6893_exp__minus__inverse,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) )
% 11.11/6.19        = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6894_exp__of__nat2__mult,axiom,
% 11.11/6.19      ! [X4: complex,N2: nat] :
% 11.11/6.19        ( ( exp_complex @ ( times_times_complex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 11.11/6.19        = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6895_exp__of__nat2__mult,axiom,
% 11.11/6.19      ! [X4: real,N2: nat] :
% 11.11/6.19        ( ( exp_real @ ( times_times_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.19        = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6896_exp__of__nat__mult,axiom,
% 11.11/6.19      ! [N2: nat,X4: complex] :
% 11.11/6.19        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X4 ) )
% 11.11/6.19        = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6897_exp__of__nat__mult,axiom,
% 11.11/6.19      ! [N2: nat,X4: real] :
% 11.11/6.19        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) )
% 11.11/6.19        = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6898_div__dvd__sgn__abs,axiom,
% 11.11/6.19      ! [L: int,K: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ L @ K )
% 11.11/6.19       => ( ( divide_divide_int @ K @ L )
% 11.11/6.19          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6899_sgn__mod,axiom,
% 11.11/6.19      ! [L: int,K: int] :
% 11.11/6.19        ( ( L != zero_zero_int )
% 11.11/6.19       => ( ~ ( dvd_dvd_int @ L @ K )
% 11.11/6.19         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 11.11/6.19            = ( sgn_sgn_int @ L ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6900_and__not__numerals_I8_J,axiom,
% 11.11/6.19      ! [M: num,N2: num] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.19        = ( 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 @ N2 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6901_minus__numeral__inc__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) )
% 11.11/6.19        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6902_minus__numeral__inc__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6903_less__mask,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.19       => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6904_even__and__iff,axiom,
% 11.11/6.19      ! [A: code_integer,B: code_integer] :
% 11.11/6.19        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 11.11/6.19        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 11.11/6.19          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6905_even__and__iff,axiom,
% 11.11/6.19      ! [A: int,B: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 11.11/6.19        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 11.11/6.19          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6906_even__and__iff,axiom,
% 11.11/6.19      ! [A: nat,B: nat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 11.11/6.19        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 11.11/6.19          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6907_sgn__1__neg,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ( sgn_sgn_real @ A )
% 11.11/6.19          = ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.19        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6908_sgn__1__neg,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ A )
% 11.11/6.19          = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.19        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6909_sgn__1__neg,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( ( sgn_sgn_Code_integer @ A )
% 11.11/6.19          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.19        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6910_sgn__1__neg,axiom,
% 11.11/6.19      ! [A: rat] :
% 11.11/6.19        ( ( ( sgn_sgn_rat @ A )
% 11.11/6.19          = ( uminus_uminus_rat @ one_one_rat ) )
% 11.11/6.19        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6911_sgn__if,axiom,
% 11.11/6.19      ( sgn_sgn_real
% 11.11/6.19      = ( ^ [X: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6912_sgn__if,axiom,
% 11.11/6.19      ( sgn_sgn_int
% 11.11/6.19      = ( ^ [X: int] : ( if_int @ ( X = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6913_sgn__if,axiom,
% 11.11/6.19      ( sgn_sgn_Code_integer
% 11.11/6.19      = ( ^ [X: code_integer] : ( if_Code_integer @ ( X = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6914_sgn__if,axiom,
% 11.11/6.19      ( sgn_sgn_rat
% 11.11/6.19      = ( ^ [X: rat] : ( if_rat @ ( X = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6915_not__int__div__2,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6916_even__not__iff__int,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 11.11/6.19        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6917_exp__ge__add__one__self__aux,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6918_even__and__iff__int,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 11.11/6.19        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 11.11/6.19          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6919_lemma__exp__total,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ Y )
% 11.11/6.19       => ? [X5: real] :
% 11.11/6.19            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 11.11/6.19            & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 11.11/6.19            & ( ( exp_real @ X5 )
% 11.11/6.19              = Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6920_ln__ge__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X4 ) )
% 11.11/6.19          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6921_zsgn__def,axiom,
% 11.11/6.19      ( sgn_sgn_int
% 11.11/6.19      = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6922_ln__x__over__x__mono,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6923_not__numeral__Bit0__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) )
% 11.11/6.19        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6924_not__numeral__Bit0__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6925_norm__sgn,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( X4 = zero_zero_real )
% 11.11/6.19         => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 11.11/6.19            = zero_zero_real ) )
% 11.11/6.19        & ( ( X4 != zero_zero_real )
% 11.11/6.19         => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 11.11/6.19            = one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6926_norm__sgn,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( ( X4 = zero_zero_complex )
% 11.11/6.19         => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 11.11/6.19            = zero_zero_real ) )
% 11.11/6.19        & ( ( X4 != zero_zero_complex )
% 11.11/6.19         => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 11.11/6.19            = one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6927_bit__minus__int__iff,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 11.11/6.19        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6928_not__numeral__BitM__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N2 ) ) )
% 11.11/6.19        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6929_not__numeral__BitM__eq,axiom,
% 11.11/6.19      ! [N2: num] :
% 11.11/6.19        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N2 ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6930_one__and__eq,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 11.11/6.19        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6931_one__and__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 11.11/6.19        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6932_one__and__eq,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 11.11/6.19        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6933_and__one__eq,axiom,
% 11.11/6.19      ! [A: code_integer] :
% 11.11/6.19        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 11.11/6.19        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6934_and__one__eq,axiom,
% 11.11/6.19      ! [A: int] :
% 11.11/6.19        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 11.11/6.19        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6935_and__one__eq,axiom,
% 11.11/6.19      ! [A: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 11.11/6.19        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6936_exp__le,axiom,
% 11.11/6.19      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6937_take__bit__eq__mask__iff,axiom,
% 11.11/6.19      ! [N2: nat,K: int] :
% 11.11/6.19        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.19          = ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.19        = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 11.11/6.19          = zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6938_exp__divide__power__eq,axiom,
% 11.11/6.19      ! [N2: nat,X4: complex] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 11.11/6.19          = ( exp_complex @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6939_exp__divide__power__eq,axiom,
% 11.11/6.19      ! [N2: nat,X4: real] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 11.11/6.19          = ( exp_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6940_eucl__rel__int__remainderI,axiom,
% 11.11/6.19      ! [R3: int,L: int,K: int,Q3: int] :
% 11.11/6.19        ( ( ( sgn_sgn_int @ R3 )
% 11.11/6.19          = ( sgn_sgn_int @ L ) )
% 11.11/6.19       => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 11.11/6.19         => ( ( K
% 11.11/6.19              = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R3 ) )
% 11.11/6.19           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6941_tanh__altdef,axiom,
% 11.11/6.19      ( tanh_real
% 11.11/6.19      = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6942_tanh__altdef,axiom,
% 11.11/6.19      ( tanh_complex
% 11.11/6.19      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6943_and__exp__eq__0__iff__not__bit,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19          = zero_zero_int )
% 11.11/6.19        = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6944_and__exp__eq__0__iff__not__bit,axiom,
% 11.11/6.19      ! [A: nat,N2: nat] :
% 11.11/6.19        ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19          = zero_zero_nat )
% 11.11/6.19        = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6945_exp__half__le2,axiom,
% 11.11/6.19      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6946_Suc__mask__eq__exp,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 11.11/6.19        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6947_mask__nat__less__exp,axiom,
% 11.11/6.19      ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6948_bit__not__iff__eq,axiom,
% 11.11/6.19      ! [A: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N2 )
% 11.11/6.19        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19           != zero_zero_int )
% 11.11/6.19          & ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6949_exp__double,axiom,
% 11.11/6.19      ! [Z: complex] :
% 11.11/6.19        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 11.11/6.19        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6950_exp__double,axiom,
% 11.11/6.19      ! [Z: real] :
% 11.11/6.19        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 11.11/6.19        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6951_eucl__rel__int_Osimps,axiom,
% 11.11/6.19      ( eucl_rel_int
% 11.11/6.19      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 11.11/6.19            ( ? [K3: int] :
% 11.11/6.19                ( ( A1 = K3 )
% 11.11/6.19                & ( A22 = zero_zero_int )
% 11.11/6.19                & ( A32
% 11.11/6.19                  = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 11.11/6.19            | ? [L2: int,K3: int,Q5: int] :
% 11.11/6.19                ( ( A1 = K3 )
% 11.11/6.19                & ( A22 = L2 )
% 11.11/6.19                & ( A32
% 11.11/6.19                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 11.11/6.19                & ( L2 != zero_zero_int )
% 11.11/6.19                & ( K3
% 11.11/6.19                  = ( times_times_int @ Q5 @ L2 ) ) )
% 11.11/6.19            | ? [R5: int,L2: int,K3: int,Q5: int] :
% 11.11/6.19                ( ( A1 = K3 )
% 11.11/6.19                & ( A22 = L2 )
% 11.11/6.19                & ( A32
% 11.11/6.19                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 11.11/6.19                & ( ( sgn_sgn_int @ R5 )
% 11.11/6.19                  = ( sgn_sgn_int @ L2 ) )
% 11.11/6.19                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 11.11/6.19                & ( K3
% 11.11/6.19                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6952_eucl__rel__int_Ocases,axiom,
% 11.11/6.19      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 11.11/6.19        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 11.11/6.19       => ( ( ( A23 = zero_zero_int )
% 11.11/6.19           => ( A33
% 11.11/6.19             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 11.11/6.19         => ( ! [Q2: int] :
% 11.11/6.19                ( ( A33
% 11.11/6.19                  = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 11.11/6.19               => ( ( A23 != zero_zero_int )
% 11.11/6.19                 => ( A12
% 11.11/6.19                   != ( times_times_int @ Q2 @ A23 ) ) ) )
% 11.11/6.19           => ~ ! [R2: int,Q2: int] :
% 11.11/6.19                  ( ( A33
% 11.11/6.19                    = ( product_Pair_int_int @ Q2 @ R2 ) )
% 11.11/6.19                 => ( ( ( sgn_sgn_int @ R2 )
% 11.11/6.19                      = ( sgn_sgn_int @ A23 ) )
% 11.11/6.19                   => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 11.11/6.19                     => ( A12
% 11.11/6.19                       != ( plus_plus_int @ ( times_times_int @ Q2 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6953_div__noneq__sgn__abs,axiom,
% 11.11/6.19      ! [L: int,K: int] :
% 11.11/6.19        ( ( L != zero_zero_int )
% 11.11/6.19       => ( ( ( sgn_sgn_int @ K )
% 11.11/6.19           != ( sgn_sgn_int @ L ) )
% 11.11/6.19         => ( ( divide_divide_int @ K @ L )
% 11.11/6.19            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 11.11/6.19              @ ( zero_n2684676970156552555ol_int
% 11.11/6.19                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6954_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6955_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6956_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.19        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6957_mask__half__int,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6958_mask__nat__def,axiom,
% 11.11/6.19      ( bit_se2002935070580805687sk_nat
% 11.11/6.19      = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6959_mask__int__def,axiom,
% 11.11/6.19      ( bit_se2000444600071755411sk_int
% 11.11/6.19      = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6960_exp__bound__half,axiom,
% 11.11/6.19      ! [Z: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6961_exp__bound__half,axiom,
% 11.11/6.19      ! [Z: complex] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6962_mask__eq__exp__minus__1,axiom,
% 11.11/6.19      ( bit_se2002935070580805687sk_nat
% 11.11/6.19      = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6963_mask__eq__exp__minus__1,axiom,
% 11.11/6.19      ( bit_se2000444600071755411sk_int
% 11.11/6.19      = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6964_exp__bound,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.19         => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6965_not__int__rec,axiom,
% 11.11/6.19      ( bit_ri7919022796975470100ot_int
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6966_and__int__rec,axiom,
% 11.11/6.19      ( bit_se725231765392027082nd_int
% 11.11/6.19      = ( ^ [K3: int,L2: int] :
% 11.11/6.19            ( plus_plus_int
% 11.11/6.19            @ ( zero_n2684676970156552555ol_int
% 11.11/6.19              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 11.11/6.19                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 11.11/6.19            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6967_real__exp__bound__lemma,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6968_exp__ge__one__plus__x__over__n__power__n,axiom,
% 11.11/6.19      ! [N2: nat,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6969_exp__ge__one__minus__x__over__n__power__n,axiom,
% 11.11/6.19      ! [X4: real,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.19       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6970_exp__bound__lemma,axiom,
% 11.11/6.19      ! [Z: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( 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 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6971_exp__bound__lemma,axiom,
% 11.11/6.19      ! [Z: complex] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( 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 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6972_take__bit__eq__mask__iff__exp__dvd,axiom,
% 11.11/6.19      ! [N2: nat,K: int] :
% 11.11/6.19        ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 11.11/6.19          = ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.19        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6973_exp__lower__Taylor__quadratic,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( divide_divide_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6974_log__base__10__eq1,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19          = ( 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 @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6975_modulo__int__def,axiom,
% 11.11/6.19      ( modulo_modulo_int
% 11.11/6.19      = ( ^ [K3: int,L2: int] :
% 11.11/6.19            ( if_int @ ( L2 = zero_zero_int ) @ K3
% 11.11/6.19            @ ( if_int
% 11.11/6.19              @ ( ( sgn_sgn_int @ K3 )
% 11.11/6.19                = ( sgn_sgn_int @ L2 ) )
% 11.11/6.19              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 11.11/6.19              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 11.11/6.19                @ ( minus_minus_int
% 11.11/6.19                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 11.11/6.19                    @ ( zero_n2684676970156552555ol_int
% 11.11/6.19                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 11.11/6.19                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6976_divide__int__def,axiom,
% 11.11/6.19      ( divide_divide_int
% 11.11/6.19      = ( ^ [K3: int,L2: int] :
% 11.11/6.19            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 11.11/6.19            @ ( if_int
% 11.11/6.19              @ ( ( sgn_sgn_int @ K3 )
% 11.11/6.19                = ( sgn_sgn_int @ L2 ) )
% 11.11/6.19              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 11.11/6.19              @ ( uminus_uminus_int
% 11.11/6.19                @ ( semiri1314217659103216013at_int
% 11.11/6.19                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 11.11/6.19                    @ ( zero_n2687167440665602831ol_nat
% 11.11/6.19                      @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6977_arctan__half,axiom,
% 11.11/6.19      ( arctan
% 11.11/6.19      = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6978_log__base__10__eq2,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6979_machin,axiom,
% 11.11/6.19      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.19      = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6980_zero__le__sgn__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X4 ) )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6981_sgn__le__0__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6982_real__sqrt__less__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6983_real__sqrt__le__iff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6984_real__sqrt__one,axiom,
% 11.11/6.19      ( ( sqrt @ one_one_real )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6985_real__sqrt__eq__1__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( sqrt @ X4 )
% 11.11/6.19          = one_one_real )
% 11.11/6.19        = ( X4 = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6986_real__sqrt__lt__0__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6987_real__sqrt__gt__0__iff,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6988_nat__numeral,axiom,
% 11.11/6.19      ! [K: num] :
% 11.11/6.19        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 11.11/6.19        = ( numeral_numeral_nat @ K ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6989_real__sqrt__le__0__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6990_real__sqrt__ge__0__iff,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6991_real__sqrt__lt__1__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( sqrt @ X4 ) @ one_one_real )
% 11.11/6.19        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6992_real__sqrt__gt__1__iff,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6993_real__sqrt__le__1__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ one_one_real )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6994_real__sqrt__ge__1__iff,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 11.11/6.19        = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6995_log__one,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( log @ A @ one_one_real )
% 11.11/6.19        = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6996_real__sqrt__four,axiom,
% 11.11/6.19      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.19      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6997_nat__1,axiom,
% 11.11/6.19      ( ( nat2 @ one_one_int )
% 11.11/6.19      = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6998_nat__0__iff,axiom,
% 11.11/6.19      ! [I2: int] :
% 11.11/6.19        ( ( ( nat2 @ I2 )
% 11.11/6.19          = zero_zero_nat )
% 11.11/6.19        = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_6999_nat__le__0,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 11.11/6.19       => ( ( nat2 @ Z )
% 11.11/6.19          = zero_zero_nat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7000_zless__nat__conj,axiom,
% 11.11/6.19      ! [W: int,Z: int] :
% 11.11/6.19        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 11.11/6.19        = ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.19          & ( ord_less_int @ W @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7001_log__eq__one,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( log @ A @ A )
% 11.11/6.19            = one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7002_log__less__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19           => ( ( ord_less_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 11.11/6.19              = ( ord_less_real @ X4 @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7003_log__less__one__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ ( log @ A @ X4 ) @ one_one_real )
% 11.11/6.19            = ( ord_less_real @ X4 @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7004_one__less__log__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X4 ) )
% 11.11/6.19            = ( ord_less_real @ A @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7005_log__less__zero__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 11.11/6.19            = ( ord_less_real @ X4 @ one_one_real ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7006_zero__less__log__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 11.11/6.19            = ( ord_less_real @ one_one_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7007_int__nat__eq,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 11.11/6.19            = Z ) )
% 11.11/6.19        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 11.11/6.19            = zero_zero_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7008_zero__less__nat__eq,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 11.11/6.19        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7009_zero__le__log__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 11.11/6.19            = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7010_log__le__zero__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 11.11/6.19            = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7011_one__le__log__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X4 ) )
% 11.11/6.19            = ( ord_less_eq_real @ A @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7012_log__le__one__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ one_one_real )
% 11.11/6.19            = ( ord_less_eq_real @ X4 @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7013_log__le__cancel__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 11.11/6.19              = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7014_diff__nat__numeral,axiom,
% 11.11/6.19      ! [V: num,V3: num] :
% 11.11/6.19        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 11.11/6.19        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7015_and__nat__numerals_I3_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7016_and__nat__numerals_I1_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.19        = zero_zero_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7017_nat__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.19      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.19        ( ( ( nat2 @ Y )
% 11.11/6.19          = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 11.11/6.19        = ( Y
% 11.11/6.19          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7018_numeral__power__eq__nat__cancel__iff,axiom,
% 11.11/6.19      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.19        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 11.11/6.19          = ( nat2 @ Y ) )
% 11.11/6.19        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.19          = Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7019_one__less__nat__eq,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 11.11/6.19        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7020_real__sqrt__abs,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( sqrt @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = ( abs_abs_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7021_log__pow__cancel,axiom,
% 11.11/6.19      ! [A: real,B: nat] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 11.11/6.19            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7022_and__nat__numerals_I2_J,axiom,
% 11.11/6.19      ! [Y: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.19        = one_one_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7023_and__nat__numerals_I4_J,axiom,
% 11.11/6.19      ! [X4: num] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.19        = one_one_nat ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7024_real__sqrt__pow2,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7025_real__sqrt__pow2__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = X4 )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7026_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 11.11/6.19      ! [X4: real,Y: real,Xa: real,Ya: real] :
% 11.11/6.19        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7027_nat__numeral__diff__1,axiom,
% 11.11/6.19      ! [V: num] :
% 11.11/6.19        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 11.11/6.19        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7028_nat__less__numeral__power__cancel__iff,axiom,
% 11.11/6.19      ! [A: int,X4: num,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 11.11/6.19        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7029_numeral__power__less__nat__cancel__iff,axiom,
% 11.11/6.19      ! [X4: num,N2: nat,A: int] :
% 11.11/6.19        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 11.11/6.19        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7030_numeral__power__le__nat__cancel__iff,axiom,
% 11.11/6.19      ! [X4: num,N2: nat,A: int] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 11.11/6.19        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7031_nat__le__numeral__power__cancel__iff,axiom,
% 11.11/6.19      ! [A: int,X4: num,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 11.11/6.19        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7032_Suc__0__and__eq,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.19        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7033_and__Suc__0__eq,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.19        = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7034_nat__mask__eq,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.19        = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7035_and__nat__def,axiom,
% 11.11/6.19      ( bit_se727722235901077358nd_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7036_real__sqrt__less__mono,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.19       => ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7037_real__sqrt__le__mono,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19       => ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7038_real__sqrt__power,axiom,
% 11.11/6.19      ! [X4: real,K: nat] :
% 11.11/6.19        ( ( sqrt @ ( power_power_real @ X4 @ K ) )
% 11.11/6.19        = ( power_power_real @ ( sqrt @ X4 ) @ K ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7039_real__sqrt__gt__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7040_real__sqrt__eq__zero__cancel,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ( sqrt @ X4 )
% 11.11/6.19            = zero_zero_real )
% 11.11/6.19         => ( X4 = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7041_real__sqrt__ge__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7042_real__sqrt__ge__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7043_nat__numeral__as__int,axiom,
% 11.11/6.19      ( numeral_numeral_nat
% 11.11/6.19      = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7044_nat__mono,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ X4 @ Y )
% 11.11/6.19       => ( ord_less_eq_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7045_ex__nat,axiom,
% 11.11/6.19      ( ( ^ [P3: nat > $o] :
% 11.11/6.19          ? [X6: nat] : ( P3 @ X6 ) )
% 11.11/6.19      = ( ^ [P4: nat > $o] :
% 11.11/6.19          ? [X: int] :
% 11.11/6.19            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 11.11/6.19            & ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7046_all__nat,axiom,
% 11.11/6.19      ( ( ^ [P3: nat > $o] :
% 11.11/6.19          ! [X6: nat] : ( P3 @ X6 ) )
% 11.11/6.19      = ( ^ [P4: nat > $o] :
% 11.11/6.19          ! [X: int] :
% 11.11/6.19            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 11.11/6.19           => ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7047_eq__nat__nat__iff,axiom,
% 11.11/6.19      ! [Z: int,Z6: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 11.11/6.19         => ( ( ( nat2 @ Z )
% 11.11/6.19              = ( nat2 @ Z6 ) )
% 11.11/6.19            = ( Z = Z6 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7048_nat__one__as__int,axiom,
% 11.11/6.19      ( one_one_nat
% 11.11/6.19      = ( nat2 @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7049_pi__not__less__zero,axiom,
% 11.11/6.19      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7050_pi__gt__zero,axiom,
% 11.11/6.19      ord_less_real @ zero_zero_real @ pi ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7051_pi__ge__zero,axiom,
% 11.11/6.19      ord_less_eq_real @ zero_zero_real @ pi ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7052_unset__bit__nat__def,axiom,
% 11.11/6.19      ( bit_se4205575877204974255it_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7053_real__div__sqrt,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( divide_divide_real @ X4 @ ( sqrt @ X4 ) )
% 11.11/6.19          = ( sqrt @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7054_sqrt__add__le__add__sqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7055_le__real__sqrt__sumsq,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7056_nat__mono__iff,axiom,
% 11.11/6.19      ! [Z: int,W: int] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 11.11/6.19          = ( ord_less_int @ W @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7057_zless__nat__eq__int__zless,axiom,
% 11.11/6.19      ! [M: nat,Z: int] :
% 11.11/6.19        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 11.11/6.19        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7058_nat__le__iff,axiom,
% 11.11/6.19      ! [X4: int,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( nat2 @ X4 ) @ N2 )
% 11.11/6.19        = ( ord_less_eq_int @ X4 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7059_nat__0__le,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 11.11/6.19          = Z ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7060_int__eq__iff,axiom,
% 11.11/6.19      ! [M: nat,Z: int] :
% 11.11/6.19        ( ( ( semiri1314217659103216013at_int @ M )
% 11.11/6.19          = Z )
% 11.11/6.19        = ( ( M
% 11.11/6.19            = ( nat2 @ Z ) )
% 11.11/6.19          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7061_nat__int__add,axiom,
% 11.11/6.19      ! [A: nat,B: nat] :
% 11.11/6.19        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 11.11/6.19        = ( plus_plus_nat @ A @ B ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7062_log__ln,axiom,
% 11.11/6.19      ( ln_ln_real
% 11.11/6.19      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7063_xor__nat__def,axiom,
% 11.11/6.19      ( bit_se6528837805403552850or_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7064_sqrt2__less__2,axiom,
% 11.11/6.19      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7065_sgn__real__def,axiom,
% 11.11/6.19      ( sgn_sgn_real
% 11.11/6.19      = ( ^ [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 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7066_log__base__change,axiom,
% 11.11/6.19      ! [A: real,B: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( log @ B @ X4 )
% 11.11/6.19            = ( divide_divide_real @ ( log @ A @ X4 ) @ ( log @ A @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7067_less__log__of__power,axiom,
% 11.11/6.19      ! [B: real,N2: nat,M: real] :
% 11.11/6.19        ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7068_log__of__power__eq,axiom,
% 11.11/6.19      ! [M: nat,B: real,N2: nat] :
% 11.11/6.19        ( ( ( semiri5074537144036343181t_real @ M )
% 11.11/6.19          = ( power_power_real @ B @ N2 ) )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ( semiri5074537144036343181t_real @ N2 )
% 11.11/6.19            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7069_nat__less__eq__zless,axiom,
% 11.11/6.19      ! [W: int,Z: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 11.11/6.19          = ( ord_less_int @ W @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7070_nat__le__eq__zle,axiom,
% 11.11/6.19      ! [W: int,Z: int] :
% 11.11/6.19        ( ( ( ord_less_int @ zero_zero_int @ W )
% 11.11/6.19          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 11.11/6.19       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 11.11/6.19          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7071_nat__eq__iff,axiom,
% 11.11/6.19      ! [W: int,M: nat] :
% 11.11/6.19        ( ( ( nat2 @ W )
% 11.11/6.19          = M )
% 11.11/6.19        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19           => ( W
% 11.11/6.19              = ( semiri1314217659103216013at_int @ M ) ) )
% 11.11/6.19          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19           => ( M = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7072_nat__eq__iff2,axiom,
% 11.11/6.19      ! [M: nat,W: int] :
% 11.11/6.19        ( ( M
% 11.11/6.19          = ( nat2 @ W ) )
% 11.11/6.19        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19           => ( W
% 11.11/6.19              = ( semiri1314217659103216013at_int @ M ) ) )
% 11.11/6.19          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19           => ( M = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7073_split__nat,axiom,
% 11.11/6.19      ! [P: nat > $o,I2: int] :
% 11.11/6.19        ( ( P @ ( nat2 @ I2 ) )
% 11.11/6.19        = ( ! [N: nat] :
% 11.11/6.19              ( ( I2
% 11.11/6.19                = ( semiri1314217659103216013at_int @ N ) )
% 11.11/6.19             => ( P @ N ) )
% 11.11/6.19          & ( ( ord_less_int @ I2 @ zero_zero_int )
% 11.11/6.19           => ( P @ zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7074_le__nat__iff,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19       => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 11.11/6.19          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7075_nat__add__distrib,axiom,
% 11.11/6.19      ! [Z: int,Z6: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 11.11/6.19         => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 11.11/6.19            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7076_nat__mult__distrib,axiom,
% 11.11/6.19      ! [Z: int,Z6: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 11.11/6.19          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7077_Suc__as__int,axiom,
% 11.11/6.19      ( suc
% 11.11/6.19      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7078_nat__diff__distrib_H,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19         => ( ( nat2 @ ( minus_minus_int @ X4 @ Y ) )
% 11.11/6.19            = ( minus_minus_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7079_nat__diff__distrib,axiom,
% 11.11/6.19      ! [Z6: int,Z: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 11.11/6.19       => ( ( ord_less_eq_int @ Z6 @ Z )
% 11.11/6.19         => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 11.11/6.19            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7080_nat__abs__triangle__ineq,axiom,
% 11.11/6.19      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7081_nat__div__distrib,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.19       => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 11.11/6.19          = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7082_nat__div__distrib_H,axiom,
% 11.11/6.19      ! [Y: int,X4: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19       => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 11.11/6.19          = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7083_nat__power__eq,axiom,
% 11.11/6.19      ! [Z: int,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 11.11/6.19          = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7084_nat__mod__distrib,axiom,
% 11.11/6.19      ! [X4: int,Y: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.19         => ( ( nat2 @ ( modulo_modulo_int @ X4 @ Y ) )
% 11.11/6.19            = ( modulo_modulo_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7085_pi__less__4,axiom,
% 11.11/6.19      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7086_pi__ge__two,axiom,
% 11.11/6.19      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7087_div__abs__eq__div__nat,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 11.11/6.19        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7088_pi__half__neq__two,axiom,
% 11.11/6.19      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7089_mod__abs__eq__div__nat,axiom,
% 11.11/6.19      ! [K: int,L: int] :
% 11.11/6.19        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 11.11/6.19        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7090_take__bit__nat__eq,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19       => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 11.11/6.19          = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7091_nat__take__bit__eq,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 11.11/6.19          = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7092_arctan__inverse,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( X4 != zero_zero_real )
% 11.11/6.19       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X4 ) )
% 11.11/6.19          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X4 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7093_bit__nat__iff,axiom,
% 11.11/6.19      ! [K: int,N2: nat] :
% 11.11/6.19        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 11.11/6.19        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19          & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7094_real__less__rsqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 11.11/6.19       => ( ord_less_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7095_sqrt__le__D,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y )
% 11.11/6.19       => ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7096_real__le__rsqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 11.11/6.19       => ( ord_less_eq_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7097_nat__2,axiom,
% 11.11/6.19      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.19      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7098_log__mult,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19           => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19             => ( ( log @ A @ ( times_times_real @ X4 @ Y ) )
% 11.11/6.19                = ( plus_plus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7099_sgn__power__injE,axiom,
% 11.11/6.19      ! [A: real,N2: nat,X4: real,B: real] :
% 11.11/6.19        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 11.11/6.19          = X4 )
% 11.11/6.19       => ( ( X4
% 11.11/6.19            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 11.11/6.19         => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.19           => ( A = B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7100_log__divide,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19           => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19             => ( ( log @ A @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.19                = ( minus_minus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7101_le__log__of__power,axiom,
% 11.11/6.19      ! [B: real,N2: nat,M: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7102_log__base__pow,axiom,
% 11.11/6.19      ! [A: real,N2: nat,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( log @ ( power_power_real @ A @ N2 ) @ X4 )
% 11.11/6.19          = ( divide_divide_real @ ( log @ A @ X4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7103_log__nat__power,axiom,
% 11.11/6.19      ! [X4: real,B: real,N2: nat] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( log @ B @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.19          = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7104_Suc__nat__eq__nat__zadd1,axiom,
% 11.11/6.19      ! [Z: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19       => ( ( suc @ ( nat2 @ Z ) )
% 11.11/6.19          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7105_nat__less__iff,axiom,
% 11.11/6.19      ! [W: int,M: nat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 11.11/6.19       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 11.11/6.19          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7106_nat__mult__distrib__neg,axiom,
% 11.11/6.19      ! [Z: int,Z6: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 11.11/6.19       => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 11.11/6.19          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7107_nat__abs__int__diff,axiom,
% 11.11/6.19      ! [A: nat,B: nat] :
% 11.11/6.19        ( ( ( ord_less_eq_nat @ A @ B )
% 11.11/6.19         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 11.11/6.19            = ( minus_minus_nat @ B @ A ) ) )
% 11.11/6.19        & ( ~ ( ord_less_eq_nat @ A @ B )
% 11.11/6.19         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 11.11/6.19            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7108_pi__half__neq__zero,axiom,
% 11.11/6.19      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19     != zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7109_pi__half__less__two,axiom,
% 11.11/6.19      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7110_pi__half__le__two,axiom,
% 11.11/6.19      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7111_real__le__lsqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19           => ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7112_real__sqrt__unique,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19          = X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( sqrt @ X4 )
% 11.11/6.19            = Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7113_lemma__real__divide__sqrt__less,axiom,
% 11.11/6.19      ! [U: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ U )
% 11.11/6.19       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7114_real__sqrt__sum__squares__eq__cancel,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19          = X4 )
% 11.11/6.19       => ( Y = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7115_real__sqrt__sum__squares__eq__cancel2,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19          = Y )
% 11.11/6.19       => ( X4 = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7116_real__sqrt__sum__squares__ge1,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7117_real__sqrt__sum__squares__ge2,axiom,
% 11.11/6.19      ! [Y: real,X4: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7118_real__sqrt__sum__squares__triangle__ineq,axiom,
% 11.11/6.19      ! [A: real,C: real,B: real,D: 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 @ D ) @ ( 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 @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7119_sqrt__ge__absD,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ Y ) )
% 11.11/6.19       => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7120_log__of__power__less,axiom,
% 11.11/6.19      ! [M: nat,B: real,N2: nat] :
% 11.11/6.19        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7121_log2__of__power__eq,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( M
% 11.11/6.19          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19       => ( ( semiri5074537144036343181t_real @ N2 )
% 11.11/6.19          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7122_log__eq__div__ln__mult__log,axiom,
% 11.11/6.19      ! [A: real,B: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.19           => ( ( B != one_one_real )
% 11.11/6.19             => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19               => ( ( log @ A @ X4 )
% 11.11/6.19                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X4 ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7123_nat__dvd__iff,axiom,
% 11.11/6.19      ! [Z: int,M: nat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 11.11/6.19        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 11.11/6.19          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.19           => ( M = zero_zero_nat ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7124_pi__half__gt__zero,axiom,
% 11.11/6.19      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7125_pi__half__ge__zero,axiom,
% 11.11/6.19      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7126_m2pi__less__pi,axiom,
% 11.11/6.19      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7127_arctan__ubound,axiom,
% 11.11/6.19      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7128_arctan__one,axiom,
% 11.11/6.19      ( ( arctan @ one_one_real )
% 11.11/6.19      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7129_real__less__lsqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( ord_less_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19           => ( ord_less_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7130_sqrt__sum__squares__le__sum,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7131_log__of__power__le,axiom,
% 11.11/6.19      ! [M: nat,B: real,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7132_sqrt__sum__squares__le__sum__abs,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7133_real__sqrt__ge__abs2,axiom,
% 11.11/6.19      ! [Y: real,X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7134_real__sqrt__ge__abs1,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7135_ln__sqrt,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ln_ln_real @ ( sqrt @ X4 ) )
% 11.11/6.19          = ( divide_divide_real @ ( ln_ln_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7136_sqrt__even__pow2,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7137_minus__pi__half__less__zero,axiom,
% 11.11/6.19      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7138_arctan__bounded,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 11.11/6.19        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7139_arctan__lbound,axiom,
% 11.11/6.19      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7140_and__nat__unfold,axiom,
% 11.11/6.19      ( bit_se727722235901077358nd_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] :
% 11.11/6.19            ( if_nat
% 11.11/6.19            @ ( ( M6 = zero_zero_nat )
% 11.11/6.19              | ( N = zero_zero_nat ) )
% 11.11/6.19            @ zero_zero_nat
% 11.11/6.19            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7141_arsinh__real__aux,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7142_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 11.11/6.19      ! [X4: real,Y: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7143_real__sqrt__power__even,axiom,
% 11.11/6.19      ! [N2: nat,X4: real] :
% 11.11/6.19        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( power_power_real @ ( sqrt @ X4 ) @ N2 )
% 11.11/6.19            = ( power_power_real @ X4 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7144_arith__geo__mean__sqrt,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X4 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7145_less__log2__of__power,axiom,
% 11.11/6.19      ! [N2: nat,M: nat] :
% 11.11/6.19        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 11.11/6.19       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7146_le__log2__of__power,axiom,
% 11.11/6.19      ! [N2: nat,M: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 11.11/6.19       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7147_and__nat__rec,axiom,
% 11.11/6.19      ( bit_se727722235901077358nd_nat
% 11.11/6.19      = ( ^ [M6: nat,N: nat] :
% 11.11/6.19            ( plus_plus_nat
% 11.11/6.19            @ ( zero_n2687167440665602831ol_nat
% 11.11/6.19              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 11.11/6.19                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.19            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7148_even__nat__iff,axiom,
% 11.11/6.19      ! [K: int] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.19       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 11.11/6.19          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7149_log2__of__power__less,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7150_cos__x__y__le__one,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7151_real__sqrt__sum__squares__less,axiom,
% 11.11/6.19      ! [X4: real,U: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7152_arcosh__real__def,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ( arcosh_real @ X4 )
% 11.11/6.19          = ( ln_ln_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7153_sqrt__sum__squares__half__less,axiom,
% 11.11/6.19      ! [X4: real,U: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ X4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7154_log2__of__power__le,axiom,
% 11.11/6.19      ! [M: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.19       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.19         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7155_machin__Euler,axiom,
% 11.11/6.19      ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7156_sin__cos__npi,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7157_ceiling__log__nat__eq__powr__iff,axiom,
% 11.11/6.19      ! [B: nat,K: nat,N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.19       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.19         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 11.11/6.19              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 11.11/6.19            = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 11.11/6.19              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7158_arsinh__real__def,axiom,
% 11.11/6.19      ( arsinh_real
% 11.11/6.19      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7159_cos__pi__eq__zero,axiom,
% 11.11/6.19      ! [M: nat] :
% 11.11/6.19        ( ( 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 ) ) ) )
% 11.11/6.19        = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7160_ceiling__log__nat__eq__if,axiom,
% 11.11/6.19      ! [B: nat,N2: nat,K: nat] :
% 11.11/6.19        ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 11.11/6.19       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 11.11/6.19         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.19           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 11.11/6.19              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7161_ceiling__log2__div2,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.19          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7162_cos__zero,axiom,
% 11.11/6.19      ( ( cos_complex @ zero_zero_complex )
% 11.11/6.19      = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7163_cos__zero,axiom,
% 11.11/6.19      ( ( cos_real @ zero_zero_real )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7164_ceiling__numeral,axiom,
% 11.11/6.19      ! [V: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 11.11/6.19        = ( numeral_numeral_int @ V ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7165_ceiling__one,axiom,
% 11.11/6.19      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 11.11/6.19      = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7166_ceiling__one,axiom,
% 11.11/6.19      ( ( archim7802044766580827645g_real @ one_one_real )
% 11.11/6.19      = one_one_int ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7167_cos__pi,axiom,
% 11.11/6.19      ( ( cos_real @ pi )
% 11.11/6.19      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7168_sin__cos__squared__add3,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ X4 ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ X4 ) ) )
% 11.11/6.19        = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7169_sin__cos__squared__add3,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ X4 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ X4 ) ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7170_ceiling__le__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7171_ceiling__le__zero,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7172_zero__less__ceiling,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7173_zero__less__ceiling,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7174_ceiling__le__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7175_ceiling__le__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7176_ceiling__less__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7177_ceiling__less__one,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7178_one__le__ceiling,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7179_one__le__ceiling,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7180_numeral__less__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7181_numeral__less__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: real] :
% 11.11/6.19        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7182_ceiling__le__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7183_ceiling__le__one,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7184_one__less__ceiling,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ one_one_rat @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7185_one__less__ceiling,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ one_one_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7186_ceiling__add__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 11.11/6.19        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7187_ceiling__add__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 11.11/6.19        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7188_ceiling__neg__numeral,axiom,
% 11.11/6.19      ! [V: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7189_ceiling__neg__numeral,axiom,
% 11.11/6.19      ! [V: num] :
% 11.11/6.19        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7190_ceiling__add__one,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 11.11/6.19        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7191_ceiling__add__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 11.11/6.19        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7192_ceiling__diff__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 11.11/6.19        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7193_ceiling__diff__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 11.11/6.19        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7194_ceiling__diff__one,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 11.11/6.19        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7195_ceiling__diff__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 11.11/6.19        = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7196_ceiling__numeral__power,axiom,
% 11.11/6.19      ! [X4: num,N2: nat] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.19        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7197_nat__ceiling__le__eq,axiom,
% 11.11/6.19      ! [X4: real,A: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) @ A )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7198_ceiling__less__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7199_ceiling__less__zero,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7200_zero__le__ceiling,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7201_zero__le__ceiling,axiom,
% 11.11/6.19      ! [X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7202_ceiling__divide__eq__div__numeral,axiom,
% 11.11/6.19      ! [A: num,B: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7203_ceiling__less__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7204_ceiling__less__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7205_numeral__le__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7206_numeral__le__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7207_ceiling__le__neg__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7208_ceiling__le__neg__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7209_neg__numeral__less__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: real] :
% 11.11/6.19        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7210_neg__numeral__less__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: rat] :
% 11.11/6.19        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7211_cos__pi__half,axiom,
% 11.11/6.19      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19      = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7212_sin__two__pi,axiom,
% 11.11/6.19      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19      = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7213_sin__pi__half,axiom,
% 11.11/6.19      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7214_cos__two__pi,axiom,
% 11.11/6.19      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19      = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7215_cos__periodic,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( cos_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 11.11/6.19        = ( cos_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7216_sin__periodic,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( sin_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 11.11/6.19        = ( sin_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7217_cos__2pi__minus,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 11.11/6.19        = ( cos_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7218_cos__npi,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 11.11/6.19        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7219_cos__npi2,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.19        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7220_ceiling__minus__divide__eq__div__numeral,axiom,
% 11.11/6.19      ! [A: num,B: num] :
% 11.11/6.19        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 11.11/6.19        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7221_sin__cos__squared__add2,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7222_sin__cos__squared__add2,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7223_sin__cos__squared__add,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7224_sin__cos__squared__add,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = one_one_complex ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7225_sin__2npi,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 11.11/6.19        = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7226_cos__2npi,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7227_sin__2pi__minus,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 11.11/6.19        = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7228_ceiling__less__neg__numeral,axiom,
% 11.11/6.19      ! [X4: real,V: num] :
% 11.11/6.19        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.19        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7229_ceiling__less__neg__numeral,axiom,
% 11.11/6.19      ! [X4: rat,V: num] :
% 11.11/6.19        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.19        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7230_neg__numeral__le__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.19        = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7231_neg__numeral__le__ceiling,axiom,
% 11.11/6.19      ! [V: num,X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.19        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7232_cos__3over2__pi,axiom,
% 11.11/6.19      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 11.11/6.19      = zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7233_sin__3over2__pi,axiom,
% 11.11/6.19      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 11.11/6.19      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7234_cos__one__sin__zero,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( ( cos_complex @ X4 )
% 11.11/6.19          = one_one_complex )
% 11.11/6.19       => ( ( sin_complex @ X4 )
% 11.11/6.19          = zero_zero_complex ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7235_cos__one__sin__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( cos_real @ X4 )
% 11.11/6.19          = one_one_real )
% 11.11/6.19       => ( ( sin_real @ X4 )
% 11.11/6.19          = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7236_sin__add,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.19        = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7237_sin__add,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( sin_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.19        = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7238_cos__diff,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 11.11/6.19        = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7239_cos__diff,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 11.11/6.19        = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7240_cos__add,axiom,
% 11.11/6.19      ! [X4: complex,Y: complex] :
% 11.11/6.19        ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.19        = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7241_cos__add,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.19        = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7242_sin__zero__norm__cos__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( sin_real @ X4 )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19       => ( ( real_V7735802525324610683m_real @ ( cos_real @ X4 ) )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7243_sin__zero__norm__cos__one,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( ( sin_complex @ X4 )
% 11.11/6.19          = zero_zero_complex )
% 11.11/6.19       => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X4 ) )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7244_sin__zero__abs__cos__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( sin_real @ X4 )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19       => ( ( abs_abs_real @ ( cos_real @ X4 ) )
% 11.11/6.19          = one_one_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7245_sin__double,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X4 ) ) @ ( cos_complex @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7246_sin__double,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X4 ) ) @ ( cos_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7247_sincos__principal__value,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19      ? [Y3: real] :
% 11.11/6.19        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 11.11/6.19        & ( ord_less_eq_real @ Y3 @ pi )
% 11.11/6.19        & ( ( sin_real @ Y3 )
% 11.11/6.19          = ( sin_real @ X4 ) )
% 11.11/6.19        & ( ( cos_real @ Y3 )
% 11.11/6.19          = ( cos_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7248_ceiling__mono,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.19       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7249_ceiling__mono,axiom,
% 11.11/6.19      ! [Y: rat,X4: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ Y @ X4 )
% 11.11/6.19       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7250_sin__x__le__x,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ ( sin_real @ X4 ) @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7251_ceiling__less__cancel,axiom,
% 11.11/6.19      ! [X4: rat,Y: rat] :
% 11.11/6.19        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 11.11/6.19       => ( ord_less_rat @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7252_ceiling__less__cancel,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) )
% 11.11/6.19       => ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7253_sin__le__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( sin_real @ X4 ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7254_cos__le__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( cos_real @ X4 ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7255_abs__sin__x__le__abs__x,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ ( abs_abs_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7256_sin__cos__le1,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7257_sin__squared__eq,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7258_sin__squared__eq,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7259_cos__squared__eq,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7260_cos__squared__eq,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.19        = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7261_of__nat__ceiling,axiom,
% 11.11/6.19      ! [R3: real] : ( ord_less_eq_real @ R3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7262_of__nat__ceiling,axiom,
% 11.11/6.19      ! [R3: rat] : ( ord_less_eq_rat @ R3 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7263_sin__gt__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ pi )
% 11.11/6.19         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7264_sin__x__ge__neg__x,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ ( sin_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7265_sin__ge__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7266_ceiling__add__le,axiom,
% 11.11/6.19      ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7267_ceiling__add__le,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7268_real__nat__ceiling__ge,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7269_sin__ge__minus__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7270_cos__inj__pi,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ pi )
% 11.11/6.19             => ( ( ( cos_real @ X4 )
% 11.11/6.19                  = ( cos_real @ Y ) )
% 11.11/6.19               => ( X4 = Y ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7271_cos__mono__le__eq,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ pi )
% 11.11/6.19             => ( ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 11.11/6.19                = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7272_cos__monotone__0__pi__le,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19           => ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7273_cos__ge__minus__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7274_abs__sin__le__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7275_abs__cos__le__one,axiom,
% 11.11/6.19      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X4 ) ) @ one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7276_sin__times__sin,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7277_sin__times__sin,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7278_sin__times__cos,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7279_sin__times__cos,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7280_cos__times__sin,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7281_cos__times__sin,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7282_sin__plus__sin,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7283_sin__plus__sin,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7284_sin__diff__sin,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7285_sin__diff__sin,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7286_cos__diff__cos,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7287_cos__diff__cos,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7288_cos__double,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7289_cos__double,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7290_cos__double__sin,axiom,
% 11.11/6.19      ! [W: complex] :
% 11.11/6.19        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 11.11/6.19        = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7291_cos__double__sin,axiom,
% 11.11/6.19      ! [W: real] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7292_cos__two__neq__zero,axiom,
% 11.11/6.19      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19     != zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7293_cos__monotone__0__pi,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19       => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19           => ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7294_cos__mono__less__eq,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.19         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ pi )
% 11.11/6.19             => ( ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 11.11/6.19                = ( ord_less_real @ Y @ X4 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7295_sin__eq__0__pi,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ pi )
% 11.11/6.19         => ( ( ( sin_real @ X4 )
% 11.11/6.19              = zero_zero_real )
% 11.11/6.19           => ( X4 = zero_zero_real ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7296_sin__zero__pi__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ pi )
% 11.11/6.19       => ( ( ( sin_real @ X4 )
% 11.11/6.19            = zero_zero_real )
% 11.11/6.19          = ( X4 = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7297_cos__monotone__minus__pi__0_H,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.19           => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7298_sincos__total__pi,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19       => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19            = one_one_real )
% 11.11/6.19         => ? [T3: real] :
% 11.11/6.19              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.19              & ( ord_less_eq_real @ T3 @ pi )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( cos_real @ T3 ) )
% 11.11/6.19              & ( Y
% 11.11/6.19                = ( sin_real @ T3 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7299_sin__cos__sqrt,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) )
% 11.11/6.19       => ( ( sin_real @ X4 )
% 11.11/6.19          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7300_sin__expansion__lemma,axiom,
% 11.11/6.19      ! [X4: real,M: nat] :
% 11.11/6.19        ( ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19        = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7301_cos__expansion__lemma,axiom,
% 11.11/6.19      ! [X4: real,M: nat] :
% 11.11/6.19        ( ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7302_mult__ceiling__le,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.19         => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7303_mult__ceiling__le,axiom,
% 11.11/6.19      ! [A: rat,B: rat] :
% 11.11/6.19        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.19       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.19         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7304_sin__gt__zero__02,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7305_cos__two__less__zero,axiom,
% 11.11/6.19      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7306_cos__is__zero,axiom,
% 11.11/6.19      ? [X5: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 11.11/6.19        & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19        & ( ( cos_real @ X5 )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19        & ! [Y4: real] :
% 11.11/6.19            ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 11.11/6.19              & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19              & ( ( cos_real @ Y4 )
% 11.11/6.19                = zero_zero_real ) )
% 11.11/6.19           => ( Y4 = X5 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7307_cos__two__le__zero,axiom,
% 11.11/6.19      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7308_cos__monotone__minus__pi__0,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 11.11/6.19       => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.19           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7309_cos__total,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.19         => ? [X5: real] :
% 11.11/6.19              ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 11.11/6.19              & ( ord_less_eq_real @ X5 @ pi )
% 11.11/6.19              & ( ( cos_real @ X5 )
% 11.11/6.19                = Y )
% 11.11/6.19              & ! [Y4: real] :
% 11.11/6.19                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 11.11/6.19                    & ( ord_less_eq_real @ Y4 @ pi )
% 11.11/6.19                    & ( ( cos_real @ Y4 )
% 11.11/6.19                      = Y ) )
% 11.11/6.19                 => ( Y4 = X5 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7310_sincos__total__pi__half,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19              = one_one_real )
% 11.11/6.19           => ? [T3: real] :
% 11.11/6.19                ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.19                & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19                & ( X4
% 11.11/6.19                  = ( cos_real @ T3 ) )
% 11.11/6.19                & ( Y
% 11.11/6.19                  = ( sin_real @ T3 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7311_sincos__total__2pi__le,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = one_one_real )
% 11.11/6.19       => ? [T3: real] :
% 11.11/6.19            ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.19            & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19            & ( X4
% 11.11/6.19              = ( cos_real @ T3 ) )
% 11.11/6.19            & ( Y
% 11.11/6.19              = ( sin_real @ T3 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7312_sincos__total__2pi,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.19          = one_one_real )
% 11.11/6.19       => ~ ! [T3: real] :
% 11.11/6.19              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.19             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19               => ( ( X4
% 11.11/6.19                    = ( cos_real @ T3 ) )
% 11.11/6.19                 => ( Y
% 11.11/6.19                   != ( sin_real @ T3 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7313_sin__pi__divide__n__ge__0,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( N2 != zero_zero_nat )
% 11.11/6.19       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7314_sin__45,axiom,
% 11.11/6.19      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7315_cos__45,axiom,
% 11.11/6.19      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7316_cos__times__cos,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7317_cos__times__cos,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 11.11/6.19        = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7318_cos__plus__cos,axiom,
% 11.11/6.19      ! [W: real,Z: real] :
% 11.11/6.19        ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7319_cos__plus__cos,axiom,
% 11.11/6.19      ! [W: complex,Z: complex] :
% 11.11/6.19        ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 11.11/6.19        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7320_sin__gt__zero2,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7321_sin__lt__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ pi @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19         => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7322_cos__double__less__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.19         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7323_sin__30,axiom,
% 11.11/6.19      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7324_cos__gt__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7325_sin__inj__pi,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19             => ( ( ( sin_real @ X4 )
% 11.11/6.19                  = ( sin_real @ Y ) )
% 11.11/6.19               => ( X4 = Y ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7326_sin__mono__le__eq,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19             => ( ( ord_less_eq_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 11.11/6.19                = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7327_sin__monotone__2pi__le,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19           => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7328_cos__60,axiom,
% 11.11/6.19      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7329_sin__60,axiom,
% 11.11/6.19      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7330_cos__30,axiom,
% 11.11/6.19      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 11.11/6.19      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7331_cos__double__cos,axiom,
% 11.11/6.19      ! [W: complex] :
% 11.11/6.19        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 11.11/6.19        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7332_cos__double__cos,axiom,
% 11.11/6.19      ! [W: real] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 11.11/6.19        = ( 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 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7333_cos__treble__cos,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7334_cos__treble__cos,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X4 ) )
% 11.11/6.19        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7335_sin__le__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ pi @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19         => ( ord_less_eq_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7336_sin__less__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.19         => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7337_sin__mono__less__eq,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.19           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19             => ( ( ord_less_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 11.11/6.19                = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7338_sin__monotone__2pi,axiom,
% 11.11/6.19      ! [Y: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.19       => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7339_sin__total,axiom,
% 11.11/6.19      ! [Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.19       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.19         => ? [X5: real] :
% 11.11/6.19              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 11.11/6.19              & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19              & ( ( sin_real @ X5 )
% 11.11/6.19                = Y )
% 11.11/6.19              & ! [Y4: real] :
% 11.11/6.19                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 11.11/6.19                    & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19                    & ( ( sin_real @ Y4 )
% 11.11/6.19                      = Y ) )
% 11.11/6.19                 => ( Y4 = X5 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7340_cos__gt__zero__pi,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7341_cos__ge__zero,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7342_cos__one__2pi,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( cos_real @ X4 )
% 11.11/6.19          = one_one_real )
% 11.11/6.19        = ( ? [X: nat] :
% 11.11/6.19              ( X4
% 11.11/6.19              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 11.11/6.19          | ? [X: nat] :
% 11.11/6.19              ( X4
% 11.11/6.19              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7343_sin__pi__divide__n__gt__0,axiom,
% 11.11/6.19      ! [N2: nat] :
% 11.11/6.19        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.19       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7344_sin__arctan,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( sin_real @ ( arctan @ X4 ) )
% 11.11/6.19        = ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7345_cos__arctan,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( cos_real @ ( arctan @ X4 ) )
% 11.11/6.19        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7346_sin__zero__lemma,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ( sin_real @ X4 )
% 11.11/6.19            = zero_zero_real )
% 11.11/6.19         => ? [N3: nat] :
% 11.11/6.19              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7347_sin__zero__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( sin_real @ X4 )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19        = ( ? [N: nat] :
% 11.11/6.19              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.19          | ? [N: nat] :
% 11.11/6.19              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7348_cos__zero__lemma,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ( cos_real @ X4 )
% 11.11/6.19            = zero_zero_real )
% 11.11/6.19         => ? [N3: nat] :
% 11.11/6.19              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7349_cos__zero__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( cos_real @ X4 )
% 11.11/6.19          = zero_zero_real )
% 11.11/6.19        = ( ? [N: nat] :
% 11.11/6.19              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.19          | ? [N: nat] :
% 11.11/6.19              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 11.11/6.19              & ( X4
% 11.11/6.19                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7350_tan__double,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( cos_real @ X4 )
% 11.11/6.19         != zero_zero_real )
% 11.11/6.19       => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19           != zero_zero_real )
% 11.11/6.19         => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19            = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X4 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7351_tan__double,axiom,
% 11.11/6.19      ! [X4: complex] :
% 11.11/6.19        ( ( ( cos_complex @ X4 )
% 11.11/6.19         != zero_zero_complex )
% 11.11/6.19       => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19           != zero_zero_complex )
% 11.11/6.19         => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.19            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7352_sin__tan,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( ( sin_real @ X4 )
% 11.11/6.19          = ( divide_divide_real @ ( tan_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7353_cos__tan,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19       => ( ( cos_real @ X4 )
% 11.11/6.19          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7354_complex__unimodular__polar,axiom,
% 11.11/6.19      ! [Z: complex] :
% 11.11/6.19        ( ( ( real_V1022390504157884413omplex @ Z )
% 11.11/6.19          = one_one_real )
% 11.11/6.19       => ~ ! [T3: real] :
% 11.11/6.19              ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.19             => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.19               => ( Z
% 11.11/6.19                 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7355_ceiling__log__eq__powr__iff,axiom,
% 11.11/6.19      ! [X4: real,B: real,K: nat] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X4 ) )
% 11.11/6.19              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 11.11/6.19            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X4 )
% 11.11/6.19              & ( ord_less_eq_real @ X4 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7356_powr__one__eq__one,axiom,
% 11.11/6.19      ! [A: real] :
% 11.11/6.19        ( ( powr_real @ one_one_real @ A )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7357_powr__zero__eq__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( X4 = zero_zero_real )
% 11.11/6.19         => ( ( powr_real @ X4 @ zero_zero_real )
% 11.11/6.19            = zero_zero_real ) )
% 11.11/6.19        & ( ( X4 != zero_zero_real )
% 11.11/6.19         => ( ( powr_real @ X4 @ zero_zero_real )
% 11.11/6.19            = one_one_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7358_powr__gt__zero,axiom,
% 11.11/6.19      ! [X4: real,A: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X4 @ A ) )
% 11.11/6.19        = ( X4 != zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7359_powr__nonneg__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ ( powr_real @ A @ X4 ) @ zero_zero_real )
% 11.11/6.19        = ( A = zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7360_powr__less__cancel__iff,axiom,
% 11.11/6.19      ! [X4: real,A: real,B: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 11.11/6.19          = ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7361_powr__eq__one__iff,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ A )
% 11.11/6.19       => ( ( ( powr_real @ A @ X4 )
% 11.11/6.19            = one_one_real )
% 11.11/6.19          = ( X4 = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7362_powr__one__gt__zero__iff,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ( powr_real @ X4 @ one_one_real )
% 11.11/6.19          = X4 )
% 11.11/6.19        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7363_powr__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( powr_real @ X4 @ one_one_real )
% 11.11/6.19          = X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7364_powr__le__cancel__iff,axiom,
% 11.11/6.19      ! [X4: real,A: real,B: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 11.11/6.19          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7365_numeral__powr__numeral__real,axiom,
% 11.11/6.19      ! [M: num,N2: num] :
% 11.11/6.19        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.19        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7366_log__powr__cancel,axiom,
% 11.11/6.19      ! [A: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 11.11/6.19            = Y ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7367_powr__log__cancel,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19           => ( ( powr_real @ A @ ( log @ A @ X4 ) )
% 11.11/6.19              = X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7368_tan__periodic__n,axiom,
% 11.11/6.19      ! [X4: real,N2: num] :
% 11.11/6.19        ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 11.11/6.19        = ( tan_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7369_norm__cos__sin,axiom,
% 11.11/6.19      ! [T2: real] :
% 11.11/6.19        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T2 ) @ ( sin_real @ T2 ) ) )
% 11.11/6.19        = one_one_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7370_powr__numeral,axiom,
% 11.11/6.19      ! [X4: real,N2: num] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( powr_real @ X4 @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.19          = ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7371_tan__periodic,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 11.11/6.19        = ( tan_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7372_square__powr__half,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( powr_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.19        = ( abs_abs_real @ X4 ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7373_powr__non__neg,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ~ ( ord_less_real @ ( powr_real @ A @ X4 ) @ zero_zero_real ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7374_powr__less__mono2__neg,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.19           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7375_powr__ge__pzero,axiom,
% 11.11/6.19      ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X4 @ Y ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7376_powr__mono2,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19           => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7377_powr__less__cancel,axiom,
% 11.11/6.19      ! [X4: real,A: real,B: real] :
% 11.11/6.19        ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.19         => ( ord_less_real @ A @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7378_powr__less__mono,axiom,
% 11.11/6.19      ! [A: real,B: real,X4: real] :
% 11.11/6.19        ( ( ord_less_real @ A @ B )
% 11.11/6.19       => ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.19         => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7379_powr__mono,axiom,
% 11.11/6.19      ! [A: real,B: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.19       => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.19         => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7380_one__complex_Ocode,axiom,
% 11.11/6.19      ( one_one_complex
% 11.11/6.19      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7381_Complex__eq__1,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( ( complex2 @ A @ B )
% 11.11/6.19          = one_one_complex )
% 11.11/6.19        = ( ( A = one_one_real )
% 11.11/6.19          & ( B = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7382_Complex__eq__numeral,axiom,
% 11.11/6.19      ! [A: real,B: real,W: num] :
% 11.11/6.19        ( ( ( complex2 @ A @ B )
% 11.11/6.19          = ( numera6690914467698888265omplex @ W ) )
% 11.11/6.19        = ( ( A
% 11.11/6.19            = ( numeral_numeral_real @ W ) )
% 11.11/6.19          & ( B = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7383_powr__mono2_H,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7384_powr__less__mono2,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.19           => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7385_powr__inj,axiom,
% 11.11/6.19      ! [A: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( A != one_one_real )
% 11.11/6.19         => ( ( ( powr_real @ A @ X4 )
% 11.11/6.19              = ( powr_real @ A @ Y ) )
% 11.11/6.19            = ( X4 = Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7386_gr__one__powr,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ord_less_real @ one_one_real @ ( powr_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7387_ge__one__powr__ge__zero,axiom,
% 11.11/6.19      ! [X4: real,A: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.19         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7388_powr__mono__both,axiom,
% 11.11/6.19      ! [A: real,B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.19         => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.19           => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.19             => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7389_powr__le1,axiom,
% 11.11/6.19      ! [A: real,X4: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.19           => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ one_one_real ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7390_powr__divide,axiom,
% 11.11/6.19      ! [X4: real,Y: real,A: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( powr_real @ ( divide_divide_real @ X4 @ Y ) @ A )
% 11.11/6.19            = ( divide_divide_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7391_powr__mult,axiom,
% 11.11/6.19      ! [X4: real,Y: real,A: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.19         => ( ( powr_real @ ( times_times_real @ X4 @ Y ) @ A )
% 11.11/6.19            = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7392_Complex__eq__neg__1,axiom,
% 11.11/6.19      ! [A: real,B: real] :
% 11.11/6.19        ( ( ( complex2 @ A @ B )
% 11.11/6.19          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 11.11/6.19        = ( ( A
% 11.11/6.19            = ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.19          & ( B = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7393_Complex__eq__neg__numeral,axiom,
% 11.11/6.19      ! [A: real,B: real,W: num] :
% 11.11/6.19        ( ( ( complex2 @ A @ B )
% 11.11/6.19          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.19        = ( ( A
% 11.11/6.19            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.19          & ( B = zero_zero_real ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7394_powr__add,axiom,
% 11.11/6.19      ! [X4: real,A: real,B: real] :
% 11.11/6.19        ( ( powr_real @ X4 @ ( plus_plus_real @ A @ B ) )
% 11.11/6.19        = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7395_powr__diff,axiom,
% 11.11/6.19      ! [W: real,Z1: real,Z22: real] :
% 11.11/6.19        ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 11.11/6.19        = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7396_tan__def,axiom,
% 11.11/6.19      ( tan_real
% 11.11/6.19      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7397_tan__def,axiom,
% 11.11/6.19      ( tan_complex
% 11.11/6.19      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7398_powr__realpow,axiom,
% 11.11/6.19      ! [X4: real,N2: nat] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( powr_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 11.11/6.19          = ( power_power_real @ X4 @ N2 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7399_less__log__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ Y @ ( log @ B @ X4 ) )
% 11.11/6.19            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7400_log__less__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ ( log @ B @ X4 ) @ Y )
% 11.11/6.19            = ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7401_less__powr__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) )
% 11.11/6.19            = ( ord_less_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7402_powr__less__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 )
% 11.11/6.19            = ( ord_less_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7403_powr__minus__divide,axiom,
% 11.11/6.19      ! [X4: real,A: real] :
% 11.11/6.19        ( ( powr_real @ X4 @ ( uminus_uminus_real @ A ) )
% 11.11/6.19        = ( divide_divide_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7404_powr__neg__one,axiom,
% 11.11/6.19      ! [X4: real] :
% 11.11/6.19        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( powr_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.19          = ( divide_divide_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7405_powr__mult__base,axiom,
% 11.11/6.19      ! [X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.19       => ( ( times_times_real @ X4 @ ( powr_real @ X4 @ Y ) )
% 11.11/6.19          = ( powr_real @ X4 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7406_le__log__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) )
% 11.11/6.19            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7407_log__le__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y )
% 11.11/6.19            = ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7408_le__powr__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.19       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.19         => ( ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) )
% 11.11/6.19            = ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 11.11/6.19  
% 11.11/6.19  thf(fact_7409_powr__le__iff,axiom,
% 11.11/6.19      ! [B: real,X4: real,Y: real] :
% 11.11/6.19        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 )
% 11.11/6.20            = ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7410_ln__powr__bound,axiom,
% 11.11/6.20      ! [X4: real,A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( divide_divide_real @ ( powr_real @ X4 @ A ) @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7411_ln__powr__bound2,axiom,
% 11.11/6.20      ! [X4: real,A: real] :
% 11.11/6.20        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X4 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7412_tan__45,axiom,
% 11.11/6.20      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7413_log__add__eq__powr,axiom,
% 11.11/6.20      ! [B: real,X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20       => ( ( B != one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20           => ( ( plus_plus_real @ ( log @ B @ X4 ) @ Y )
% 11.11/6.20              = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7414_add__log__eq__powr,axiom,
% 11.11/6.20      ! [B: real,X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20       => ( ( B != one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20           => ( ( plus_plus_real @ Y @ ( log @ B @ X4 ) )
% 11.11/6.20              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7415_minus__log__eq__powr,axiom,
% 11.11/6.20      ! [B: real,X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20       => ( ( B != one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20           => ( ( minus_minus_real @ Y @ ( log @ B @ X4 ) )
% 11.11/6.20              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7416_tan__60,axiom,
% 11.11/6.20      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 11.11/6.20      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7417_lemma__tan__total,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ Y )
% 11.11/6.20       => ? [X5: real] :
% 11.11/6.20            ( ( ord_less_real @ zero_zero_real @ X5 )
% 11.11/6.20            & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20            & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7418_tan__gt__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7419_tan__total,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20      ? [X5: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 11.11/6.20        & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20        & ( ( tan_real @ X5 )
% 11.11/6.20          = Y )
% 11.11/6.20        & ! [Y4: real] :
% 11.11/6.20            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 11.11/6.20              & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20              & ( ( tan_real @ Y4 )
% 11.11/6.20                = Y ) )
% 11.11/6.20           => ( Y4 = X5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7420_tan__monotone,axiom,
% 11.11/6.20      ! [Y: real,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.20       => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.20         => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7421_tan__monotone_H,axiom,
% 11.11/6.20      ! [Y: real,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.20       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20           => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20             => ( ( ord_less_real @ Y @ X4 )
% 11.11/6.20                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7422_tan__mono__lt__eq,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.20           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20             => ( ( ord_less_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 11.11/6.20                = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7423_lemma__tan__total1,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20      ? [X5: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 11.11/6.20        & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20        & ( ( tan_real @ X5 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7424_tan__minus__45,axiom,
% 11.11/6.20      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.20      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7425_tan__inverse,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 11.11/6.20        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7426_log__minus__eq__powr,axiom,
% 11.11/6.20      ! [B: real,X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20       => ( ( B != one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20           => ( ( minus_minus_real @ ( log @ B @ X4 ) @ Y )
% 11.11/6.20              = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7427_complex__norm,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( real_V1022390504157884413omplex @ ( complex2 @ X4 @ Y ) )
% 11.11/6.20        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7428_add__tan__eq,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( ( cos_real @ Y )
% 11.11/6.20           != zero_zero_real )
% 11.11/6.20         => ( ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 11.11/6.20            = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7429_add__tan__eq,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( ( cos_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( ( cos_complex @ Y )
% 11.11/6.20           != zero_zero_complex )
% 11.11/6.20         => ( ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) )
% 11.11/6.20            = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7430_powr__half__sqrt,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20          = ( sqrt @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7431_powr__neg__numeral,axiom,
% 11.11/6.20      ! [X4: real,N2: num] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( powr_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.20          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7432_tan__total__pos,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.20       => ? [X5: real] :
% 11.11/6.20            ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 11.11/6.20            & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20            & ( ( tan_real @ X5 )
% 11.11/6.20              = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7433_tan__pos__pi2__le,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7434_tan__less__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ ( tan_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7435_tan__mono__le__eq,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 11.11/6.20           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20             => ( ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 11.11/6.20                = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7436_tan__mono__le,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.20         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20           => ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7437_tan__bound__pi2,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X4 ) ) @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7438_tan__30,axiom,
% 11.11/6.20      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 11.11/6.20      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7439_arctan__unique,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( ( tan_real @ X4 )
% 11.11/6.20              = Y )
% 11.11/6.20           => ( ( arctan @ Y )
% 11.11/6.20              = X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7440_arctan__tan,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( arctan @ ( tan_real @ X4 ) )
% 11.11/6.20            = X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7441_arctan,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 11.11/6.20        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20        & ( ( tan_real @ ( arctan @ Y ) )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7442_lemma__tan__add1,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( ( cos_real @ Y )
% 11.11/6.20           != zero_zero_real )
% 11.11/6.20         => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) )
% 11.11/6.20            = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7443_lemma__tan__add1,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( ( cos_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( ( cos_complex @ Y )
% 11.11/6.20           != zero_zero_complex )
% 11.11/6.20         => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) )
% 11.11/6.20            = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7444_tan__diff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( ( cos_real @ Y )
% 11.11/6.20           != zero_zero_real )
% 11.11/6.20         => ( ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 11.11/6.20             != zero_zero_real )
% 11.11/6.20           => ( ( tan_real @ ( minus_minus_real @ X4 @ Y ) )
% 11.11/6.20              = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7445_tan__diff,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( ( cos_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( ( cos_complex @ Y )
% 11.11/6.20           != zero_zero_complex )
% 11.11/6.20         => ( ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 11.11/6.20             != zero_zero_complex )
% 11.11/6.20           => ( ( tan_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 11.11/6.20              = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7446_tan__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( ( cos_real @ Y )
% 11.11/6.20           != zero_zero_real )
% 11.11/6.20         => ( ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20             != zero_zero_real )
% 11.11/6.20           => ( ( tan_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20              = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7447_tan__add,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( ( cos_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( ( cos_complex @ Y )
% 11.11/6.20           != zero_zero_complex )
% 11.11/6.20         => ( ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.20             != zero_zero_complex )
% 11.11/6.20           => ( ( tan_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.20              = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7448_tan__total__pi4,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ? [Z2: real] :
% 11.11/6.20            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 11.11/6.20            & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20            & ( ( tan_real @ Z2 )
% 11.11/6.20              = X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7449_tan__half,axiom,
% 11.11/6.20      ( tan_real
% 11.11/6.20      = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7450_tan__half,axiom,
% 11.11/6.20      ( tan_complex
% 11.11/6.20      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7451_arcosh__def,axiom,
% 11.11/6.20      ( arcosh_real
% 11.11/6.20      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7452_cos__arcsin,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( cos_real @ ( arcsin @ X4 ) )
% 11.11/6.20            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7453_sin__arccos__abs,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20       => ( ( sin_real @ ( arccos @ Y ) )
% 11.11/6.20          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7454_sin__arccos,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( sin_real @ ( arccos @ X4 ) )
% 11.11/6.20            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7455_arsinh__def,axiom,
% 11.11/6.20      ( arsinh_real
% 11.11/6.20      = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7456_of__real__eq__1__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( real_V1803761363581548252l_real @ X4 )
% 11.11/6.20          = one_one_real )
% 11.11/6.20        = ( X4 = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7457_of__real__eq__1__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( real_V4546457046886955230omplex @ X4 )
% 11.11/6.20          = one_one_complex )
% 11.11/6.20        = ( X4 = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7458_of__real__1,axiom,
% 11.11/6.20      ( ( real_V1803761363581548252l_real @ one_one_real )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7459_of__real__1,axiom,
% 11.11/6.20      ( ( real_V4546457046886955230omplex @ one_one_real )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7460_of__real__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.20        = ( numeral_numeral_real @ W ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7461_of__real__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 11.11/6.20        = ( numera6690914467698888265omplex @ W ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7462_of__real__divide,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.20        = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7463_of__real__divide,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.20        = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7464_of__real__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7465_of__real__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7466_of__real__power,axiom,
% 11.11/6.20      ! [X4: real,N2: nat] :
% 11.11/6.20        ( ( real_V1803761363581548252l_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.20        = ( power_power_real @ ( real_V1803761363581548252l_real @ X4 ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7467_of__real__power,axiom,
% 11.11/6.20      ! [X4: real,N2: nat] :
% 11.11/6.20        ( ( real_V4546457046886955230omplex @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.20        = ( power_power_complex @ ( real_V4546457046886955230omplex @ X4 ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7468_arccos__1,axiom,
% 11.11/6.20      ( ( arccos @ one_one_real )
% 11.11/6.20      = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7469_arccos__minus__1,axiom,
% 11.11/6.20      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.20      = pi ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7470_of__real__neg__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.20        = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7471_of__real__neg__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.20        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7472_cos__of__real__pi,axiom,
% 11.11/6.20      ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 11.11/6.20      = ( uminus_uminus_real @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7473_cos__of__real__pi,axiom,
% 11.11/6.20      ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 11.11/6.20      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7474_cos__arccos,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( cos_real @ ( arccos @ Y ) )
% 11.11/6.20            = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7475_sin__arcsin,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( sin_real @ ( arcsin @ Y ) )
% 11.11/6.20            = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7476_norm__of__real__add1,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ one_one_real ) )
% 11.11/6.20        = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7477_norm__of__real__add1,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ one_one_complex ) )
% 11.11/6.20        = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7478_norm__of__real__addn,axiom,
% 11.11/6.20      ! [X4: real,B: num] :
% 11.11/6.20        ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( numeral_numeral_real @ B ) ) )
% 11.11/6.20        = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7479_norm__of__real__addn,axiom,
% 11.11/6.20      ! [X4: real,B: num] :
% 11.11/6.20        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 11.11/6.20        = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7480_arccos__0,axiom,
% 11.11/6.20      ( ( arccos @ zero_zero_real )
% 11.11/6.20      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7481_arcsin__1,axiom,
% 11.11/6.20      ( ( arcsin @ one_one_real )
% 11.11/6.20      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7482_cos__of__real__pi__half,axiom,
% 11.11/6.20      ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20      = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7483_cos__of__real__pi__half,axiom,
% 11.11/6.20      ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 11.11/6.20      = zero_zero_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7484_sin__of__real__pi__half,axiom,
% 11.11/6.20      ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7485_sin__of__real__pi__half,axiom,
% 11.11/6.20      ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7486_arcsin__minus__1,axiom,
% 11.11/6.20      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 11.11/6.20      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7487_nonzero__of__real__divide,axiom,
% 11.11/6.20      ! [Y: real,X4: real] :
% 11.11/6.20        ( ( Y != zero_zero_real )
% 11.11/6.20       => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.20          = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7488_nonzero__of__real__divide,axiom,
% 11.11/6.20      ! [Y: real,X4: real] :
% 11.11/6.20        ( ( Y != zero_zero_real )
% 11.11/6.20       => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 11.11/6.20          = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7489_arccos__le__arccos,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.20         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20           => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7490_arccos__le__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 11.11/6.20            = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7491_arccos__eq__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20          & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 11.11/6.20       => ( ( ( arccos @ X4 )
% 11.11/6.20            = ( arccos @ Y ) )
% 11.11/6.20          = ( X4 = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7492_arcsin__minus,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( arcsin @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.20            = ( uminus_uminus_real @ ( arcsin @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7493_arcsin__le__arcsin,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.20         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20           => ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7494_arcsin__le__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 11.11/6.20            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7495_arcsin__eq__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20         => ( ( ( arcsin @ X4 )
% 11.11/6.20              = ( arcsin @ Y ) )
% 11.11/6.20            = ( X4 = Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7496_norm__less__p1,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X4 ) ) @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7497_norm__less__p1,axiom,
% 11.11/6.20      ! [X4: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X4 ) ) @ one_one_complex ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7498_arccos__lbound,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7499_arccos__less__arccos,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.20         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7500_arccos__less__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 11.11/6.20            = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7501_arccos__ubound,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7502_arccos__cos,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.20         => ( ( arccos @ ( cos_real @ X4 ) )
% 11.11/6.20            = X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7503_arcsin__less__arcsin,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.20         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20           => ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7504_arcsin__less__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 11.11/6.20            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7505_cos__arccos__abs,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 11.11/6.20       => ( ( cos_real @ ( arccos @ Y ) )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7506_norm__of__real__diff,axiom,
% 11.11/6.20      ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7507_norm__of__real__diff,axiom,
% 11.11/6.20      ! [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 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7508_arccos__cos__eq__abs,axiom,
% 11.11/6.20      ! [Theta: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 11.11/6.20       => ( ( arccos @ ( cos_real @ Theta ) )
% 11.11/6.20          = ( abs_abs_real @ Theta ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7509_arccos__lt__bounded,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 11.11/6.20            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7510_arccos__bounded,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 11.11/6.20            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7511_sin__arccos__nonzero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( sin_real @ ( arccos @ X4 ) )
% 11.11/6.20           != zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7512_arccos__cos2,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 11.11/6.20         => ( ( arccos @ ( cos_real @ X4 ) )
% 11.11/6.20            = ( uminus_uminus_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7513_arccos__minus,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.20            = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7514_cos__arcsin__nonzero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( cos_real @ ( arcsin @ X4 ) )
% 11.11/6.20           != zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7515_arccos,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 11.11/6.20            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 11.11/6.20            & ( ( cos_real @ ( arccos @ Y ) )
% 11.11/6.20              = Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7516_arccos__minus__abs,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20       => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.20          = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7517_cos__sin__eq,axiom,
% 11.11/6.20      ( cos_real
% 11.11/6.20      = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7518_cos__sin__eq,axiom,
% 11.11/6.20      ( cos_complex
% 11.11/6.20      = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7519_sin__cos__eq,axiom,
% 11.11/6.20      ( sin_real
% 11.11/6.20      = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7520_sin__cos__eq,axiom,
% 11.11/6.20      ( sin_complex
% 11.11/6.20      = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7521_minus__sin__cos__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( uminus_uminus_real @ ( sin_real @ X4 ) )
% 11.11/6.20        = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7522_minus__sin__cos__eq,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( uminus1482373934393186551omplex @ ( sin_complex @ X4 ) )
% 11.11/6.20        = ( cos_complex @ ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7523_arccos__le__pi2,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7524_arcsin__lt__bounded,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 11.11/6.20            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7525_arcsin__bounded,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 11.11/6.20            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7526_arcsin__ubound,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7527_arcsin__lbound,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7528_arcsin__sin,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ( arcsin @ ( sin_real @ X4 ) )
% 11.11/6.20            = X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7529_arcsin,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 11.11/6.20            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20            & ( ( sin_real @ ( arcsin @ Y ) )
% 11.11/6.20              = Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7530_arcsin__pi,axiom,
% 11.11/6.20      ! [Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 11.11/6.20            & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 11.11/6.20            & ( ( sin_real @ ( arcsin @ Y ) )
% 11.11/6.20              = Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7531_arcsin__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 11.11/6.20           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20             => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ Y )
% 11.11/6.20                = ( ord_less_eq_real @ X4 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7532_le__arcsin__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 11.11/6.20           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20             => ( ( ord_less_eq_real @ Y @ ( arcsin @ X4 ) )
% 11.11/6.20                = ( ord_less_eq_real @ ( sin_real @ Y ) @ X4 ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7533_floor__log__nat__eq__powr__iff,axiom,
% 11.11/6.20      ! [B: nat,K: nat,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.20       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 11.11/6.20              = ( semiri1314217659103216013at_int @ N2 ) )
% 11.11/6.20            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 11.11/6.20              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7534_cos__npi__int,axiom,
% 11.11/6.20      ! [N2: int] :
% 11.11/6.20        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.20         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 11.11/6.20            = one_one_real ) )
% 11.11/6.20        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.20         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 11.11/6.20            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7535_cot__less__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ ( cot_real @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7536_floor__log__nat__eq__if,axiom,
% 11.11/6.20      ! [B: nat,N2: nat,K: nat] :
% 11.11/6.20        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 11.11/6.20       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 11.11/6.20         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 11.11/6.20           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 11.11/6.20              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7537_cot__periodic,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( cot_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 11.11/6.20        = ( cot_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7538_of__int__floor__cancel,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ? [N: int] :
% 11.11/6.20              ( X4
% 11.11/6.20              = ( ring_1_of_int_real @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7539_of__int__floor__cancel,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ? [N: int] :
% 11.11/6.20              ( X4
% 11.11/6.20              = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7540_of__int__ceiling__cancel,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ? [N: int] :
% 11.11/6.20              ( X4
% 11.11/6.20              = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7541_of__int__ceiling__cancel,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ? [N: int] :
% 11.11/6.20              ( X4
% 11.11/6.20              = ( ring_1_of_int_real @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7542_of__int__le__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7543_of__int__le__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7544_of__int__le__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7545_of__int__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( numeral_numeral_rat @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7546_of__int__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( numera6690914467698888265omplex @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7547_of__int__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( numeral_numeral_real @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7548_of__int__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( numeral_numeral_int @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7549_of__int__eq__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ Z )
% 11.11/6.20          = ( numeral_numeral_rat @ N2 ) )
% 11.11/6.20        = ( Z
% 11.11/6.20          = ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7550_of__int__eq__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ( ring_17405671764205052669omplex @ Z )
% 11.11/6.20          = ( numera6690914467698888265omplex @ N2 ) )
% 11.11/6.20        = ( Z
% 11.11/6.20          = ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7551_of__int__eq__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ Z )
% 11.11/6.20          = ( numeral_numeral_real @ N2 ) )
% 11.11/6.20        = ( Z
% 11.11/6.20          = ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7552_of__int__eq__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ( ring_1_of_int_int @ Z )
% 11.11/6.20          = ( numeral_numeral_int @ N2 ) )
% 11.11/6.20        = ( Z
% 11.11/6.20          = ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7553_of__int__less__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7554_of__int__less__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7555_of__int__less__iff,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_int @ W @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7556_of__int__1,axiom,
% 11.11/6.20      ( ( ring_17405671764205052669omplex @ one_one_int )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7557_of__int__1,axiom,
% 11.11/6.20      ( ( ring_1_of_int_int @ one_one_int )
% 11.11/6.20      = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7558_of__int__1,axiom,
% 11.11/6.20      ( ( ring_1_of_int_real @ one_one_int )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7559_of__int__1,axiom,
% 11.11/6.20      ( ( ring_1_of_int_rat @ one_one_int )
% 11.11/6.20      = one_one_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7560_of__int__eq__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ( ring_17405671764205052669omplex @ Z )
% 11.11/6.20          = one_one_complex )
% 11.11/6.20        = ( Z = one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7561_of__int__eq__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ( ring_1_of_int_int @ Z )
% 11.11/6.20          = one_one_int )
% 11.11/6.20        = ( Z = one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7562_of__int__eq__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ Z )
% 11.11/6.20          = one_one_real )
% 11.11/6.20        = ( Z = one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7563_of__int__eq__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ Z )
% 11.11/6.20          = one_one_rat )
% 11.11/6.20        = ( Z = one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7564_of__int__add,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 11.11/6.20        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7565_of__int__add,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 11.11/6.20        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7566_of__int__add,axiom,
% 11.11/6.20      ! [W: int,Z: int] :
% 11.11/6.20        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 11.11/6.20        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7567_floor__numeral,axiom,
% 11.11/6.20      ! [V: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 11.11/6.20        = ( numeral_numeral_int @ V ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7568_floor__numeral,axiom,
% 11.11/6.20      ! [V: num] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 11.11/6.20        = ( numeral_numeral_int @ V ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7569_floor__one,axiom,
% 11.11/6.20      ( ( archim6058952711729229775r_real @ one_one_real )
% 11.11/6.20      = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7570_floor__one,axiom,
% 11.11/6.20      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 11.11/6.20      = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7571_of__int__power,axiom,
% 11.11/6.20      ! [Z: int,N2: nat] :
% 11.11/6.20        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N2 ) )
% 11.11/6.20        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7572_of__int__power,axiom,
% 11.11/6.20      ! [Z: int,N2: nat] :
% 11.11/6.20        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 11.11/6.20        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7573_of__int__power,axiom,
% 11.11/6.20      ! [Z: int,N2: nat] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 11.11/6.20        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7574_of__int__power,axiom,
% 11.11/6.20      ! [Z: int,N2: nat] :
% 11.11/6.20        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 11.11/6.20        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7575_of__int__eq__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 11.11/6.20          = ( ring_1_of_int_rat @ X4 ) )
% 11.11/6.20        = ( ( power_power_int @ B @ W )
% 11.11/6.20          = X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7576_of__int__eq__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 11.11/6.20          = ( ring_1_of_int_real @ X4 ) )
% 11.11/6.20        = ( ( power_power_int @ B @ W )
% 11.11/6.20          = X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7577_of__int__eq__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 11.11/6.20          = ( ring_1_of_int_int @ X4 ) )
% 11.11/6.20        = ( ( power_power_int @ B @ W )
% 11.11/6.20          = X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7578_of__int__eq__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 11.11/6.20          = ( ring_17405671764205052669omplex @ X4 ) )
% 11.11/6.20        = ( ( power_power_int @ B @ W )
% 11.11/6.20          = X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7579_of__int__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ X4 )
% 11.11/6.20          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 11.11/6.20        = ( X4
% 11.11/6.20          = ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7580_of__int__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ X4 )
% 11.11/6.20          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 11.11/6.20        = ( X4
% 11.11/6.20          = ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7581_of__int__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_int @ X4 )
% 11.11/6.20          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 11.11/6.20        = ( X4
% 11.11/6.20          = ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7582_of__int__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ( ring_17405671764205052669omplex @ X4 )
% 11.11/6.20          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 11.11/6.20        = ( X4
% 11.11/6.20          = ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7583_ceiling__add__of__int,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 11.11/6.20        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7584_ceiling__add__of__int,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 11.11/6.20        = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7585_of__nat__nat__take__bit__eq,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 11.11/6.20        = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7586_of__nat__nat__take__bit__eq,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 11.11/6.20        = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7587_of__nat__nat__take__bit__eq,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 11.11/6.20        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7588_of__int__0__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7589_of__int__0__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7590_of__int__0__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7591_of__int__le__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7592_of__int__le__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7593_of__int__le__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7594_of__int__0__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7595_of__int__0__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7596_of__int__0__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7597_of__int__less__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7598_of__int__less__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 11.11/6.20        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7599_of__int__less__0__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7600_of__int__numeral__le__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7601_of__int__numeral__le__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7602_of__int__numeral__le__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7603_of__int__le__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7604_of__int__le__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7605_of__int__le__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7606_of__int__less__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7607_of__int__less__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7608_of__int__less__numeral__iff,axiom,
% 11.11/6.20      ! [Z: int,N2: num] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7609_of__int__numeral__less__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7610_of__int__numeral__less__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7611_of__int__numeral__less__iff,axiom,
% 11.11/6.20      ! [N2: num,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7612_of__int__le__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7613_of__int__le__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7614_of__int__le__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 11.11/6.20        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7615_of__int__1__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7616_of__int__1__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7617_of__int__1__le__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7618_zero__le__floor,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7619_zero__le__floor,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ zero_zero_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7620_of__int__1__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7621_of__int__1__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7622_of__int__1__less__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 11.11/6.20        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7623_of__int__less__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 11.11/6.20        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7624_of__int__less__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 11.11/6.20        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7625_of__int__less__1__iff,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 11.11/6.20        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7626_floor__less__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7627_floor__less__zero,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_rat @ X4 @ zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7628_numeral__le__floor,axiom,
% 11.11/6.20      ! [V: num,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7629_numeral__le__floor,axiom,
% 11.11/6.20      ! [V: num,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7630_zero__less__floor,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7631_zero__less__floor,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7632_floor__le__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7633_floor__le__zero,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7634_floor__less__numeral,axiom,
% 11.11/6.20      ! [X4: real,V: num] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7635_floor__less__numeral,axiom,
% 11.11/6.20      ! [X4: rat,V: num] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7636_one__le__floor,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7637_one__le__floor,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7638_floor__less__one,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 11.11/6.20        = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7639_floor__less__one,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 11.11/6.20        = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7640_floor__neg__numeral,axiom,
% 11.11/6.20      ! [V: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7641_floor__neg__numeral,axiom,
% 11.11/6.20      ! [V: num] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7642_floor__diff__numeral,axiom,
% 11.11/6.20      ! [X4: real,V: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 11.11/6.20        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7643_floor__diff__numeral,axiom,
% 11.11/6.20      ! [X4: rat,V: num] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 11.11/6.20        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7644_of__int__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7645_of__int__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7646_of__int__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7647_of__int__le__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7648_of__int__le__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7649_of__int__le__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7650_numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_rat @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7651_numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 11.11/6.20          = ( ring_17405671764205052669omplex @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7652_numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_real @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7653_numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_int @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7654_of__int__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ Y )
% 11.11/6.20          = ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7655_of__int__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_17405671764205052669omplex @ Y )
% 11.11/6.20          = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7656_of__int__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ Y )
% 11.11/6.20          = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7657_of__int__eq__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_int @ Y )
% 11.11/6.20          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7658_floor__diff__one,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 11.11/6.20        = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7659_floor__diff__one,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 11.11/6.20        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7660_of__int__less__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7661_of__int__less__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7662_of__int__less__of__int__power__cancel__iff,axiom,
% 11.11/6.20      ! [B: int,W: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7663_of__int__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7664_of__int__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7665_of__int__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: int,B: int,W: nat] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 11.11/6.20        = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7666_of__nat__nat,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 11.11/6.20          = ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7667_of__nat__nat,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 11.11/6.20          = ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7668_of__nat__nat,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 11.11/6.20          = ( ring_1_of_int_int @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7669_floor__numeral__power,axiom,
% 11.11/6.20      ! [X4: num,N2: nat] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.20        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7670_floor__numeral__power,axiom,
% 11.11/6.20      ! [X4: num,N2: nat] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 11.11/6.20        = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7671_floor__divide__eq__div__numeral,axiom,
% 11.11/6.20      ! [A: num,B: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 11.11/6.20        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7672_numeral__less__floor,axiom,
% 11.11/6.20      ! [V: num,X4: real] :
% 11.11/6.20        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7673_numeral__less__floor,axiom,
% 11.11/6.20      ! [V: num,X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7674_floor__le__numeral,axiom,
% 11.11/6.20      ! [X4: real,V: num] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7675_floor__le__numeral,axiom,
% 11.11/6.20      ! [X4: rat,V: num] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7676_one__less__floor,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7677_one__less__floor,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7678_floor__le__one,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7679_floor__le__one,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7680_neg__numeral__le__floor,axiom,
% 11.11/6.20      ! [V: num,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7681_neg__numeral__le__floor,axiom,
% 11.11/6.20      ! [V: num,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7682_floor__less__neg__numeral,axiom,
% 11.11/6.20      ! [X4: real,V: num] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7683_floor__less__neg__numeral,axiom,
% 11.11/6.20      ! [X4: rat,V: num] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7684_numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7685_numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7686_numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7687_of__int__le__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7688_of__int__le__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7689_of__int__le__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7690_numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7691_numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7692_numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7693_of__int__less__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7694_of__int__less__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7695_of__int__less__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7696_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_real @ Y )
% 11.11/6.20          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7697_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_int @ Y )
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7698_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_17405671764205052669omplex @ Y )
% 11.11/6.20          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7699_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_18347121197199848620nteger @ Y )
% 11.11/6.20          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7700_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [Y: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ( ring_1_of_int_rat @ Y )
% 11.11/6.20          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( Y
% 11.11/6.20          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7701_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_real @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7702_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_int @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7703_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 )
% 11.11/6.20          = ( ring_17405671764205052669omplex @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7704_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 )
% 11.11/6.20          = ( ring_18347121197199848620nteger @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7705_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,Y: int] :
% 11.11/6.20        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 )
% 11.11/6.20          = ( ring_1_of_int_rat @ Y ) )
% 11.11/6.20        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 11.11/6.20          = Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7706_floor__one__divide__eq__div__numeral,axiom,
% 11.11/6.20      ! [B: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 11.11/6.20        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7707_floor__minus__divide__eq__div__numeral,axiom,
% 11.11/6.20      ! [A: num,B: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 11.11/6.20        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7708_sin__int__2pin,axiom,
% 11.11/6.20      ! [N2: int] :
% 11.11/6.20        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 11.11/6.20        = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7709_cos__int__2pin,axiom,
% 11.11/6.20      ! [N2: int] :
% 11.11/6.20        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 11.11/6.20        = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7710_neg__numeral__less__floor,axiom,
% 11.11/6.20      ! [V: num,X4: real] :
% 11.11/6.20        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7711_neg__numeral__less__floor,axiom,
% 11.11/6.20      ! [V: num,X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7712_floor__le__neg__numeral,axiom,
% 11.11/6.20      ! [X4: real,V: num] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7713_floor__le__neg__numeral,axiom,
% 11.11/6.20      ! [X4: rat,V: num] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7714_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7715_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7716_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7717_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7718_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7719_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7720_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7721_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 11.11/6.20        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7722_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7723_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7724_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7725_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 11.11/6.20      ! [X4: num,N2: nat,A: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 11.11/6.20        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7726_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7727_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7728_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7729_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 11.11/6.20      ! [A: int,X4: num,N2: nat] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 11.11/6.20        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7730_floor__minus__one__divide__eq__div__numeral,axiom,
% 11.11/6.20      ! [B: num] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 11.11/6.20        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7731_ex__le__of__int,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7732_ex__le__of__int,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7733_ex__of__int__less,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X4 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7734_ex__of__int__less,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7735_ex__less__of__int,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7736_ex__less__of__int,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20      ? [Z2: int] : ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7737_int__add__floor,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7738_int__add__floor,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7739_floor__add__int,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 11.11/6.20        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7740_floor__add__int,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 11.11/6.20        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7741_floor__divide__of__int__eq,axiom,
% 11.11/6.20      ! [K: int,L: int] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 11.11/6.20        = ( divide_divide_int @ K @ L ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7742_floor__divide__of__int__eq,axiom,
% 11.11/6.20      ! [K: int,L: int] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 11.11/6.20        = ( divide_divide_int @ K @ L ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7743_of__int__floor__le,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7744_of__int__floor__le,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7745_floor__less__iff,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7746_floor__less__iff,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7747_le__floor__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7748_le__floor__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7749_floor__power,axiom,
% 11.11/6.20      ! [X4: real,N2: nat] :
% 11.11/6.20        ( ( X4
% 11.11/6.20          = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) )
% 11.11/6.20       => ( ( archim6058952711729229775r_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.20          = ( power_power_int @ ( archim6058952711729229775r_real @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7750_floor__power,axiom,
% 11.11/6.20      ! [X4: rat,N2: nat] :
% 11.11/6.20        ( ( X4
% 11.11/6.20          = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) )
% 11.11/6.20       => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X4 @ N2 ) )
% 11.11/6.20          = ( power_power_int @ ( archim3151403230148437115or_rat @ X4 ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7751_real__of__int__floor__add__one__gt,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7752_floor__eq,axiom,
% 11.11/6.20      ! [N2: int,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 11.11/6.20         => ( ( archim6058952711729229775r_real @ X4 )
% 11.11/6.20            = N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7753_real__of__int__floor__add__one__ge,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_eq_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7754_real__of__int__floor__gt__diff__one,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7755_real__of__int__floor__ge__diff__one,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7756_floor__split,axiom,
% 11.11/6.20      ! [P: int > $o,T2: real] :
% 11.11/6.20        ( ( P @ ( archim6058952711729229775r_real @ T2 ) )
% 11.11/6.20        = ( ! [I3: int] :
% 11.11/6.20              ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T2 )
% 11.11/6.20                & ( ord_less_real @ T2 @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 11.11/6.20             => ( P @ I3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7757_floor__split,axiom,
% 11.11/6.20      ! [P: int > $o,T2: rat] :
% 11.11/6.20        ( ( P @ ( archim3151403230148437115or_rat @ T2 ) )
% 11.11/6.20        = ( ! [I3: int] :
% 11.11/6.20              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T2 )
% 11.11/6.20                & ( ord_less_rat @ T2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 11.11/6.20             => ( P @ I3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7758_floor__eq__iff,axiom,
% 11.11/6.20      ! [X4: real,A: int] :
% 11.11/6.20        ( ( ( archim6058952711729229775r_real @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X4 )
% 11.11/6.20          & ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7759_floor__eq__iff,axiom,
% 11.11/6.20      ! [X4: rat,A: int] :
% 11.11/6.20        ( ( ( archim3151403230148437115or_rat @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X4 )
% 11.11/6.20          & ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7760_floor__unique,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 11.11/6.20         => ( ( archim6058952711729229775r_real @ X4 )
% 11.11/6.20            = Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7761_floor__unique,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 )
% 11.11/6.20       => ( ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 11.11/6.20         => ( ( archim3151403230148437115or_rat @ X4 )
% 11.11/6.20            = Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7762_less__floor__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7763_less__floor__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7764_floor__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7765_floor__le__iff,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7766_floor__correct,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 )
% 11.11/6.20        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7767_floor__correct,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 )
% 11.11/6.20        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7768_floor__eq2,axiom,
% 11.11/6.20      ! [N2: int,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 11.11/6.20         => ( ( archim6058952711729229775r_real @ X4 )
% 11.11/6.20            = N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7769_floor__divide__real__eq__div,axiom,
% 11.11/6.20      ! [B: int,A: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 11.11/6.20       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 11.11/6.20          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7770_floor__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.20       => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7771_floor__mono,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.20       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7772_floor__less__cancel,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) )
% 11.11/6.20       => ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7773_floor__less__cancel,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 11.11/6.20       => ( ord_less_rat @ X4 @ Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7774_floor__le__ceiling,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7775_floor__le__ceiling,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7776_le__of__int__ceiling,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7777_le__of__int__ceiling,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7778_floor__divide__lower,axiom,
% 11.11/6.20      ! [Q3: real,P2: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 11.11/6.20       => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7779_floor__divide__lower,axiom,
% 11.11/6.20      ! [Q3: rat,P2: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 11.11/6.20       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7780_take__bit__of__int,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 11.11/6.20        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7781_of__int__and__eq,axiom,
% 11.11/6.20      ! [K: int,L: int] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 11.11/6.20        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7782_of__int__not__eq,axiom,
% 11.11/6.20      ! [K: int] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 11.11/6.20        = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7783_of__int__xor__eq,axiom,
% 11.11/6.20      ! [K: int,L: int] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 11.11/6.20        = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7784_of__int__mask__eq,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.20        = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7785_floor__divide__upper,axiom,
% 11.11/6.20      ! [Q3: real,P2: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 11.11/6.20       => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7786_floor__divide__upper,axiom,
% 11.11/6.20      ! [Q3: rat,P2: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 11.11/6.20       => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7787_le__floor__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7788_le__floor__add,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7789_ceiling__le,axiom,
% 11.11/6.20      ! [X4: real,A: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) )
% 11.11/6.20       => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7790_ceiling__le,axiom,
% 11.11/6.20      ! [X4: rat,A: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) )
% 11.11/6.20       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7791_ceiling__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7792_ceiling__le__iff,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7793_less__ceiling__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7794_less__ceiling__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.20        = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7795_real__of__int__div4,axiom,
% 11.11/6.20      ! [N2: int,X4: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7796_real__of__int__div,axiom,
% 11.11/6.20      ! [D: int,N2: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ D @ N2 )
% 11.11/6.20       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 11.11/6.20          = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7797_of__nat__floor,axiom,
% 11.11/6.20      ! [R3: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 11.11/6.20       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R3 ) ) ) @ R3 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7798_of__nat__floor,axiom,
% 11.11/6.20      ! [R3: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 11.11/6.20       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R3 ) ) ) @ R3 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7799_one__add__floor,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 11.11/6.20        = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7800_one__add__floor,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 11.11/6.20        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7801_le__mult__nat__floor,axiom,
% 11.11/6.20      ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7802_le__mult__nat__floor,axiom,
% 11.11/6.20      ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7803_floor__divide__of__nat__eq,axiom,
% 11.11/6.20      ! [M: nat,N2: nat] :
% 11.11/6.20        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.20        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7804_floor__divide__of__nat__eq,axiom,
% 11.11/6.20      ! [M: nat,N2: nat] :
% 11.11/6.20        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) )
% 11.11/6.20        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7805_nat__floor__neg,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20       => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20          = zero_zero_nat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7806_floor__log__eq__powr__iff,axiom,
% 11.11/6.20      ! [X4: real,B: real,K: int] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.20         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X4 ) )
% 11.11/6.20              = K )
% 11.11/6.20            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X4 )
% 11.11/6.20              & ( ord_less_real @ X4 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7807_of__int__nonneg,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7808_of__int__nonneg,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7809_of__int__nonneg,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7810_of__int__leD,axiom,
% 11.11/6.20      ! [N2: int,X4: code_integer] :
% 11.11/6.20        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7811_of__int__leD,axiom,
% 11.11/6.20      ! [N2: int,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7812_of__int__leD,axiom,
% 11.11/6.20      ! [N2: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7813_of__int__leD,axiom,
% 11.11/6.20      ! [N2: int,X4: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_eq_int @ one_one_int @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7814_of__int__pos,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7815_of__int__pos,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7816_of__int__pos,axiom,
% 11.11/6.20      ! [Z: int] :
% 11.11/6.20        ( ( ord_less_int @ zero_zero_int @ Z )
% 11.11/6.20       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7817_of__int__lessD,axiom,
% 11.11/6.20      ! [N2: int,X4: code_integer] :
% 11.11/6.20        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7818_of__int__lessD,axiom,
% 11.11/6.20      ! [N2: int,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7819_of__int__lessD,axiom,
% 11.11/6.20      ! [N2: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7820_of__int__lessD,axiom,
% 11.11/6.20      ! [N2: int,X4: int] :
% 11.11/6.20        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 11.11/6.20       => ( ( N2 = zero_zero_int )
% 11.11/6.20          | ( ord_less_int @ one_one_int @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7821_floor__eq3,axiom,
% 11.11/6.20      ! [N2: nat,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 11.11/6.20         => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20            = N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7822_le__nat__floor,axiom,
% 11.11/6.20      ! [X4: nat,A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ A )
% 11.11/6.20       => ( ord_less_eq_nat @ X4 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7823_floor__exists1,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20      ? [X5: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X4 )
% 11.11/6.20        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 11.11/6.20        & ! [Y4: int] :
% 11.11/6.20            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X4 )
% 11.11/6.20              & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 11.11/6.20           => ( Y4 = X5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7824_floor__exists1,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20      ? [X5: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X4 )
% 11.11/6.20        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 11.11/6.20        & ! [Y4: int] :
% 11.11/6.20            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X4 )
% 11.11/6.20              & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 11.11/6.20           => ( Y4 = X5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7825_floor__exists,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20      ? [Z2: int] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 11.11/6.20        & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7826_floor__exists,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20      ? [Z2: int] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 11.11/6.20        & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7827_of__int__ceiling__le__add__one,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ ( plus_plus_real @ R3 @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7828_of__int__ceiling__le__add__one,axiom,
% 11.11/6.20      ! [R3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ ( plus_plus_rat @ R3 @ one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7829_of__int__neg__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7830_of__int__neg__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7831_of__int__neg__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7832_of__int__neg__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7833_of__int__neg__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7834_of__int__ceiling__diff__one__le,axiom,
% 11.11/6.20      ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ one_one_real ) @ R3 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7835_of__int__ceiling__diff__one__le,axiom,
% 11.11/6.20      ! [R3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ one_one_rat ) @ R3 ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7836_ceiling__diff__floor__le__1,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim6058952711729229775r_real @ X4 ) ) @ one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7837_ceiling__diff__floor__le__1,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim3151403230148437115or_rat @ X4 ) ) @ one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7838_of__nat__less__of__int__iff,axiom,
% 11.11/6.20      ! [N2: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7839_of__nat__less__of__int__iff,axiom,
% 11.11/6.20      ! [N2: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7840_of__nat__less__of__int__iff,axiom,
% 11.11/6.20      ! [N2: nat,X4: int] :
% 11.11/6.20        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X4 ) )
% 11.11/6.20        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7841_int__le__real__less,axiom,
% 11.11/6.20      ( ord_less_eq_int
% 11.11/6.20      = ( ^ [N: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7842_int__less__real__le,axiom,
% 11.11/6.20      ( ord_less_int
% 11.11/6.20      = ( ^ [N: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7843_of__int__not__numeral,axiom,
% 11.11/6.20      ! [K: num] :
% 11.11/6.20        ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7844_ceiling__divide__eq__div,axiom,
% 11.11/6.20      ! [A: int,B: int] :
% 11.11/6.20        ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7845_ceiling__divide__eq__div,axiom,
% 11.11/6.20      ! [A: int,B: int] :
% 11.11/6.20        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7846_real__of__int__div__aux,axiom,
% 11.11/6.20      ! [X4: int,D: int] :
% 11.11/6.20        ( ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ D ) )
% 11.11/6.20        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X4 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X4 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7847_le__mult__floor,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.20         => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7848_le__mult__floor,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 11.11/6.20         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7849_floor__eq4,axiom,
% 11.11/6.20      ! [N2: nat,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 11.11/6.20         => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 11.11/6.20            = N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7850_ceiling__split,axiom,
% 11.11/6.20      ! [P: int > $o,T2: real] :
% 11.11/6.20        ( ( P @ ( archim7802044766580827645g_real @ T2 ) )
% 11.11/6.20        = ( ! [I3: int] :
% 11.11/6.20              ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T2 )
% 11.11/6.20                & ( ord_less_eq_real @ T2 @ ( ring_1_of_int_real @ I3 ) ) )
% 11.11/6.20             => ( P @ I3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7851_ceiling__split,axiom,
% 11.11/6.20      ! [P: int > $o,T2: rat] :
% 11.11/6.20        ( ( P @ ( archim2889992004027027881ng_rat @ T2 ) )
% 11.11/6.20        = ( ! [I3: int] :
% 11.11/6.20              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T2 )
% 11.11/6.20                & ( ord_less_eq_rat @ T2 @ ( ring_1_of_int_rat @ I3 ) ) )
% 11.11/6.20             => ( P @ I3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7852_ceiling__eq__iff,axiom,
% 11.11/6.20      ! [X4: real,A: int] :
% 11.11/6.20        ( ( ( archim7802044766580827645g_real @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X4 )
% 11.11/6.20          & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7853_ceiling__eq__iff,axiom,
% 11.11/6.20      ! [X4: rat,A: int] :
% 11.11/6.20        ( ( ( archim2889992004027027881ng_rat @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X4 )
% 11.11/6.20          & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7854_ceiling__unique,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) )
% 11.11/6.20         => ( ( archim7802044766580827645g_real @ X4 )
% 11.11/6.20            = Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7855_ceiling__unique,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) )
% 11.11/6.20         => ( ( archim2889992004027027881ng_rat @ X4 )
% 11.11/6.20            = Z ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7856_ceiling__correct,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) @ one_one_real ) @ X4 )
% 11.11/6.20        & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7857_ceiling__correct,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) @ one_one_rat ) @ X4 )
% 11.11/6.20        & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7858_cot__def,axiom,
% 11.11/6.20      ( cot_real
% 11.11/6.20      = ( ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7859_cot__def,axiom,
% 11.11/6.20      ( cot_complex
% 11.11/6.20      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X ) @ ( sin_complex @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7860_ceiling__less__iff,axiom,
% 11.11/6.20      ! [X4: real,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7861_ceiling__less__iff,axiom,
% 11.11/6.20      ! [X4: rat,Z: int] :
% 11.11/6.20        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 11.11/6.20        = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7862_le__ceiling__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 11.11/6.20        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7863_le__ceiling__iff,axiom,
% 11.11/6.20      ! [Z: int,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 11.11/6.20        = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7864_real__of__int__div2,axiom,
% 11.11/6.20      ! [N2: int,X4: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7865_real__of__int__div3,axiom,
% 11.11/6.20      ! [N2: int,X4: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7866_ceiling__divide__upper,axiom,
% 11.11/6.20      ! [Q3: real,P2: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 11.11/6.20       => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7867_ceiling__divide__upper,axiom,
% 11.11/6.20      ! [Q3: rat,P2: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 11.11/6.20       => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7868_even__of__int__iff,axiom,
% 11.11/6.20      ! [K: int] :
% 11.11/6.20        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 11.11/6.20        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7869_even__of__int__iff,axiom,
% 11.11/6.20      ! [K: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 11.11/6.20        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7870_of__int__of__nat,axiom,
% 11.11/6.20      ( ring_17405671764205052669omplex
% 11.11/6.20      = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7871_of__int__of__nat,axiom,
% 11.11/6.20      ( ring_18347121197199848620nteger
% 11.11/6.20      = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7872_of__int__of__nat,axiom,
% 11.11/6.20      ( ring_1_of_int_rat
% 11.11/6.20      = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7873_of__int__of__nat,axiom,
% 11.11/6.20      ( ring_1_of_int_real
% 11.11/6.20      = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7874_of__int__of__nat,axiom,
% 11.11/6.20      ( ring_1_of_int_int
% 11.11/6.20      = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7875_ceiling__divide__lower,axiom,
% 11.11/6.20      ! [Q3: rat,P2: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 11.11/6.20       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7876_ceiling__divide__lower,axiom,
% 11.11/6.20      ! [Q3: real,P2: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ Q3 )
% 11.11/6.20       => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7877_ceiling__eq,axiom,
% 11.11/6.20      ! [N2: int,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 11.11/6.20         => ( ( archim7802044766580827645g_real @ X4 )
% 11.11/6.20            = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7878_ceiling__eq,axiom,
% 11.11/6.20      ! [N2: int,X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( ring_1_of_int_rat @ N2 ) @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N2 ) @ one_one_rat ) )
% 11.11/6.20         => ( ( archim2889992004027027881ng_rat @ X4 )
% 11.11/6.20            = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7879_cos__one__2pi__int,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20          = one_one_real )
% 11.11/6.20        = ( ? [X: int] :
% 11.11/6.20              ( X4
% 11.11/6.20              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7880_arccos__cos__eq__abs__2pi,axiom,
% 11.11/6.20      ! [Theta: real] :
% 11.11/6.20        ~ ! [K2: int] :
% 11.11/6.20            ( ( arccos @ ( cos_real @ Theta ) )
% 11.11/6.20           != ( 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 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7881_cot__gt__zero,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7882_floor__log2__div2,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.20       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.20          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7883_tan__cot_H,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 11.11/6.20        = ( cot_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7884_cos__zero__iff__int,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20          = zero_zero_real )
% 11.11/6.20        = ( ? [I3: int] :
% 11.11/6.20              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.20              & ( X4
% 11.11/6.20                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7885_sin__zero__iff__int,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( sin_real @ X4 )
% 11.11/6.20          = zero_zero_real )
% 11.11/6.20        = ( ? [I3: int] :
% 11.11/6.20              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.20              & ( X4
% 11.11/6.20                = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7886_powr__int,axiom,
% 11.11/6.20      ! [X4: real,I2: int] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 11.11/6.20           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 11.11/6.20              = ( power_power_real @ X4 @ ( nat2 @ I2 ) ) ) )
% 11.11/6.20          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 11.11/6.20           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 11.11/6.20              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7887_round__unique,axiom,
% 11.11/6.20      ! [X4: real,Y: int] :
% 11.11/6.20        ( ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 11.11/6.20       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20         => ( ( archim8280529875227126926d_real @ X4 )
% 11.11/6.20            = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7888_round__unique,axiom,
% 11.11/6.20      ! [X4: rat,Y: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 11.11/6.20       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20         => ( ( archim7778729529865785530nd_rat @ X4 )
% 11.11/6.20            = Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7889_round__unique_H,axiom,
% 11.11/6.20      ! [X4: rat,N2: int] :
% 11.11/6.20        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 11.11/6.20       => ( ( archim7778729529865785530nd_rat @ X4 )
% 11.11/6.20          = N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7890_round__unique_H,axiom,
% 11.11/6.20      ! [X4: real,N2: int] :
% 11.11/6.20        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20       => ( ( archim8280529875227126926d_real @ X4 )
% 11.11/6.20          = N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7891_of__int__round__abs__le,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ X4 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7892_of__int__round__abs__le,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ X4 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7893_of__int__round__gt,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7894_of__int__round__gt,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7895_of__int__round__ge,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7896_of__int__round__ge,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7897_round__numeral,axiom,
% 11.11/6.20      ! [N2: num] :
% 11.11/6.20        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 11.11/6.20        = ( numeral_numeral_int @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7898_round__1,axiom,
% 11.11/6.20      ( ( archim8280529875227126926d_real @ one_one_real )
% 11.11/6.20      = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7899_round__1,axiom,
% 11.11/6.20      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 11.11/6.20      = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7900_round__neg__numeral,axiom,
% 11.11/6.20      ! [N2: num] :
% 11.11/6.20        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7901_round__neg__numeral,axiom,
% 11.11/6.20      ! [N2: num] :
% 11.11/6.20        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7902_round__mono,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ X4 @ Y )
% 11.11/6.20       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7903_floor__le__round,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim8280529875227126926d_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7904_floor__le__round,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7905_ceiling__ge__round,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7906_round__diff__minimal,axiom,
% 11.11/6.20      ! [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 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7907_round__diff__minimal,axiom,
% 11.11/6.20      ! [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 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7908_round__def,axiom,
% 11.11/6.20      ( archim8280529875227126926d_real
% 11.11/6.20      = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7909_round__def,axiom,
% 11.11/6.20      ( archim7778729529865785530nd_rat
% 11.11/6.20      = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7910_of__int__round__le,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7911_of__int__round__le,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7912_round__altdef,axiom,
% 11.11/6.20      ( archim8280529875227126926d_real
% 11.11/6.20      = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7913_round__altdef,axiom,
% 11.11/6.20      ( archim7778729529865785530nd_rat
% 11.11/6.20      = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7914_powr__real__of__int,axiom,
% 11.11/6.20      ! [X4: real,N2: int] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 11.11/6.20           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 11.11/6.20              = ( power_power_real @ X4 @ ( nat2 @ N2 ) ) ) )
% 11.11/6.20          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 11.11/6.20           => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 11.11/6.20              = ( inverse_inverse_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7915_cis__2pi,axiom,
% 11.11/6.20      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7916_i__even__power,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7917_gbinomial__absorption_H,axiom,
% 11.11/6.20      ! [K: nat,A: rat] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_rat @ A @ K )
% 11.11/6.20          = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7918_gbinomial__absorption_H,axiom,
% 11.11/6.20      ! [K: nat,A: complex] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_complex @ A @ K )
% 11.11/6.20          = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7919_gbinomial__absorption_H,axiom,
% 11.11/6.20      ! [K: nat,A: real] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_real @ A @ K )
% 11.11/6.20          = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7920_inverse__inverse__eq,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20        = A ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7921_inverse__inverse__eq,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 11.11/6.20        = A ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7922_inverse__eq__iff__eq,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ A )
% 11.11/6.20          = ( inverse_inverse_real @ B ) )
% 11.11/6.20        = ( A = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7923_inverse__eq__iff__eq,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20        = ( A = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7924_inverse__nonzero__iff__nonzero,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ( inverse_inverse_rat @ A )
% 11.11/6.20          = zero_zero_rat )
% 11.11/6.20        = ( A = zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7925_inverse__nonzero__iff__nonzero,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ A )
% 11.11/6.20          = zero_zero_real )
% 11.11/6.20        = ( A = zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7926_inverse__nonzero__iff__nonzero,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = zero_zero_complex )
% 11.11/6.20        = ( A = zero_zero_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7927_inverse__zero,axiom,
% 11.11/6.20      ( ( inverse_inverse_rat @ zero_zero_rat )
% 11.11/6.20      = zero_zero_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7928_inverse__zero,axiom,
% 11.11/6.20      ( ( inverse_inverse_real @ zero_zero_real )
% 11.11/6.20      = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7929_inverse__zero,axiom,
% 11.11/6.20      ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 11.11/6.20      = zero_zero_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7930_inverse__mult__distrib,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 11.11/6.20        = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7931_inverse__mult__distrib,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 11.11/6.20        = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7932_inverse__eq__1__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ( inverse_inverse_rat @ X4 )
% 11.11/6.20          = one_one_rat )
% 11.11/6.20        = ( X4 = one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7933_inverse__eq__1__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ X4 )
% 11.11/6.20          = one_one_real )
% 11.11/6.20        = ( X4 = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7934_inverse__eq__1__iff,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ X4 )
% 11.11/6.20          = one_one_complex )
% 11.11/6.20        = ( X4 = one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7935_inverse__1,axiom,
% 11.11/6.20      ( ( inverse_inverse_rat @ one_one_rat )
% 11.11/6.20      = one_one_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7936_inverse__1,axiom,
% 11.11/6.20      ( ( inverse_inverse_real @ one_one_real )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7937_inverse__1,axiom,
% 11.11/6.20      ( ( invers8013647133539491842omplex @ one_one_complex )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7938_inverse__divide,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 11.11/6.20        = ( divide_divide_real @ B @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7939_inverse__divide,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 11.11/6.20        = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7940_inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.20        = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7941_inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.20        = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7942_inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.20        = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7943_abs__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20        = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7944_abs__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20        = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7945_abs__inverse,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 11.11/6.20        = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7946_inverse__sgn,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 11.11/6.20        = ( sgn_sgn_rat @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7947_inverse__sgn,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 11.11/6.20        = ( sgn_sgn_real @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7948_sgn__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20        = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7949_sgn__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20        = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7950_sgn__inverse,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 11.11/6.20        = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7951_inverse__nonnegative__iff__nonnegative,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7952_inverse__nonnegative__iff__nonnegative,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7953_inverse__nonpositive__iff__nonpositive,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 11.11/6.20        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7954_inverse__nonpositive__iff__nonpositive,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7955_inverse__positive__iff__positive,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7956_inverse__positive__iff__positive,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7957_inverse__negative__iff__negative,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 11.11/6.20        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7958_inverse__negative__iff__negative,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7959_inverse__less__iff__less__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7960_inverse__less__iff__less__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7961_inverse__less__iff__less,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.20         => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( ord_less_rat @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7962_inverse__less__iff__less,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20         => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( ord_less_real @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7963_gbinomial__0_I2_J,axiom,
% 11.11/6.20      ! [K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 11.11/6.20        = zero_zero_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7964_gbinomial__0_I2_J,axiom,
% 11.11/6.20      ! [K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 11.11/6.20        = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7965_gbinomial__0_I2_J,axiom,
% 11.11/6.20      ! [K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 11.11/6.20        = zero_zero_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7966_gbinomial__0_I2_J,axiom,
% 11.11/6.20      ! [K: nat] :
% 11.11/6.20        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 11.11/6.20        = zero_zero_nat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7967_gbinomial__0_I2_J,axiom,
% 11.11/6.20      ! [K: nat] :
% 11.11/6.20        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 11.11/6.20        = zero_zero_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7968_gbinomial__0_I1_J,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( gbinomial_complex @ A @ zero_zero_nat )
% 11.11/6.20        = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7969_gbinomial__0_I1_J,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( gbinomial_real @ A @ zero_zero_nat )
% 11.11/6.20        = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7970_gbinomial__0_I1_J,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 11.11/6.20        = one_one_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7971_gbinomial__0_I1_J,axiom,
% 11.11/6.20      ! [A: nat] :
% 11.11/6.20        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 11.11/6.20        = one_one_nat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7972_gbinomial__0_I1_J,axiom,
% 11.11/6.20      ! [A: int] :
% 11.11/6.20        ( ( gbinomial_int @ A @ zero_zero_nat )
% 11.11/6.20        = one_one_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7973_norm__ii,axiom,
% 11.11/6.20      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7974_norm__cis,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 11.11/6.20        = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7975_inverse__le__iff__le__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7976_inverse__le__iff__le__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7977_inverse__le__iff__le,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 11.11/6.20         => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7978_inverse__le__iff__le,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7979_right__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20          = one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7980_right__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 11.11/6.20          = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7981_right__inverse,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 11.11/6.20          = one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7982_left__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 11.11/6.20          = one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7983_left__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 11.11/6.20          = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7984_left__inverse,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 11.11/6.20          = one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7985_inverse__eq__divide__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 11.11/6.20        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7986_inverse__eq__divide__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 11.11/6.20        = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7987_inverse__eq__divide__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 11.11/6.20        = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7988_inverse__eq__divide__neg__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 11.11/6.20        = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7989_inverse__eq__divide__neg__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 11.11/6.20        = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7990_inverse__eq__divide__neg__numeral,axiom,
% 11.11/6.20      ! [W: num] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.20        = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7991_exp__two__pi__i_H,axiom,
% 11.11/6.20      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7992_exp__two__pi__i,axiom,
% 11.11/6.20      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7993_cis__pi__half,axiom,
% 11.11/6.20      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.20      = imaginary_unit ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7994_power2__i,axiom,
% 11.11/6.20      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7995_cis__minus__pi__half,axiom,
% 11.11/6.20      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.20      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7996_mult__commute__imp__mult__inverse__commute,axiom,
% 11.11/6.20      ! [Y: real,X4: real] :
% 11.11/6.20        ( ( ( times_times_real @ Y @ X4 )
% 11.11/6.20          = ( times_times_real @ X4 @ Y ) )
% 11.11/6.20       => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X4 )
% 11.11/6.20          = ( times_times_real @ X4 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7997_mult__commute__imp__mult__inverse__commute,axiom,
% 11.11/6.20      ! [Y: complex,X4: complex] :
% 11.11/6.20        ( ( ( times_times_complex @ Y @ X4 )
% 11.11/6.20          = ( times_times_complex @ X4 @ Y ) )
% 11.11/6.20       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X4 )
% 11.11/6.20          = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7998_power__inverse,axiom,
% 11.11/6.20      ! [A: real,N2: nat] :
% 11.11/6.20        ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N2 )
% 11.11/6.20        = ( inverse_inverse_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_7999_power__inverse,axiom,
% 11.11/6.20      ! [A: complex,N2: nat] :
% 11.11/6.20        ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N2 )
% 11.11/6.20        = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8000_inverse__eq__imp__eq,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ A )
% 11.11/6.20          = ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( A = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8001_inverse__eq__imp__eq,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20       => ( A = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8002_field__class_Ofield__inverse__zero,axiom,
% 11.11/6.20      ( ( inverse_inverse_rat @ zero_zero_rat )
% 11.11/6.20      = zero_zero_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8003_field__class_Ofield__inverse__zero,axiom,
% 11.11/6.20      ( ( inverse_inverse_real @ zero_zero_real )
% 11.11/6.20      = zero_zero_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8004_field__class_Ofield__inverse__zero,axiom,
% 11.11/6.20      ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 11.11/6.20      = zero_zero_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8005_inverse__zero__imp__zero,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ( inverse_inverse_rat @ A )
% 11.11/6.20          = zero_zero_rat )
% 11.11/6.20       => ( A = zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8006_inverse__zero__imp__zero,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ A )
% 11.11/6.20          = zero_zero_real )
% 11.11/6.20       => ( A = zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8007_inverse__zero__imp__zero,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = zero_zero_complex )
% 11.11/6.20       => ( A = zero_zero_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8008_nonzero__inverse__eq__imp__eq,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ( inverse_inverse_rat @ A )
% 11.11/6.20          = ( inverse_inverse_rat @ B ) )
% 11.11/6.20       => ( ( A != zero_zero_rat )
% 11.11/6.20         => ( ( B != zero_zero_rat )
% 11.11/6.20           => ( A = B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8009_nonzero__inverse__eq__imp__eq,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ( inverse_inverse_real @ A )
% 11.11/6.20          = ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( ( A != zero_zero_real )
% 11.11/6.20         => ( ( B != zero_zero_real )
% 11.11/6.20           => ( A = B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8010_nonzero__inverse__eq__imp__eq,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20       => ( ( A != zero_zero_complex )
% 11.11/6.20         => ( ( B != zero_zero_complex )
% 11.11/6.20           => ( A = B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8011_nonzero__inverse__inverse__eq,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20          = A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8012_nonzero__inverse__inverse__eq,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20          = A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8013_nonzero__inverse__inverse__eq,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 11.11/6.20          = A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8014_nonzero__imp__inverse__nonzero,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( inverse_inverse_rat @ A )
% 11.11/6.20         != zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8015_nonzero__imp__inverse__nonzero,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( inverse_inverse_real @ A )
% 11.11/6.20         != zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8016_nonzero__imp__inverse__nonzero,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20         != zero_zero_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8017_norm__inverse__le__norm,axiom,
% 11.11/6.20      ! [R3: real,X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ R3 @ ( real_V7735802525324610683m_real @ X4 ) )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ R3 )
% 11.11/6.20         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8018_norm__inverse__le__norm,axiom,
% 11.11/6.20      ! [R3: real,X4: complex] :
% 11.11/6.20        ( ( ord_less_eq_real @ R3 @ ( real_V1022390504157884413omplex @ X4 ) )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ R3 )
% 11.11/6.20         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8019_positive__imp__inverse__positive,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8020_positive__imp__inverse__positive,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8021_negative__imp__inverse__negative,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ A @ zero_zero_rat )
% 11.11/6.20       => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8022_negative__imp__inverse__negative,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.20       => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8023_inverse__positive__imp__positive,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20       => ( ( A != zero_zero_rat )
% 11.11/6.20         => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8024_inverse__positive__imp__positive,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20       => ( ( A != zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8025_inverse__negative__imp__negative,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 11.11/6.20       => ( ( A != zero_zero_rat )
% 11.11/6.20         => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8026_inverse__negative__imp__negative,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 11.11/6.20       => ( ( A != zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8027_less__imp__inverse__less__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ A @ B )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8028_less__imp__inverse__less__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ A @ B )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8029_inverse__less__imp__less__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ord_less_rat @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8030_inverse__less__imp__less__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ord_less_real @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8031_less__imp__inverse__less,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ A @ B )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20         => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8032_less__imp__inverse__less,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ A @ B )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8033_inverse__less__imp__less,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20         => ( ord_less_rat @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8034_inverse__less__imp__less,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_real @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8035_nonzero__inverse__mult__distrib,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( B != zero_zero_rat )
% 11.11/6.20         => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.20            = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8036_nonzero__inverse__mult__distrib,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( B != zero_zero_real )
% 11.11/6.20         => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 11.11/6.20            = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8037_nonzero__inverse__mult__distrib,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( B != zero_zero_complex )
% 11.11/6.20         => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 11.11/6.20            = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8038_nonzero__inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 11.11/6.20          = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8039_nonzero__inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 11.11/6.20          = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8040_nonzero__inverse__minus__eq,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 11.11/6.20          = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8041_inverse__unique,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ( times_times_rat @ A @ B )
% 11.11/6.20          = one_one_rat )
% 11.11/6.20       => ( ( inverse_inverse_rat @ A )
% 11.11/6.20          = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8042_inverse__unique,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ( times_times_real @ A @ B )
% 11.11/6.20          = one_one_real )
% 11.11/6.20       => ( ( inverse_inverse_real @ A )
% 11.11/6.20          = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8043_inverse__unique,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( ( times_times_complex @ A @ B )
% 11.11/6.20          = one_one_complex )
% 11.11/6.20       => ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = B ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8044_inverse__numeral__1,axiom,
% 11.11/6.20      ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 11.11/6.20      = ( numeral_numeral_real @ one ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8045_inverse__numeral__1,axiom,
% 11.11/6.20      ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 11.11/6.20      = ( numera6690914467698888265omplex @ one ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8046_divide__inverse__commute,axiom,
% 11.11/6.20      ( divide_divide_real
% 11.11/6.20      = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8047_divide__inverse__commute,axiom,
% 11.11/6.20      ( divide1717551699836669952omplex
% 11.11/6.20      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8048_divide__inverse,axiom,
% 11.11/6.20      ( divide_divide_real
% 11.11/6.20      = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8049_divide__inverse,axiom,
% 11.11/6.20      ( divide1717551699836669952omplex
% 11.11/6.20      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8050_field__class_Ofield__divide__inverse,axiom,
% 11.11/6.20      ( divide_divide_real
% 11.11/6.20      = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8051_field__class_Ofield__divide__inverse,axiom,
% 11.11/6.20      ( divide1717551699836669952omplex
% 11.11/6.20      = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8052_inverse__eq__divide,axiom,
% 11.11/6.20      ( inverse_inverse_rat
% 11.11/6.20      = ( divide_divide_rat @ one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8053_inverse__eq__divide,axiom,
% 11.11/6.20      ( inverse_inverse_real
% 11.11/6.20      = ( divide_divide_real @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8054_inverse__eq__divide,axiom,
% 11.11/6.20      ( invers8013647133539491842omplex
% 11.11/6.20      = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8055_power__mult__inverse__distrib,axiom,
% 11.11/6.20      ! [X4: real,M: nat] :
% 11.11/6.20        ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( inverse_inverse_real @ X4 ) )
% 11.11/6.20        = ( times_times_real @ ( inverse_inverse_real @ X4 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8056_power__mult__inverse__distrib,axiom,
% 11.11/6.20      ! [X4: complex,M: nat] :
% 11.11/6.20        ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( invers8013647133539491842omplex @ X4 ) )
% 11.11/6.20        = ( times_times_complex @ ( invers8013647133539491842omplex @ X4 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8057_power__mult__power__inverse__commute,axiom,
% 11.11/6.20      ! [X4: real,M: nat,N2: nat] :
% 11.11/6.20        ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) )
% 11.11/6.20        = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8058_power__mult__power__inverse__commute,axiom,
% 11.11/6.20      ! [X4: complex,M: nat,N2: nat] :
% 11.11/6.20        ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) )
% 11.11/6.20        = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8059_mult__inverse__of__nat__commute,axiom,
% 11.11/6.20      ! [Xa: nat,X4: real] :
% 11.11/6.20        ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X4 )
% 11.11/6.20        = ( times_times_real @ X4 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8060_mult__inverse__of__nat__commute,axiom,
% 11.11/6.20      ! [Xa: nat,X4: complex] :
% 11.11/6.20        ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X4 )
% 11.11/6.20        = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8061_nonzero__abs__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 11.11/6.20          = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8062_nonzero__abs__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 11.11/6.20          = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8063_divide__real__def,axiom,
% 11.11/6.20      ( divide_divide_real
% 11.11/6.20      = ( ^ [X: real,Y5: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y5 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8064_frac__ge__0,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8065_frac__ge__0,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8066_frac__lt__1,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X4 ) @ one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8067_frac__lt__1,axiom,
% 11.11/6.20      ! [X4: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X4 ) @ one_one_rat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8068_frac__1__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 11.11/6.20        = ( archim2898591450579166408c_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8069_frac__1__eq,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 11.11/6.20        = ( archimedean_frac_rat @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8070_le__imp__inverse__le__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8071_le__imp__inverse__le__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8072_inverse__le__imp__le__neg,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8073_inverse__le__imp__le__neg,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( ( ord_less_real @ B @ zero_zero_real )
% 11.11/6.20         => ( ord_less_eq_real @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8074_le__imp__inverse__le,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ A @ B )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20         => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8075_le__imp__inverse__le,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8076_inverse__le__imp__le,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20         => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8077_inverse__le__imp__le,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20         => ( ord_less_eq_real @ B @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8078_inverse__le__1__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 11.11/6.20        = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.20          | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8079_inverse__le__1__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 11.11/6.20        = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20          | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8080_one__less__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( ord_less_rat @ A @ one_one_rat )
% 11.11/6.20         => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8081_one__less__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( ord_less_real @ A @ one_one_real )
% 11.11/6.20         => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8082_one__less__inverse__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 11.11/6.20        = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.20          & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8083_one__less__inverse__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 11.11/6.20        = ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20          & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8084_field__class_Ofield__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 11.11/6.20          = one_one_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8085_field__class_Ofield__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 11.11/6.20          = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8086_field__class_Ofield__inverse,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 11.11/6.20          = one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8087_division__ring__inverse__add,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( B != zero_zero_rat )
% 11.11/6.20         => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8088_division__ring__inverse__add,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( B != zero_zero_real )
% 11.11/6.20         => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8089_division__ring__inverse__add,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( B != zero_zero_complex )
% 11.11/6.20         => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20            = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8090_inverse__add,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( B != zero_zero_rat )
% 11.11/6.20         => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8091_inverse__add,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( B != zero_zero_real )
% 11.11/6.20         => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8092_inverse__add,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( B != zero_zero_complex )
% 11.11/6.20         => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20            = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8093_division__ring__inverse__diff,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( B != zero_zero_rat )
% 11.11/6.20         => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8094_division__ring__inverse__diff,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( B != zero_zero_real )
% 11.11/6.20         => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8095_division__ring__inverse__diff,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( B != zero_zero_complex )
% 11.11/6.20         => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20            = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8096_nonzero__inverse__eq__divide,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( inverse_inverse_rat @ A )
% 11.11/6.20          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8097_nonzero__inverse__eq__divide,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( inverse_inverse_real @ A )
% 11.11/6.20          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8098_nonzero__inverse__eq__divide,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( invers8013647133539491842omplex @ A )
% 11.11/6.20          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8099_gbinomial__Suc__Suc,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8100_gbinomial__Suc__Suc,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8101_gbinomial__Suc__Suc,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8102_gbinomial__of__nat__symmetric,axiom,
% 11.11/6.20      ! [K: nat,N2: nat] :
% 11.11/6.20        ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.20       => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 11.11/6.20          = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8103_inverse__powr,axiom,
% 11.11/6.20      ! [Y: real,A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.20       => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 11.11/6.20          = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8104_Complex__eq__i,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( complex2 @ X4 @ Y )
% 11.11/6.20          = imaginary_unit )
% 11.11/6.20        = ( ( X4 = zero_zero_real )
% 11.11/6.20          & ( Y = one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8105_imaginary__unit_Ocode,axiom,
% 11.11/6.20      ( imaginary_unit
% 11.11/6.20      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8106_inverse__le__iff,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20        = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.20           => ( ord_less_eq_rat @ B @ A ) )
% 11.11/6.20          & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.20           => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8107_inverse__le__iff,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20        = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.20           => ( ord_less_eq_real @ B @ A ) )
% 11.11/6.20          & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 11.11/6.20           => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8108_inverse__less__iff,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20        = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 11.11/6.20           => ( ord_less_rat @ B @ A ) )
% 11.11/6.20          & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 11.11/6.20           => ( ord_less_rat @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8109_inverse__less__iff,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20        = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 11.11/6.20           => ( ord_less_real @ B @ A ) )
% 11.11/6.20          & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 11.11/6.20           => ( ord_less_real @ A @ B ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8110_one__le__inverse,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8111_one__le__inverse,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.20         => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8112_inverse__less__1__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 11.11/6.20        = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 11.11/6.20          | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8113_inverse__less__1__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 11.11/6.20        = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20          | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8114_one__le__inverse__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 11.11/6.20        = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.20          & ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8115_one__le__inverse__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 11.11/6.20        = ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20          & ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8116_inverse__diff__inverse,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( A != zero_zero_rat )
% 11.11/6.20       => ( ( B != zero_zero_rat )
% 11.11/6.20         => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 11.11/6.20            = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8117_inverse__diff__inverse,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( A != zero_zero_real )
% 11.11/6.20       => ( ( B != zero_zero_real )
% 11.11/6.20         => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 11.11/6.20            = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8118_inverse__diff__inverse,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( A != zero_zero_complex )
% 11.11/6.20       => ( ( B != zero_zero_complex )
% 11.11/6.20         => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 11.11/6.20            = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8119_reals__Archimedean,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.20       => ? [N3: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8120_reals__Archimedean,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ? [N3: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8121_gbinomial__addition__formula,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8122_gbinomial__addition__formula,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ A @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8123_gbinomial__addition__formula,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 11.11/6.20        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8124_gbinomial__absorb__comp,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 11.11/6.20        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8125_gbinomial__absorb__comp,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 11.11/6.20        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8126_gbinomial__absorb__comp,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 11.11/6.20        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8127_gbinomial__ge__n__over__k__pow__k,axiom,
% 11.11/6.20      ! [K: nat,A: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 11.11/6.20       => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8128_gbinomial__ge__n__over__k__pow__k,axiom,
% 11.11/6.20      ! [K: nat,A: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 11.11/6.20       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8129_gbinomial__mult__1,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 11.11/6.20        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8130_gbinomial__mult__1,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 11.11/6.20        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8131_gbinomial__mult__1,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 11.11/6.20        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8132_gbinomial__mult__1_H,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 11.11/6.20        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8133_gbinomial__mult__1_H,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 11.11/6.20        = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8134_gbinomial__mult__1_H,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 11.11/6.20        = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8135_forall__pos__mono__1,axiom,
% 11.11/6.20      ! [P: real > $o,E2: real] :
% 11.11/6.20        ( ! [D3: real,E: real] :
% 11.11/6.20            ( ( ord_less_real @ D3 @ E )
% 11.11/6.20           => ( ( P @ D3 )
% 11.11/6.20             => ( P @ E ) ) )
% 11.11/6.20       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.20           => ( P @ E2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8136_forall__pos__mono,axiom,
% 11.11/6.20      ! [P: real > $o,E2: real] :
% 11.11/6.20        ( ! [D3: real,E: real] :
% 11.11/6.20            ( ( ord_less_real @ D3 @ E )
% 11.11/6.20           => ( ( P @ D3 )
% 11.11/6.20             => ( P @ E ) ) )
% 11.11/6.20       => ( ! [N3: nat] :
% 11.11/6.20              ( ( N3 != zero_zero_nat )
% 11.11/6.20             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.20           => ( P @ E2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8137_real__arch__inverse,axiom,
% 11.11/6.20      ! [E2: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.20        = ( ? [N: nat] :
% 11.11/6.20              ( ( N != zero_zero_nat )
% 11.11/6.20              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 11.11/6.20              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8138_sqrt__divide__self__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( divide_divide_real @ ( sqrt @ X4 ) @ X4 )
% 11.11/6.20          = ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8139_ln__inverse,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ln_ln_real @ ( inverse_inverse_real @ X4 ) )
% 11.11/6.20          = ( uminus_uminus_real @ ( ln_ln_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8140_ex__inverse__of__nat__less,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 11.11/6.20       => ? [N3: nat] :
% 11.11/6.20            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.20            & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N3 ) ) @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8141_ex__inverse__of__nat__less,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ? [N3: nat] :
% 11.11/6.20            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 11.11/6.20            & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8142_power__diff__conv__inverse,axiom,
% 11.11/6.20      ! [X4: rat,M: nat,N2: nat] :
% 11.11/6.20        ( ( X4 != zero_zero_rat )
% 11.11/6.20       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.20         => ( ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.20            = ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ M ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8143_power__diff__conv__inverse,axiom,
% 11.11/6.20      ! [X4: real,M: nat,N2: nat] :
% 11.11/6.20        ( ( X4 != zero_zero_real )
% 11.11/6.20       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.20         => ( ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.20            = ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ M ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8144_power__diff__conv__inverse,axiom,
% 11.11/6.20      ! [X4: complex,M: nat,N2: nat] :
% 11.11/6.20        ( ( X4 != zero_zero_complex )
% 11.11/6.20       => ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.20         => ( ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 11.11/6.20            = ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ M ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8145_Suc__times__gbinomial,axiom,
% 11.11/6.20      ! [K: nat,A: rat] :
% 11.11/6.20        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8146_Suc__times__gbinomial,axiom,
% 11.11/6.20      ! [K: nat,A: complex] :
% 11.11/6.20        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8147_Suc__times__gbinomial,axiom,
% 11.11/6.20      ! [K: nat,A: real] :
% 11.11/6.20        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8148_gbinomial__absorption,axiom,
% 11.11/6.20      ! [K: nat,A: rat] :
% 11.11/6.20        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8149_gbinomial__absorption,axiom,
% 11.11/6.20      ! [K: nat,A: complex] :
% 11.11/6.20        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8150_gbinomial__absorption,axiom,
% 11.11/6.20      ! [K: nat,A: real] :
% 11.11/6.20        ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 11.11/6.20        = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8151_gbinomial__trinomial__revision,axiom,
% 11.11/6.20      ! [K: nat,M: nat,A: rat] :
% 11.11/6.20        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.20       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 11.11/6.20          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8152_gbinomial__trinomial__revision,axiom,
% 11.11/6.20      ! [K: nat,M: nat,A: complex] :
% 11.11/6.20        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.20       => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 11.11/6.20          = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8153_gbinomial__trinomial__revision,axiom,
% 11.11/6.20      ! [K: nat,M: nat,A: real] :
% 11.11/6.20        ( ( ord_less_eq_nat @ K @ M )
% 11.11/6.20       => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 11.11/6.20          = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8154_log__inverse,axiom,
% 11.11/6.20      ! [A: real,X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( A != one_one_real )
% 11.11/6.20         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20           => ( ( log @ A @ ( inverse_inverse_real @ X4 ) )
% 11.11/6.20              = ( uminus_uminus_real @ ( log @ A @ X4 ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8155_frac__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( archim2898591450579166408c_real @ X4 )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20          & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8156_frac__eq,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ( archimedean_frac_rat @ X4 )
% 11.11/6.20          = X4 )
% 11.11/6.20        = ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 11.11/6.20          & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8157_frac__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 11.11/6.20         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 11.11/6.20        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 11.11/6.20         => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20            = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8158_frac__add,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 11.11/6.20         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 11.11/6.20        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 11.11/6.20         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 11.11/6.20            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8159_gbinomial__rec,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8160_gbinomial__rec,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8161_gbinomial__rec,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8162_gbinomial__factors,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8163_gbinomial__factors,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8164_gbinomial__factors,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 11.11/6.20        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8165_gbinomial__negated__upper,axiom,
% 11.11/6.20      ( gbinomial_complex
% 11.11/6.20      = ( ^ [A3: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A3 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8166_gbinomial__negated__upper,axiom,
% 11.11/6.20      ( gbinomial_rat
% 11.11/6.20      = ( ^ [A3: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A3 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8167_gbinomial__negated__upper,axiom,
% 11.11/6.20      ( gbinomial_real
% 11.11/6.20      = ( ^ [A3: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A3 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8168_gbinomial__index__swap,axiom,
% 11.11/6.20      ! [K: nat,N2: nat] :
% 11.11/6.20        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 11.11/6.20        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8169_gbinomial__index__swap,axiom,
% 11.11/6.20      ! [K: nat,N2: nat] :
% 11.11/6.20        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 11.11/6.20        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8170_gbinomial__index__swap,axiom,
% 11.11/6.20      ! [K: nat,N2: nat] :
% 11.11/6.20        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 11.11/6.20        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8171_exp__plus__inverse__exp,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8172_cmod__unit__one,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 11.11/6.20        = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8173_gbinomial__minus,axiom,
% 11.11/6.20      ! [A: complex,K: nat] :
% 11.11/6.20        ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 11.11/6.20        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8174_gbinomial__minus,axiom,
% 11.11/6.20      ! [A: rat,K: nat] :
% 11.11/6.20        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 11.11/6.20        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8175_gbinomial__minus,axiom,
% 11.11/6.20      ! [A: real,K: nat] :
% 11.11/6.20        ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 11.11/6.20        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8176_plus__inverse__ge__2,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8177_real__inv__sqrt__pow2,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20          = ( inverse_inverse_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8178_gbinomial__reduce__nat,axiom,
% 11.11/6.20      ! [K: nat,A: complex] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_complex @ A @ K )
% 11.11/6.20          = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8179_gbinomial__reduce__nat,axiom,
% 11.11/6.20      ! [K: nat,A: real] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_real @ A @ K )
% 11.11/6.20          = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8180_gbinomial__reduce__nat,axiom,
% 11.11/6.20      ! [K: nat,A: rat] :
% 11.11/6.20        ( ( ord_less_nat @ zero_zero_nat @ K )
% 11.11/6.20       => ( ( gbinomial_rat @ A @ K )
% 11.11/6.20          = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8181_gbinomial__pochhammer,axiom,
% 11.11/6.20      ( gbinomial_complex
% 11.11/6.20      = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8182_gbinomial__pochhammer,axiom,
% 11.11/6.20      ( gbinomial_rat
% 11.11/6.20      = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8183_gbinomial__pochhammer,axiom,
% 11.11/6.20      ( gbinomial_real
% 11.11/6.20      = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8184_gbinomial__pochhammer_H,axiom,
% 11.11/6.20      ( gbinomial_rat
% 11.11/6.20      = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8185_gbinomial__pochhammer_H,axiom,
% 11.11/6.20      ( gbinomial_complex
% 11.11/6.20      = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8186_gbinomial__pochhammer_H,axiom,
% 11.11/6.20      ( gbinomial_real
% 11.11/6.20      = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8187_tan__cot,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 11.11/6.20        = ( inverse_inverse_real @ ( tan_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8188_floor__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 11.11/6.20         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 11.11/6.20        & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 11.11/6.20         => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8189_floor__add,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 11.11/6.20         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 11.11/6.20        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 11.11/6.20         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 11.11/6.20            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8190_real__le__x__sinh,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ord_less_eq_real @ X4 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8191_real__le__abs__sinh,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8192_tan__sec,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( cos_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20          = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8193_tan__sec,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( ( cos_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20          = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8194_Arg__minus__ii,axiom,
% 11.11/6.20      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 11.11/6.20      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8195_csqrt__ii,axiom,
% 11.11/6.20      ( ( csqrt @ imaginary_unit )
% 11.11/6.20      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8196_Arg__ii,axiom,
% 11.11/6.20      ( ( arg @ imaginary_unit )
% 11.11/6.20      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8197_sinh__ln__real,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( sinh_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.20          = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8198_cis__multiple__2pi,axiom,
% 11.11/6.20      ! [N2: real] :
% 11.11/6.20        ( ( member_real @ N2 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 11.11/6.20          = one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8199_sinh__real__less__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 11.11/6.20        = ( ord_less_real @ X4 @ Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8200_sinh__real__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 11.11/6.20        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8201_sinh__real__neg__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8202_sinh__real__pos__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 11.11/6.20        = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8203_sinh__real__nonneg__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 11.11/6.20        = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8204_sinh__real__nonpos__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 11.11/6.20        = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8205_floor__add2,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20          | ( member_real @ Y @ ring_1_Ints_real ) )
% 11.11/6.20       => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20          = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8206_floor__add2,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20          | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 11.11/6.20       => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 11.11/6.20          = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8207_frac__gt__0__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) )
% 11.11/6.20        = ( ~ ( member_real @ X4 @ ring_1_Ints_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8208_frac__gt__0__iff,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) )
% 11.11/6.20        = ( ~ ( member_rat @ X4 @ ring_1_Ints_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8209_power2__csqrt,axiom,
% 11.11/6.20      ! [Z: complex] :
% 11.11/6.20        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20        = Z ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8210_Ints__power,axiom,
% 11.11/6.20      ! [A: real,N2: nat] :
% 11.11/6.20        ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20       => ( member_real @ ( power_power_real @ A @ N2 ) @ ring_1_Ints_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8211_Ints__power,axiom,
% 11.11/6.20      ! [A: int,N2: nat] :
% 11.11/6.20        ( ( member_int @ A @ ring_1_Ints_int )
% 11.11/6.20       => ( member_int @ ( power_power_int @ A @ N2 ) @ ring_1_Ints_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8212_Ints__power,axiom,
% 11.11/6.20      ! [A: complex,N2: nat] :
% 11.11/6.20        ( ( member_complex @ A @ ring_1_Ints_complex )
% 11.11/6.20       => ( member_complex @ ( power_power_complex @ A @ N2 ) @ ring_1_Ints_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8213_Ints__numeral,axiom,
% 11.11/6.20      ! [N2: num] : ( member_complex @ ( numera6690914467698888265omplex @ N2 ) @ ring_1_Ints_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8214_Ints__numeral,axiom,
% 11.11/6.20      ! [N2: num] : ( member_real @ ( numeral_numeral_real @ N2 ) @ ring_1_Ints_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8215_Ints__numeral,axiom,
% 11.11/6.20      ! [N2: num] : ( member_int @ ( numeral_numeral_int @ N2 ) @ ring_1_Ints_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8216_Ints__1,axiom,
% 11.11/6.20      member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8217_Ints__1,axiom,
% 11.11/6.20      member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8218_Ints__1,axiom,
% 11.11/6.20      member_int @ one_one_int @ ring_1_Ints_int ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8219_Ints__1,axiom,
% 11.11/6.20      member_real @ one_one_real @ ring_1_Ints_real ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8220_Ints__add,axiom,
% 11.11/6.20      ! [A: complex,B: complex] :
% 11.11/6.20        ( ( member_complex @ A @ ring_1_Ints_complex )
% 11.11/6.20       => ( ( member_complex @ B @ ring_1_Ints_complex )
% 11.11/6.20         => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8221_Ints__add,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20       => ( ( member_real @ B @ ring_1_Ints_real )
% 11.11/6.20         => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8222_Ints__add,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 11.11/6.20         => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8223_Ints__add,axiom,
% 11.11/6.20      ! [A: int,B: int] :
% 11.11/6.20        ( ( member_int @ A @ ring_1_Ints_int )
% 11.11/6.20       => ( ( member_int @ B @ ring_1_Ints_int )
% 11.11/6.20         => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8224_Ints__double__eq__0__iff,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( member_complex @ A @ ring_1_Ints_complex )
% 11.11/6.20       => ( ( ( plus_plus_complex @ A @ A )
% 11.11/6.20            = zero_zero_complex )
% 11.11/6.20          = ( A = zero_zero_complex ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8225_Ints__double__eq__0__iff,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20       => ( ( ( plus_plus_real @ A @ A )
% 11.11/6.20            = zero_zero_real )
% 11.11/6.20          = ( A = zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8226_Ints__double__eq__0__iff,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( ( plus_plus_rat @ A @ A )
% 11.11/6.20            = zero_zero_rat )
% 11.11/6.20          = ( A = zero_zero_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8227_Ints__double__eq__0__iff,axiom,
% 11.11/6.20      ! [A: int] :
% 11.11/6.20        ( ( member_int @ A @ ring_1_Ints_int )
% 11.11/6.20       => ( ( ( plus_plus_int @ A @ A )
% 11.11/6.20            = zero_zero_int )
% 11.11/6.20          = ( A = zero_zero_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8228_Ints__odd__nonzero,axiom,
% 11.11/6.20      ! [A: complex] :
% 11.11/6.20        ( ( member_complex @ A @ ring_1_Ints_complex )
% 11.11/6.20       => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 11.11/6.20         != zero_zero_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8229_Ints__odd__nonzero,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20       => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 11.11/6.20         != zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8230_Ints__odd__nonzero,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 11.11/6.20         != zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8231_Ints__odd__nonzero,axiom,
% 11.11/6.20      ! [A: int] :
% 11.11/6.20        ( ( member_int @ A @ ring_1_Ints_int )
% 11.11/6.20       => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 11.11/6.20         != zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8232_of__int__divide__in__Ints,axiom,
% 11.11/6.20      ! [B: int,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.20       => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8233_of__int__divide__in__Ints,axiom,
% 11.11/6.20      ! [B: int,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.20       => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8234_of__int__divide__in__Ints,axiom,
% 11.11/6.20      ! [B: int,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.20       => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8235_of__int__divide__in__Ints,axiom,
% 11.11/6.20      ! [B: int,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.20       => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8236_of__int__divide__in__Ints,axiom,
% 11.11/6.20      ! [B: int,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ B @ A )
% 11.11/6.20       => ( member_Code_integer @ ( divide6298287555418463151nteger @ ( ring_18347121197199848620nteger @ A ) @ ( ring_18347121197199848620nteger @ B ) ) @ ring_11222124179247155820nteger ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8237_Ints__odd__less__0,axiom,
% 11.11/6.20      ! [A: real] :
% 11.11/6.20        ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20       => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 11.11/6.20          = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8238_Ints__odd__less__0,axiom,
% 11.11/6.20      ! [A: rat] :
% 11.11/6.20        ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 11.11/6.20          = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8239_Ints__odd__less__0,axiom,
% 11.11/6.20      ! [A: int] :
% 11.11/6.20        ( ( member_int @ A @ ring_1_Ints_int )
% 11.11/6.20       => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 11.11/6.20          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8240_Ints__nonzero__abs__ge1,axiom,
% 11.11/6.20      ! [X4: code_integer] :
% 11.11/6.20        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 11.11/6.20       => ( ( X4 != zero_z3403309356797280102nteger )
% 11.11/6.20         => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8241_Ints__nonzero__abs__ge1,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( X4 != zero_zero_real )
% 11.11/6.20         => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8242_Ints__nonzero__abs__ge1,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( X4 != zero_zero_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8243_Ints__nonzero__abs__ge1,axiom,
% 11.11/6.20      ! [X4: int] :
% 11.11/6.20        ( ( member_int @ X4 @ ring_1_Ints_int )
% 11.11/6.20       => ( ( X4 != zero_zero_int )
% 11.11/6.20         => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8244_Ints__nonzero__abs__less1,axiom,
% 11.11/6.20      ! [X4: code_integer] :
% 11.11/6.20        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 11.11/6.20       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer )
% 11.11/6.20         => ( X4 = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8245_Ints__nonzero__abs__less1,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.20         => ( X4 = zero_zero_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8246_Ints__nonzero__abs__less1,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat )
% 11.11/6.20         => ( X4 = zero_zero_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8247_Ints__nonzero__abs__less1,axiom,
% 11.11/6.20      ! [X4: int] :
% 11.11/6.20        ( ( member_int @ X4 @ ring_1_Ints_int )
% 11.11/6.20       => ( ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int )
% 11.11/6.20         => ( X4 = zero_zero_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8248_Ints__eq__abs__less1,axiom,
% 11.11/6.20      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.20        ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 11.11/6.20       => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 11.11/6.20         => ( ( X4 = Y )
% 11.11/6.20            = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8249_Ints__eq__abs__less1,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( member_real @ Y @ ring_1_Ints_real )
% 11.11/6.20         => ( ( X4 = Y )
% 11.11/6.20            = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y ) ) @ one_one_real ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8250_Ints__eq__abs__less1,axiom,
% 11.11/6.20      ! [X4: rat,Y: rat] :
% 11.11/6.20        ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20       => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 11.11/6.20         => ( ( X4 = Y )
% 11.11/6.20            = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8251_Ints__eq__abs__less1,axiom,
% 11.11/6.20      ! [X4: int,Y: int] :
% 11.11/6.20        ( ( member_int @ X4 @ ring_1_Ints_int )
% 11.11/6.20       => ( ( member_int @ Y @ ring_1_Ints_int )
% 11.11/6.20         => ( ( X4 = Y )
% 11.11/6.20            = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Y ) ) @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8252_of__real__sqrt,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X4 ) )
% 11.11/6.20          = ( csqrt @ ( real_V4546457046886955230omplex @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8253_frac__neg,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20         => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.20            = zero_zero_real ) )
% 11.11/6.20        & ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 11.11/6.20         => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 11.11/6.20            = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8254_frac__neg,axiom,
% 11.11/6.20      ! [X4: rat] :
% 11.11/6.20        ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 11.11/6.20            = zero_zero_rat ) )
% 11.11/6.20        & ( ~ ( member_rat @ X4 @ ring_1_Ints_rat )
% 11.11/6.20         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 11.11/6.20            = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X4 ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8255_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8256_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8257_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8258_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8259_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8260_le__mult__floor__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8261_frac__unique__iff,axiom,
% 11.11/6.20      ! [X4: real,A: real] :
% 11.11/6.20        ( ( ( archim2898591450579166408c_real @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( member_real @ ( minus_minus_real @ X4 @ A ) @ ring_1_Ints_real )
% 11.11/6.20          & ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20          & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8262_frac__unique__iff,axiom,
% 11.11/6.20      ! [X4: rat,A: rat] :
% 11.11/6.20        ( ( ( archimedean_frac_rat @ X4 )
% 11.11/6.20          = A )
% 11.11/6.20        = ( ( member_rat @ ( minus_minus_rat @ X4 @ A ) @ ring_1_Ints_rat )
% 11.11/6.20          & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20          & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8263_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8264_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8265_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.20       => ( ( member_real @ A @ ring_1_Ints_real )
% 11.11/6.20         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8266_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8267_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8268_mult__ceiling__le__Ints,axiom,
% 11.11/6.20      ! [A: rat,B: rat] :
% 11.11/6.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 11.11/6.20       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 11.11/6.20         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8269_Arg__bounded,axiom,
% 11.11/6.20      ! [Z: complex] :
% 11.11/6.20        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 11.11/6.20        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8270_sin__integer__2pi,axiom,
% 11.11/6.20      ! [N2: real] :
% 11.11/6.20        ( ( member_real @ N2 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 11.11/6.20          = zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8271_cos__integer__2pi,axiom,
% 11.11/6.20      ! [N2: real] :
% 11.11/6.20        ( ( member_real @ N2 @ ring_1_Ints_real )
% 11.11/6.20       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 11.11/6.20          = one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8272_complex__inverse,axiom,
% 11.11/6.20      ! [A: real,B: real] :
% 11.11/6.20        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 11.11/6.20        = ( 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 ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8273_sinh__field__def,axiom,
% 11.11/6.20      ( sinh_real
% 11.11/6.20      = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8274_sinh__field__def,axiom,
% 11.11/6.20      ( sinh_complex
% 11.11/6.20      = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8275_cis__Arg__unique,axiom,
% 11.11/6.20      ! [Z: complex,X4: real] :
% 11.11/6.20        ( ( ( sgn_sgn_complex @ Z )
% 11.11/6.20          = ( cis @ X4 ) )
% 11.11/6.20       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 11.11/6.20         => ( ( ord_less_eq_real @ X4 @ pi )
% 11.11/6.20           => ( ( arg @ Z )
% 11.11/6.20              = X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8276_Arg__correct,axiom,
% 11.11/6.20      ! [Z: complex] :
% 11.11/6.20        ( ( Z != zero_zero_complex )
% 11.11/6.20       => ( ( ( sgn_sgn_complex @ Z )
% 11.11/6.20            = ( cis @ ( arg @ Z ) ) )
% 11.11/6.20          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 11.11/6.20          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8277_cosh__ln__real,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( cosh_real @ ( ln_ln_real @ X4 ) )
% 11.11/6.20          = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8278_cosh__double,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.20        = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8279_cosh__double,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.20        = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8280_horner__sum__of__bool__2__less,axiom,
% 11.11/6.20      ! [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 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8281_cosh__zero__iff,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ( cosh_real @ X4 )
% 11.11/6.20          = zero_zero_real )
% 11.11/6.20        = ( ( power_power_real @ ( exp_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8282_cosh__zero__iff,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( ( cosh_complex @ X4 )
% 11.11/6.20          = zero_zero_complex )
% 11.11/6.20        = ( ( power_power_complex @ ( exp_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8283_push__bit__numeral__minus__1,axiom,
% 11.11/6.20      ! [N2: num] :
% 11.11/6.20        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.20        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8284_push__bit__numeral__minus__1,axiom,
% 11.11/6.20      ! [N2: num] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8285_push__bit__nonnegative__int__iff,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 11.11/6.20        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8286_push__bit__negative__int__iff,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.20        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8287_push__bit__eq__0__iff,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( ( bit_se545348938243370406it_int @ N2 @ A )
% 11.11/6.20          = zero_zero_int )
% 11.11/6.20        = ( A = zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8288_push__bit__eq__0__iff,axiom,
% 11.11/6.20      ! [N2: nat,A: nat] :
% 11.11/6.20        ( ( ( bit_se547839408752420682it_nat @ N2 @ A )
% 11.11/6.20          = zero_zero_nat )
% 11.11/6.20        = ( A = zero_zero_nat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8289_push__bit__of__0,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ zero_zero_int )
% 11.11/6.20        = zero_zero_int ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8290_push__bit__of__0,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ zero_zero_nat )
% 11.11/6.20        = zero_zero_nat ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8291_push__bit__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8292_push__bit__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8293_push__bit__and,axiom,
% 11.11/6.20      ! [N2: nat,A: int,B: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 11.11/6.20        = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8294_push__bit__and,axiom,
% 11.11/6.20      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 11.11/6.20        = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8295_push__bit__xor,axiom,
% 11.11/6.20      ! [N2: nat,A: int,B: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 11.11/6.20        = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8296_push__bit__xor,axiom,
% 11.11/6.20      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 11.11/6.20        = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8297_concat__bit__of__zero__1,axiom,
% 11.11/6.20      ! [N2: nat,L: int] :
% 11.11/6.20        ( ( bit_concat_bit @ N2 @ zero_zero_int @ L )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ N2 @ L ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8298_cosh__0,axiom,
% 11.11/6.20      ( ( cosh_complex @ zero_zero_complex )
% 11.11/6.20      = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8299_cosh__0,axiom,
% 11.11/6.20      ( ( cosh_real @ zero_zero_real )
% 11.11/6.20      = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8300_push__bit__Suc__numeral,axiom,
% 11.11/6.20      ! [N2: nat,K: num] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8301_push__bit__Suc__numeral,axiom,
% 11.11/6.20      ! [N2: nat,K: num] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8302_push__bit__Suc__minus__numeral,axiom,
% 11.11/6.20      ! [N2: nat,K: num] :
% 11.11/6.20        ( ( bit_se7788150548672797655nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 11.11/6.20        = ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8303_push__bit__Suc__minus__numeral,axiom,
% 11.11/6.20      ! [N2: nat,K: num] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8304_push__bit__numeral,axiom,
% 11.11/6.20      ! [L: num,K: num] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ K ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8305_push__bit__numeral,axiom,
% 11.11/6.20      ! [L: num,K: num] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8306_push__bit__minus__one__eq__not__mask,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 11.11/6.20        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8307_push__bit__minus__one__eq__not__mask,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.20        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8308_push__bit__Suc,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ A )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8309_push__bit__Suc,axiom,
% 11.11/6.20      ! [N2: nat,A: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ A )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8310_push__bit__of__1,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ one_one_int )
% 11.11/6.20        = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8311_push__bit__of__1,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ one_one_nat )
% 11.11/6.20        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8312_push__bit__of__Suc__0,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.20        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8313_even__push__bit__iff,axiom,
% 11.11/6.20      ! [N2: nat,A: code_integer] :
% 11.11/6.20        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N2 @ A ) )
% 11.11/6.20        = ( ( N2 != zero_zero_nat )
% 11.11/6.20          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8314_even__push__bit__iff,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 11.11/6.20        = ( ( N2 != zero_zero_nat )
% 11.11/6.20          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8315_even__push__bit__iff,axiom,
% 11.11/6.20      ! [N2: nat,A: nat] :
% 11.11/6.20        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 11.11/6.20        = ( ( N2 != zero_zero_nat )
% 11.11/6.20          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8316_push__bit__minus__numeral,axiom,
% 11.11/6.20      ! [L: num,K: num] :
% 11.11/6.20        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 11.11/6.20        = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8317_push__bit__minus__numeral,axiom,
% 11.11/6.20      ! [L: num,K: num] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8318_push__bit__of__int,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 11.11/6.20        = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8319_of__nat__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat] :
% 11.11/6.20        ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8320_of__nat__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat] :
% 11.11/6.20        ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8321_push__bit__of__nat,axiom,
% 11.11/6.20      ! [N2: nat,M: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 11.11/6.20        = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8322_push__bit__of__nat,axiom,
% 11.11/6.20      ! [N2: nat,M: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 11.11/6.20        = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8323_push__bit__nat__eq,axiom,
% 11.11/6.20      ! [N2: nat,K: int] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 11.11/6.20        = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8324_push__bit__minus,axiom,
% 11.11/6.20      ! [N2: nat,A: code_integer] :
% 11.11/6.20        ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ A ) )
% 11.11/6.20        = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N2 @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8325_push__bit__minus,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ A ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8326_push__bit__add,axiom,
% 11.11/6.20      ! [N2: nat,A: int,B: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 11.11/6.20        = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8327_push__bit__add,axiom,
% 11.11/6.20      ! [N2: nat,A: nat,B: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 11.11/6.20        = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8328_cosh__real__pos,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8329_cosh__real__nonpos__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 11.11/6.20            = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8330_cosh__real__nonneg__le__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.20         => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 11.11/6.20            = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8331_cosh__real__nonneg,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8332_cosh__real__ge__1,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8333_push__bit__take__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 11.11/6.20        = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8334_push__bit__take__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 11.11/6.20        = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8335_take__bit__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 11.11/6.20        = ( bit_se545348938243370406it_int @ N2 @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8336_take__bit__push__bit,axiom,
% 11.11/6.20      ! [M: nat,N2: nat,A: nat] :
% 11.11/6.20        ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 11.11/6.20        = ( bit_se547839408752420682it_nat @ N2 @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8337_sinh__less__cosh__real,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8338_sinh__le__cosh__real,axiom,
% 11.11/6.20      ! [X4: real] : ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8339_flip__bit__nat__def,axiom,
% 11.11/6.20      ( bit_se2161824704523386999it_nat
% 11.11/6.20      = ( ^ [M6: nat,N: nat] : ( bit_se6528837805403552850or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8340_cosh__real__strict__mono,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.20         => ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8341_cosh__real__nonneg__less__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.20         => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 11.11/6.20            = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8342_cosh__real__nonpos__less__iff,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.20       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 11.11/6.20         => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 11.11/6.20            = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8343_bit__push__bit__iff__int,axiom,
% 11.11/6.20      ! [M: nat,K: int,N2: nat] :
% 11.11/6.20        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 11.11/6.20        = ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.20          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8344_bit__push__bit__iff__nat,axiom,
% 11.11/6.20      ! [M: nat,Q3: nat,N2: nat] :
% 11.11/6.20        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N2 )
% 11.11/6.20        = ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.20          & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8345_concat__bit__eq,axiom,
% 11.11/6.20      ( bit_concat_bit
% 11.11/6.20      = ( ^ [N: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8346_arcosh__cosh__real,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.20       => ( ( arcosh_real @ ( cosh_real @ X4 ) )
% 11.11/6.20          = X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8347_flip__bit__eq__xor,axiom,
% 11.11/6.20      ( bit_se2159334234014336723it_int
% 11.11/6.20      = ( ^ [N: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8348_flip__bit__eq__xor,axiom,
% 11.11/6.20      ( bit_se2161824704523386999it_nat
% 11.11/6.20      = ( ^ [N: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8349_cosh__add,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( cosh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_complex @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8350_cosh__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( cosh_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8351_sinh__add,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( sinh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_complex @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8352_sinh__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( sinh_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20        = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8353_cosh__plus__sinh,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( plus_plus_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ X4 ) )
% 11.11/6.20        = ( exp_complex @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8354_cosh__plus__sinh,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( plus_plus_real @ ( cosh_real @ X4 ) @ ( sinh_real @ X4 ) )
% 11.11/6.20        = ( exp_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8355_sinh__plus__cosh,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( plus_plus_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ X4 ) )
% 11.11/6.20        = ( exp_complex @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8356_sinh__plus__cosh,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( plus_plus_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) )
% 11.11/6.20        = ( exp_real @ X4 ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8357_flip__bit__int__def,axiom,
% 11.11/6.20      ( bit_se2159334234014336723it_int
% 11.11/6.20      = ( ^ [N: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8358_tanh__def,axiom,
% 11.11/6.20      ( tanh_real
% 11.11/6.20      = ( ^ [X: real] : ( divide_divide_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8359_tanh__def,axiom,
% 11.11/6.20      ( tanh_complex
% 11.11/6.20      = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8360_push__bit__double,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 11.11/6.20        = ( times_times_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8361_push__bit__double,axiom,
% 11.11/6.20      ! [N2: nat,A: nat] :
% 11.11/6.20        ( ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20        = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8362_bit__iff__and__push__bit__not__eq__0,axiom,
% 11.11/6.20      ( bit_se1146084159140164899it_int
% 11.11/6.20      = ( ^ [A3: int,N: nat] :
% 11.11/6.20            ( ( bit_se725231765392027082nd_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 11.11/6.20           != zero_zero_int ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8363_bit__iff__and__push__bit__not__eq__0,axiom,
% 11.11/6.20      ( bit_se1148574629649215175it_nat
% 11.11/6.20      = ( ^ [A3: nat,N: nat] :
% 11.11/6.20            ( ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 11.11/6.20           != zero_zero_nat ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8364_push__bit__mask__eq,axiom,
% 11.11/6.20      ! [M: nat,N2: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 11.11/6.20        = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8365_unset__bit__eq__and__not,axiom,
% 11.11/6.20      ( bit_se4203085406695923979it_int
% 11.11/6.20      = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8366_unset__bit__int__def,axiom,
% 11.11/6.20      ( bit_se4203085406695923979it_int
% 11.11/6.20      = ( ^ [N: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8367_push__bit__int__def,axiom,
% 11.11/6.20      ( bit_se545348938243370406it_int
% 11.11/6.20      = ( ^ [N: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8368_push__bit__nat__def,axiom,
% 11.11/6.20      ( bit_se547839408752420682it_nat
% 11.11/6.20      = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8369_push__bit__eq__mult,axiom,
% 11.11/6.20      ( bit_se545348938243370406it_int
% 11.11/6.20      = ( ^ [N: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8370_push__bit__eq__mult,axiom,
% 11.11/6.20      ( bit_se547839408752420682it_nat
% 11.11/6.20      = ( ^ [N: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8371_exp__dvdE,axiom,
% 11.11/6.20      ! [N2: nat,A: code_integer] :
% 11.11/6.20        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A )
% 11.11/6.20       => ~ ! [B5: code_integer] :
% 11.11/6.20              ( A
% 11.11/6.20             != ( bit_se7788150548672797655nteger @ N2 @ B5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8372_exp__dvdE,axiom,
% 11.11/6.20      ! [N2: nat,A: int] :
% 11.11/6.20        ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A )
% 11.11/6.20       => ~ ! [B5: int] :
% 11.11/6.20              ( A
% 11.11/6.20             != ( bit_se545348938243370406it_int @ N2 @ B5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8373_exp__dvdE,axiom,
% 11.11/6.20      ! [N2: nat,A: nat] :
% 11.11/6.20        ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A )
% 11.11/6.20       => ~ ! [B5: nat] :
% 11.11/6.20              ( A
% 11.11/6.20             != ( bit_se547839408752420682it_nat @ N2 @ B5 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8374_sinh__double,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.20        = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X4 ) ) @ ( cosh_complex @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8375_sinh__double,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 11.11/6.20        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X4 ) ) @ ( cosh_real @ X4 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8376_push__bit__minus__one,axiom,
% 11.11/6.20      ! [N2: nat] :
% 11.11/6.20        ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.20        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8377_tanh__add,axiom,
% 11.11/6.20      ! [X4: real,Y: real] :
% 11.11/6.20        ( ( ( cosh_real @ X4 )
% 11.11/6.20         != zero_zero_real )
% 11.11/6.20       => ( ( ( cosh_real @ Y )
% 11.11/6.20           != zero_zero_real )
% 11.11/6.20         => ( ( tanh_real @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.20            = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8378_tanh__add,axiom,
% 11.11/6.20      ! [X4: complex,Y: complex] :
% 11.11/6.20        ( ( ( cosh_complex @ X4 )
% 11.11/6.20         != zero_zero_complex )
% 11.11/6.20       => ( ( ( cosh_complex @ Y )
% 11.11/6.20           != zero_zero_complex )
% 11.11/6.20         => ( ( tanh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 11.11/6.20            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8379_cosh__field__def,axiom,
% 11.11/6.20      ( cosh_real
% 11.11/6.20      = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8380_cosh__field__def,axiom,
% 11.11/6.20      ( cosh_complex
% 11.11/6.20      = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8381_cosh__square__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20        = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8382_cosh__square__eq,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20        = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8383_sinh__square__eq,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20        = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8384_sinh__square__eq,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.20        = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8385_hyperbolic__pythagoras,axiom,
% 11.11/6.20      ! [X4: complex] :
% 11.11/6.20        ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20        = one_one_complex ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8386_hyperbolic__pythagoras,axiom,
% 11.11/6.20      ! [X4: real] :
% 11.11/6.20        ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.20        = one_one_real ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8387_bit__horner__sum__bit__iff,axiom,
% 11.11/6.20      ! [Bs: list_o,N2: nat] :
% 11.11/6.20        ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 11.11/6.20        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 11.11/6.20          & ( nth_o @ Bs @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8388_bit__horner__sum__bit__iff,axiom,
% 11.11/6.20      ! [Bs: list_o,N2: nat] :
% 11.11/6.20        ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 11.11/6.20        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 11.11/6.20          & ( nth_o @ Bs @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8389_bit__horner__sum__bit__iff,axiom,
% 11.11/6.20      ! [Bs: list_o,N2: nat] :
% 11.11/6.20        ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 11.11/6.20        = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 11.11/6.20          & ( nth_o @ Bs @ N2 ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8390_Cauchy__iff2,axiom,
% 11.11/6.20      ( topolo4055970368930404560y_real
% 11.11/6.20      = ( ^ [X3: nat > real] :
% 11.11/6.20          ! [J3: nat] :
% 11.11/6.20          ? [M8: nat] :
% 11.11/6.20          ! [M6: nat] :
% 11.11/6.20            ( ( ord_less_eq_nat @ M8 @ M6 )
% 11.11/6.20           => ! [N: nat] :
% 11.11/6.20                ( ( ord_less_eq_nat @ M8 @ N )
% 11.11/6.20               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8391_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 11.11/6.20      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.20        ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.20       => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.20              ( X4
% 11.11/6.20             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.20         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 11.11/6.20                ( X4
% 11.11/6.20               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 11.11/6.20           => ( ! [Mi3: nat,Ma3: nat] :
% 11.11/6.20                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.20                      ( X4
% 11.11/6.20                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.20                 => ( ( Xa = Mi3 )
% 11.11/6.20                    | ( Xa = Ma3 ) ) )
% 11.11/6.20             => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.20                    ( ? [Vc: vEBT_VEBT] :
% 11.11/6.20                        ( X4
% 11.11/6.20                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.20                   => ( ( Xa = Mi3 )
% 11.11/6.20                      | ( Xa = Ma3 )
% 11.11/6.20                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.20                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.20                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 11.11/6.20               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.20                      ( ? [Vd: vEBT_VEBT] :
% 11.11/6.20                          ( X4
% 11.11/6.20                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.20                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.20                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.20                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8392_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 11.11/6.20      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.20        ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.20          = Y )
% 11.11/6.20       => ( ( ? [Uu2: $o,Uv2: $o] :
% 11.11/6.20                ( X4
% 11.11/6.20                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.20           => Y )
% 11.11/6.20         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 11.11/6.20                  ( X4
% 11.11/6.20                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 11.11/6.20             => Y )
% 11.11/6.20           => ( ! [Mi3: nat,Ma3: nat] :
% 11.11/6.20                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.20                      ( X4
% 11.11/6.20                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.20                 => ( Y
% 11.11/6.20                    = ( ~ ( ( Xa = Mi3 )
% 11.11/6.20                          | ( Xa = Ma3 ) ) ) ) )
% 11.11/6.20             => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.20                    ( ? [Vc: vEBT_VEBT] :
% 11.11/6.20                        ( X4
% 11.11/6.20                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.20                   => ( Y
% 11.11/6.20                      = ( ~ ( ( Xa = Mi3 )
% 11.11/6.20                            | ( Xa = Ma3 )
% 11.11/6.20                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.20                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.20                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 11.11/6.20               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.20                      ( ? [Vd: vEBT_VEBT] :
% 11.11/6.20                          ( X4
% 11.11/6.20                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.20                     => ( Y
% 11.11/6.20                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.20                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.20                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8393_csqrt_Osimps_I1_J,axiom,
% 11.11/6.20      ! [Z: complex] :
% 11.11/6.20        ( ( re @ ( csqrt @ Z ) )
% 11.11/6.20        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8394_complex__Re__numeral,axiom,
% 11.11/6.20      ! [V: num] :
% 11.11/6.20        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 11.11/6.20        = ( numeral_numeral_real @ V ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8395_Re__divide__numeral,axiom,
% 11.11/6.20      ! [Z: complex,W: num] :
% 11.11/6.20        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.20        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8396_lambda__zero,axiom,
% 11.11/6.20      ( ( ^ [H2: rat] : zero_zero_rat )
% 11.11/6.20      = ( times_times_rat @ zero_zero_rat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8397_lambda__zero,axiom,
% 11.11/6.20      ( ( ^ [H2: complex] : zero_zero_complex )
% 11.11/6.20      = ( times_times_complex @ zero_zero_complex ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8398_lambda__zero,axiom,
% 11.11/6.20      ( ( ^ [H2: real] : zero_zero_real )
% 11.11/6.20      = ( times_times_real @ zero_zero_real ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8399_lambda__zero,axiom,
% 11.11/6.20      ( ( ^ [H2: nat] : zero_zero_nat )
% 11.11/6.20      = ( times_times_nat @ zero_zero_nat ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8400_lambda__zero,axiom,
% 11.11/6.20      ( ( ^ [H2: int] : zero_zero_int )
% 11.11/6.20      = ( times_times_int @ zero_zero_int ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8401_less__set__def,axiom,
% 11.11/6.20      ( ord_less_set_real
% 11.11/6.20      = ( ^ [A6: set_real,B6: set_real] :
% 11.11/6.20            ( ord_less_real_o
% 11.11/6.20            @ ^ [X: real] : ( member_real @ X @ A6 )
% 11.11/6.20            @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8402_less__set__def,axiom,
% 11.11/6.20      ( ord_less_set_nat
% 11.11/6.20      = ( ^ [A6: set_nat,B6: set_nat] :
% 11.11/6.20            ( ord_less_nat_o
% 11.11/6.20            @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 11.11/6.20            @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8403_less__set__def,axiom,
% 11.11/6.20      ( ord_less_set_complex
% 11.11/6.20      = ( ^ [A6: set_complex,B6: set_complex] :
% 11.11/6.20            ( ord_less_complex_o
% 11.11/6.20            @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 11.11/6.20            @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8404_less__set__def,axiom,
% 11.11/6.20      ( ord_less_set_int
% 11.11/6.20      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.20            ( ord_less_int_o
% 11.11/6.20            @ ^ [X: int] : ( member_int @ X @ A6 )
% 11.11/6.20            @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8405_less__set__def,axiom,
% 11.11/6.20      ( ord_le7866589430770878221at_nat
% 11.11/6.20      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 11.11/6.20            ( ord_le549003669493604880_nat_o
% 11.11/6.20            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 11.11/6.20            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.20  
% 11.11/6.20  thf(fact_8406_less__eq__set__def,axiom,
% 11.11/6.20      ( ord_less_eq_set_real
% 11.11/6.20      = ( ^ [A6: set_real,B6: set_real] :
% 11.11/6.21            ( ord_less_eq_real_o
% 11.11/6.21            @ ^ [X: real] : ( member_real @ X @ A6 )
% 11.11/6.21            @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8407_less__eq__set__def,axiom,
% 11.11/6.21      ( ord_less_eq_set_nat
% 11.11/6.21      = ( ^ [A6: set_nat,B6: set_nat] :
% 11.11/6.21            ( ord_less_eq_nat_o
% 11.11/6.21            @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 11.11/6.21            @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8408_less__eq__set__def,axiom,
% 11.11/6.21      ( ord_le211207098394363844omplex
% 11.11/6.21      = ( ^ [A6: set_complex,B6: set_complex] :
% 11.11/6.21            ( ord_le4573692005234683329plex_o
% 11.11/6.21            @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 11.11/6.21            @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8409_less__eq__set__def,axiom,
% 11.11/6.21      ( ord_le3146513528884898305at_nat
% 11.11/6.21      = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 11.11/6.21            ( ord_le704812498762024988_nat_o
% 11.11/6.21            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 11.11/6.21            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8410_less__eq__set__def,axiom,
% 11.11/6.21      ( ord_less_eq_set_int
% 11.11/6.21      = ( ^ [A6: set_int,B6: set_int] :
% 11.11/6.21            ( ord_less_eq_int_o
% 11.11/6.21            @ ^ [X: int] : ( member_int @ X @ A6 )
% 11.11/6.21            @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8411_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 11.11/6.21        ( ord_le3146513528884898305at_nat
% 11.11/6.21        @ ( collec3392354462482085612at_nat
% 11.11/6.21          @ ^ [X: product_prod_nat_nat] :
% 11.11/6.21              ( ( member8440522571783428010at_nat @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8412_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_complex,P: complex > $o] :
% 11.11/6.21        ( ord_le211207098394363844omplex
% 11.11/6.21        @ ( collect_complex
% 11.11/6.21          @ ^ [X: complex] :
% 11.11/6.21              ( ( member_complex @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8413_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_real,P: real > $o] :
% 11.11/6.21        ( ord_less_eq_set_real
% 11.11/6.21        @ ( collect_real
% 11.11/6.21          @ ^ [X: real] :
% 11.11/6.21              ( ( member_real @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8414_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_list_nat,P: list_nat > $o] :
% 11.11/6.21        ( ord_le6045566169113846134st_nat
% 11.11/6.21        @ ( collect_list_nat
% 11.11/6.21          @ ^ [X: list_nat] :
% 11.11/6.21              ( ( member_list_nat @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8415_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_nat,P: nat > $o] :
% 11.11/6.21        ( ord_less_eq_set_nat
% 11.11/6.21        @ ( collect_nat
% 11.11/6.21          @ ^ [X: nat] :
% 11.11/6.21              ( ( member_nat @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8416_Collect__subset,axiom,
% 11.11/6.21      ! [A2: set_int,P: int > $o] :
% 11.11/6.21        ( ord_less_eq_set_int
% 11.11/6.21        @ ( collect_int
% 11.11/6.21          @ ^ [X: int] :
% 11.11/6.21              ( ( member_int @ X @ A2 )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        @ A2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8417_subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: complex,B: complex] :
% 11.11/6.21        ( ( ord_le211207098394363844omplex
% 11.11/6.21          @ ( collect_complex
% 11.11/6.21            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 11.11/6.21          @ ( collect_complex
% 11.11/6.21            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 11.11/6.21        = ( dvd_dvd_complex @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8418_subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_eq_set_real
% 11.11/6.21          @ ( collect_real
% 11.11/6.21            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 11.11/6.21          @ ( collect_real
% 11.11/6.21            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 11.11/6.21        = ( dvd_dvd_real @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8419_subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: nat,B: nat] :
% 11.11/6.21        ( ( ord_less_eq_set_nat
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 11.11/6.21        = ( dvd_dvd_nat @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8420_subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: code_integer,B: code_integer] :
% 11.11/6.21        ( ( ord_le7084787975880047091nteger
% 11.11/6.21          @ ( collect_Code_integer
% 11.11/6.21            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 11.11/6.21          @ ( collect_Code_integer
% 11.11/6.21            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 11.11/6.21        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8421_subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: int,B: int] :
% 11.11/6.21        ( ( ord_less_eq_set_int
% 11.11/6.21          @ ( collect_int
% 11.11/6.21            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 11.11/6.21          @ ( collect_int
% 11.11/6.21            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 11.11/6.21        = ( dvd_dvd_int @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8422_strict__subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: complex,B: complex] :
% 11.11/6.21        ( ( ord_less_set_complex
% 11.11/6.21          @ ( collect_complex
% 11.11/6.21            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 11.11/6.21          @ ( collect_complex
% 11.11/6.21            @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 11.11/6.21        = ( ( dvd_dvd_complex @ A @ B )
% 11.11/6.21          & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8423_strict__subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_set_real
% 11.11/6.21          @ ( collect_real
% 11.11/6.21            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 11.11/6.21          @ ( collect_real
% 11.11/6.21            @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 11.11/6.21        = ( ( dvd_dvd_real @ A @ B )
% 11.11/6.21          & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8424_strict__subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: nat,B: nat] :
% 11.11/6.21        ( ( ord_less_set_nat
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 11.11/6.21        = ( ( dvd_dvd_nat @ A @ B )
% 11.11/6.21          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8425_strict__subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: int,B: int] :
% 11.11/6.21        ( ( ord_less_set_int
% 11.11/6.21          @ ( collect_int
% 11.11/6.21            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 11.11/6.21          @ ( collect_int
% 11.11/6.21            @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 11.11/6.21        = ( ( dvd_dvd_int @ A @ B )
% 11.11/6.21          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8426_strict__subset__divisors__dvd,axiom,
% 11.11/6.21      ! [A: code_integer,B: code_integer] :
% 11.11/6.21        ( ( ord_le1307284697595431911nteger
% 11.11/6.21          @ ( collect_Code_integer
% 11.11/6.21            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 11.11/6.21          @ ( collect_Code_integer
% 11.11/6.21            @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 11.11/6.21        = ( ( dvd_dvd_Code_integer @ A @ B )
% 11.11/6.21          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8427_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8428_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8429_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8430_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8431_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8432_numeral__code_I2_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 11.11/6.21        = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8433_lambda__one,axiom,
% 11.11/6.21      ( ( ^ [X: rat] : X )
% 11.11/6.21      = ( times_times_rat @ one_one_rat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8434_lambda__one,axiom,
% 11.11/6.21      ( ( ^ [X: complex] : X )
% 11.11/6.21      = ( times_times_complex @ one_one_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8435_lambda__one,axiom,
% 11.11/6.21      ( ( ^ [X: real] : X )
% 11.11/6.21      = ( times_times_real @ one_one_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8436_lambda__one,axiom,
% 11.11/6.21      ( ( ^ [X: nat] : X )
% 11.11/6.21      = ( times_times_nat @ one_one_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8437_lambda__one,axiom,
% 11.11/6.21      ( ( ^ [X: int] : X )
% 11.11/6.21      = ( times_times_int @ one_one_int ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8438_nat__less__as__int,axiom,
% 11.11/6.21      ( ord_less_nat
% 11.11/6.21      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8439_nat__leq__as__int,axiom,
% 11.11/6.21      ( ord_less_eq_nat
% 11.11/6.21      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8440_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8441_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8442_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8443_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8444_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8445_numeral__code_I3_J,axiom,
% 11.11/6.21      ! [N2: num] :
% 11.11/6.21        ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 11.11/6.21        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8446_power__numeral__even,axiom,
% 11.11/6.21      ! [Z: complex,W: num] :
% 11.11/6.21        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 11.11/6.21        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8447_power__numeral__even,axiom,
% 11.11/6.21      ! [Z: real,W: num] :
% 11.11/6.21        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 11.11/6.21        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8448_power__numeral__even,axiom,
% 11.11/6.21      ! [Z: nat,W: num] :
% 11.11/6.21        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 11.11/6.21        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8449_power__numeral__even,axiom,
% 11.11/6.21      ! [Z: int,W: num] :
% 11.11/6.21        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 11.11/6.21        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8450_power__numeral__odd,axiom,
% 11.11/6.21      ! [Z: complex,W: num] :
% 11.11/6.21        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 11.11/6.21        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8451_power__numeral__odd,axiom,
% 11.11/6.21      ! [Z: real,W: num] :
% 11.11/6.21        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 11.11/6.21        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8452_power__numeral__odd,axiom,
% 11.11/6.21      ! [Z: nat,W: num] :
% 11.11/6.21        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 11.11/6.21        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8453_power__numeral__odd,axiom,
% 11.11/6.21      ! [Z: int,W: num] :
% 11.11/6.21        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 11.11/6.21        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8454_nat__plus__as__int,axiom,
% 11.11/6.21      ( plus_plus_nat
% 11.11/6.21      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8455_nat__div__as__int,axiom,
% 11.11/6.21      ( divide_divide_nat
% 11.11/6.21      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8456_nat__mod__as__int,axiom,
% 11.11/6.21      ( modulo_modulo_nat
% 11.11/6.21      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8457_complex__Re__le__cmod,axiom,
% 11.11/6.21      ! [X4: complex] : ( ord_less_eq_real @ ( re @ X4 ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8458_one__complex_Osimps_I1_J,axiom,
% 11.11/6.21      ( ( re @ one_one_complex )
% 11.11/6.21      = one_one_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8459_set__conv__nth,axiom,
% 11.11/6.21      ( set_complex2
% 11.11/6.21      = ( ^ [Xs3: list_complex] :
% 11.11/6.21            ( collect_complex
% 11.11/6.21            @ ^ [Uu3: complex] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_complex @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8460_set__conv__nth,axiom,
% 11.11/6.21      ( set_real2
% 11.11/6.21      = ( ^ [Xs3: list_real] :
% 11.11/6.21            ( collect_real
% 11.11/6.21            @ ^ [Uu3: real] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_real @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8461_set__conv__nth,axiom,
% 11.11/6.21      ( set_list_nat2
% 11.11/6.21      = ( ^ [Xs3: list_list_nat] :
% 11.11/6.21            ( collect_list_nat
% 11.11/6.21            @ ^ [Uu3: list_nat] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_list_nat @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_s3023201423986296836st_nat @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8462_set__conv__nth,axiom,
% 11.11/6.21      ( set_VEBT_VEBT2
% 11.11/6.21      = ( ^ [Xs3: list_VEBT_VEBT] :
% 11.11/6.21            ( collect_VEBT_VEBT
% 11.11/6.21            @ ^ [Uu3: vEBT_VEBT] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_VEBT_VEBT @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8463_set__conv__nth,axiom,
% 11.11/6.21      ( set_o2
% 11.11/6.21      = ( ^ [Xs3: list_o] :
% 11.11/6.21            ( collect_o
% 11.11/6.21            @ ^ [Uu3: $o] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_o @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8464_set__conv__nth,axiom,
% 11.11/6.21      ( set_nat2
% 11.11/6.21      = ( ^ [Xs3: list_nat] :
% 11.11/6.21            ( collect_nat
% 11.11/6.21            @ ^ [Uu3: nat] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_nat @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8465_set__conv__nth,axiom,
% 11.11/6.21      ( set_int2
% 11.11/6.21      = ( ^ [Xs3: list_int] :
% 11.11/6.21            ( collect_int
% 11.11/6.21            @ ^ [Uu3: int] :
% 11.11/6.21              ? [I3: nat] :
% 11.11/6.21                ( ( Uu3
% 11.11/6.21                  = ( nth_int @ Xs3 @ I3 ) )
% 11.11/6.21                & ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8466_diff__nat__eq__if,axiom,
% 11.11/6.21      ! [Z6: int,Z: int] :
% 11.11/6.21        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 11.11/6.21         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 11.11/6.21            = ( nat2 @ Z ) ) )
% 11.11/6.21        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 11.11/6.21         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 11.11/6.21            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8467_abs__Re__le__cmod,axiom,
% 11.11/6.21      ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8468_Re__csqrt,axiom,
% 11.11/6.21      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8469_set__decode__def,axiom,
% 11.11/6.21      ( nat_set_decode
% 11.11/6.21      = ( ^ [X: nat] :
% 11.11/6.21            ( collect_nat
% 11.11/6.21            @ ^ [N: nat] :
% 11.11/6.21                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8470_signed__take__bit__code,axiom,
% 11.11/6.21      ( bit_ri6519982836138164636nteger
% 11.11/6.21      = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8471_signed__take__bit__code,axiom,
% 11.11/6.21      ( bit_ri631733984087533419it_int
% 11.11/6.21      = ( ^ [N: nat,A3: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8472_pochhammer__code,axiom,
% 11.11/6.21      ( comm_s4028243227959126397er_rat
% 11.11/6.21      = ( ^ [A3: rat,N: nat] :
% 11.11/6.21            ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 11.11/6.21            @ ( set_fo1949268297981939178at_rat
% 11.11/6.21              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 11.11/6.21              @ zero_zero_nat
% 11.11/6.21              @ ( minus_minus_nat @ N @ one_one_nat )
% 11.11/6.21              @ one_one_rat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8473_pochhammer__code,axiom,
% 11.11/6.21      ( comm_s2602460028002588243omplex
% 11.11/6.21      = ( ^ [A3: complex,N: nat] :
% 11.11/6.21            ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 11.11/6.21            @ ( set_fo1517530859248394432omplex
% 11.11/6.21              @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 11.11/6.21              @ zero_zero_nat
% 11.11/6.21              @ ( minus_minus_nat @ N @ one_one_nat )
% 11.11/6.21              @ one_one_complex ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8474_pochhammer__code,axiom,
% 11.11/6.21      ( comm_s7457072308508201937r_real
% 11.11/6.21      = ( ^ [A3: real,N: nat] :
% 11.11/6.21            ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 11.11/6.21            @ ( set_fo3111899725591712190t_real
% 11.11/6.21              @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 11.11/6.21              @ zero_zero_nat
% 11.11/6.21              @ ( minus_minus_nat @ N @ one_one_nat )
% 11.11/6.21              @ one_one_real ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8475_pochhammer__code,axiom,
% 11.11/6.21      ( comm_s4660882817536571857er_int
% 11.11/6.21      = ( ^ [A3: int,N: nat] :
% 11.11/6.21            ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 11.11/6.21            @ ( set_fo2581907887559384638at_int
% 11.11/6.21              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 11.11/6.21              @ zero_zero_nat
% 11.11/6.21              @ ( minus_minus_nat @ N @ one_one_nat )
% 11.11/6.21              @ one_one_int ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8476_pochhammer__code,axiom,
% 11.11/6.21      ( comm_s4663373288045622133er_nat
% 11.11/6.21      = ( ^ [A3: nat,N: nat] :
% 11.11/6.21            ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 11.11/6.21            @ ( set_fo2584398358068434914at_nat
% 11.11/6.21              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 11.11/6.21              @ zero_zero_nat
% 11.11/6.21              @ ( minus_minus_nat @ N @ one_one_nat )
% 11.11/6.21              @ one_one_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8477_cmod__plus__Re__le__0__iff,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 11.11/6.21        = ( ( re @ Z )
% 11.11/6.21          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8478_gbinomial__code,axiom,
% 11.11/6.21      ( gbinomial_rat
% 11.11/6.21      = ( ^ [A3: rat,K3: nat] :
% 11.11/6.21            ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 11.11/6.21            @ ( divide_divide_rat
% 11.11/6.21              @ ( set_fo1949268297981939178at_rat
% 11.11/6.21                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 11.11/6.21                @ zero_zero_nat
% 11.11/6.21                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 11.11/6.21                @ one_one_rat )
% 11.11/6.21              @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8479_gbinomial__code,axiom,
% 11.11/6.21      ( gbinomial_complex
% 11.11/6.21      = ( ^ [A3: complex,K3: nat] :
% 11.11/6.21            ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 11.11/6.21            @ ( divide1717551699836669952omplex
% 11.11/6.21              @ ( set_fo1517530859248394432omplex
% 11.11/6.21                @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 11.11/6.21                @ zero_zero_nat
% 11.11/6.21                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 11.11/6.21                @ one_one_complex )
% 11.11/6.21              @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8480_gbinomial__code,axiom,
% 11.11/6.21      ( gbinomial_real
% 11.11/6.21      = ( ^ [A3: real,K3: nat] :
% 11.11/6.21            ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 11.11/6.21            @ ( divide_divide_real
% 11.11/6.21              @ ( set_fo3111899725591712190t_real
% 11.11/6.21                @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 11.11/6.21                @ zero_zero_nat
% 11.11/6.21                @ ( minus_minus_nat @ K3 @ one_one_nat )
% 11.11/6.21                @ one_one_real )
% 11.11/6.21              @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8481_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 11.11/6.21      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 11.11/6.21        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X4 )
% 11.11/6.21        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 11.11/6.21           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21          & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8482_CauchyD,axiom,
% 11.11/6.21      ! [X8: nat > complex,E2: real] :
% 11.11/6.21        ( ( topolo6517432010174082258omplex @ X8 )
% 11.11/6.21       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.21         => ? [M9: nat] :
% 11.11/6.21            ! [M2: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ M9 @ M2 )
% 11.11/6.21             => ! [N6: nat] :
% 11.11/6.21                  ( ( ord_less_eq_nat @ M9 @ N6 )
% 11.11/6.21                 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8483_CauchyD,axiom,
% 11.11/6.21      ! [X8: nat > real,E2: real] :
% 11.11/6.21        ( ( topolo4055970368930404560y_real @ X8 )
% 11.11/6.21       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.21         => ? [M9: nat] :
% 11.11/6.21            ! [M2: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ M9 @ M2 )
% 11.11/6.21             => ! [N6: nat] :
% 11.11/6.21                  ( ( ord_less_eq_nat @ M9 @ N6 )
% 11.11/6.21                 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8484_CauchyI,axiom,
% 11.11/6.21      ! [X8: nat > complex] :
% 11.11/6.21        ( ! [E: real] :
% 11.11/6.21            ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.21           => ? [M10: nat] :
% 11.11/6.21              ! [M5: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M10 @ M5 )
% 11.11/6.21               => ! [N3: nat] :
% 11.11/6.21                    ( ( ord_less_eq_nat @ M10 @ N3 )
% 11.11/6.21                   => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 11.11/6.21       => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8485_CauchyI,axiom,
% 11.11/6.21      ! [X8: nat > real] :
% 11.11/6.21        ( ! [E: real] :
% 11.11/6.21            ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.21           => ? [M10: nat] :
% 11.11/6.21              ! [M5: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M10 @ M5 )
% 11.11/6.21               => ! [N3: nat] :
% 11.11/6.21                    ( ( ord_less_eq_nat @ M10 @ N3 )
% 11.11/6.21                   => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 11.11/6.21       => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8486_Cauchy__iff,axiom,
% 11.11/6.21      ( topolo6517432010174082258omplex
% 11.11/6.21      = ( ^ [X3: nat > complex] :
% 11.11/6.21          ! [E3: real] :
% 11.11/6.21            ( ( ord_less_real @ zero_zero_real @ E3 )
% 11.11/6.21           => ? [M8: nat] :
% 11.11/6.21              ! [M6: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M8 @ M6 )
% 11.11/6.21               => ! [N: nat] :
% 11.11/6.21                    ( ( ord_less_eq_nat @ M8 @ N )
% 11.11/6.21                   => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8487_Cauchy__iff,axiom,
% 11.11/6.21      ( topolo4055970368930404560y_real
% 11.11/6.21      = ( ^ [X3: nat > real] :
% 11.11/6.21          ! [E3: real] :
% 11.11/6.21            ( ( ord_less_real @ zero_zero_real @ E3 )
% 11.11/6.21           => ? [M8: nat] :
% 11.11/6.21              ! [M6: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M8 @ M6 )
% 11.11/6.21               => ! [N: nat] :
% 11.11/6.21                    ( ( ord_less_eq_nat @ M8 @ N )
% 11.11/6.21                   => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8488_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 11.11/6.21      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 11.11/6.21        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X4 )
% 11.11/6.21        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 11.11/6.21           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21          & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8489_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 11.11/6.21      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 11.11/6.21        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ X4 )
% 11.11/6.21        = ( ( X4 = Mi )
% 11.11/6.21          | ( X4 = Ma )
% 11.11/6.21          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 11.11/6.21             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21            & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8490_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.21        ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21          = Y )
% 11.11/6.21       => ( ! [A5: $o,B5: $o] :
% 11.11/6.21              ( ( X4
% 11.11/6.21                = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21             => ( Y
% 11.11/6.21                = ( ~ ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                       => A5 )
% 11.11/6.21                      & ( ( Xa != zero_zero_nat )
% 11.11/6.21                       => ( ( ( Xa = one_one_nat )
% 11.11/6.21                           => B5 )
% 11.11/6.21                          & ( Xa = one_one_nat ) ) ) ) ) ) )
% 11.11/6.21         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 11.11/6.21                  ( X4
% 11.11/6.21                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 11.11/6.21             => Y )
% 11.11/6.21           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.21                  ( ? [S3: vEBT_VEBT] :
% 11.11/6.21                      ( X4
% 11.11/6.21                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21                 => ( Y
% 11.11/6.21                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8491_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21       => ( ! [A5: $o,B5: $o] :
% 11.11/6.21              ( ( X4
% 11.11/6.21                = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21             => ~ ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                   => A5 )
% 11.11/6.21                  & ( ( Xa != zero_zero_nat )
% 11.11/6.21                   => ( ( ( Xa = one_one_nat )
% 11.11/6.21                       => B5 )
% 11.11/6.21                      & ( Xa = one_one_nat ) ) ) ) )
% 11.11/6.21         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.21                ( ? [S3: vEBT_VEBT] :
% 11.11/6.21                    ( X4
% 11.11/6.21                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8492_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21       => ( ! [A5: $o,B5: $o] :
% 11.11/6.21              ( ( X4
% 11.11/6.21                = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21             => ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                 => A5 )
% 11.11/6.21                & ( ( Xa != zero_zero_nat )
% 11.11/6.21                 => ( ( ( Xa = one_one_nat )
% 11.11/6.21                     => B5 )
% 11.11/6.21                    & ( Xa = one_one_nat ) ) ) ) )
% 11.11/6.21         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 11.11/6.21                ( X4
% 11.11/6.21               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 11.11/6.21           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.21                  ( ? [S3: vEBT_VEBT] :
% 11.11/6.21                      ( X4
% 11.11/6.21                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8493_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.21       => ( ! [Mi3: nat,Ma3: nat] :
% 11.11/6.21              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.21                  ( X4
% 11.11/6.21                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.21             => ~ ( ( Xa = Mi3 )
% 11.11/6.21                  | ( Xa = Ma3 ) ) )
% 11.11/6.21         => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.21                ( ? [Vc: vEBT_VEBT] :
% 11.11/6.21                    ( X4
% 11.11/6.21                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.21               => ~ ( ( Xa = Mi3 )
% 11.11/6.21                    | ( Xa = Ma3 )
% 11.11/6.21                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 11.11/6.21           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 11.11/6.21                  ( ? [Vd: vEBT_VEBT] :
% 11.11/6.21                      ( X4
% 11.11/6.21                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.21                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8494_of__int__code__if,axiom,
% 11.11/6.21      ( ring_1_of_int_real
% 11.11/6.21      = ( ^ [K3: int] :
% 11.11/6.21            ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 11.11/6.21            @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.21              @ ( if_real
% 11.11/6.21                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21                  = zero_zero_int )
% 11.11/6.21                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21                @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8495_of__int__code__if,axiom,
% 11.11/6.21      ( ring_1_of_int_int
% 11.11/6.21      = ( ^ [K3: int] :
% 11.11/6.21            ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 11.11/6.21            @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.21              @ ( if_int
% 11.11/6.21                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21                  = zero_zero_int )
% 11.11/6.21                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21                @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8496_of__int__code__if,axiom,
% 11.11/6.21      ( ring_17405671764205052669omplex
% 11.11/6.21      = ( ^ [K3: int] :
% 11.11/6.21            ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 11.11/6.21            @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.21              @ ( if_complex
% 11.11/6.21                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21                  = zero_zero_int )
% 11.11/6.21                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8497_of__int__code__if,axiom,
% 11.11/6.21      ( ring_18347121197199848620nteger
% 11.11/6.21      = ( ^ [K3: int] :
% 11.11/6.21            ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 11.11/6.21            @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.21              @ ( if_Code_integer
% 11.11/6.21                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21                  = zero_zero_int )
% 11.11/6.21                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8498_of__int__code__if,axiom,
% 11.11/6.21      ( ring_1_of_int_rat
% 11.11/6.21      = ( ^ [K3: int] :
% 11.11/6.21            ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 11.11/6.21            @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.21              @ ( if_rat
% 11.11/6.21                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21                  = zero_zero_int )
% 11.11/6.21                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21                @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8499_monoseq__arctan__series,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.21       => ( topolo6980174941875973593q_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8500_csqrt_Ocode,axiom,
% 11.11/6.21      ( csqrt
% 11.11/6.21      = ( ^ [Z5: complex] :
% 11.11/6.21            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.21            @ ( times_times_real
% 11.11/6.21              @ ( if_real
% 11.11/6.21                @ ( ( im @ Z5 )
% 11.11/6.21                  = zero_zero_real )
% 11.11/6.21                @ one_one_real
% 11.11/6.21                @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 11.11/6.21              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8501_ln__series,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.21       => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.21         => ( ( ln_ln_real @ X4 )
% 11.11/6.21            = ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8502_powser__zero,axiom,
% 11.11/6.21      ! [F: nat > complex] :
% 11.11/6.21        ( ( suminf_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 11.11/6.21        = ( F @ zero_zero_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8503_powser__zero,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( suminf_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 11.11/6.21        = ( F @ zero_zero_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8504_Re__power__real,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( ( im @ X4 )
% 11.11/6.21          = zero_zero_real )
% 11.11/6.21       => ( ( re @ ( power_power_complex @ X4 @ N2 ) )
% 11.11/6.21          = ( power_power_real @ ( re @ X4 ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8505_Im__divide__numeral,axiom,
% 11.11/6.21      ! [Z: complex,W: num] :
% 11.11/6.21        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 11.11/6.21        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8506_csqrt__of__real__nonneg,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( ( im @ X4 )
% 11.11/6.21          = zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) )
% 11.11/6.21         => ( ( csqrt @ X4 )
% 11.11/6.21            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X4 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8507_csqrt__minus,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( ( ord_less_real @ ( im @ X4 ) @ zero_zero_real )
% 11.11/6.21          | ( ( ( im @ X4 )
% 11.11/6.21              = zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) ) ) )
% 11.11/6.21       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X4 ) )
% 11.11/6.21          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8508_csqrt__of__real__nonpos,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( ( im @ X4 )
% 11.11/6.21          = zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ ( re @ X4 ) @ zero_zero_real )
% 11.11/6.21         => ( ( csqrt @ X4 )
% 11.11/6.21            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X4 ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8509_imaginary__unit_Osimps_I2_J,axiom,
% 11.11/6.21      ( ( im @ imaginary_unit )
% 11.11/6.21      = one_one_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8510_abs__Im__le__cmod,axiom,
% 11.11/6.21      ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8511_cmod__Im__le__iff,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( ( ( re @ X4 )
% 11.11/6.21          = ( re @ Y ) )
% 11.11/6.21       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 11.11/6.21          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8512_cmod__Re__le__iff,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( ( ( im @ X4 )
% 11.11/6.21          = ( im @ Y ) )
% 11.11/6.21       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 11.11/6.21          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8513_csqrt__principal,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 11.11/6.21        | ( ( ( re @ ( csqrt @ Z ) )
% 11.11/6.21            = zero_zero_real )
% 11.11/6.21          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8514_cmod__le,axiom,
% 11.11/6.21      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8515_monoseq__realpow,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.21         => ( topolo6980174941875973593q_real @ ( power_power_real @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8516_cmod__power2,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.21        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8517_Im__power2,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( im @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.21        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X4 ) ) @ ( im @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8518_Re__power2,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( re @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.21        = ( minus_minus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8519_complex__eq__0,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( Z = zero_zero_complex )
% 11.11/6.21        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.21          = zero_zero_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8520_norm__complex__def,axiom,
% 11.11/6.21      ( real_V1022390504157884413omplex
% 11.11/6.21      = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8521_inverse__complex_Osimps_I1_J,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( re @ ( invers8013647133539491842omplex @ X4 ) )
% 11.11/6.21        = ( divide_divide_real @ ( re @ X4 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8522_complex__neq__0,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( Z != zero_zero_complex )
% 11.11/6.21        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8523_Re__divide,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( ( re @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 11.11/6.21        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8524_csqrt__unique,axiom,
% 11.11/6.21      ! [W: complex,Z: complex] :
% 11.11/6.21        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.21          = Z )
% 11.11/6.21       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 11.11/6.21            | ( ( ( re @ W )
% 11.11/6.21                = zero_zero_real )
% 11.11/6.21              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 11.11/6.21         => ( ( csqrt @ Z )
% 11.11/6.21            = W ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8525_csqrt__square,axiom,
% 11.11/6.21      ! [B: complex] :
% 11.11/6.21        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 11.11/6.21          | ( ( ( re @ B )
% 11.11/6.21              = zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 11.11/6.21       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.21          = B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8526_inverse__complex_Osimps_I2_J,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( im @ ( invers8013647133539491842omplex @ X4 ) )
% 11.11/6.21        = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X4 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8527_Im__divide,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( ( im @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 11.11/6.21        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8528_complex__abs__le__norm,axiom,
% 11.11/6.21      ! [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 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8529_complex__unit__circle,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( Z != zero_zero_complex )
% 11.11/6.21       => ( ( 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 ) ) ) )
% 11.11/6.21          = one_one_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8530_inverse__complex_Ocode,axiom,
% 11.11/6.21      ( invers8013647133539491842omplex
% 11.11/6.21      = ( ^ [X: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8531_Complex__divide,axiom,
% 11.11/6.21      ( divide1717551699836669952omplex
% 11.11/6.21      = ( ^ [X: complex,Y5: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8532_pi__series,axiom,
% 11.11/6.21      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 11.11/6.21      = ( suminf_real
% 11.11/6.21        @ ^ [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 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8533_csqrt_Osimps_I2_J,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( im @ ( csqrt @ Z ) )
% 11.11/6.21        = ( times_times_real
% 11.11/6.21          @ ( if_real
% 11.11/6.21            @ ( ( im @ Z )
% 11.11/6.21              = zero_zero_real )
% 11.11/6.21            @ one_one_real
% 11.11/6.21            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 11.11/6.21          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8534_arctan__series,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.21       => ( ( arctan @ X4 )
% 11.11/6.21          = ( suminf_real
% 11.11/6.21            @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8535_suminf__geometric,axiom,
% 11.11/6.21      ! [C: real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 11.11/6.21       => ( ( suminf_real @ ( power_power_real @ C ) )
% 11.11/6.21          = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8536_suminf__geometric,axiom,
% 11.11/6.21      ! [C: complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 11.11/6.21       => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 11.11/6.21          = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8537_summable__arctan__series,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.21       => ( summable_real
% 11.11/6.21          @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8538_vebt__buildup_Oelims,axiom,
% 11.11/6.21      ! [X4: nat,Y: vEBT_VEBT] :
% 11.11/6.21        ( ( ( vEBT_vebt_buildup @ X4 )
% 11.11/6.21          = Y )
% 11.11/6.21       => ( ( ( X4 = zero_zero_nat )
% 11.11/6.21           => ( Y
% 11.11/6.21             != ( vEBT_Leaf @ $false @ $false ) ) )
% 11.11/6.21         => ( ( ( X4
% 11.11/6.21                = ( suc @ zero_zero_nat ) )
% 11.11/6.21             => ( Y
% 11.11/6.21               != ( vEBT_Leaf @ $false @ $false ) ) )
% 11.11/6.21           => ~ ! [Va2: nat] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.21                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.21                       => ( Y
% 11.11/6.21                          = ( 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 ) ) ) ) ) ) )
% 11.11/6.21                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.21                       => ( Y
% 11.11/6.21                          = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8539_Im__Reals__divide,axiom,
% 11.11/6.21      ! [R3: complex,Z: complex] :
% 11.11/6.21        ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 11.11/6.21          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8540_intind,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,P: nat > $o,X4: nat] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( P @ X4 )
% 11.11/6.21         => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8541_intind,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,P: int > $o,X4: int] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( P @ X4 )
% 11.11/6.21         => ( P @ ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8542_intind,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( P @ X4 )
% 11.11/6.21         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8543_replicate__eq__replicate,axiom,
% 11.11/6.21      ! [M: nat,X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 11.11/6.21        ( ( ( replicate_VEBT_VEBT @ M @ X4 )
% 11.11/6.21          = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 11.11/6.21        = ( ( M = N2 )
% 11.11/6.21          & ( ( M != zero_zero_nat )
% 11.11/6.21           => ( X4 = Y ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8544_length__replicate,axiom,
% 11.11/6.21      ! [N2: nat,X4: vEBT_VEBT] :
% 11.11/6.21        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) )
% 11.11/6.21        = N2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8545_length__replicate,axiom,
% 11.11/6.21      ! [N2: nat,X4: $o] :
% 11.11/6.21        ( ( size_size_list_o @ ( replicate_o @ N2 @ X4 ) )
% 11.11/6.21        = N2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8546_length__replicate,axiom,
% 11.11/6.21      ! [N2: nat,X4: nat] :
% 11.11/6.21        ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X4 ) )
% 11.11/6.21        = N2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8547_length__replicate,axiom,
% 11.11/6.21      ! [N2: nat,X4: int] :
% 11.11/6.21        ( ( size_size_list_int @ ( replicate_int @ N2 @ X4 ) )
% 11.11/6.21        = N2 ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8548_summable__iff__shift,axiom,
% 11.11/6.21      ! [F: nat > real,K: nat] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 11.11/6.21        = ( summable_real @ F ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8549_Ball__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: int,P: int > $o] :
% 11.11/6.21        ( ( ! [X: int] :
% 11.11/6.21              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 11.11/6.21             => ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8550_Ball__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: nat,P: nat > $o] :
% 11.11/6.21        ( ( ! [X: nat] :
% 11.11/6.21              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 11.11/6.21             => ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8551_Ball__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 11.11/6.21        ( ( ! [X: vEBT_VEBT] :
% 11.11/6.21              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 11.11/6.21             => ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          | ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8552_Bex__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: int,P: int > $o] :
% 11.11/6.21        ( ( ? [X: int] :
% 11.11/6.21              ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8553_Bex__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: nat,P: nat > $o] :
% 11.11/6.21        ( ( ? [X: nat] :
% 11.11/6.21              ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8554_Bex__set__replicate,axiom,
% 11.11/6.21      ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 11.11/6.21        ( ( ? [X: vEBT_VEBT] :
% 11.11/6.21              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 11.11/6.21              & ( P @ X ) ) )
% 11.11/6.21        = ( ( P @ A )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8555_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Y: real] :
% 11.11/6.21        ( ( member_real @ X4 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8556_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat,Y: complex] :
% 11.11/6.21        ( ( member_complex @ X4 @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8557_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: product_prod_nat_nat,N2: nat,Y: product_prod_nat_nat] :
% 11.11/6.21        ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8558_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: int,N2: nat,Y: int] :
% 11.11/6.21        ( ( member_int @ X4 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8559_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: nat,N2: nat,Y: nat] :
% 11.11/6.21        ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8560_in__set__replicate,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 11.11/6.21        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 11.11/6.21        = ( ( X4 = Y )
% 11.11/6.21          & ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8561_nth__replicate,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,X4: nat] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 )
% 11.11/6.21          = X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8562_nth__replicate,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,X4: int] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 )
% 11.11/6.21          = X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8563_nth__replicate,axiom,
% 11.11/6.21      ! [I2: nat,N2: nat,X4: vEBT_VEBT] :
% 11.11/6.21        ( ( ord_less_nat @ I2 @ N2 )
% 11.11/6.21       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 )
% 11.11/6.21          = X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8564_summable__divide__iff,axiom,
% 11.11/6.21      ! [F: nat > real,C: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 11.11/6.21        = ( ( C = zero_zero_real )
% 11.11/6.21          | ( summable_real @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8565_summable__divide__iff,axiom,
% 11.11/6.21      ! [F: nat > complex,C: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 11.11/6.21        = ( ( C = zero_zero_complex )
% 11.11/6.21          | ( summable_complex @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8566_summable__geometric__iff,axiom,
% 11.11/6.21      ! [C: real] :
% 11.11/6.21        ( ( summable_real @ ( power_power_real @ C ) )
% 11.11/6.21        = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8567_summable__geometric__iff,axiom,
% 11.11/6.21      ! [C: complex] :
% 11.11/6.21        ( ( summable_complex @ ( power_power_complex @ C ) )
% 11.11/6.21        = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8568_summable__comparison__test,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real] :
% 11.11/6.21        ( ? [N7: nat] :
% 11.11/6.21          ! [N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ N7 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( summable_real @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8569_summable__comparison__test,axiom,
% 11.11/6.21      ! [F: nat > complex,G: nat > real] :
% 11.11/6.21        ( ? [N7: nat] :
% 11.11/6.21          ! [N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ N7 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( summable_complex @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8570_summable__comparison__test_H,axiom,
% 11.11/6.21      ! [G: nat > real,N4: nat,F: nat > real] :
% 11.11/6.21        ( ( summable_real @ G )
% 11.11/6.21       => ( ! [N3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21         => ( summable_real @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8571_summable__comparison__test_H,axiom,
% 11.11/6.21      ! [G: nat > real,N4: nat,F: nat > complex] :
% 11.11/6.21        ( ( summable_real @ G )
% 11.11/6.21       => ( ! [N3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21         => ( summable_complex @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8572_suminf__le,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( summable_real @ F )
% 11.11/6.21         => ( ( summable_real @ G )
% 11.11/6.21           => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8573_suminf__le,axiom,
% 11.11/6.21      ! [F: nat > nat,G: nat > nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( summable_nat @ F )
% 11.11/6.21         => ( ( summable_nat @ G )
% 11.11/6.21           => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8574_suminf__le,axiom,
% 11.11/6.21      ! [F: nat > int,G: nat > int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( summable_int @ F )
% 11.11/6.21         => ( ( summable_int @ G )
% 11.11/6.21           => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8575_Reals__power,axiom,
% 11.11/6.21      ! [A: real,N2: nat] :
% 11.11/6.21        ( ( member_real @ A @ real_V470468836141973256s_real )
% 11.11/6.21       => ( member_real @ ( power_power_real @ A @ N2 ) @ real_V470468836141973256s_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8576_Reals__power,axiom,
% 11.11/6.21      ! [A: complex,N2: nat] :
% 11.11/6.21        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( member_complex @ ( power_power_complex @ A @ N2 ) @ real_V2521375963428798218omplex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8577_Reals__divide,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( member_real @ A @ real_V470468836141973256s_real )
% 11.11/6.21       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 11.11/6.21         => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8578_Reals__divide,axiom,
% 11.11/6.21      ! [A: complex,B: complex] :
% 11.11/6.21        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 11.11/6.21         => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8579_Reals__add,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( member_real @ A @ real_V470468836141973256s_real )
% 11.11/6.21       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 11.11/6.21         => ( member_real @ ( plus_plus_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8580_Reals__add,axiom,
% 11.11/6.21      ! [A: complex,B: complex] :
% 11.11/6.21        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 11.11/6.21         => ( member_complex @ ( plus_plus_complex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8581_Reals__1,axiom,
% 11.11/6.21      member_real @ one_one_real @ real_V470468836141973256s_real ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8582_Reals__1,axiom,
% 11.11/6.21      member_complex @ one_one_complex @ real_V2521375963428798218omplex ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8583_Reals__numeral,axiom,
% 11.11/6.21      ! [W: num] : ( member_complex @ ( numera6690914467698888265omplex @ W ) @ real_V2521375963428798218omplex ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8584_Reals__numeral,axiom,
% 11.11/6.21      ! [W: num] : ( member_real @ ( numeral_numeral_real @ W ) @ real_V470468836141973256s_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8585_summable__divide,axiom,
% 11.11/6.21      ! [F: nat > real,C: real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8586_summable__divide,axiom,
% 11.11/6.21      ! [F: nat > complex,C: complex] :
% 11.11/6.21        ( ( summable_complex @ F )
% 11.11/6.21       => ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8587_summable__ignore__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > real,K: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8588_summable__add,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8589_summable__add,axiom,
% 11.11/6.21      ! [F: nat > nat,G: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ( summable_nat @ G )
% 11.11/6.21         => ( summable_nat
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8590_summable__add,axiom,
% 11.11/6.21      ! [F: nat > int,G: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ( summable_int @ G )
% 11.11/6.21         => ( summable_int
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8591_summable__Suc__iff,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 11.11/6.21        = ( summable_real @ F ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8592_summable__zero__power,axiom,
% 11.11/6.21      summable_real @ ( power_power_real @ zero_zero_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8593_summable__zero__power,axiom,
% 11.11/6.21      summable_int @ ( power_power_int @ zero_zero_int ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8594_summable__zero__power,axiom,
% 11.11/6.21      summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8595_suminf__add,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 11.11/6.21            = ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8596_suminf__add,axiom,
% 11.11/6.21      ! [F: nat > nat,G: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ( summable_nat @ G )
% 11.11/6.21         => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 11.11/6.21            = ( suminf_nat
% 11.11/6.21              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8597_suminf__add,axiom,
% 11.11/6.21      ! [F: nat > int,G: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ( summable_int @ G )
% 11.11/6.21         => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 11.11/6.21            = ( suminf_int
% 11.11/6.21              @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8598_suminf__divide,axiom,
% 11.11/6.21      ! [F: nat > real,C: real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 11.11/6.21          = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8599_suminf__divide,axiom,
% 11.11/6.21      ! [F: nat > complex,C: complex] :
% 11.11/6.21        ( ( summable_complex @ F )
% 11.11/6.21       => ( ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 11.11/6.21          = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8600_series__comparison__complex,axiom,
% 11.11/6.21      ! [G: nat > complex,N4: nat,F: nat > real] :
% 11.11/6.21        ( ( summable_complex @ G )
% 11.11/6.21       => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 11.11/6.21         => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 11.11/6.21           => ( ! [N3: nat] :
% 11.11/6.21                  ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21                 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 11.11/6.21             => ( summable_real @ F ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8601_series__comparison__complex,axiom,
% 11.11/6.21      ! [G: nat > complex,N4: nat,F: nat > complex] :
% 11.11/6.21        ( ( summable_complex @ G )
% 11.11/6.21       => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 11.11/6.21         => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 11.11/6.21           => ( ! [N3: nat] :
% 11.11/6.21                  ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21                 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 11.11/6.21             => ( summable_complex @ F ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8602_powser__insidea,axiom,
% 11.11/6.21      ! [F: nat > real,X4: real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8603_powser__insidea,axiom,
% 11.11/6.21      ! [F: nat > complex,X4: complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8604_suminf__nonneg,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8605_suminf__nonneg,axiom,
% 11.11/6.21      ! [F: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8606_suminf__nonneg,axiom,
% 11.11/6.21      ! [F: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8607_suminf__eq__zero__iff,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ( suminf_real @ F )
% 11.11/6.21              = zero_zero_real )
% 11.11/6.21            = ( ! [N: nat] :
% 11.11/6.21                  ( ( F @ N )
% 11.11/6.21                  = zero_zero_real ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8608_suminf__eq__zero__iff,axiom,
% 11.11/6.21      ! [F: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ( suminf_nat @ F )
% 11.11/6.21              = zero_zero_nat )
% 11.11/6.21            = ( ! [N: nat] :
% 11.11/6.21                  ( ( F @ N )
% 11.11/6.21                  = zero_zero_nat ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8609_suminf__eq__zero__iff,axiom,
% 11.11/6.21      ! [F: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ( suminf_int @ F )
% 11.11/6.21              = zero_zero_int )
% 11.11/6.21            = ( ! [N: nat] :
% 11.11/6.21                  ( ( F @ N )
% 11.11/6.21                  = zero_zero_int ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8610_suminf__pos,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8611_suminf__pos,axiom,
% 11.11/6.21      ! [F: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8612_suminf__pos,axiom,
% 11.11/6.21      ! [F: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21         => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8613_summable__0__powser,axiom,
% 11.11/6.21      ! [F: nat > complex] :
% 11.11/6.21        ( summable_complex
% 11.11/6.21        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8614_summable__0__powser,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8615_summable__zero__power_H,axiom,
% 11.11/6.21      ! [F: nat > complex] :
% 11.11/6.21        ( summable_complex
% 11.11/6.21        @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8616_summable__zero__power_H,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8617_summable__zero__power_H,axiom,
% 11.11/6.21      ! [F: nat > int] :
% 11.11/6.21        ( summable_int
% 11.11/6.21        @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8618_summable__powser__split__head,axiom,
% 11.11/6.21      ! [F: nat > complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21        = ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8619_summable__powser__split__head,axiom,
% 11.11/6.21      ! [F: nat > real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21        = ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8620_powser__split__head_I3_J,axiom,
% 11.11/6.21      ! [F: nat > complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21       => ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8621_powser__split__head_I3_J,axiom,
% 11.11/6.21      ! [F: nat > real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21       => ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8622_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_real,N2: nat,X4: real] :
% 11.11/6.21        ( ( ( size_size_list_real @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: real] :
% 11.11/6.21              ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_real @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8623_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_complex,N2: nat,X4: complex] :
% 11.11/6.21        ( ( ( size_s3451745648224563538omplex @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: complex] :
% 11.11/6.21              ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_complex @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8624_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_P6011104703257516679at_nat,N2: nat,X4: product_prod_nat_nat] :
% 11.11/6.21        ( ( ( size_s5460976970255530739at_nat @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: product_prod_nat_nat] :
% 11.11/6.21              ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replic4235873036481779905at_nat @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8625_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_VEBT_VEBT,N2: nat,X4: vEBT_VEBT] :
% 11.11/6.21        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: vEBT_VEBT] :
% 11.11/6.21              ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_VEBT_VEBT @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8626_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_o,N2: nat,X4: $o] :
% 11.11/6.21        ( ( ( size_size_list_o @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: $o] :
% 11.11/6.21              ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_o @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8627_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_nat,N2: nat,X4: nat] :
% 11.11/6.21        ( ( ( size_size_list_nat @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: nat] :
% 11.11/6.21              ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_nat @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8628_replicate__eqI,axiom,
% 11.11/6.21      ! [Xs: list_int,N2: nat,X4: int] :
% 11.11/6.21        ( ( ( size_size_list_int @ Xs )
% 11.11/6.21          = N2 )
% 11.11/6.21       => ( ! [Y3: int] :
% 11.11/6.21              ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 11.11/6.21             => ( Y3 = X4 ) )
% 11.11/6.21         => ( Xs
% 11.11/6.21            = ( replicate_int @ N2 @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8629_replicate__length__same,axiom,
% 11.11/6.21      ! [Xs: list_VEBT_VEBT,X4: vEBT_VEBT] :
% 11.11/6.21        ( ! [X5: vEBT_VEBT] :
% 11.11/6.21            ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 11.11/6.21           => ( X5 = X4 ) )
% 11.11/6.21       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X4 )
% 11.11/6.21          = Xs ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8630_replicate__length__same,axiom,
% 11.11/6.21      ! [Xs: list_o,X4: $o] :
% 11.11/6.21        ( ! [X5: $o] :
% 11.11/6.21            ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 11.11/6.21           => ( X5 = X4 ) )
% 11.11/6.21       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X4 )
% 11.11/6.21          = Xs ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8631_replicate__length__same,axiom,
% 11.11/6.21      ! [Xs: list_nat,X4: nat] :
% 11.11/6.21        ( ! [X5: nat] :
% 11.11/6.21            ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 11.11/6.21           => ( X5 = X4 ) )
% 11.11/6.21       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X4 )
% 11.11/6.21          = Xs ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8632_replicate__length__same,axiom,
% 11.11/6.21      ! [Xs: list_int,X4: int] :
% 11.11/6.21        ( ! [X5: int] :
% 11.11/6.21            ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 11.11/6.21           => ( X5 = X4 ) )
% 11.11/6.21       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X4 )
% 11.11/6.21          = Xs ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8633_summable__powser__ignore__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > complex,M: nat,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21        = ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8634_summable__powser__ignore__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > real,M: nat,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21        = ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8635_summable__norm__comparison__test,axiom,
% 11.11/6.21      ! [F: nat > complex,G: nat > real] :
% 11.11/6.21        ( ? [N7: nat] :
% 11.11/6.21          ! [N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ N7 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8636_summable__rabs__comparison__test,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real] :
% 11.11/6.21        ( ? [N7: nat] :
% 11.11/6.21          ! [N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ N7 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 11.11/6.21       => ( ( summable_real @ G )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8637_nonzero__Reals__divide,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( member_real @ A @ real_V470468836141973256s_real )
% 11.11/6.21       => ( ( member_real @ B @ real_V470468836141973256s_real )
% 11.11/6.21         => ( ( B != zero_zero_real )
% 11.11/6.21           => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8638_nonzero__Reals__divide,axiom,
% 11.11/6.21      ! [A: complex,B: complex] :
% 11.11/6.21        ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 11.11/6.21         => ( ( B != zero_zero_complex )
% 11.11/6.21           => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8639_summable__rabs,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 11.11/6.21          @ ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8640_suminf__pos2,axiom,
% 11.11/6.21      ! [F: nat > real,I2: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 11.11/6.21           => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8641_suminf__pos2,axiom,
% 11.11/6.21      ! [F: nat > nat,I2: nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 11.11/6.21           => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8642_suminf__pos2,axiom,
% 11.11/6.21      ! [F: nat > int,I2: nat] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 11.11/6.21           => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8643_suminf__pos__iff,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 11.11/6.21            = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8644_suminf__pos__iff,axiom,
% 11.11/6.21      ! [F: nat > nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 11.11/6.21            = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8645_suminf__pos__iff,axiom,
% 11.11/6.21      ! [F: nat > int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21         => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 11.11/6.21            = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8646_summable__geometric,axiom,
% 11.11/6.21      ! [C: real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 11.11/6.21       => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8647_summable__geometric,axiom,
% 11.11/6.21      ! [C: complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 11.11/6.21       => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8648_complete__algebra__summable__geometric,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ one_one_real )
% 11.11/6.21       => ( summable_real @ ( power_power_real @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8649_complete__algebra__summable__geometric,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ one_one_real )
% 11.11/6.21       => ( summable_complex @ ( power_power_complex @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8650_suminf__split__head,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 11.11/6.21          = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8651_summable__norm,axiom,
% 11.11/6.21      ! [F: nat > real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 11.11/6.21          @ ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8652_summable__norm,axiom,
% 11.11/6.21      ! [F: nat > complex] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 11.11/6.21          @ ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8653_powser__inside,axiom,
% 11.11/6.21      ! [F: nat > real,X4: real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8654_powser__inside,axiom,
% 11.11/6.21      ! [F: nat > complex,X4: complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 11.11/6.21         => ( summable_complex
% 11.11/6.21            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8655_summable__exp,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( summable_complex
% 11.11/6.21        @ ^ [N: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8656_summable__exp,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8657_powser__split__head_I1_J,axiom,
% 11.11/6.21      ! [F: nat > complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21       => ( ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21          = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 11.11/6.21            @ ( times_times_complex
% 11.11/6.21              @ ( suminf_complex
% 11.11/6.21                @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21              @ Z ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8658_powser__split__head_I1_J,axiom,
% 11.11/6.21      ! [F: nat > real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21       => ( ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21          = ( plus_plus_real @ ( F @ zero_zero_nat )
% 11.11/6.21            @ ( times_times_real
% 11.11/6.21              @ ( suminf_real
% 11.11/6.21                @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21              @ Z ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8659_powser__split__head_I2_J,axiom,
% 11.11/6.21      ! [F: nat > complex,Z: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21       => ( ( times_times_complex
% 11.11/6.21            @ ( suminf_complex
% 11.11/6.21              @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21            @ Z )
% 11.11/6.21          = ( minus_minus_complex
% 11.11/6.21            @ ( suminf_complex
% 11.11/6.21              @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 11.11/6.21            @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8660_powser__split__head_I2_J,axiom,
% 11.11/6.21      ! [F: nat > real,Z: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21       => ( ( times_times_real
% 11.11/6.21            @ ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21            @ Z )
% 11.11/6.21          = ( minus_minus_real
% 11.11/6.21            @ ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 11.11/6.21            @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8661_suminf__exist__split,axiom,
% 11.11/6.21      ! [R3: real,F: nat > real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ R3 )
% 11.11/6.21       => ( ( summable_real @ F )
% 11.11/6.21         => ? [N8: nat] :
% 11.11/6.21            ! [N6: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N8 @ N6 )
% 11.11/6.21             => ( ord_less_real
% 11.11/6.21                @ ( real_V7735802525324610683m_real
% 11.11/6.21                  @ ( suminf_real
% 11.11/6.21                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 11.11/6.21                @ R3 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8662_suminf__exist__split,axiom,
% 11.11/6.21      ! [R3: real,F: nat > complex] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ R3 )
% 11.11/6.21       => ( ( summable_complex @ F )
% 11.11/6.21         => ? [N8: nat] :
% 11.11/6.21            ! [N6: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N8 @ N6 )
% 11.11/6.21             => ( ord_less_real
% 11.11/6.21                @ ( real_V1022390504157884413omplex
% 11.11/6.21                  @ ( suminf_complex
% 11.11/6.21                    @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 11.11/6.21                @ R3 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8663_summable__power__series,axiom,
% 11.11/6.21      ! [F: nat > real,Z: real] :
% 11.11/6.21        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 11.11/6.21       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 11.11/6.21         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 11.11/6.21           => ( ( ord_less_real @ Z @ one_one_real )
% 11.11/6.21             => ( summable_real
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8664_Abel__lemma,axiom,
% 11.11/6.21      ! [R3: real,R0: real,A: nat > complex,M7: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 11.11/6.21       => ( ( ord_less_real @ R3 @ R0 )
% 11.11/6.21         => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 11.11/6.21           => ( summable_real
% 11.11/6.21              @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R3 @ N ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8665_summable__ratio__test,axiom,
% 11.11/6.21      ! [C: real,N4: nat,F: nat > real] :
% 11.11/6.21        ( ( ord_less_real @ C @ one_one_real )
% 11.11/6.21       => ( ! [N3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 11.11/6.21         => ( summable_real @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8666_summable__ratio__test,axiom,
% 11.11/6.21      ! [C: real,N4: nat,F: nat > complex] :
% 11.11/6.21        ( ( ord_less_real @ C @ one_one_real )
% 11.11/6.21       => ( ! [N3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N4 @ N3 )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 11.11/6.21         => ( summable_complex @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8667_Re__Reals__divide,axiom,
% 11.11/6.21      ! [R3: complex,Z: complex] :
% 11.11/6.21        ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 11.11/6.21       => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 11.11/6.21          = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8668_vebt__buildup_Osimps_I3_J,axiom,
% 11.11/6.21      ! [Va: nat] :
% 11.11/6.21        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 11.11/6.21         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 11.11/6.21            = ( 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 ) ) ) ) ) ) )
% 11.11/6.21        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 11.11/6.21         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 11.11/6.21            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8669_sin__paired,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 11.11/6.21        @ ( sin_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8670_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.21        ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.21          = Y )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.21               => ( ~ Y
% 11.11/6.21                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 11.11/6.21           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 11.11/6.21                 => ( ~ Y
% 11.11/6.21                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 11.11/6.21             => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.21                    ( ( X4
% 11.11/6.21                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.21                   => ( ( Y
% 11.11/6.21                        = ( ( Xa = Mi3 )
% 11.11/6.21                          | ( Xa = Ma3 ) ) )
% 11.11/6.21                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 11.11/6.21               => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 11.11/6.21                      ( ( X4
% 11.11/6.21                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.21                     => ( ( Y
% 11.11/6.21                          = ( ( Xa = Mi3 )
% 11.11/6.21                            | ( Xa = Ma3 )
% 11.11/6.21                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 11.11/6.21                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) ) ) )
% 11.11/6.21                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 11.11/6.21                        ( ( X4
% 11.11/6.21                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.21                       => ( ( Y
% 11.11/6.21                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 11.11/6.21                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8671_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.21               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 11.11/6.21           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 11.11/6.21                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 11.11/6.21             => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.21                    ( ( X4
% 11.11/6.21                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.21                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 11.11/6.21                     => ( ( Xa = Mi3 )
% 11.11/6.21                        | ( Xa = Ma3 ) ) ) )
% 11.11/6.21               => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 11.11/6.21                      ( ( X4
% 11.11/6.21                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.21                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 11.11/6.21                       => ( ( Xa = Mi3 )
% 11.11/6.21                          | ( Xa = Ma3 )
% 11.11/6.21                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 11.11/6.21                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 11.11/6.21                        ( ( X4
% 11.11/6.21                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.21                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 11.11/6.21                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8672_geometric__deriv__sums,axiom,
% 11.11/6.21      ! [Z: real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 11.11/6.21       => ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) )
% 11.11/6.21          @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8673_geometric__deriv__sums,axiom,
% 11.11/6.21      ! [Z: complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 11.11/6.21       => ( sums_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) )
% 11.11/6.21          @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8674_powser__sums__zero__iff,axiom,
% 11.11/6.21      ! [A: nat > complex,X4: complex] :
% 11.11/6.21        ( ( sums_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 11.11/6.21          @ X4 )
% 11.11/6.21        = ( ( A @ zero_zero_nat )
% 11.11/6.21          = X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8675_powser__sums__zero__iff,axiom,
% 11.11/6.21      ! [A: nat > real,X4: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 11.11/6.21          @ X4 )
% 11.11/6.21        = ( ( A @ zero_zero_nat )
% 11.11/6.21          = X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8676_sums__le,axiom,
% 11.11/6.21      ! [F: nat > real,G: nat > real,S: real,T2: real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( sums_real @ F @ S )
% 11.11/6.21         => ( ( sums_real @ G @ T2 )
% 11.11/6.21           => ( ord_less_eq_real @ S @ T2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8677_sums__le,axiom,
% 11.11/6.21      ! [F: nat > nat,G: nat > nat,S: nat,T2: nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( sums_nat @ F @ S )
% 11.11/6.21         => ( ( sums_nat @ G @ T2 )
% 11.11/6.21           => ( ord_less_eq_nat @ S @ T2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8678_sums__le,axiom,
% 11.11/6.21      ! [F: nat > int,G: nat > int,S: int,T2: int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.21       => ( ( sums_int @ F @ S )
% 11.11/6.21         => ( ( sums_int @ G @ T2 )
% 11.11/6.21           => ( ord_less_eq_int @ S @ T2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8679_sums__divide,axiom,
% 11.11/6.21      ! [F: nat > real,A: real,C: real] :
% 11.11/6.21        ( ( sums_real @ F @ A )
% 11.11/6.21       => ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C )
% 11.11/6.21          @ ( divide_divide_real @ A @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8680_sums__divide,axiom,
% 11.11/6.21      ! [F: nat > complex,A: complex,C: complex] :
% 11.11/6.21        ( ( sums_complex @ F @ A )
% 11.11/6.21       => ( sums_complex
% 11.11/6.21          @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C )
% 11.11/6.21          @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8681_sums__add,axiom,
% 11.11/6.21      ! [F: nat > real,A: real,G: nat > real,B: real] :
% 11.11/6.21        ( ( sums_real @ F @ A )
% 11.11/6.21       => ( ( sums_real @ G @ B )
% 11.11/6.21         => ( sums_real
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 11.11/6.21            @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8682_sums__add,axiom,
% 11.11/6.21      ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 11.11/6.21        ( ( sums_nat @ F @ A )
% 11.11/6.21       => ( ( sums_nat @ G @ B )
% 11.11/6.21         => ( sums_nat
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 11.11/6.21            @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8683_sums__add,axiom,
% 11.11/6.21      ! [F: nat > int,A: int,G: nat > int,B: int] :
% 11.11/6.21        ( ( sums_int @ F @ A )
% 11.11/6.21       => ( ( sums_int @ G @ B )
% 11.11/6.21         => ( sums_int
% 11.11/6.21            @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 11.11/6.21            @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8684_sums__mult__D,axiom,
% 11.11/6.21      ! [C: real,F: nat > real,A: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 11.11/6.21          @ A )
% 11.11/6.21       => ( ( C != zero_zero_real )
% 11.11/6.21         => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8685_sums__mult__D,axiom,
% 11.11/6.21      ! [C: complex,F: nat > complex,A: complex] :
% 11.11/6.21        ( ( sums_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 11.11/6.21          @ A )
% 11.11/6.21       => ( ( C != zero_zero_complex )
% 11.11/6.21         => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8686_sums__Suc__imp,axiom,
% 11.11/6.21      ! [F: nat > complex,S: complex] :
% 11.11/6.21        ( ( ( F @ zero_zero_nat )
% 11.11/6.21          = zero_zero_complex )
% 11.11/6.21       => ( ( sums_complex
% 11.11/6.21            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21            @ S )
% 11.11/6.21         => ( sums_complex @ F @ S ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8687_sums__Suc__imp,axiom,
% 11.11/6.21      ! [F: nat > real,S: real] :
% 11.11/6.21        ( ( ( F @ zero_zero_nat )
% 11.11/6.21          = zero_zero_real )
% 11.11/6.21       => ( ( sums_real
% 11.11/6.21            @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21            @ S )
% 11.11/6.21         => ( sums_real @ F @ S ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8688_sums__Suc__iff,axiom,
% 11.11/6.21      ! [F: nat > real,S: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21          @ S )
% 11.11/6.21        = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8689_sums__Suc,axiom,
% 11.11/6.21      ! [F: nat > real,L: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21          @ L )
% 11.11/6.21       => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8690_sums__Suc,axiom,
% 11.11/6.21      ! [F: nat > nat,L: nat] :
% 11.11/6.21        ( ( sums_nat
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21          @ L )
% 11.11/6.21       => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8691_sums__Suc,axiom,
% 11.11/6.21      ! [F: nat > int,L: int] :
% 11.11/6.21        ( ( sums_int
% 11.11/6.21          @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 11.11/6.21          @ L )
% 11.11/6.21       => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8692_sums__zero__iff__shift,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > complex,S: complex] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ I4 @ N2 )
% 11.11/6.21           => ( ( F @ I4 )
% 11.11/6.21              = zero_zero_complex ) )
% 11.11/6.21       => ( ( sums_complex
% 11.11/6.21            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 11.11/6.21            @ S )
% 11.11/6.21          = ( sums_complex @ F @ S ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8693_sums__zero__iff__shift,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > real,S: real] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ I4 @ N2 )
% 11.11/6.21           => ( ( F @ I4 )
% 11.11/6.21              = zero_zero_real ) )
% 11.11/6.21       => ( ( sums_real
% 11.11/6.21            @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 11.11/6.21            @ S )
% 11.11/6.21          = ( sums_real @ F @ S ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8694_powser__sums__if,axiom,
% 11.11/6.21      ! [M: nat,Z: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N ) )
% 11.11/6.21        @ ( power_power_complex @ Z @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8695_powser__sums__if,axiom,
% 11.11/6.21      ! [M: nat,Z: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N ) )
% 11.11/6.21        @ ( power_power_real @ Z @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8696_powser__sums__if,axiom,
% 11.11/6.21      ! [M: nat,Z: int] :
% 11.11/6.21        ( sums_int
% 11.11/6.21        @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N ) )
% 11.11/6.21        @ ( power_power_int @ Z @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8697_powser__sums__zero,axiom,
% 11.11/6.21      ! [A: nat > complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 11.11/6.21        @ ( A @ zero_zero_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8698_powser__sums__zero,axiom,
% 11.11/6.21      ! [A: nat > real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 11.11/6.21        @ ( A @ zero_zero_nat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8699_geometric__sums,axiom,
% 11.11/6.21      ! [C: real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 11.11/6.21       => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8700_geometric__sums,axiom,
% 11.11/6.21      ! [C: complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 11.11/6.21       => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8701_power__half__series,axiom,
% 11.11/6.21      ( sums_real
% 11.11/6.21      @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 11.11/6.21      @ one_one_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8702_sums__if_H,axiom,
% 11.11/6.21      ! [G: nat > real,X4: real] :
% 11.11/6.21        ( ( sums_real @ G @ X4 )
% 11.11/6.21       => ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21          @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8703_sums__if,axiom,
% 11.11/6.21      ! [G: nat > real,X4: real,F: nat > real,Y: real] :
% 11.11/6.21        ( ( sums_real @ G @ X4 )
% 11.11/6.21       => ( ( sums_real @ F @ Y )
% 11.11/6.21         => ( sums_real
% 11.11/6.21            @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( F @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.21            @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8704_cos__paired,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_real @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.21        @ ( cos_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8705_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 11.11/6.21               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 11.11/6.21                 => ~ ( ( Xa = Mi3 )
% 11.11/6.21                      | ( Xa = Ma3 ) ) ) )
% 11.11/6.21           => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 11.11/6.21                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 11.11/6.21                   => ~ ( ( Xa = Mi3 )
% 11.11/6.21                        | ( Xa = Ma3 )
% 11.11/6.21                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 11.11/6.21             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 11.11/6.21                    ( ( X4
% 11.11/6.21                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 11.11/6.21                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 11.11/6.21                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8706_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [A5: $o,B5: $o] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 11.11/6.21                 => ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                     => A5 )
% 11.11/6.21                    & ( ( Xa != zero_zero_nat )
% 11.11/6.21                     => ( ( ( Xa = one_one_nat )
% 11.11/6.21                         => B5 )
% 11.11/6.21                        & ( Xa = one_one_nat ) ) ) ) ) )
% 11.11/6.21           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 11.11/6.21                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 11.11/6.21             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 11.11/6.21                    ( ( X4
% 11.11/6.21                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 11.11/6.21                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8707_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.21        ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [A5: $o,B5: $o] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 11.11/6.21                 => ~ ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                       => A5 )
% 11.11/6.21                      & ( ( Xa != zero_zero_nat )
% 11.11/6.21                       => ( ( ( Xa = one_one_nat )
% 11.11/6.21                           => B5 )
% 11.11/6.21                          & ( Xa = one_one_nat ) ) ) ) ) )
% 11.11/6.21           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 11.11/6.21                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8708_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 11.11/6.21      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.21        ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 11.11/6.21          = Y )
% 11.11/6.21       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.21         => ( ! [A5: $o,B5: $o] :
% 11.11/6.21                ( ( X4
% 11.11/6.21                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 11.11/6.21               => ( ( Y
% 11.11/6.21                    = ( ( ( Xa = zero_zero_nat )
% 11.11/6.21                       => A5 )
% 11.11/6.21                      & ( ( Xa != zero_zero_nat )
% 11.11/6.21                       => ( ( ( Xa = one_one_nat )
% 11.11/6.21                           => B5 )
% 11.11/6.21                          & ( Xa = one_one_nat ) ) ) ) )
% 11.11/6.21                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 11.11/6.21           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 11.11/6.21                  ( ( X4
% 11.11/6.21                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 11.11/6.21                 => ( ~ Y
% 11.11/6.21                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 11.11/6.21             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 11.11/6.21                    ( ( X4
% 11.11/6.21                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 11.11/6.21                   => ( ( Y
% 11.11/6.21                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 11.11/6.21                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.21                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 11.11/6.21                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8709_diffs__equiv,axiom,
% 11.11/6.21      ! [C: nat > complex,X4: complex] :
% 11.11/6.21        ( ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 11.11/6.21       => ( sums_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 11.11/6.21          @ ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8710_diffs__equiv,axiom,
% 11.11/6.21      ! [C: nat > real,X4: real] :
% 11.11/6.21        ( ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 11.11/6.21       => ( sums_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 11.11/6.21          @ ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8711_diffs__def,axiom,
% 11.11/6.21      ( diffs_complex
% 11.11/6.21      = ( ^ [C2: nat > complex,N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8712_diffs__def,axiom,
% 11.11/6.21      ( diffs_real
% 11.11/6.21      = ( ^ [C2: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8713_diffs__def,axiom,
% 11.11/6.21      ( diffs_int
% 11.11/6.21      = ( ^ [C2: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8714_termdiff__converges__all,axiom,
% 11.11/6.21      ! [C: nat > complex,X4: complex] :
% 11.11/6.21        ( ! [X5: complex] :
% 11.11/6.21            ( summable_complex
% 11.11/6.21            @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) )
% 11.11/6.21       => ( summable_complex
% 11.11/6.21          @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8715_termdiff__converges__all,axiom,
% 11.11/6.21      ! [C: nat > real,X4: real] :
% 11.11/6.21        ( ! [X5: real] :
% 11.11/6.21            ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) )
% 11.11/6.21       => ( summable_real
% 11.11/6.21          @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8716_termdiff__converges,axiom,
% 11.11/6.21      ! [X4: real,K5: real,C: nat > real] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 11.11/6.21       => ( ! [X5: real] :
% 11.11/6.21              ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 11.11/6.21             => ( summable_real
% 11.11/6.21                @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) ) )
% 11.11/6.21         => ( summable_real
% 11.11/6.21            @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8717_termdiff__converges,axiom,
% 11.11/6.21      ! [X4: complex,K5: real,C: nat > complex] :
% 11.11/6.21        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 11.11/6.21       => ( ! [X5: complex] :
% 11.11/6.21              ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 11.11/6.21             => ( summable_complex
% 11.11/6.21                @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) ) )
% 11.11/6.21         => ( summable_complex
% 11.11/6.21            @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8718_exp__first__two__terms,axiom,
% 11.11/6.21      ( exp_real
% 11.11/6.21      = ( ^ [X: real] :
% 11.11/6.21            ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X )
% 11.11/6.21            @ ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8719_exp__first__two__terms,axiom,
% 11.11/6.21      ( exp_complex
% 11.11/6.21      = ( ^ [X: complex] :
% 11.11/6.21            ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ X )
% 11.11/6.21            @ ( suminf_complex
% 11.11/6.21              @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8720_monoseq__def,axiom,
% 11.11/6.21      ( topolo6980174941875973593q_real
% 11.11/6.21      = ( ^ [X3: nat > real] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8721_monoseq__def,axiom,
% 11.11/6.21      ( topolo3100542954746470799et_int
% 11.11/6.21      = ( ^ [X3: nat > set_int] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_set_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8722_monoseq__def,axiom,
% 11.11/6.21      ( topolo4267028734544971653eq_rat
% 11.11/6.21      = ( ^ [X3: nat > rat] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_rat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8723_monoseq__def,axiom,
% 11.11/6.21      ( topolo1459490580787246023eq_num
% 11.11/6.21      = ( ^ [X3: nat > num] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_num @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8724_monoseq__def,axiom,
% 11.11/6.21      ( topolo4902158794631467389eq_nat
% 11.11/6.21      = ( ^ [X3: nat > nat] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_nat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8725_monoseq__def,axiom,
% 11.11/6.21      ( topolo4899668324122417113eq_int
% 11.11/6.21      = ( ^ [X3: nat > int] :
% 11.11/6.21            ( ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 11.11/6.21            | ! [M6: nat,N: nat] :
% 11.11/6.21                ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.21               => ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8726_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > real] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8727_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > set_int] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8728_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > rat] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8729_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > num] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8730_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > nat] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8731_monoI2,axiom,
% 11.11/6.21      ! [X8: nat > int] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 11.11/6.21       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8732_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > real] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8733_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > set_int] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_set_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8734_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > rat] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8735_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > num] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8736_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > nat] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8737_monoI1,axiom,
% 11.11/6.21      ! [X8: nat > int] :
% 11.11/6.21        ( ! [M5: nat,N3: nat] :
% 11.11/6.21            ( ( ord_less_eq_nat @ M5 @ N3 )
% 11.11/6.21           => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 11.11/6.21       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8738_scaleR__eq__iff,axiom,
% 11.11/6.21      ! [B: real,U: real,A: real] :
% 11.11/6.21        ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 11.11/6.21          = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 11.11/6.21        = ( ( A = B )
% 11.11/6.21          | ( U = one_one_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8739_scaleR__power,axiom,
% 11.11/6.21      ! [X4: real,Y: real,N2: nat] :
% 11.11/6.21        ( ( power_power_real @ ( real_V1485227260804924795R_real @ X4 @ Y ) @ N2 )
% 11.11/6.21        = ( real_V1485227260804924795R_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8740_scaleR__power,axiom,
% 11.11/6.21      ! [X4: real,Y: complex,N2: nat] :
% 11.11/6.21        ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X4 @ Y ) @ N2 )
% 11.11/6.21        = ( real_V2046097035970521341omplex @ ( power_power_real @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8741_scaleR__minus1__left,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.21        = ( uminus_uminus_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8742_scaleR__minus1__left,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.21        = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8743_scaleR__collapse,axiom,
% 11.11/6.21      ! [U: real,A: real] :
% 11.11/6.21        ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 11.11/6.21        = A ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8744_scaleR__times,axiom,
% 11.11/6.21      ! [U: num,W: num,A: complex] :
% 11.11/6.21        ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 11.11/6.21        = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8745_scaleR__times,axiom,
% 11.11/6.21      ! [U: num,W: num,A: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 11.11/6.21        = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8746_inverse__scaleR__times,axiom,
% 11.11/6.21      ! [V: num,W: num,A: complex] :
% 11.11/6.21        ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 11.11/6.21        = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8747_inverse__scaleR__times,axiom,
% 11.11/6.21      ! [V: num,W: num,A: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 11.11/6.21        = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8748_fraction__scaleR__times,axiom,
% 11.11/6.21      ! [U: num,V: num,W: num,A: complex] :
% 11.11/6.21        ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 11.11/6.21        = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8749_fraction__scaleR__times,axiom,
% 11.11/6.21      ! [U: num,V: num,W: num,A: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 11.11/6.21        = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8750_scaleR__half__double,axiom,
% 11.11/6.21      ! [A: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 11.11/6.21        = A ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8751_scaleR__right__distrib,axiom,
% 11.11/6.21      ! [A: real,X4: real,Y: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X4 @ Y ) )
% 11.11/6.21        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8752_scaleR__left__distrib,axiom,
% 11.11/6.21      ! [A: real,B: real,X4: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X4 )
% 11.11/6.21        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8753_scaleR__left_Oadd,axiom,
% 11.11/6.21      ! [X4: real,Y: real,Xa: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X4 @ Y ) @ Xa )
% 11.11/6.21        = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X4 @ Xa ) @ ( real_V1485227260804924795R_real @ Y @ Xa ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8754_of__real__def,axiom,
% 11.11/6.21      ( real_V1803761363581548252l_real
% 11.11/6.21      = ( ^ [R5: real] : ( real_V1485227260804924795R_real @ R5 @ one_one_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8755_of__real__def,axiom,
% 11.11/6.21      ( real_V4546457046886955230omplex
% 11.11/6.21      = ( ^ [R5: real] : ( real_V2046097035970521341omplex @ R5 @ one_one_complex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8756_scaleR__right__mono,axiom,
% 11.11/6.21      ! [A: real,B: real,X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.21       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8757_scaleR__right__mono__neg,axiom,
% 11.11/6.21      ! [B: real,A: real,C: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ B @ A )
% 11.11/6.21       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 11.11/6.21         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8758_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 11.11/6.21      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 11.11/6.21        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8759_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 11.11/6.21      ! [A: real,E2: real,C: real,B: real,D: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 11.11/6.21        = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8760_zero__le__scaleR__iff,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 11.11/6.21        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.21          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 11.11/6.21          | ( A = zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8761_scaleR__le__0__iff,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 11.11/6.21        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.21            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 11.11/6.21          | ( ( ord_less_real @ A @ zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.21          | ( A = zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8762_scaleR__nonpos__nonpos,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 11.11/6.21         => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8763_scaleR__nonpos__nonneg,axiom,
% 11.11/6.21      ! [A: real,X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8764_scaleR__nonneg__nonpos,axiom,
% 11.11/6.21      ! [A: real,X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.21       => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.21         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8765_scaleR__nonneg__nonneg,axiom,
% 11.11/6.21      ! [A: real,X4: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.21       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21         => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X4 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8766_split__scaleR__pos__le,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 11.11/6.21          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8767_split__scaleR__neg__le,axiom,
% 11.11/6.21      ! [A: real,X4: real] :
% 11.11/6.21        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.21            & ( ord_less_eq_real @ X4 @ zero_zero_real ) )
% 11.11/6.21          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 11.11/6.21            & ( ord_less_eq_real @ zero_zero_real @ X4 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8768_scaleR__mono_H,axiom,
% 11.11/6.21      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.21       => ( ( ord_less_eq_real @ C @ D )
% 11.11/6.21         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 11.11/6.21           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8769_scaleR__mono,axiom,
% 11.11/6.21      ! [A: real,B: real,X4: real,Y: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.21       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.21         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 11.11/6.21           => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21             => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ Y ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8770_scaleR__left__le__one__le,axiom,
% 11.11/6.21      ! [X4: real,A: real] :
% 11.11/6.21        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.21       => ( ( ord_less_eq_real @ A @ one_one_real )
% 11.11/6.21         => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8771_scaleR__2,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.21        = ( plus_plus_real @ X4 @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8772_real__vector__affinity__eq,axiom,
% 11.11/6.21      ! [M: real,X4: real,C: real,Y: real] :
% 11.11/6.21        ( ( M != zero_zero_real )
% 11.11/6.21       => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C )
% 11.11/6.21            = Y )
% 11.11/6.21          = ( X4
% 11.11/6.21            = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8773_real__vector__eq__affinity,axiom,
% 11.11/6.21      ! [M: real,Y: real,X4: real,C: real] :
% 11.11/6.21        ( ( M != zero_zero_real )
% 11.11/6.21       => ( ( Y
% 11.11/6.21            = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C ) )
% 11.11/6.21          = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 11.11/6.21            = X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8774_neg__less__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 11.11/6.21          = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8775_neg__divideR__less__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 11.11/6.21          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8776_pos__less__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 11.11/6.21          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8777_pos__divideR__less__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 11.11/6.21          = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8778_summable__exp__generic,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8779_summable__exp__generic,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( summable_complex
% 11.11/6.21        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8780_sin__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 11.11/6.21        @ ( sin_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8781_sin__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 11.11/6.21        @ ( sin_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8782_sin__def,axiom,
% 11.11/6.21      ( sin_real
% 11.11/6.21      = ( ^ [X: real] :
% 11.11/6.21            ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8783_sin__def,axiom,
% 11.11/6.21      ( sin_complex
% 11.11/6.21      = ( ^ [X: complex] :
% 11.11/6.21            ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8784_cos__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 11.11/6.21        @ ( cos_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8785_cos__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 11.11/6.21        @ ( cos_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8786_cos__def,axiom,
% 11.11/6.21      ( cos_real
% 11.11/6.21      = ( ^ [X: real] :
% 11.11/6.21            ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8787_cos__def,axiom,
% 11.11/6.21      ( cos_complex
% 11.11/6.21      = ( ^ [X: complex] :
% 11.11/6.21            ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8788_summable__norm__sin,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8789_summable__norm__sin,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8790_summable__norm__cos,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8791_summable__norm__cos,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8792_pos__le__minus__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 11.11/6.21          = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8793_pos__minus__divideR__le__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 11.11/6.21          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8794_neg__le__minus__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 11.11/6.21          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8795_neg__minus__divideR__le__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 11.11/6.21          = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8796_neg__minus__divideR__less__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 11.11/6.21          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8797_neg__less__minus__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ C @ zero_zero_real )
% 11.11/6.21       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 11.11/6.21          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8798_pos__minus__divideR__less__eq,axiom,
% 11.11/6.21      ! [C: real,B: real,A: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 11.11/6.21          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8799_pos__less__minus__divideR__eq,axiom,
% 11.11/6.21      ! [C: real,A: real,B: real] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.21       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 11.11/6.21          = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8800_exp__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) )
% 11.11/6.21        @ ( exp_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8801_exp__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) )
% 11.11/6.21        @ ( exp_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8802_exp__def,axiom,
% 11.11/6.21      ( exp_real
% 11.11/6.21      = ( ^ [X: real] :
% 11.11/6.21            ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8803_exp__def,axiom,
% 11.11/6.21      ( exp_complex
% 11.11/6.21      = ( ^ [X: complex] :
% 11.11/6.21            ( suminf_complex
% 11.11/6.21            @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8804_summable__norm__exp,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8805_summable__norm__exp,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( summable_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8806_sin__minus__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) ) )
% 11.11/6.21        @ ( sin_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8807_sin__minus__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) ) )
% 11.11/6.21        @ ( sin_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8808_cos__minus__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) )
% 11.11/6.21        @ ( cos_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8809_cos__minus__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) )
% 11.11/6.21        @ ( cos_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8810_cosh__def,axiom,
% 11.11/6.21      ( cosh_real
% 11.11/6.21      = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8811_cosh__def,axiom,
% 11.11/6.21      ( cosh_complex
% 11.11/6.21      = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8812_sinh__def,axiom,
% 11.11/6.21      ( sinh_real
% 11.11/6.21      = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8813_sinh__def,axiom,
% 11.11/6.21      ( sinh_complex
% 11.11/6.21      = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8814_exp__first__term,axiom,
% 11.11/6.21      ( exp_real
% 11.11/6.21      = ( ^ [X: real] :
% 11.11/6.21            ( plus_plus_real @ one_one_real
% 11.11/6.21            @ ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8815_exp__first__term,axiom,
% 11.11/6.21      ( exp_complex
% 11.11/6.21      = ( ^ [X: complex] :
% 11.11/6.21            ( plus_plus_complex @ one_one_complex
% 11.11/6.21            @ ( suminf_complex
% 11.11/6.21              @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8816_cosh__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) @ zero_zero_real )
% 11.11/6.21        @ ( cosh_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8817_cosh__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) @ zero_zero_complex )
% 11.11/6.21        @ ( cosh_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8818_sinh__converges,axiom,
% 11.11/6.21      ! [X4: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) )
% 11.11/6.21        @ ( sinh_real @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8819_sinh__converges,axiom,
% 11.11/6.21      ! [X4: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) )
% 11.11/6.21        @ ( sinh_complex @ X4 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8820_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8821_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > set_int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8822_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > rat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8823_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > num] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8824_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8825_mono__SucI1,axiom,
% 11.11/6.21      ! [X8: nat > int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 11.11/6.21       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8826_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8827_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > set_int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8828_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > rat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8829_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > num] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8830_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8831_mono__SucI2,axiom,
% 11.11/6.21      ! [X8: nat > int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 11.11/6.21       => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8832_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo6980174941875973593q_real
% 11.11/6.21      = ( ^ [X3: nat > real] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_real @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8833_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo3100542954746470799et_int
% 11.11/6.21      = ( ^ [X3: nat > set_int] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8834_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo4267028734544971653eq_rat
% 11.11/6.21      = ( ^ [X3: nat > rat] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8835_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo1459490580787246023eq_num
% 11.11/6.21      = ( ^ [X3: nat > num] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_num @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8836_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo4902158794631467389eq_nat
% 11.11/6.21      = ( ^ [X3: nat > nat] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8837_monoseq__Suc,axiom,
% 11.11/6.21      ( topolo4899668324122417113eq_int
% 11.11/6.21      = ( ^ [X3: nat > int] :
% 11.11/6.21            ( ! [N: nat] : ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 11.11/6.21            | ! [N: nat] : ( ord_less_eq_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8838_of__nat__code,axiom,
% 11.11/6.21      ( semiri8010041392384452111omplex
% 11.11/6.21      = ( ^ [N: nat] :
% 11.11/6.21            ( semiri2816024913162550771omplex
% 11.11/6.21            @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 11.11/6.21            @ N
% 11.11/6.21            @ zero_zero_complex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8839_of__nat__code,axiom,
% 11.11/6.21      ( semiri681578069525770553at_rat
% 11.11/6.21      = ( ^ [N: nat] :
% 11.11/6.21            ( semiri7787848453975740701ux_rat
% 11.11/6.21            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 11.11/6.21            @ N
% 11.11/6.21            @ zero_zero_rat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8840_of__nat__code,axiom,
% 11.11/6.21      ( semiri5074537144036343181t_real
% 11.11/6.21      = ( ^ [N: nat] :
% 11.11/6.21            ( semiri7260567687927622513x_real
% 11.11/6.21            @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 11.11/6.21            @ N
% 11.11/6.21            @ zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8841_of__nat__code,axiom,
% 11.11/6.21      ( semiri1314217659103216013at_int
% 11.11/6.21      = ( ^ [N: nat] :
% 11.11/6.21            ( semiri8420488043553186161ux_int
% 11.11/6.21            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 11.11/6.21            @ N
% 11.11/6.21            @ zero_zero_int ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8842_of__nat__code,axiom,
% 11.11/6.21      ( semiri1316708129612266289at_nat
% 11.11/6.21      = ( ^ [N: nat] :
% 11.11/6.21            ( semiri8422978514062236437ux_nat
% 11.11/6.21            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 11.11/6.21            @ N
% 11.11/6.21            @ zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8843_Arg__def,axiom,
% 11.11/6.21      ( arg
% 11.11/6.21      = ( ^ [Z5: complex] :
% 11.11/6.21            ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 11.11/6.21            @ ( fChoice_real
% 11.11/6.21              @ ^ [A3: real] :
% 11.11/6.21                  ( ( ( sgn_sgn_complex @ Z5 )
% 11.11/6.21                    = ( cis @ A3 ) )
% 11.11/6.21                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 11.11/6.21                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8844_set__vebt__def,axiom,
% 11.11/6.21      ( vEBT_set_vebt
% 11.11/6.21      = ( ^ [T: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8845_sin__x__sin__y,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [N: nat] :
% 11.11/6.21                ( if_complex
% 11.11/6.21                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 11.11/6.21                  & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.21                @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 11.11/6.21                @ zero_zero_complex )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8846_sin__x__sin__y,axiom,
% 11.11/6.21      ! [X4: real,Y: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [N: nat] :
% 11.11/6.21                ( if_real
% 11.11/6.21                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 11.11/6.21                  & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.21                @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 11.11/6.21                @ zero_zero_real )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8847_atMost__eq__iff,axiom,
% 11.11/6.21      ! [X4: nat,Y: nat] :
% 11.11/6.21        ( ( ( set_ord_atMost_nat @ X4 )
% 11.11/6.21          = ( set_ord_atMost_nat @ Y ) )
% 11.11/6.21        = ( X4 = Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8848_atMost__eq__iff,axiom,
% 11.11/6.21      ! [X4: int,Y: int] :
% 11.11/6.21        ( ( ( set_ord_atMost_int @ X4 )
% 11.11/6.21          = ( set_ord_atMost_int @ Y ) )
% 11.11/6.21        = ( X4 = Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8849_atMost__iff,axiom,
% 11.11/6.21      ! [I2: real,K: real] :
% 11.11/6.21        ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 11.11/6.21        = ( ord_less_eq_real @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8850_atMost__iff,axiom,
% 11.11/6.21      ! [I2: set_int,K: set_int] :
% 11.11/6.21        ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 11.11/6.21        = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8851_atMost__iff,axiom,
% 11.11/6.21      ! [I2: rat,K: rat] :
% 11.11/6.21        ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 11.11/6.21        = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8852_atMost__iff,axiom,
% 11.11/6.21      ! [I2: num,K: num] :
% 11.11/6.21        ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 11.11/6.21        = ( ord_less_eq_num @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8853_atMost__iff,axiom,
% 11.11/6.21      ! [I2: nat,K: nat] :
% 11.11/6.21        ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 11.11/6.21        = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8854_atMost__iff,axiom,
% 11.11/6.21      ! [I2: int,K: int] :
% 11.11/6.21        ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 11.11/6.21        = ( ord_less_eq_int @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8855_atMost__subset__iff,axiom,
% 11.11/6.21      ! [X4: set_int,Y: set_int] :
% 11.11/6.21        ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X4 ) @ ( set_or58775011639299419et_int @ Y ) )
% 11.11/6.21        = ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8856_atMost__subset__iff,axiom,
% 11.11/6.21      ! [X4: rat,Y: rat] :
% 11.11/6.21        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X4 ) @ ( set_ord_atMost_rat @ Y ) )
% 11.11/6.21        = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8857_atMost__subset__iff,axiom,
% 11.11/6.21      ! [X4: num,Y: num] :
% 11.11/6.21        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X4 ) @ ( set_ord_atMost_num @ Y ) )
% 11.11/6.21        = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8858_atMost__subset__iff,axiom,
% 11.11/6.21      ! [X4: nat,Y: nat] :
% 11.11/6.21        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X4 ) @ ( set_ord_atMost_nat @ Y ) )
% 11.11/6.21        = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8859_atMost__subset__iff,axiom,
% 11.11/6.21      ! [X4: int,Y: int] :
% 11.11/6.21        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X4 ) @ ( set_ord_atMost_int @ Y ) )
% 11.11/6.21        = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8860_sum_OatMost__Suc,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8861_sum_OatMost__Suc,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8862_sum_OatMost__Suc,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8863_sum_OatMost__Suc,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8864_norm__sum,axiom,
% 11.11/6.21      ! [F: nat > complex,A2: set_nat] :
% 11.11/6.21        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 11.11/6.21        @ ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8865_norm__sum,axiom,
% 11.11/6.21      ! [F: nat > real,A2: set_nat] :
% 11.11/6.21        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 11.11/6.21        @ ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8866_norm__sum,axiom,
% 11.11/6.21      ! [F: complex > complex,A2: set_complex] :
% 11.11/6.21        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 11.11/6.21        @ ( groups5808333547571424918x_real
% 11.11/6.21          @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8867_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_real,F: real > complex,G: real > real] :
% 11.11/6.21        ( ! [X5: real] :
% 11.11/6.21            ( ( member_real @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8868_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_int,F: int > complex,G: int > real] :
% 11.11/6.21        ( ! [X5: int] :
% 11.11/6.21            ( ( member_int @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8869_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 11.11/6.21        ( ! [X5: product_prod_nat_nat] :
% 11.11/6.21            ( ( member8440522571783428010at_nat @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8870_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 11.11/6.21        ( ! [X5: nat] :
% 11.11/6.21            ( ( member_nat @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8871_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 11.11/6.21        ( ! [X5: nat] :
% 11.11/6.21            ( ( member_nat @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8872_sum__norm__le,axiom,
% 11.11/6.21      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 11.11/6.21        ( ! [X5: complex] :
% 11.11/6.21            ( ( member_complex @ X5 @ S2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 11.11/6.21       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8873_sum__choose__upper,axiom,
% 11.11/6.21      ! [M: nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8874_mod__sum__eq,axiom,
% 11.11/6.21      ! [F: nat > nat,A: nat,A2: set_nat] :
% 11.11/6.21        ( ( modulo_modulo_nat
% 11.11/6.21          @ ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 11.11/6.21            @ A2 )
% 11.11/6.21          @ A )
% 11.11/6.21        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8875_mod__sum__eq,axiom,
% 11.11/6.21      ! [F: int > int,A: int,A2: set_int] :
% 11.11/6.21        ( ( modulo_modulo_int
% 11.11/6.21          @ ( groups4538972089207619220nt_int
% 11.11/6.21            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 11.11/6.21            @ A2 )
% 11.11/6.21          @ A )
% 11.11/6.21        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8876_sum_OatMost__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8877_sum_OatMost__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8878_sum_OatMost__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8879_sum_OatMost__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8880_sum__telescope,axiom,
% 11.11/6.21      ! [F: nat > rat,I2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ I2 ) )
% 11.11/6.21        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8881_sum__telescope,axiom,
% 11.11/6.21      ! [F: nat > int,I2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ I2 ) )
% 11.11/6.21        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8882_sum__telescope,axiom,
% 11.11/6.21      ! [F: nat > real,I2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ I2 ) )
% 11.11/6.21        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8883_polyfun__eq__coeffs,axiom,
% 11.11/6.21      ! [C: nat > complex,N2: nat,D: nat > complex] :
% 11.11/6.21        ( ( ! [X: complex] :
% 11.11/6.21              ( ( groups2073611262835488442omplex
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21              = ( groups2073611262835488442omplex
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 11.11/6.21        = ( ! [I3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ I3 @ N2 )
% 11.11/6.21             => ( ( C @ I3 )
% 11.11/6.21                = ( D @ I3 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8884_polyfun__eq__coeffs,axiom,
% 11.11/6.21      ! [C: nat > real,N2: nat,D: nat > real] :
% 11.11/6.21        ( ( ! [X: real] :
% 11.11/6.21              ( ( groups6591440286371151544t_real
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21              = ( groups6591440286371151544t_real
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 11.11/6.21        = ( ! [I3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ I3 @ N2 )
% 11.11/6.21             => ( ( C @ I3 )
% 11.11/6.21                = ( D @ I3 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8885_bounded__imp__summable,axiom,
% 11.11/6.21      ! [A: nat > int,B3: int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 11.11/6.21         => ( summable_int @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8886_bounded__imp__summable,axiom,
% 11.11/6.21      ! [A: nat > nat,B3: nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 11.11/6.21         => ( summable_nat @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8887_bounded__imp__summable,axiom,
% 11.11/6.21      ! [A: nat > real,B3: real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 11.11/6.21         => ( summable_real @ A ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8888_atMost__def,axiom,
% 11.11/6.21      ( set_ord_atMost_real
% 11.11/6.21      = ( ^ [U2: real] :
% 11.11/6.21            ( collect_real
% 11.11/6.21            @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8889_atMost__def,axiom,
% 11.11/6.21      ( set_or58775011639299419et_int
% 11.11/6.21      = ( ^ [U2: set_int] :
% 11.11/6.21            ( collect_set_int
% 11.11/6.21            @ ^ [X: set_int] : ( ord_less_eq_set_int @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8890_atMost__def,axiom,
% 11.11/6.21      ( set_ord_atMost_rat
% 11.11/6.21      = ( ^ [U2: rat] :
% 11.11/6.21            ( collect_rat
% 11.11/6.21            @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8891_atMost__def,axiom,
% 11.11/6.21      ( set_ord_atMost_num
% 11.11/6.21      = ( ^ [U2: num] :
% 11.11/6.21            ( collect_num
% 11.11/6.21            @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8892_atMost__def,axiom,
% 11.11/6.21      ( set_ord_atMost_nat
% 11.11/6.21      = ( ^ [U2: nat] :
% 11.11/6.21            ( collect_nat
% 11.11/6.21            @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8893_atMost__def,axiom,
% 11.11/6.21      ( set_ord_atMost_int
% 11.11/6.21      = ( ^ [U2: int] :
% 11.11/6.21            ( collect_int
% 11.11/6.21            @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8894_sum__choose__lower,axiom,
% 11.11/6.21      ! [R3: nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N2 ) ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8895_choose__rising__sum_I2_J,axiom,
% 11.11/6.21      ! [N2: nat,M: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8896_choose__rising__sum_I1_J,axiom,
% 11.11/6.21      ! [N2: nat,M: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8897_polyfun__eq__0,axiom,
% 11.11/6.21      ! [C: nat > complex,N2: nat] :
% 11.11/6.21        ( ( ! [X: complex] :
% 11.11/6.21              ( ( groups2073611262835488442omplex
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21              = zero_zero_complex ) )
% 11.11/6.21        = ( ! [I3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ I3 @ N2 )
% 11.11/6.21             => ( ( C @ I3 )
% 11.11/6.21                = zero_zero_complex ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8898_polyfun__eq__0,axiom,
% 11.11/6.21      ! [C: nat > real,N2: nat] :
% 11.11/6.21        ( ( ! [X: real] :
% 11.11/6.21              ( ( groups6591440286371151544t_real
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21              = zero_zero_real ) )
% 11.11/6.21        = ( ! [I3: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ I3 @ N2 )
% 11.11/6.21             => ( ( C @ I3 )
% 11.11/6.21                = zero_zero_real ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8899_zero__polynom__imp__zero__coeffs,axiom,
% 11.11/6.21      ! [C: nat > complex,N2: nat,K: nat] :
% 11.11/6.21        ( ! [W2: complex] :
% 11.11/6.21            ( ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W2 @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_complex )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.21         => ( ( C @ K )
% 11.11/6.21            = zero_zero_complex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8900_zero__polynom__imp__zero__coeffs,axiom,
% 11.11/6.21      ! [C: nat > real,N2: nat,K: nat] :
% 11.11/6.21        ( ! [W2: real] :
% 11.11/6.21            ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W2 @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_real )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ N2 )
% 11.11/6.21         => ( ( C @ K )
% 11.11/6.21            = zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8901_gbinomial__parallel__sum,axiom,
% 11.11/6.21      ! [A: complex,N2: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8902_gbinomial__parallel__sum,axiom,
% 11.11/6.21      ! [A: rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8903_gbinomial__parallel__sum,axiom,
% 11.11/6.21      ! [A: real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8904_sum__choose__diagonal,axiom,
% 11.11/6.21      ! [M: nat,N2: nat] :
% 11.11/6.21        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.21       => ( ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21          = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8905_vandermonde,axiom,
% 11.11/6.21      ! [M: nat,N2: nat,R3: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ R3 ) )
% 11.11/6.21        = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R3 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8906_sum__gp__basic,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8907_sum__gp__basic,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21        = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8908_sum__gp__basic,axiom,
% 11.11/6.21      ! [X4: int,N2: nat] :
% 11.11/6.21        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8909_sum__gp__basic,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21        = ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8910_choose__row__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8911_binomial,axiom,
% 11.11/6.21      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.21        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8912_sum_Oin__pairs__0,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [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 ) ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8913_sum_Oin__pairs__0,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.21        = ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [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 ) ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8914_sum_Oin__pairs__0,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.21        = ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [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 ) ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8915_sum_Oin__pairs__0,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [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 ) ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8916_polynomial__product,axiom,
% 11.11/6.21      ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X4: rat] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ M @ I4 )
% 11.11/6.21           => ( ( A @ I4 )
% 11.11/6.21              = zero_zero_rat ) )
% 11.11/6.21       => ( ! [J2: nat] :
% 11.11/6.21              ( ( ord_less_nat @ N2 @ J2 )
% 11.11/6.21             => ( ( B @ J2 )
% 11.11/6.21                = zero_zero_rat ) )
% 11.11/6.21         => ( ( times_times_rat
% 11.11/6.21              @ ( groups2906978787729119204at_rat
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21              @ ( groups2906978787729119204at_rat
% 11.11/6.21                @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X4 @ J3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21            = ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [R5: nat] :
% 11.11/6.21                  ( times_times_rat
% 11.11/6.21                  @ ( groups2906978787729119204at_rat
% 11.11/6.21                    @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ R5 ) )
% 11.11/6.21                  @ ( power_power_rat @ X4 @ R5 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8917_polynomial__product,axiom,
% 11.11/6.21      ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X4: complex] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ M @ I4 )
% 11.11/6.21           => ( ( A @ I4 )
% 11.11/6.21              = zero_zero_complex ) )
% 11.11/6.21       => ( ! [J2: nat] :
% 11.11/6.21              ( ( ord_less_nat @ N2 @ J2 )
% 11.11/6.21             => ( ( B @ J2 )
% 11.11/6.21                = zero_zero_complex ) )
% 11.11/6.21         => ( ( times_times_complex
% 11.11/6.21              @ ( groups2073611262835488442omplex
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21              @ ( groups2073611262835488442omplex
% 11.11/6.21                @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X4 @ J3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21            = ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [R5: nat] :
% 11.11/6.21                  ( times_times_complex
% 11.11/6.21                  @ ( groups2073611262835488442omplex
% 11.11/6.21                    @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ R5 ) )
% 11.11/6.21                  @ ( power_power_complex @ X4 @ R5 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8918_polynomial__product,axiom,
% 11.11/6.21      ! [M: nat,A: nat > int,N2: nat,B: nat > int,X4: int] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ M @ I4 )
% 11.11/6.21           => ( ( A @ I4 )
% 11.11/6.21              = zero_zero_int ) )
% 11.11/6.21       => ( ! [J2: nat] :
% 11.11/6.21              ( ( ord_less_nat @ N2 @ J2 )
% 11.11/6.21             => ( ( B @ J2 )
% 11.11/6.21                = zero_zero_int ) )
% 11.11/6.21         => ( ( times_times_int
% 11.11/6.21              @ ( groups3539618377306564664at_int
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21              @ ( groups3539618377306564664at_int
% 11.11/6.21                @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X4 @ J3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21            = ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [R5: nat] :
% 11.11/6.21                  ( times_times_int
% 11.11/6.21                  @ ( groups3539618377306564664at_int
% 11.11/6.21                    @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ R5 ) )
% 11.11/6.21                  @ ( power_power_int @ X4 @ R5 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8919_polynomial__product,axiom,
% 11.11/6.21      ! [M: nat,A: nat > real,N2: nat,B: nat > real,X4: real] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ M @ I4 )
% 11.11/6.21           => ( ( A @ I4 )
% 11.11/6.21              = zero_zero_real ) )
% 11.11/6.21       => ( ! [J2: nat] :
% 11.11/6.21              ( ( ord_less_nat @ N2 @ J2 )
% 11.11/6.21             => ( ( B @ J2 )
% 11.11/6.21                = zero_zero_real ) )
% 11.11/6.21         => ( ( times_times_real
% 11.11/6.21              @ ( groups6591440286371151544t_real
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21              @ ( groups6591440286371151544t_real
% 11.11/6.21                @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X4 @ J3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21            = ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [R5: nat] :
% 11.11/6.21                  ( times_times_real
% 11.11/6.21                  @ ( groups6591440286371151544t_real
% 11.11/6.21                    @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ R5 ) )
% 11.11/6.21                  @ ( power_power_real @ X4 @ R5 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8920_gbinomial__sum__lower__neg,axiom,
% 11.11/6.21      ! [A: complex,M: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8921_gbinomial__sum__lower__neg,axiom,
% 11.11/6.21      ! [A: rat,M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8922_gbinomial__sum__lower__neg,axiom,
% 11.11/6.21      ! [A: real,M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8923_binomial__ring,axiom,
% 11.11/6.21      ! [A: rat,B: rat,N2: nat] :
% 11.11/6.21        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8924_binomial__ring,axiom,
% 11.11/6.21      ! [A: complex,B: complex,N2: nat] :
% 11.11/6.21        ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8925_binomial__ring,axiom,
% 11.11/6.21      ! [A: int,B: int,N2: nat] :
% 11.11/6.21        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8926_binomial__ring,axiom,
% 11.11/6.21      ! [A: nat,B: nat,N2: nat] :
% 11.11/6.21        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8927_binomial__ring,axiom,
% 11.11/6.21      ! [A: real,B: real,N2: nat] :
% 11.11/6.21        ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8928_polynomial__product__nat,axiom,
% 11.11/6.21      ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X4: nat] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( ord_less_nat @ M @ I4 )
% 11.11/6.21           => ( ( A @ I4 )
% 11.11/6.21              = zero_zero_nat ) )
% 11.11/6.21       => ( ! [J2: nat] :
% 11.11/6.21              ( ( ord_less_nat @ N2 @ J2 )
% 11.11/6.21             => ( ( B @ J2 )
% 11.11/6.21                = zero_zero_nat ) )
% 11.11/6.21         => ( ( times_times_nat
% 11.11/6.21              @ ( groups3542108847815614940at_nat
% 11.11/6.21                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X4 @ I3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21              @ ( groups3542108847815614940at_nat
% 11.11/6.21                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X4 @ J3 ) )
% 11.11/6.21                @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21            = ( groups3542108847815614940at_nat
% 11.11/6.21              @ ^ [R5: nat] :
% 11.11/6.21                  ( times_times_nat
% 11.11/6.21                  @ ( groups3542108847815614940at_nat
% 11.11/6.21                    @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ R5 ) )
% 11.11/6.21                  @ ( power_power_nat @ X4 @ R5 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8929_choose__square__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8930_pochhammer__binomial__sum,axiom,
% 11.11/6.21      ! [A: rat,B: rat,N2: nat] :
% 11.11/6.21        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8931_pochhammer__binomial__sum,axiom,
% 11.11/6.21      ! [A: complex,B: complex,N2: nat] :
% 11.11/6.21        ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8932_pochhammer__binomial__sum,axiom,
% 11.11/6.21      ! [A: int,B: int,N2: nat] :
% 11.11/6.21        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8933_pochhammer__binomial__sum,axiom,
% 11.11/6.21      ! [A: real,B: real,N2: nat] :
% 11.11/6.21        ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8934_sum__power__add,axiom,
% 11.11/6.21      ! [X4: complex,M: nat,I5: set_nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 11.11/6.21          @ I5 )
% 11.11/6.21        = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ I5 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8935_sum__power__add,axiom,
% 11.11/6.21      ! [X4: int,M: nat,I5: set_nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [I3: nat] : ( power_power_int @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 11.11/6.21          @ I5 )
% 11.11/6.21        = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ I5 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8936_sum__power__add,axiom,
% 11.11/6.21      ! [X4: real,M: nat,I5: set_nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( power_power_real @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 11.11/6.21          @ I5 )
% 11.11/6.21        = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ I5 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8937_sum_Ozero__middle,axiom,
% 11.11/6.21      ! [P2: nat,K: nat,G: nat > complex,H: nat > complex] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ P2 )
% 11.11/6.21         => ( ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ P2 ) )
% 11.11/6.21            = ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8938_sum_Ozero__middle,axiom,
% 11.11/6.21      ! [P2: nat,K: nat,G: nat > rat,H: nat > rat] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ P2 )
% 11.11/6.21         => ( ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ P2 ) )
% 11.11/6.21            = ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8939_sum_Ozero__middle,axiom,
% 11.11/6.21      ! [P2: nat,K: nat,G: nat > int,H: nat > int] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ P2 )
% 11.11/6.21         => ( ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ P2 ) )
% 11.11/6.21            = ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8940_sum_Ozero__middle,axiom,
% 11.11/6.21      ! [P2: nat,K: nat,G: nat > nat,H: nat > nat] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ P2 )
% 11.11/6.21         => ( ( groups3542108847815614940at_nat
% 11.11/6.21              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ P2 ) )
% 11.11/6.21            = ( groups3542108847815614940at_nat
% 11.11/6.21              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8941_sum_Ozero__middle,axiom,
% 11.11/6.21      ! [P2: nat,K: nat,G: nat > real,H: nat > real] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 11.11/6.21       => ( ( ord_less_eq_nat @ K @ P2 )
% 11.11/6.21         => ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ P2 ) )
% 11.11/6.21            = ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8942_gbinomial__partial__sum__poly,axiom,
% 11.11/6.21      ! [M: nat,A: complex,X4: complex,Y: complex] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8943_gbinomial__partial__sum__poly,axiom,
% 11.11/6.21      ! [M: nat,A: rat,X4: rat,Y: rat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8944_gbinomial__partial__sum__poly,axiom,
% 11.11/6.21      ! [M: nat,A: real,X4: real,Y: real] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8945_exp__series__add__commuting,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex,N2: nat] :
% 11.11/6.21        ( ( ( times_times_complex @ X4 @ Y )
% 11.11/6.21          = ( times_times_complex @ Y @ X4 ) )
% 11.11/6.21       => ( ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ N2 ) )
% 11.11/6.21          = ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_complex @ X4 @ I3 ) ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8946_exp__series__add__commuting,axiom,
% 11.11/6.21      ! [X4: real,Y: real,N2: nat] :
% 11.11/6.21        ( ( ( times_times_real @ X4 @ Y )
% 11.11/6.21          = ( times_times_real @ Y @ X4 ) )
% 11.11/6.21       => ( ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ N2 ) )
% 11.11/6.21          = ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_real @ X4 @ I3 ) ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8947_root__polyfun,axiom,
% 11.11/6.21      ! [N2: nat,Z: int,A: int] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( ( power_power_int @ Z @ N2 )
% 11.11/6.21            = A )
% 11.11/6.21          = ( ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_int @ ( if_int @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I3 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_int ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8948_root__polyfun,axiom,
% 11.11/6.21      ! [N2: nat,Z: complex,A: complex] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( ( power_power_complex @ Z @ N2 )
% 11.11/6.21            = A )
% 11.11/6.21          = ( ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_complex @ ( if_complex @ ( I3 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I3 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_complex ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8949_root__polyfun,axiom,
% 11.11/6.21      ! [N2: nat,Z: code_integer,A: code_integer] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( ( power_8256067586552552935nteger @ Z @ N2 )
% 11.11/6.21            = A )
% 11.11/6.21          = ( ( groups7501900531339628137nteger
% 11.11/6.21              @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I3 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_z3403309356797280102nteger ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8950_root__polyfun,axiom,
% 11.11/6.21      ! [N2: nat,Z: rat,A: rat] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( ( power_power_rat @ Z @ N2 )
% 11.11/6.21            = A )
% 11.11/6.21          = ( ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_rat @ ( if_rat @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I3 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_rat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8951_root__polyfun,axiom,
% 11.11/6.21      ! [N2: nat,Z: real,A: real] :
% 11.11/6.21        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( ( power_power_real @ Z @ N2 )
% 11.11/6.21            = A )
% 11.11/6.21          = ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_real @ ( if_real @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I3 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I3 ) )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = zero_zero_real ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8952_sum__gp0,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_rat )
% 11.11/6.21         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 11.11/6.21        & ( ( X4 != one_one_rat )
% 11.11/6.21         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8953_sum__gp0,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_complex )
% 11.11/6.21         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 11.11/6.21        & ( ( X4 != one_one_complex )
% 11.11/6.21         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8954_sum__gp0,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_real )
% 11.11/6.21         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 11.11/6.21        & ( ( X4 != one_one_real )
% 11.11/6.21         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8955_choose__alternating__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( N2 != one_one_nat )
% 11.11/6.21       => ( ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8956_choose__alternating__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( N2 != one_one_nat )
% 11.11/6.21       => ( ( groups7501900531339628137nteger
% 11.11/6.21            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8957_choose__alternating__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( N2 != one_one_nat )
% 11.11/6.21       => ( ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_rat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8958_choose__alternating__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( N2 != one_one_nat )
% 11.11/6.21       => ( ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_int ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8959_choose__alternating__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( N2 != one_one_nat )
% 11.11/6.21       => ( ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ I3 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8960_gbinomial__sum__nat__pow2,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8961_gbinomial__sum__nat__pow2,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8962_gbinomial__partial__sum__poly__xpos,axiom,
% 11.11/6.21      ! [M: nat,A: rat,X4: rat,Y: rat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8963_gbinomial__partial__sum__poly__xpos,axiom,
% 11.11/6.21      ! [M: nat,A: complex,X4: complex,Y: complex] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8964_gbinomial__partial__sum__poly__xpos,axiom,
% 11.11/6.21      ! [M: nat,A: real,X4: real,Y: real] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8965_binomial__r__part__sum,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8966_choose__linear__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8967_choose__alternating__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8968_choose__alternating__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( groups7501900531339628137nteger
% 11.11/6.21            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_z3403309356797280102nteger ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8969_choose__alternating__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_rat ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8970_choose__alternating__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_int ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8971_choose__alternating__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_real ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8972_polyfun__extremal__lemma,axiom,
% 11.11/6.21      ! [E2: real,C: nat > complex,N2: nat] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.21       => ? [M9: real] :
% 11.11/6.21          ! [Z3: complex] :
% 11.11/6.21            ( ( ord_less_eq_real @ M9 @ ( real_V1022390504157884413omplex @ Z3 ) )
% 11.11/6.21           => ( ord_less_eq_real
% 11.11/6.21              @ ( real_V1022390504157884413omplex
% 11.11/6.21                @ ( groups2073611262835488442omplex
% 11.11/6.21                  @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 11.11/6.21                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8973_polyfun__extremal__lemma,axiom,
% 11.11/6.21      ! [E2: real,C: nat > real,N2: nat] :
% 11.11/6.21        ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.21       => ? [M9: real] :
% 11.11/6.21          ! [Z3: real] :
% 11.11/6.21            ( ( ord_less_eq_real @ M9 @ ( real_V7735802525324610683m_real @ Z3 ) )
% 11.11/6.21           => ( ord_less_eq_real
% 11.11/6.21              @ ( real_V7735802525324610683m_real
% 11.11/6.21                @ ( groups6591440286371151544t_real
% 11.11/6.21                  @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 11.11/6.21                  @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21              @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8974_gbinomial__r__part__sum,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8975_gbinomial__r__part__sum,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8976_gbinomial__r__part__sum,axiom,
% 11.11/6.21      ! [M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8977_choose__odd__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [I3: nat] :
% 11.11/6.21                  ( if_rat
% 11.11/6.21                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.21                  @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) )
% 11.11/6.21                  @ zero_zero_rat )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8978_choose__odd__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [I3: nat] :
% 11.11/6.21                  ( if_complex
% 11.11/6.21                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.21                  @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) )
% 11.11/6.21                  @ zero_zero_complex )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8979_choose__odd__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [I3: nat] :
% 11.11/6.21                  ( if_int
% 11.11/6.21                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.21                  @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) )
% 11.11/6.21                  @ zero_zero_int )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8980_choose__odd__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [I3: nat] :
% 11.11/6.21                  ( if_real
% 11.11/6.21                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 11.11/6.21                  @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) )
% 11.11/6.21                  @ zero_zero_real )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8981_choose__even__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) @ zero_zero_rat )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8982_choose__even__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) @ zero_zero_complex )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8983_choose__even__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) @ zero_zero_int )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8984_choose__even__sum,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 11.11/6.21            @ ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) @ zero_zero_real )
% 11.11/6.21              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.21          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8985_gbinomial__partial__row__sum,axiom,
% 11.11/6.21      ! [A: rat,M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8986_gbinomial__partial__row__sum,axiom,
% 11.11/6.21      ! [A: complex,M: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8987_gbinomial__partial__row__sum,axiom,
% 11.11/6.21      ! [A: real,M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ M ) )
% 11.11/6.21        = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8988_mask__eq__sum__exp,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 11.11/6.21        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8989_mask__eq__sum__exp,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 11.11/6.21        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8990_mask__eq__sum__exp__nat,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.21        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 11.11/6.21          @ ( collect_nat
% 11.11/6.21            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8991_cos__x__cos__y,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [N: nat] :
% 11.11/6.21                ( if_complex
% 11.11/6.21                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 11.11/6.21                  & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.21                @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 11.11/6.21                @ zero_zero_complex )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8992_cos__x__cos__y,axiom,
% 11.11/6.21      ! [X4: real,Y: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [N: nat] :
% 11.11/6.21                ( if_real
% 11.11/6.21                @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 11.11/6.21                  & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 11.11/6.21                @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 11.11/6.21                @ zero_zero_real )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8993_sums__cos__x__plus__y,axiom,
% 11.11/6.21      ! [X4: complex,Y: complex] :
% 11.11/6.21        ( sums_complex
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_complex )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8994_sums__cos__x__plus__y,axiom,
% 11.11/6.21      ! [X4: real,Y: real] :
% 11.11/6.21        ( sums_real
% 11.11/6.21        @ ^ [P5: nat] :
% 11.11/6.21            ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_real )
% 11.11/6.21            @ ( set_ord_atMost_nat @ P5 ) )
% 11.11/6.21        @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8995_sum__abs__ge__zero,axiom,
% 11.11/6.21      ! [F: nat > real,A2: set_nat] :
% 11.11/6.21        ( ord_less_eq_real @ zero_zero_real
% 11.11/6.21        @ ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8996_sum__abs__ge__zero,axiom,
% 11.11/6.21      ! [F: int > int,A2: set_int] :
% 11.11/6.21        ( ord_less_eq_int @ zero_zero_int
% 11.11/6.21        @ ( groups4538972089207619220nt_int
% 11.11/6.21          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8997_sum__abs,axiom,
% 11.11/6.21      ! [F: nat > real,A2: set_nat] :
% 11.11/6.21        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 11.11/6.21        @ ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8998_sum__abs,axiom,
% 11.11/6.21      ! [F: int > int,A2: set_int] :
% 11.11/6.21        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 11.11/6.21        @ ( groups4538972089207619220nt_int
% 11.11/6.21          @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 11.11/6.21          @ A2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_8999_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_real,X4: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 11.11/6.21        ( ! [I4: real] :
% 11.11/6.21            ( ( member_real @ I4 @ I5 )
% 11.11/6.21           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups7713935264441627589nteger @ X4 @ I5 )
% 11.11/6.21            = one_one_Code_integer )
% 11.11/6.21         => ( ! [I4: real] :
% 11.11/6.21                ( ( member_real @ I4 @ I5 )
% 11.11/6.21               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_le3102999989581377725nteger
% 11.11/6.21              @ ( abs_abs_Code_integer
% 11.11/6.21                @ ( minus_8373710615458151222nteger
% 11.11/6.21                  @ ( groups7713935264441627589nteger
% 11.11/6.21                    @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9000_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_nat,X4: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( member_nat @ I4 @ I5 )
% 11.11/6.21           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups7501900531339628137nteger @ X4 @ I5 )
% 11.11/6.21            = one_one_Code_integer )
% 11.11/6.21         => ( ! [I4: nat] :
% 11.11/6.21                ( ( member_nat @ I4 @ I5 )
% 11.11/6.21               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_le3102999989581377725nteger
% 11.11/6.21              @ ( abs_abs_Code_integer
% 11.11/6.21                @ ( minus_8373710615458151222nteger
% 11.11/6.21                  @ ( groups7501900531339628137nteger
% 11.11/6.21                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9001_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_complex,X4: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 11.11/6.21        ( ! [I4: complex] :
% 11.11/6.21            ( ( member_complex @ I4 @ I5 )
% 11.11/6.21           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups6621422865394947399nteger @ X4 @ I5 )
% 11.11/6.21            = one_one_Code_integer )
% 11.11/6.21         => ( ! [I4: complex] :
% 11.11/6.21                ( ( member_complex @ I4 @ I5 )
% 11.11/6.21               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_le3102999989581377725nteger
% 11.11/6.21              @ ( abs_abs_Code_integer
% 11.11/6.21                @ ( minus_8373710615458151222nteger
% 11.11/6.21                  @ ( groups6621422865394947399nteger
% 11.11/6.21                    @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9002_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_int,X4: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 11.11/6.21        ( ! [I4: int] :
% 11.11/6.21            ( ( member_int @ I4 @ I5 )
% 11.11/6.21           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups7873554091576472773nteger @ X4 @ I5 )
% 11.11/6.21            = one_one_Code_integer )
% 11.11/6.21         => ( ! [I4: int] :
% 11.11/6.21                ( ( member_int @ I4 @ I5 )
% 11.11/6.21               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_le3102999989581377725nteger
% 11.11/6.21              @ ( abs_abs_Code_integer
% 11.11/6.21                @ ( minus_8373710615458151222nteger
% 11.11/6.21                  @ ( groups7873554091576472773nteger
% 11.11/6.21                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9003_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_real,X4: real > real,A: real > real,B: real,Delta: real] :
% 11.11/6.21        ( ! [I4: real] :
% 11.11/6.21            ( ( member_real @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups8097168146408367636l_real @ X4 @ I5 )
% 11.11/6.21            = one_one_real )
% 11.11/6.21         => ( ! [I4: real] :
% 11.11/6.21                ( ( member_real @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_real
% 11.11/6.21              @ ( abs_abs_real
% 11.11/6.21                @ ( minus_minus_real
% 11.11/6.21                  @ ( groups8097168146408367636l_real
% 11.11/6.21                    @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9004_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_complex,X4: complex > real,A: complex > real,B: real,Delta: real] :
% 11.11/6.21        ( ! [I4: complex] :
% 11.11/6.21            ( ( member_complex @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups5808333547571424918x_real @ X4 @ I5 )
% 11.11/6.21            = one_one_real )
% 11.11/6.21         => ( ! [I4: complex] :
% 11.11/6.21                ( ( member_complex @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_real
% 11.11/6.21              @ ( abs_abs_real
% 11.11/6.21                @ ( minus_minus_real
% 11.11/6.21                  @ ( groups5808333547571424918x_real
% 11.11/6.21                    @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9005_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_int,X4: int > real,A: int > real,B: real,Delta: real] :
% 11.11/6.21        ( ! [I4: int] :
% 11.11/6.21            ( ( member_int @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups8778361861064173332t_real @ X4 @ I5 )
% 11.11/6.21            = one_one_real )
% 11.11/6.21         => ( ! [I4: int] :
% 11.11/6.21                ( ( member_int @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_real
% 11.11/6.21              @ ( abs_abs_real
% 11.11/6.21                @ ( minus_minus_real
% 11.11/6.21                  @ ( groups8778361861064173332t_real
% 11.11/6.21                    @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9006_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_real,X4: real > rat,A: real > rat,B: rat,Delta: rat] :
% 11.11/6.21        ( ! [I4: real] :
% 11.11/6.21            ( ( member_real @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups1300246762558778688al_rat @ X4 @ I5 )
% 11.11/6.21            = one_one_rat )
% 11.11/6.21         => ( ! [I4: real] :
% 11.11/6.21                ( ( member_real @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_rat
% 11.11/6.21              @ ( abs_abs_rat
% 11.11/6.21                @ ( minus_minus_rat
% 11.11/6.21                  @ ( groups1300246762558778688al_rat
% 11.11/6.21                    @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9007_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_nat,X4: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 11.11/6.21        ( ! [I4: nat] :
% 11.11/6.21            ( ( member_nat @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups2906978787729119204at_rat @ X4 @ I5 )
% 11.11/6.21            = one_one_rat )
% 11.11/6.21         => ( ! [I4: nat] :
% 11.11/6.21                ( ( member_nat @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_rat
% 11.11/6.21              @ ( abs_abs_rat
% 11.11/6.21                @ ( minus_minus_rat
% 11.11/6.21                  @ ( groups2906978787729119204at_rat
% 11.11/6.21                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9008_convex__sum__bound__le,axiom,
% 11.11/6.21      ! [I5: set_complex,X4: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 11.11/6.21        ( ! [I4: complex] :
% 11.11/6.21            ( ( member_complex @ I4 @ I5 )
% 11.11/6.21           => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 11.11/6.21       => ( ( ( groups5058264527183730370ex_rat @ X4 @ I5 )
% 11.11/6.21            = one_one_rat )
% 11.11/6.21         => ( ! [I4: complex] :
% 11.11/6.21                ( ( member_complex @ I4 @ I5 )
% 11.11/6.21               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 11.11/6.21           => ( ord_less_eq_rat
% 11.11/6.21              @ ( abs_abs_rat
% 11.11/6.21                @ ( minus_minus_rat
% 11.11/6.21                  @ ( groups5058264527183730370ex_rat
% 11.11/6.21                    @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 11.11/6.21                    @ I5 )
% 11.11/6.21                  @ B ) )
% 11.11/6.21              @ Delta ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9009_Maclaurin__minus__cos__expansion,axiom,
% 11.11/6.21      ! [N2: nat,X4: real] :
% 11.11/6.21        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.21       => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.21         => ? [T3: real] :
% 11.11/6.21              ( ( ord_less_real @ X4 @ T3 )
% 11.11/6.21              & ( ord_less_real @ T3 @ zero_zero_real )
% 11.11/6.21              & ( ( cos_real @ X4 )
% 11.11/6.21                = ( plus_plus_real
% 11.11/6.21                  @ ( groups6591440286371151544t_real
% 11.11/6.21                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.21                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9010_lessThan__eq__iff,axiom,
% 11.11/6.21      ! [X4: nat,Y: nat] :
% 11.11/6.21        ( ( ( set_ord_lessThan_nat @ X4 )
% 11.11/6.21          = ( set_ord_lessThan_nat @ Y ) )
% 11.11/6.21        = ( X4 = Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9011_lessThan__eq__iff,axiom,
% 11.11/6.21      ! [X4: int,Y: int] :
% 11.11/6.21        ( ( ( set_ord_lessThan_int @ X4 )
% 11.11/6.21          = ( set_ord_lessThan_int @ Y ) )
% 11.11/6.21        = ( X4 = Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9012_lessThan__eq__iff,axiom,
% 11.11/6.21      ! [X4: real,Y: real] :
% 11.11/6.21        ( ( ( set_or5984915006950818249n_real @ X4 )
% 11.11/6.21          = ( set_or5984915006950818249n_real @ Y ) )
% 11.11/6.21        = ( X4 = Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9013_of__nat__id,axiom,
% 11.11/6.21      ( semiri1316708129612266289at_nat
% 11.11/6.21      = ( ^ [N: nat] : N ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9014_lessThan__iff,axiom,
% 11.11/6.21      ! [I2: rat,K: rat] :
% 11.11/6.21        ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 11.11/6.21        = ( ord_less_rat @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9015_lessThan__iff,axiom,
% 11.11/6.21      ! [I2: num,K: num] :
% 11.11/6.21        ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 11.11/6.21        = ( ord_less_num @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9016_lessThan__iff,axiom,
% 11.11/6.21      ! [I2: nat,K: nat] :
% 11.11/6.21        ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 11.11/6.21        = ( ord_less_nat @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9017_lessThan__iff,axiom,
% 11.11/6.21      ! [I2: int,K: int] :
% 11.11/6.21        ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 11.11/6.21        = ( ord_less_int @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9018_lessThan__iff,axiom,
% 11.11/6.21      ! [I2: real,K: real] :
% 11.11/6.21        ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 11.11/6.21        = ( ord_less_real @ I2 @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9019_lessThan__subset__iff,axiom,
% 11.11/6.21      ! [X4: rat,Y: rat] :
% 11.11/6.21        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X4 ) @ ( set_ord_lessThan_rat @ Y ) )
% 11.11/6.21        = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9020_lessThan__subset__iff,axiom,
% 11.11/6.21      ! [X4: num,Y: num] :
% 11.11/6.21        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X4 ) @ ( set_ord_lessThan_num @ Y ) )
% 11.11/6.21        = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9021_lessThan__subset__iff,axiom,
% 11.11/6.21      ! [X4: nat,Y: nat] :
% 11.11/6.21        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X4 ) @ ( set_ord_lessThan_nat @ Y ) )
% 11.11/6.21        = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9022_lessThan__subset__iff,axiom,
% 11.11/6.21      ! [X4: int,Y: int] :
% 11.11/6.21        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X4 ) @ ( set_ord_lessThan_int @ Y ) )
% 11.11/6.21        = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9023_lessThan__subset__iff,axiom,
% 11.11/6.21      ! [X4: real,Y: real] :
% 11.11/6.21        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X4 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 11.11/6.21        = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9024_sum_OlessThan__Suc,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9025_sum_OlessThan__Suc,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9026_sum_OlessThan__Suc,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9027_sum_OlessThan__Suc,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9028_sumr__cos__zero__one,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = one_one_real ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9029_sum__diff__distrib,axiom,
% 11.11/6.21      ! [Q: int > nat,P: int > nat,N2: int] :
% 11.11/6.21        ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 11.11/6.21       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 11.11/6.21          = ( groups4541462559716669496nt_nat
% 11.11/6.21            @ ^ [X: int] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 11.11/6.21            @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9030_sum__diff__distrib,axiom,
% 11.11/6.21      ! [Q: real > nat,P: real > nat,N2: real] :
% 11.11/6.21        ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 11.11/6.21       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 11.11/6.21          = ( groups1935376822645274424al_nat
% 11.11/6.21            @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 11.11/6.21            @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9031_sum__diff__distrib,axiom,
% 11.11/6.21      ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 11.11/6.21        ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 11.11/6.21       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 11.11/6.21          = ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9032_lessThan__def,axiom,
% 11.11/6.21      ( set_ord_lessThan_rat
% 11.11/6.21      = ( ^ [U2: rat] :
% 11.11/6.21            ( collect_rat
% 11.11/6.21            @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9033_lessThan__def,axiom,
% 11.11/6.21      ( set_ord_lessThan_num
% 11.11/6.21      = ( ^ [U2: num] :
% 11.11/6.21            ( collect_num
% 11.11/6.21            @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9034_lessThan__def,axiom,
% 11.11/6.21      ( set_ord_lessThan_nat
% 11.11/6.21      = ( ^ [U2: nat] :
% 11.11/6.21            ( collect_nat
% 11.11/6.21            @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9035_lessThan__def,axiom,
% 11.11/6.21      ( set_ord_lessThan_int
% 11.11/6.21      = ( ^ [U2: int] :
% 11.11/6.21            ( collect_int
% 11.11/6.21            @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9036_lessThan__def,axiom,
% 11.11/6.21      ( set_or5984915006950818249n_real
% 11.11/6.21      = ( ^ [U2: real] :
% 11.11/6.21            ( collect_real
% 11.11/6.21            @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9037_sum__subtractf__nat,axiom,
% 11.11/6.21      ! [A2: set_real,G: real > nat,F: real > nat] :
% 11.11/6.21        ( ! [X5: real] :
% 11.11/6.21            ( ( member_real @ X5 @ A2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 11.11/6.21       => ( ( groups1935376822645274424al_nat
% 11.11/6.21            @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 11.11/6.21            @ A2 )
% 11.11/6.21          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9038_sum__subtractf__nat,axiom,
% 11.11/6.21      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 11.11/6.21        ( ! [X5: complex] :
% 11.11/6.21            ( ( member_complex @ X5 @ A2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 11.11/6.21       => ( ( groups5693394587270226106ex_nat
% 11.11/6.21            @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 11.11/6.21            @ A2 )
% 11.11/6.21          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9039_sum__subtractf__nat,axiom,
% 11.11/6.21      ! [A2: set_int,G: int > nat,F: int > nat] :
% 11.11/6.21        ( ! [X5: int] :
% 11.11/6.21            ( ( member_int @ X5 @ A2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 11.11/6.21       => ( ( groups4541462559716669496nt_nat
% 11.11/6.21            @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 11.11/6.21            @ A2 )
% 11.11/6.21          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9040_sum__subtractf__nat,axiom,
% 11.11/6.21      ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 11.11/6.21        ( ! [X5: product_prod_nat_nat] :
% 11.11/6.21            ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 11.11/6.21       => ( ( groups977919841031483927at_nat
% 11.11/6.21            @ ^ [X: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 11.11/6.21            @ A2 )
% 11.11/6.21          = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9041_sum__subtractf__nat,axiom,
% 11.11/6.21      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 11.11/6.21        ( ! [X5: nat] :
% 11.11/6.21            ( ( member_nat @ X5 @ A2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 11.11/6.21       => ( ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 11.11/6.21            @ A2 )
% 11.11/6.21          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9042_sum__SucD,axiom,
% 11.11/6.21      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 11.11/6.21        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 11.11/6.21          = ( suc @ N2 ) )
% 11.11/6.21       => ? [X5: nat] :
% 11.11/6.21            ( ( member_nat @ X5 @ A2 )
% 11.11/6.21            & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9043_lessThan__strict__subset__iff,axiom,
% 11.11/6.21      ! [M: rat,N2: rat] :
% 11.11/6.21        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 11.11/6.21        = ( ord_less_rat @ M @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9044_lessThan__strict__subset__iff,axiom,
% 11.11/6.21      ! [M: num,N2: num] :
% 11.11/6.21        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 11.11/6.21        = ( ord_less_num @ M @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9045_lessThan__strict__subset__iff,axiom,
% 11.11/6.21      ! [M: nat,N2: nat] :
% 11.11/6.21        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9046_lessThan__strict__subset__iff,axiom,
% 11.11/6.21      ! [M: int,N2: int] :
% 11.11/6.21        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 11.11/6.21        = ( ord_less_int @ M @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9047_lessThan__strict__subset__iff,axiom,
% 11.11/6.21      ! [M: real,N2: real] :
% 11.11/6.21        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 11.11/6.21        = ( ord_less_real @ M @ N2 ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9048_lessThan__Suc__atMost,axiom,
% 11.11/6.21      ! [K: nat] :
% 11.11/6.21        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 11.11/6.21        = ( set_ord_atMost_nat @ K ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9049_Iic__subset__Iio__iff,axiom,
% 11.11/6.21      ! [A: rat,B: rat] :
% 11.11/6.21        ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 11.11/6.21        = ( ord_less_rat @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9050_Iic__subset__Iio__iff,axiom,
% 11.11/6.21      ! [A: num,B: num] :
% 11.11/6.21        ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 11.11/6.21        = ( ord_less_num @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9051_Iic__subset__Iio__iff,axiom,
% 11.11/6.21      ! [A: nat,B: nat] :
% 11.11/6.21        ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 11.11/6.21        = ( ord_less_nat @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9052_Iic__subset__Iio__iff,axiom,
% 11.11/6.21      ! [A: int,B: int] :
% 11.11/6.21        ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 11.11/6.21        = ( ord_less_int @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9053_Iic__subset__Iio__iff,axiom,
% 11.11/6.21      ! [A: real,B: real] :
% 11.11/6.21        ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 11.11/6.21        = ( ord_less_real @ A @ B ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9054_sum_Onat__diff__reindex,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat
% 11.11/6.21          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9055_sum_Onat__diff__reindex,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9056_suminf__le__const,axiom,
% 11.11/6.21      ! [F: nat > int,X4: int] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( ord_less_eq_int @ ( suminf_int @ F ) @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9057_suminf__le__const,axiom,
% 11.11/6.21      ! [F: nat > nat,X4: nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9058_suminf__le__const,axiom,
% 11.11/6.21      ! [F: nat > real,X4: real] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( ord_less_eq_real @ ( suminf_real @ F ) @ X4 ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9059_sum_OlessThan__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9060_sum_OlessThan__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9061_sum_OlessThan__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9062_sum_OlessThan__Suc__shift,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9063_sum__lessThan__telescope_H,axiom,
% 11.11/6.21      ! [F: nat > rat,M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9064_sum__lessThan__telescope_H,axiom,
% 11.11/6.21      ! [F: nat > int,M: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9065_sum__lessThan__telescope_H,axiom,
% 11.11/6.21      ! [F: nat > real,M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9066_sum__lessThan__telescope,axiom,
% 11.11/6.21      ! [F: nat > rat,M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9067_sum__lessThan__telescope,axiom,
% 11.11/6.21      ! [F: nat > int,M: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9068_sum__lessThan__telescope,axiom,
% 11.11/6.21      ! [F: nat > real,M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9069_summableI__nonneg__bounded,axiom,
% 11.11/6.21      ! [F: nat > int,X4: int] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( summable_int @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9070_summableI__nonneg__bounded,axiom,
% 11.11/6.21      ! [F: nat > nat,X4: nat] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( summable_nat @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9071_summableI__nonneg__bounded,axiom,
% 11.11/6.21      ! [F: nat > real,X4: real] :
% 11.11/6.21        ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 11.11/6.21       => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 11.11/6.21         => ( summable_real @ F ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9072_sums__iff__shift,axiom,
% 11.11/6.21      ! [F: nat > real,N2: nat,S: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 11.11/6.21          @ S )
% 11.11/6.21        = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9073_sums__iff__shift_H,axiom,
% 11.11/6.21      ! [F: nat > real,N2: nat,S: real] :
% 11.11/6.21        ( ( sums_real
% 11.11/6.21          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 11.11/6.21          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 11.11/6.21        = ( sums_real @ F @ S ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9074_sums__split__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > real,S: real,N2: nat] :
% 11.11/6.21        ( ( sums_real @ F @ S )
% 11.11/6.21       => ( sums_real
% 11.11/6.21          @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 11.11/6.21          @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9075_sum__nth__roots,axiom,
% 11.11/6.21      ! [N2: nat,C: complex] :
% 11.11/6.21        ( ( ord_less_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( groups7754918857620584856omplex
% 11.11/6.21            @ ^ [X: complex] : X
% 11.11/6.21            @ ( collect_complex
% 11.11/6.21              @ ^ [Z5: complex] :
% 11.11/6.21                  ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.21                  = C ) ) )
% 11.11/6.21          = zero_zero_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9076_power__diff__1__eq,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat )
% 11.11/6.21        = ( times_times_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9077_power__diff__1__eq,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex )
% 11.11/6.21        = ( times_times_complex @ ( minus_minus_complex @ X4 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9078_power__diff__1__eq,axiom,
% 11.11/6.21      ! [X4: int,N2: nat] :
% 11.11/6.21        ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ one_one_int )
% 11.11/6.21        = ( times_times_int @ ( minus_minus_int @ X4 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9079_power__diff__1__eq,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real )
% 11.11/6.21        = ( times_times_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9080_one__diff__power__eq,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9081_one__diff__power__eq,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9082_one__diff__power__eq,axiom,
% 11.11/6.21      ! [X4: int,N2: nat] :
% 11.11/6.21        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9083_one__diff__power__eq,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9084_geometric__sum,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( X4 != one_one_rat )
% 11.11/6.21       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9085_geometric__sum,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( X4 != one_one_complex )
% 11.11/6.21       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9086_geometric__sum,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( X4 != one_one_real )
% 11.11/6.21       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9087_sum_OatMost__shift,axiom,
% 11.11/6.21      ! [G: nat > rat,N2: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9088_sum_OatMost__shift,axiom,
% 11.11/6.21      ! [G: nat > int,N2: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9089_sum_OatMost__shift,axiom,
% 11.11/6.21      ! [G: nat > nat,N2: nat] :
% 11.11/6.21        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups3542108847815614940at_nat
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9090_sum_OatMost__shift,axiom,
% 11.11/6.21      ! [G: nat > real,N2: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9091_suminf__split__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > real,K: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( suminf_real @ F )
% 11.11/6.21          = ( plus_plus_real
% 11.11/6.21            @ ( suminf_real
% 11.11/6.21              @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 11.11/6.21            @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9092_suminf__minus__initial__segment,axiom,
% 11.11/6.21      ! [F: nat > real,K: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ( suminf_real
% 11.11/6.21            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 11.11/6.21          = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9093_sum__roots__unity,axiom,
% 11.11/6.21      ! [N2: nat] :
% 11.11/6.21        ( ( ord_less_nat @ one_one_nat @ N2 )
% 11.11/6.21       => ( ( groups7754918857620584856omplex
% 11.11/6.21            @ ^ [X: complex] : X
% 11.11/6.21            @ ( collect_complex
% 11.11/6.21              @ ^ [Z5: complex] :
% 11.11/6.21                  ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.21                  = one_one_complex ) ) )
% 11.11/6.21          = zero_zero_complex ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9094_sum__less__suminf,axiom,
% 11.11/6.21      ! [F: nat > int,N2: nat] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9095_sum__less__suminf,axiom,
% 11.11/6.21      ! [F: nat > nat,N2: nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9096_sum__less__suminf,axiom,
% 11.11/6.21      ! [F: nat > real,N2: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9097_sum__gp__strict,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_rat )
% 11.11/6.21         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( semiri681578069525770553at_rat @ N2 ) ) )
% 11.11/6.21        & ( ( X4 != one_one_rat )
% 11.11/6.21         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9098_sum__gp__strict,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_complex )
% 11.11/6.21         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( semiri8010041392384452111omplex @ N2 ) ) )
% 11.11/6.21        & ( ( X4 != one_one_complex )
% 11.11/6.21         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9099_sum__gp__strict,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( ( X4 = one_one_real )
% 11.11/6.21         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.21        & ( ( X4 != one_one_real )
% 11.11/6.21         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9100_lemma__termdiff1,axiom,
% 11.11/6.21      ! [Z: rat,H: rat,M: nat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9101_lemma__termdiff1,axiom,
% 11.11/6.21      ! [Z: complex,H: complex,M: nat] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9102_lemma__termdiff1,axiom,
% 11.11/6.21      ! [Z: int,H: int,M: nat] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9103_lemma__termdiff1,axiom,
% 11.11/6.21      ! [Z: real,H: real,M: nat] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) )
% 11.11/6.21        = ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 11.11/6.21          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9104_diff__power__eq__sum,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat,Y: rat] :
% 11.11/6.21        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X4 @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9105_diff__power__eq__sum,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat,Y: complex] :
% 11.11/6.21        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 11.11/6.21          @ ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X4 @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9106_diff__power__eq__sum,axiom,
% 11.11/6.21      ! [X4: int,N2: nat,Y: int] :
% 11.11/6.21        ( ( minus_minus_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X4 @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9107_diff__power__eq__sum,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Y: real] :
% 11.11/6.21        ( ( minus_minus_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 11.11/6.21        = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X4 @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9108_power__diff__sumr2,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat,Y: rat] :
% 11.11/6.21        ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 11.11/6.21        = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X4 @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9109_power__diff__sumr2,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat,Y: complex] :
% 11.11/6.21        ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 11.11/6.21        = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 11.11/6.21          @ ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X4 @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9110_power__diff__sumr2,axiom,
% 11.11/6.21      ! [X4: int,N2: nat,Y: int] :
% 11.11/6.21        ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 11.11/6.21        = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X4 @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9111_power__diff__sumr2,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Y: real] :
% 11.11/6.21        ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 11.11/6.21        = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_real @ X4 @ I3 ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9112_polyfun__linear__factor__root,axiom,
% 11.11/6.21      ! [C: nat > rat,A: rat,N2: nat] :
% 11.11/6.21        ( ( ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_rat )
% 11.11/6.21       => ~ ! [B5: nat > rat] :
% 11.11/6.21              ~ ! [Z3: rat] :
% 11.11/6.21                  ( ( groups2906978787729119204at_rat
% 11.11/6.21                    @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21                  = ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 11.11/6.21                    @ ( groups2906978787729119204at_rat
% 11.11/6.21                      @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 11.11/6.21                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9113_polyfun__linear__factor__root,axiom,
% 11.11/6.21      ! [C: nat > complex,A: complex,N2: nat] :
% 11.11/6.21        ( ( ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_complex )
% 11.11/6.21       => ~ ! [B5: nat > complex] :
% 11.11/6.21              ~ ! [Z3: complex] :
% 11.11/6.21                  ( ( groups2073611262835488442omplex
% 11.11/6.21                    @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21                  = ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 11.11/6.21                    @ ( groups2073611262835488442omplex
% 11.11/6.21                      @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 11.11/6.21                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9114_polyfun__linear__factor__root,axiom,
% 11.11/6.21      ! [C: nat > int,A: int,N2: nat] :
% 11.11/6.21        ( ( ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_int )
% 11.11/6.21       => ~ ! [B5: nat > int] :
% 11.11/6.21              ~ ! [Z3: int] :
% 11.11/6.21                  ( ( groups3539618377306564664at_int
% 11.11/6.21                    @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21                  = ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 11.11/6.21                    @ ( groups3539618377306564664at_int
% 11.11/6.21                      @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 11.11/6.21                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9115_polyfun__linear__factor__root,axiom,
% 11.11/6.21      ! [C: nat > real,A: real,N2: nat] :
% 11.11/6.21        ( ( ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21          = zero_zero_real )
% 11.11/6.21       => ~ ! [B5: nat > real] :
% 11.11/6.21              ~ ! [Z3: real] :
% 11.11/6.21                  ( ( groups6591440286371151544t_real
% 11.11/6.21                    @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 11.11/6.21                    @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21                  = ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 11.11/6.21                    @ ( groups6591440286371151544t_real
% 11.11/6.21                      @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 11.11/6.21                      @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9116_polyfun__linear__factor,axiom,
% 11.11/6.21      ! [C: nat > rat,N2: nat,A: rat] :
% 11.11/6.21      ? [B5: nat > rat] :
% 11.11/6.21      ! [Z3: rat] :
% 11.11/6.21        ( ( groups2906978787729119204at_rat
% 11.11/6.21          @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_rat
% 11.11/6.21          @ ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 11.11/6.21            @ ( groups2906978787729119204at_rat
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9117_polyfun__linear__factor,axiom,
% 11.11/6.21      ! [C: nat > complex,N2: nat,A: complex] :
% 11.11/6.21      ? [B5: nat > complex] :
% 11.11/6.21      ! [Z3: complex] :
% 11.11/6.21        ( ( groups2073611262835488442omplex
% 11.11/6.21          @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_complex
% 11.11/6.21          @ ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 11.11/6.21            @ ( groups2073611262835488442omplex
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 11.11/6.21          @ ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9118_polyfun__linear__factor,axiom,
% 11.11/6.21      ! [C: nat > int,N2: nat,A: int] :
% 11.11/6.21      ? [B5: nat > int] :
% 11.11/6.21      ! [Z3: int] :
% 11.11/6.21        ( ( groups3539618377306564664at_int
% 11.11/6.21          @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_int
% 11.11/6.21          @ ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 11.11/6.21            @ ( groups3539618377306564664at_int
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9119_polyfun__linear__factor,axiom,
% 11.11/6.21      ! [C: nat > real,N2: nat,A: real] :
% 11.11/6.21      ? [B5: nat > real] :
% 11.11/6.21      ! [Z3: real] :
% 11.11/6.21        ( ( groups6591440286371151544t_real
% 11.11/6.21          @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 11.11/6.21          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.21        = ( plus_plus_real
% 11.11/6.21          @ ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 11.11/6.21            @ ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) ) )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 11.11/6.21            @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9120_real__sum__nat__ivl__bounded2,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 11.11/6.21        ( ! [P7: nat] :
% 11.11/6.21            ( ( ord_less_nat @ P7 @ N2 )
% 11.11/6.21           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 11.11/6.21       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 11.11/6.21         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9121_real__sum__nat__ivl__bounded2,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 11.11/6.21        ( ! [P7: nat] :
% 11.11/6.21            ( ( ord_less_nat @ P7 @ N2 )
% 11.11/6.21           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 11.11/6.21       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 11.11/6.21         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9122_real__sum__nat__ivl__bounded2,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 11.11/6.21        ( ! [P7: nat] :
% 11.11/6.21            ( ( ord_less_nat @ P7 @ N2 )
% 11.11/6.21           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 11.11/6.21       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 11.11/6.21         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9123_real__sum__nat__ivl__bounded2,axiom,
% 11.11/6.21      ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 11.11/6.21        ( ! [P7: nat] :
% 11.11/6.21            ( ( ord_less_nat @ P7 @ N2 )
% 11.11/6.21           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 11.11/6.21       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 11.11/6.21         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9124_sum__less__suminf2,axiom,
% 11.11/6.21      ! [F: nat > int,N2: nat,I2: nat] :
% 11.11/6.21        ( ( summable_int @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 11.11/6.21           => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 11.11/6.21             => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9125_sum__less__suminf2,axiom,
% 11.11/6.21      ! [F: nat > nat,N2: nat,I2: nat] :
% 11.11/6.21        ( ( summable_nat @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 11.11/6.21           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 11.11/6.21             => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9126_sum__less__suminf2,axiom,
% 11.11/6.21      ! [F: nat > real,N2: nat,I2: nat] :
% 11.11/6.21        ( ( summable_real @ F )
% 11.11/6.21       => ( ! [M5: nat] :
% 11.11/6.21              ( ( ord_less_eq_nat @ N2 @ M5 )
% 11.11/6.21             => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 11.11/6.21         => ( ( ord_less_eq_nat @ N2 @ I2 )
% 11.11/6.21           => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 11.11/6.21             => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9127_one__diff__power__eq_H,axiom,
% 11.11/6.21      ! [X4: rat,N2: nat] :
% 11.11/6.21        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 )
% 11.11/6.21          @ ( groups2906978787729119204at_rat
% 11.11/6.21            @ ^ [I3: nat] : ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9128_one__diff__power__eq_H,axiom,
% 11.11/6.21      ! [X4: complex,N2: nat] :
% 11.11/6.21        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 )
% 11.11/6.21          @ ( groups2073611262835488442omplex
% 11.11/6.21            @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9129_one__diff__power__eq_H,axiom,
% 11.11/6.21      ! [X4: int,N2: nat] :
% 11.11/6.21        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 )
% 11.11/6.21          @ ( groups3539618377306564664at_int
% 11.11/6.21            @ ^ [I3: nat] : ( power_power_int @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9130_one__diff__power__eq_H,axiom,
% 11.11/6.21      ! [X4: real,N2: nat] :
% 11.11/6.21        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.21        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 )
% 11.11/6.21          @ ( groups6591440286371151544t_real
% 11.11/6.21            @ ^ [I3: nat] : ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 11.11/6.21            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9131_Maclaurin__zero,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Diff: nat > complex > real] :
% 11.11/6.21        ( ( X4 = zero_zero_real )
% 11.11/6.21       => ( ( N2 != zero_zero_nat )
% 11.11/6.21         => ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9132_Maclaurin__zero,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Diff: nat > real > real] :
% 11.11/6.21        ( ( X4 = zero_zero_real )
% 11.11/6.21       => ( ( N2 != zero_zero_nat )
% 11.11/6.21         => ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9133_Maclaurin__zero,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Diff: nat > rat > real] :
% 11.11/6.21        ( ( X4 = zero_zero_real )
% 11.11/6.21       => ( ( N2 != zero_zero_nat )
% 11.11/6.21         => ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.21            = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 11.11/6.21  
% 11.11/6.21  thf(fact_9134_Maclaurin__zero,axiom,
% 11.11/6.21      ! [X4: real,N2: nat,Diff: nat > nat > real] :
% 11.11/6.21        ( ( X4 = zero_zero_real )
% 11.11/6.21       => ( ( N2 != zero_zero_nat )
% 11.11/6.21         => ( ( groups6591440286371151544t_real
% 11.11/6.21              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.21              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22            = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9135_Maclaurin__zero,axiom,
% 11.11/6.22      ! [X4: real,N2: nat,Diff: nat > int > real] :
% 11.11/6.22        ( ( X4 = zero_zero_real )
% 11.11/6.22       => ( ( N2 != zero_zero_nat )
% 11.11/6.22         => ( ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22            = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9136_Maclaurin__lemma,axiom,
% 11.11/6.22      ! [H: real,F: real > real,J: nat > real,N2: nat] :
% 11.11/6.22        ( ( ord_less_real @ zero_zero_real @ H )
% 11.11/6.22       => ? [B7: real] :
% 11.11/6.22            ( ( F @ H )
% 11.11/6.22            = ( plus_plus_real
% 11.11/6.22              @ ( groups6591440286371151544t_real
% 11.11/6.22                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 11.11/6.22                @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22              @ ( times_times_real @ B7 @ ( divide_divide_real @ ( power_power_real @ H @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9137_sum__split__even__odd,axiom,
% 11.11/6.22      ! [F: nat > real,G: nat > real,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_real
% 11.11/6.22          @ ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 11.11/6.22            @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22          @ ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 11.11/6.22            @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9138_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_real,F: real > rat,G: real > rat] :
% 11.11/6.22        ( ! [I4: real] :
% 11.11/6.22            ( ( member_real @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9139_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 11.11/6.22        ( ! [I4: nat] :
% 11.11/6.22            ( ( member_nat @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9140_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 11.11/6.22        ( ! [I4: complex] :
% 11.11/6.22            ( ( member_complex @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9141_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_int,F: int > rat,G: int > rat] :
% 11.11/6.22        ( ! [I4: int] :
% 11.11/6.22            ( ( member_int @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9142_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_real,F: real > nat,G: real > nat] :
% 11.11/6.22        ( ! [I4: real] :
% 11.11/6.22            ( ( member_real @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9143_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 11.11/6.22        ( ! [I4: complex] :
% 11.11/6.22            ( ( member_complex @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9144_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_int,F: int > nat,G: int > nat] :
% 11.11/6.22        ( ! [I4: int] :
% 11.11/6.22            ( ( member_int @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9145_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_real,F: real > int,G: real > int] :
% 11.11/6.22        ( ! [I4: real] :
% 11.11/6.22            ( ( member_real @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9146_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 11.11/6.22        ( ! [I4: nat] :
% 11.11/6.22            ( ( member_nat @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9147_sum__mono,axiom,
% 11.11/6.22      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 11.11/6.22        ( ! [I4: complex] :
% 11.11/6.22            ( ( member_complex @ I4 @ K5 )
% 11.11/6.22           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9148_sum_Odistrib,axiom,
% 11.11/6.22      ! [G: nat > nat,H: nat > nat,A2: set_nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H @ X ) )
% 11.11/6.22          @ A2 )
% 11.11/6.22        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9149_sum_Odistrib,axiom,
% 11.11/6.22      ! [G: nat > real,H: nat > real,A2: set_nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H @ X ) )
% 11.11/6.22          @ A2 )
% 11.11/6.22        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9150_sum_Odistrib,axiom,
% 11.11/6.22      ! [G: complex > complex,H: complex > complex,A2: set_complex] :
% 11.11/6.22        ( ( groups7754918857620584856omplex
% 11.11/6.22          @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H @ X ) )
% 11.11/6.22          @ A2 )
% 11.11/6.22        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9151_sum_Odistrib,axiom,
% 11.11/6.22      ! [G: int > int,H: int > int,A2: set_int] :
% 11.11/6.22        ( ( groups4538972089207619220nt_int
% 11.11/6.22          @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H @ X ) )
% 11.11/6.22          @ A2 )
% 11.11/6.22        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9152_sum__divide__distrib,axiom,
% 11.11/6.22      ! [F: nat > real,A2: set_nat,R3: real] :
% 11.11/6.22        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R3 )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ R3 )
% 11.11/6.22          @ A2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9153_sum__divide__distrib,axiom,
% 11.11/6.22      ! [F: complex > complex,A2: set_complex,R3: complex] :
% 11.11/6.22        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R3 )
% 11.11/6.22        = ( groups7754918857620584856omplex
% 11.11/6.22          @ ^ [N: complex] : ( divide1717551699836669952omplex @ ( F @ N ) @ R3 )
% 11.11/6.22          @ A2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9154_Maclaurin__exp__le,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22      ? [T3: real] :
% 11.11/6.22        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.22        & ( ( exp_real @ X4 )
% 11.11/6.22          = ( plus_plus_real
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9155_polyfun__diff__alt,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_rat
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( groups2906978787729119204at_rat
% 11.11/6.22                  @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X4 @ J3 ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9156_polyfun__diff__alt,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_complex
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( groups2073611262835488442omplex
% 11.11/6.22                  @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X4 @ J3 ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9157_polyfun__diff__alt,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_int
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( groups3539618377306564664at_int
% 11.11/6.22                  @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X4 @ J3 ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9158_polyfun__diff__alt,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_real
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( groups6591440286371151544t_real
% 11.11/6.22                  @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X4 @ J3 ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9159_exp__first__terms,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( exp_complex
% 11.11/6.22        = ( ^ [X: complex] :
% 11.11/6.22              ( plus_plus_complex
% 11.11/6.22              @ ( groups2073611262835488442omplex
% 11.11/6.22                @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) )
% 11.11/6.22                @ ( set_ord_lessThan_nat @ K ) )
% 11.11/6.22              @ ( suminf_complex
% 11.11/6.22                @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9160_exp__first__terms,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( exp_real
% 11.11/6.22        = ( ^ [X: real] :
% 11.11/6.22              ( plus_plus_real
% 11.11/6.22              @ ( groups6591440286371151544t_real
% 11.11/6.22                @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) )
% 11.11/6.22                @ ( set_ord_lessThan_nat @ K ) )
% 11.11/6.22              @ ( suminf_real
% 11.11/6.22                @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9161_Maclaurin__sin__bound,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22        ( ord_less_eq_real
% 11.11/6.22        @ ( abs_abs_real
% 11.11/6.22          @ ( minus_minus_real @ ( sin_real @ X4 )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 11.11/6.22        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X4 ) @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9162_sum__pos__lt__pair,axiom,
% 11.11/6.22      ! [F: nat > real,K: nat] :
% 11.11/6.22        ( ( summable_real @ F )
% 11.11/6.22       => ( ! [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 ) ) ) ) )
% 11.11/6.22         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9163_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > real] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 11.11/6.22       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9164_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > real] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 11.11/6.22       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9165_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > real] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 11.11/6.22       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9166_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > rat] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9167_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > rat] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9168_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > rat] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9169_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > rat] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 11.11/6.22       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9170_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > nat] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9171_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > nat] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9172_sum__nonpos,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > nat] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9173_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > real] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9174_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > real] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9175_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > real] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9176_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > rat] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9177_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > rat] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9178_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > rat] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9179_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > rat] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9180_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_real,F: real > nat] :
% 11.11/6.22        ( ! [X5: real] :
% 11.11/6.22            ( ( member_real @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9181_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_complex,F: complex > nat] :
% 11.11/6.22        ( ! [X5: complex] :
% 11.11/6.22            ( ( member_complex @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9182_sum__nonneg,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > nat] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9183_sum__cong__Suc,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 11.11/6.22        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 11.11/6.22       => ( ! [X5: nat] :
% 11.11/6.22              ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 11.11/6.22             => ( ( F @ ( suc @ X5 ) )
% 11.11/6.22                = ( G @ ( suc @ X5 ) ) ) )
% 11.11/6.22         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 11.11/6.22            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9184_sum__cong__Suc,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 11.11/6.22        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 11.11/6.22       => ( ! [X5: nat] :
% 11.11/6.22              ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 11.11/6.22             => ( ( F @ ( suc @ X5 ) )
% 11.11/6.22                = ( G @ ( suc @ X5 ) ) ) )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 11.11/6.22            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9185_Maclaurin__exp__lt,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22        ( ( X4 != zero_zero_real )
% 11.11/6.22       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ? [T3: real] :
% 11.11/6.22              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 11.11/6.22              & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.22              & ( ( exp_real @ X4 )
% 11.11/6.22                = ( plus_plus_real
% 11.11/6.22                  @ ( groups6591440286371151544t_real
% 11.11/6.22                    @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 11.11/6.22                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9186_lemma__termdiff2,axiom,
% 11.11/6.22      ! [H: rat,Z: rat,N2: nat] :
% 11.11/6.22        ( ( H != zero_zero_rat )
% 11.11/6.22       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ N2 ) @ ( power_power_rat @ Z @ N2 ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.22          = ( times_times_rat @ H
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [P5: nat] :
% 11.11/6.22                  ( groups2906978787729119204at_rat
% 11.11/6.22                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9187_lemma__termdiff2,axiom,
% 11.11/6.22      ! [H: complex,Z: complex,N2: nat] :
% 11.11/6.22        ( ( H != zero_zero_complex )
% 11.11/6.22       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.22          = ( times_times_complex @ H
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [P5: nat] :
% 11.11/6.22                  ( groups2073611262835488442omplex
% 11.11/6.22                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9188_lemma__termdiff2,axiom,
% 11.11/6.22      ! [H: real,Z: real,N2: nat] :
% 11.11/6.22        ( ( H != zero_zero_real )
% 11.11/6.22       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 11.11/6.22          = ( times_times_real @ H
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [P5: nat] :
% 11.11/6.22                  ( groups6591440286371151544t_real
% 11.11/6.22                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9189_Maclaurin__sin__expansion,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22      ? [T3: real] :
% 11.11/6.22        ( ( sin_real @ X4 )
% 11.11/6.22        = ( plus_plus_real
% 11.11/6.22          @ ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22            @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9190_Maclaurin__sin__expansion2,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22      ? [T3: real] :
% 11.11/6.22        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.22        & ( ( sin_real @ X4 )
% 11.11/6.22          = ( plus_plus_real
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9191_Maclaurin__cos__expansion,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22      ? [T3: real] :
% 11.11/6.22        ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.22        & ( ( cos_real @ X4 )
% 11.11/6.22          = ( plus_plus_real
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9192_Maclaurin__sin__expansion4,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22       => ? [T3: real] :
% 11.11/6.22            ( ( ord_less_real @ zero_zero_real @ T3 )
% 11.11/6.22            & ( ord_less_eq_real @ T3 @ X4 )
% 11.11/6.22            & ( ( sin_real @ X4 )
% 11.11/6.22              = ( plus_plus_real
% 11.11/6.22                @ ( groups6591440286371151544t_real
% 11.11/6.22                  @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22                  @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9193_Maclaurin__sin__expansion3,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ? [T3: real] :
% 11.11/6.22              ( ( ord_less_real @ zero_zero_real @ T3 )
% 11.11/6.22              & ( ord_less_real @ T3 @ X4 )
% 11.11/6.22              & ( ( sin_real @ X4 )
% 11.11/6.22                = ( plus_plus_real
% 11.11/6.22                  @ ( groups6591440286371151544t_real
% 11.11/6.22                    @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9194_Maclaurin__cos__expansion2,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ? [T3: real] :
% 11.11/6.22              ( ( ord_less_real @ zero_zero_real @ T3 )
% 11.11/6.22              & ( ord_less_real @ T3 @ X4 )
% 11.11/6.22              & ( ( cos_real @ X4 )
% 11.11/6.22                = ( plus_plus_real
% 11.11/6.22                  @ ( groups6591440286371151544t_real
% 11.11/6.22                    @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.22                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.22                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9195_bij__betw__roots__unity,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( bij_betw_nat_complex
% 11.11/6.22          @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ N2 )
% 11.11/6.22          @ ( collect_complex
% 11.11/6.22            @ ^ [Z5: complex] :
% 11.11/6.22                ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                = one_one_complex ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9196_sum__gp,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,X4: rat] :
% 11.11/6.22        ( ( ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_rat ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( ( X4 = one_one_rat )
% 11.11/6.22             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 11.11/6.22            & ( ( X4 != one_one_rat )
% 11.11/6.22             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9197_sum__gp,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,X4: complex] :
% 11.11/6.22        ( ( ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_complex ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( ( X4 = one_one_complex )
% 11.11/6.22             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 11.11/6.22            & ( ( X4 != one_one_complex )
% 11.11/6.22             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9198_sum__gp,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,X4: real] :
% 11.11/6.22        ( ( ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_real ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ N2 @ M )
% 11.11/6.22         => ( ( ( X4 = one_one_real )
% 11.11/6.22             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 11.11/6.22            & ( ( X4 != one_one_real )
% 11.11/6.22             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9199_gchoose__row__sum__weighted,axiom,
% 11.11/6.22      ! [R3: rat,M: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat
% 11.11/6.22          @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 11.11/6.22        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9200_gchoose__row__sum__weighted,axiom,
% 11.11/6.22      ! [R3: complex,M: nat] :
% 11.11/6.22        ( ( groups2073611262835488442omplex
% 11.11/6.22          @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 11.11/6.22        = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9201_gchoose__row__sum__weighted,axiom,
% 11.11/6.22      ! [R3: real,M: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 11.11/6.22        = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9202_gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9203_gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9204_gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9205_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: set_int,L: set_int,U: set_int] :
% 11.11/6.22        ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_set_int @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9206_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: rat,L: rat,U: rat] :
% 11.11/6.22        ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_rat @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9207_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: num,L: num,U: num] :
% 11.11/6.22        ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_num @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9208_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: nat,L: nat,U: nat] :
% 11.11/6.22        ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_nat @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9209_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: int,L: int,U: int] :
% 11.11/6.22        ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_int @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9210_atLeastAtMost__iff,axiom,
% 11.11/6.22      ! [I2: real,L: real,U: real] :
% 11.11/6.22        ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 11.11/6.22        = ( ( ord_less_eq_real @ L @ I2 )
% 11.11/6.22          & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9211_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: set_int,H: set_int,L3: set_int,H3: set_int] :
% 11.11/6.22        ( ( ( set_or370866239135849197et_int @ L @ H )
% 11.11/6.22          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_set_int @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9212_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: rat,H: rat,L3: rat,H3: rat] :
% 11.11/6.22        ( ( ( set_or633870826150836451st_rat @ L @ H )
% 11.11/6.22          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_rat @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9213_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: num,H: num,L3: num,H3: num] :
% 11.11/6.22        ( ( ( set_or7049704709247886629st_num @ L @ H )
% 11.11/6.22          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_num @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9214_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: nat,H: nat,L3: nat,H3: nat] :
% 11.11/6.22        ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 11.11/6.22          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_nat @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9215_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: int,H: int,L3: int,H3: int] :
% 11.11/6.22        ( ( ( set_or1266510415728281911st_int @ L @ H )
% 11.11/6.22          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_int @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9216_Icc__eq__Icc,axiom,
% 11.11/6.22      ! [L: real,H: real,L3: real,H3: real] :
% 11.11/6.22        ( ( ( set_or1222579329274155063t_real @ L @ H )
% 11.11/6.22          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 11.11/6.22        = ( ( ( L = L3 )
% 11.11/6.22            & ( H = H3 ) )
% 11.11/6.22          | ( ~ ( ord_less_eq_real @ L @ H )
% 11.11/6.22            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9217_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 11.11/6.22        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_set_int @ C @ A )
% 11.11/6.22            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9218_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.22        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_rat @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_rat @ C @ A )
% 11.11/6.22            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9219_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: num,B: num,C: num,D: num] :
% 11.11/6.22        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_num @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_num @ C @ A )
% 11.11/6.22            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9220_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_nat @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_nat @ C @ A )
% 11.11/6.22            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9221_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.22        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_int @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_int @ C @ A )
% 11.11/6.22            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9222_atLeastatMost__subset__iff,axiom,
% 11.11/6.22      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.22        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_real @ A @ B )
% 11.11/6.22          | ( ( ord_less_eq_real @ C @ A )
% 11.11/6.22            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9223_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: set_int,H: set_int,H3: set_int] :
% 11.11/6.22        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H ) @ ( set_or58775011639299419et_int @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_set_int @ L @ H )
% 11.11/6.22          | ( ord_less_eq_set_int @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9224_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: rat,H: rat,H3: rat] :
% 11.11/6.22        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_rat @ L @ H )
% 11.11/6.22          | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9225_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: num,H: num,H3: num] :
% 11.11/6.22        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_num @ L @ H )
% 11.11/6.22          | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9226_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: nat,H: nat,H3: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_nat @ L @ H )
% 11.11/6.22          | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9227_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: int,H: int,H3: int] :
% 11.11/6.22        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_int @ L @ H )
% 11.11/6.22          | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9228_Icc__subset__Iic__iff,axiom,
% 11.11/6.22      ! [L: real,H: real,H3: real] :
% 11.11/6.22        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 11.11/6.22        = ( ~ ( ord_less_eq_real @ L @ H )
% 11.11/6.22          | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9229_sum_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > complex] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = zero_zero_complex ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9230_sum_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > rat] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = zero_zero_rat ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9231_sum_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > int] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = zero_zero_int ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9232_sum_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > nat] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = zero_zero_nat ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9233_sum_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > real] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = zero_zero_real ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9234_not__Iic__eq__Icc,axiom,
% 11.11/6.22      ! [H3: int,L: int,H: int] :
% 11.11/6.22        ( ( set_ord_atMost_int @ H3 )
% 11.11/6.22       != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9235_not__Iic__eq__Icc,axiom,
% 11.11/6.22      ! [H3: real,L: real,H: real] :
% 11.11/6.22        ( ( set_ord_atMost_real @ H3 )
% 11.11/6.22       != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9236_not__Iic__le__Icc,axiom,
% 11.11/6.22      ! [H: int,L3: int,H3: int] :
% 11.11/6.22        ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9237_not__Iic__le__Icc,axiom,
% 11.11/6.22      ! [H: real,L3: real,H3: real] :
% 11.11/6.22        ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9238_all__nat__less,axiom,
% 11.11/6.22      ! [N2: nat,P: nat > $o] :
% 11.11/6.22        ( ( ! [M6: nat] :
% 11.11/6.22              ( ( ord_less_eq_nat @ M6 @ N2 )
% 11.11/6.22             => ( P @ M6 ) ) )
% 11.11/6.22        = ( ! [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22             => ( P @ X ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9239_ex__nat__less,axiom,
% 11.11/6.22      ! [N2: nat,P: nat > $o] :
% 11.11/6.22        ( ( ? [M6: nat] :
% 11.11/6.22              ( ( ord_less_eq_nat @ M6 @ N2 )
% 11.11/6.22              & ( P @ M6 ) ) )
% 11.11/6.22        = ( ? [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22              & ( P @ X ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9240_atMost__atLeast0,axiom,
% 11.11/6.22      ( set_ord_atMost_nat
% 11.11/6.22      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9241_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 11.11/6.22      ! [G: nat > nat,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9242_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 11.11/6.22      ! [G: nat > real,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9243_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 11.11/6.22      ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9244_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 11.11/6.22      ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9245_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 11.11/6.22        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_set_int @ C @ A )
% 11.11/6.22              & ( ord_less_eq_set_int @ B @ D )
% 11.11/6.22              & ( ( ord_less_set_int @ C @ A )
% 11.11/6.22                | ( ord_less_set_int @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9246_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: rat,B: rat,C: rat,D: rat] :
% 11.11/6.22        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_rat @ C @ A )
% 11.11/6.22              & ( ord_less_eq_rat @ B @ D )
% 11.11/6.22              & ( ( ord_less_rat @ C @ A )
% 11.11/6.22                | ( ord_less_rat @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9247_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: num,B: num,C: num,D: num] :
% 11.11/6.22        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_num @ C @ A )
% 11.11/6.22              & ( ord_less_eq_num @ B @ D )
% 11.11/6.22              & ( ( ord_less_num @ C @ A )
% 11.11/6.22                | ( ord_less_num @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9248_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: nat,B: nat,C: nat,D: nat] :
% 11.11/6.22        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_nat @ C @ A )
% 11.11/6.22              & ( ord_less_eq_nat @ B @ D )
% 11.11/6.22              & ( ( ord_less_nat @ C @ A )
% 11.11/6.22                | ( ord_less_nat @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9249_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: int,B: int,C: int,D: int] :
% 11.11/6.22        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_int @ C @ A )
% 11.11/6.22              & ( ord_less_eq_int @ B @ D )
% 11.11/6.22              & ( ( ord_less_int @ C @ A )
% 11.11/6.22                | ( ord_less_int @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9250_atLeastatMost__psubset__iff,axiom,
% 11.11/6.22      ! [A: real,B: real,C: real,D: real] :
% 11.11/6.22        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 11.11/6.22        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 11.11/6.22            | ( ( ord_less_eq_real @ C @ A )
% 11.11/6.22              & ( ord_less_eq_real @ B @ D )
% 11.11/6.22              & ( ( ord_less_real @ C @ A )
% 11.11/6.22                | ( ord_less_real @ B @ D ) ) ) )
% 11.11/6.22          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9251_sum_OatLeastAtMost__rev,axiom,
% 11.11/6.22      ! [G: nat > nat,N2: nat,M: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9252_sum_OatLeastAtMost__rev,axiom,
% 11.11/6.22      ! [G: nat > real,N2: nat,M: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9253_sum__shift__lb__Suc0__0,axiom,
% 11.11/6.22      ! [F: nat > complex,K: nat] :
% 11.11/6.22        ( ( ( F @ zero_zero_nat )
% 11.11/6.22          = zero_zero_complex )
% 11.11/6.22       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 11.11/6.22          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9254_sum__shift__lb__Suc0__0,axiom,
% 11.11/6.22      ! [F: nat > rat,K: nat] :
% 11.11/6.22        ( ( ( F @ zero_zero_nat )
% 11.11/6.22          = zero_zero_rat )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 11.11/6.22          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9255_sum__shift__lb__Suc0__0,axiom,
% 11.11/6.22      ! [F: nat > int,K: nat] :
% 11.11/6.22        ( ( ( F @ zero_zero_nat )
% 11.11/6.22          = zero_zero_int )
% 11.11/6.22       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 11.11/6.22          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9256_sum__shift__lb__Suc0__0,axiom,
% 11.11/6.22      ! [F: nat > nat,K: nat] :
% 11.11/6.22        ( ( ( F @ zero_zero_nat )
% 11.11/6.22          = zero_zero_nat )
% 11.11/6.22       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 11.11/6.22          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9257_sum__shift__lb__Suc0__0,axiom,
% 11.11/6.22      ! [F: nat > real,K: nat] :
% 11.11/6.22        ( ( ( F @ zero_zero_nat )
% 11.11/6.22          = zero_zero_real )
% 11.11/6.22       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 11.11/6.22          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9258_sum_OatLeast0__atMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > rat,N2: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9259_sum_OatLeast0__atMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > int,N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9260_sum_OatLeast0__atMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9261_sum_OatLeast0__atMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > real,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9262_sum_OatLeast__Suc__atMost,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9263_sum_OatLeast__Suc__atMost,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9264_sum_OatLeast__Suc__atMost,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9265_sum_OatLeast__Suc__atMost,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9266_sum_Onat__ivl__Suc_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9267_sum_Onat__ivl__Suc_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9268_sum_Onat__ivl__Suc_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9269_sum_Onat__ivl__Suc_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9270_sum_OSuc__reindex__ivl,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_rat @ ( G @ M )
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9271_sum_OSuc__reindex__ivl,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_int @ ( G @ M )
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9272_sum_OSuc__reindex__ivl,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_nat @ ( G @ M )
% 11.11/6.22            @ ( groups3542108847815614940at_nat
% 11.11/6.22              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9273_sum_OSuc__reindex__ivl,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 11.11/6.22          = ( plus_plus_real @ ( G @ M )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9274_sum__Suc__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat
% 11.11/6.22            @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9275_sum__Suc__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups3539618377306564664at_int
% 11.11/6.22            @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9276_sum__Suc__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9277_sum_OatLeast1__atMost__eq,axiom,
% 11.11/6.22      ! [G: nat > nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9278_sum_OatLeast1__atMost__eq,axiom,
% 11.11/6.22      ! [G: nat > real,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9279_sum__bounds__lt__plus1,axiom,
% 11.11/6.22      ! [F: nat > nat,Mm: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ Mm ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9280_sum__bounds__lt__plus1,axiom,
% 11.11/6.22      ! [F: nat > real,Mm: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ Mm ) )
% 11.11/6.22        = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9281_sum_Onested__swap_H,axiom,
% 11.11/6.22      ! [A: nat > nat > nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 11.11/6.22          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [J3: nat] :
% 11.11/6.22              ( groups3542108847815614940at_nat
% 11.11/6.22              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9282_sum_Onested__swap_H,axiom,
% 11.11/6.22      ! [A: nat > nat > real,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 11.11/6.22          @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [J3: nat] :
% 11.11/6.22              ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22          @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9283_sum__atLeastAtMost__code,axiom,
% 11.11/6.22      ! [F: nat > complex,A: nat,B: nat] :
% 11.11/6.22        ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.22        = ( set_fo1517530859248394432omplex
% 11.11/6.22          @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 11.11/6.22          @ A
% 11.11/6.22          @ B
% 11.11/6.22          @ zero_zero_complex ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9284_sum__atLeastAtMost__code,axiom,
% 11.11/6.22      ! [F: nat > rat,A: nat,B: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.22        = ( set_fo1949268297981939178at_rat
% 11.11/6.22          @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 11.11/6.22          @ A
% 11.11/6.22          @ B
% 11.11/6.22          @ zero_zero_rat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9285_sum__atLeastAtMost__code,axiom,
% 11.11/6.22      ! [F: nat > int,A: nat,B: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.22        = ( set_fo2581907887559384638at_int
% 11.11/6.22          @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 11.11/6.22          @ A
% 11.11/6.22          @ B
% 11.11/6.22          @ zero_zero_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9286_sum__atLeastAtMost__code,axiom,
% 11.11/6.22      ! [F: nat > nat,A: nat,B: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.22        = ( set_fo2584398358068434914at_nat
% 11.11/6.22          @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 11.11/6.22          @ A
% 11.11/6.22          @ B
% 11.11/6.22          @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9287_sum__atLeastAtMost__code,axiom,
% 11.11/6.22      ! [F: nat > real,A: nat,B: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.22        = ( set_fo3111899725591712190t_real
% 11.11/6.22          @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 11.11/6.22          @ A
% 11.11/6.22          @ B
% 11.11/6.22          @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9288_sum_Oub__add__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 11.11/6.22          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9289_sum_Oub__add__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 11.11/6.22       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 11.11/6.22          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9290_sum_Oub__add__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 11.11/6.22       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 11.11/6.22          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9291_sum_Oub__add__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 11.11/6.22       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 11.11/6.22          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9292_sum__up__index__split,axiom,
% 11.11/6.22      ! [F: nat > rat,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9293_sum__up__index__split,axiom,
% 11.11/6.22      ! [F: nat > int,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9294_sum__up__index__split,axiom,
% 11.11/6.22      ! [F: nat > nat,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9295_sum__up__index__split,axiom,
% 11.11/6.22      ! [F: nat > real,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22        = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9296_sum__natinterval__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > complex] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9297_sum__natinterval__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > rat] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_rat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9298_sum__natinterval__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > int] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9299_sum__natinterval__diff,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > real] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22            = zero_zero_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9300_sum__telescope_H_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups2906978787729119204at_rat
% 11.11/6.22            @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 11.11/6.22          = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9301_sum__telescope_H_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups3539618377306564664at_int
% 11.11/6.22            @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 11.11/6.22          = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9302_sum__telescope_H_H,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,F: nat > real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 11.11/6.22          = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9303_sum__power__shift,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: complex] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9304_sum__power__shift,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9305_sum__power__shift,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22          = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9306_summable__partial__sum__bound,axiom,
% 11.11/6.22      ! [F: nat > complex,E2: real] :
% 11.11/6.22        ( ( summable_complex @ F )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.22         => ~ ! [N8: nat] :
% 11.11/6.22                ~ ! [M2: nat] :
% 11.11/6.22                    ( ( ord_less_eq_nat @ N8 @ M2 )
% 11.11/6.22                   => ! [N6: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9307_summable__partial__sum__bound,axiom,
% 11.11/6.22      ! [F: nat > real,E2: real] :
% 11.11/6.22        ( ( summable_real @ F )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ E2 )
% 11.11/6.22         => ~ ! [N8: nat] :
% 11.11/6.22                ~ ! [M2: nat] :
% 11.11/6.22                    ( ( ord_less_eq_nat @ N8 @ M2 )
% 11.11/6.22                   => ! [N6: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9308_sum__gp__multiplied,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 11.11/6.22          = ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9309_sum__gp__multiplied,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: complex] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 11.11/6.22          = ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9310_sum__gp__multiplied,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 11.11/6.22          = ( minus_minus_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9311_sum__gp__multiplied,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 11.11/6.22          = ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9312_sum_Oin__pairs,axiom,
% 11.11/6.22      ! [G: nat > rat,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.22        = ( groups2906978787729119204at_rat
% 11.11/6.22          @ ^ [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 ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9313_sum_Oin__pairs,axiom,
% 11.11/6.22      ! [G: nat > int,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.22        = ( groups3539618377306564664at_int
% 11.11/6.22          @ ^ [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 ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9314_sum_Oin__pairs,axiom,
% 11.11/6.22      ! [G: nat > nat,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.22        = ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [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 ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9315_sum_Oin__pairs,axiom,
% 11.11/6.22      ! [G: nat > real,M: nat,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 11.11/6.22        = ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [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 ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9316_polyfun__eq__const,axiom,
% 11.11/6.22      ! [C: nat > complex,N2: nat,K: complex] :
% 11.11/6.22        ( ( ! [X: complex] :
% 11.11/6.22              ( ( groups2073611262835488442omplex
% 11.11/6.22                @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 11.11/6.22                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22              = K ) )
% 11.11/6.22        = ( ( ( C @ zero_zero_nat )
% 11.11/6.22            = K )
% 11.11/6.22          & ! [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 11.11/6.22             => ( ( C @ X )
% 11.11/6.22                = zero_zero_complex ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9317_polyfun__eq__const,axiom,
% 11.11/6.22      ! [C: nat > real,N2: nat,K: real] :
% 11.11/6.22        ( ( ! [X: real] :
% 11.11/6.22              ( ( groups6591440286371151544t_real
% 11.11/6.22                @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 11.11/6.22                @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22              = K ) )
% 11.11/6.22        = ( ( ( C @ zero_zero_nat )
% 11.11/6.22            = K )
% 11.11/6.22          & ! [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 11.11/6.22             => ( ( C @ X )
% 11.11/6.22                = zero_zero_real ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9318_gbinomial__sum__up__index,axiom,
% 11.11/6.22      ! [K: nat,N2: nat] :
% 11.11/6.22        ( ( groups2073611262835488442omplex
% 11.11/6.22          @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9319_gbinomial__sum__up__index,axiom,
% 11.11/6.22      ! [K: nat,N2: nat] :
% 11.11/6.22        ( ( groups2906978787729119204at_rat
% 11.11/6.22          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9320_gbinomial__sum__up__index,axiom,
% 11.11/6.22      ! [K: nat,N2: nat] :
% 11.11/6.22        ( ( groups6591440286371151544t_real
% 11.11/6.22          @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9321_gauss__sum__nat,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : X
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9322_double__arith__series,axiom,
% 11.11/6.22      ! [A: rat,D: rat,N2: nat] :
% 11.11/6.22        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups2906978787729119204at_rat
% 11.11/6.22            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9323_double__arith__series,axiom,
% 11.11/6.22      ! [A: extended_enat,D: extended_enat,N2: nat] :
% 11.11/6.22        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups7108830773950497114d_enat
% 11.11/6.22            @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9324_double__arith__series,axiom,
% 11.11/6.22      ! [A: complex,D: complex,N2: nat] :
% 11.11/6.22        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups2073611262835488442omplex
% 11.11/6.22            @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9325_double__arith__series,axiom,
% 11.11/6.22      ! [A: int,D: int,N2: nat] :
% 11.11/6.22        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups3539618377306564664at_int
% 11.11/6.22            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9326_double__arith__series,axiom,
% 11.11/6.22      ! [A: nat,D: nat,N2: nat] :
% 11.11/6.22        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups3542108847815614940at_nat
% 11.11/6.22            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9327_double__arith__series,axiom,
% 11.11/6.22      ! [A: real,D: real,N2: nat] :
% 11.11/6.22        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 11.11/6.22          @ ( groups6591440286371151544t_real
% 11.11/6.22            @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9328_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9329_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9330_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9331_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9332_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9333_double__gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9334_arith__series__nat,axiom,
% 11.11/6.22      ! [A: nat,D: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9335_Sum__Icc__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : X
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9336_arith__series,axiom,
% 11.11/6.22      ! [A: code_integer,D: code_integer,N2: nat] :
% 11.11/6.22        ( ( groups7501900531339628137nteger
% 11.11/6.22          @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9337_arith__series,axiom,
% 11.11/6.22      ! [A: int,D: int,N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int
% 11.11/6.22          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9338_arith__series,axiom,
% 11.11/6.22      ! [A: nat,D: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9339_gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9340_gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9341_gauss__sum,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9342_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9343_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9344_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9345_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9346_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9347_double__gauss__sum__from__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 11.11/6.22        = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9348_sum__gp__offset,axiom,
% 11.11/6.22      ! [X4: rat,M: nat,N2: nat] :
% 11.11/6.22        ( ( ( X4 = one_one_rat )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 11.11/6.22        & ( ( X4 != one_one_rat )
% 11.11/6.22         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X4 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9349_sum__gp__offset,axiom,
% 11.11/6.22      ! [X4: complex,M: nat,N2: nat] :
% 11.11/6.22        ( ( ( X4 = one_one_complex )
% 11.11/6.22         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 11.11/6.22        & ( ( X4 != one_one_complex )
% 11.11/6.22         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9350_sum__gp__offset,axiom,
% 11.11/6.22      ! [X4: real,M: nat,N2: nat] :
% 11.11/6.22        ( ( ( X4 = one_one_real )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 11.11/6.22        & ( ( X4 != one_one_real )
% 11.11/6.22         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 11.11/6.22            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9351_polyfun__diff,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_rat
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 11.11/6.22            @ ( groups2906978787729119204at_rat
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( times_times_rat
% 11.11/6.22                  @ ( groups2906978787729119204at_rat
% 11.11/6.22                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 11.11/6.22                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22                  @ ( power_power_rat @ X4 @ J3 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9352_polyfun__diff,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_complex
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 11.11/6.22            @ ( groups2073611262835488442omplex
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( times_times_complex
% 11.11/6.22                  @ ( groups2073611262835488442omplex
% 11.11/6.22                    @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 11.11/6.22                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22                  @ ( power_power_complex @ X4 @ J3 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9353_polyfun__diff,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_int
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 11.11/6.22            @ ( groups3539618377306564664at_int
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( times_times_int
% 11.11/6.22                  @ ( groups3539618377306564664at_int
% 11.11/6.22                    @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 11.11/6.22                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22                  @ ( power_power_int @ X4 @ J3 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9354_polyfun__diff,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 11.11/6.22       => ( ( minus_minus_real
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 11.11/6.22              @ ( set_ord_atMost_nat @ N2 ) ) )
% 11.11/6.22          = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 11.11/6.22            @ ( groups6591440286371151544t_real
% 11.11/6.22              @ ^ [J3: nat] :
% 11.11/6.22                  ( times_times_real
% 11.11/6.22                  @ ( groups6591440286371151544t_real
% 11.11/6.22                    @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 11.11/6.22                    @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 11.11/6.22                  @ ( power_power_real @ X4 @ J3 ) )
% 11.11/6.22              @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9355_pochhammer__times__pochhammer__half,axiom,
% 11.11/6.22      ! [Z: rat,N2: nat] :
% 11.11/6.22        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( groups73079841787564623at_rat
% 11.11/6.22          @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9356_pochhammer__times__pochhammer__half,axiom,
% 11.11/6.22      ! [Z: complex,N2: nat] :
% 11.11/6.22        ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( groups6464643781859351333omplex
% 11.11/6.22          @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9357_pochhammer__times__pochhammer__half,axiom,
% 11.11/6.22      ! [Z: real,N2: nat] :
% 11.11/6.22        ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( groups129246275422532515t_real
% 11.11/6.22          @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.22          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9358_vebt__buildup_Opelims,axiom,
% 11.11/6.22      ! [X4: nat,Y: vEBT_VEBT] :
% 11.11/6.22        ( ( ( vEBT_vebt_buildup @ X4 )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X4 )
% 11.11/6.22         => ( ( ( X4 = zero_zero_nat )
% 11.11/6.22             => ( ( Y
% 11.11/6.22                  = ( vEBT_Leaf @ $false @ $false ) )
% 11.11/6.22               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 11.11/6.22           => ( ( ( X4
% 11.11/6.22                  = ( suc @ zero_zero_nat ) )
% 11.11/6.22               => ( ( Y
% 11.11/6.22                    = ( vEBT_Leaf @ $false @ $false ) )
% 11.11/6.22                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 11.11/6.22             => ~ ! [Va2: nat] :
% 11.11/6.22                    ( ( X4
% 11.11/6.22                      = ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.22                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                            = ( 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 ) ) ) ) ) ) )
% 11.11/6.22                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                            = ( 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 ) ) ) ) ) ) ) ) )
% 11.11/6.22                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9359_divmod__algorithm__code_I6_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc4245557441103728435nt_int
% 11.11/6.22          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 11.11/6.22          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9360_divmod__algorithm__code_I6_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc2626176000494625587at_nat
% 11.11/6.22          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 11.11/6.22          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9361_divmod__algorithm__code_I6_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc6916734918728496179nteger
% 11.11/6.22          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 11.11/6.22          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9362_arctan__def,axiom,
% 11.11/6.22      ( arctan
% 11.11/6.22      = ( ^ [Y5: real] :
% 11.11/6.22            ( the_real
% 11.11/6.22            @ ^ [X: real] :
% 11.11/6.22                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 11.11/6.22                & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.22                & ( ( tan_real @ X )
% 11.11/6.22                  = Y5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9363_prod_Oneutral__const,axiom,
% 11.11/6.22      ! [A2: set_nat] :
% 11.11/6.22        ( ( groups708209901874060359at_nat
% 11.11/6.22          @ ^ [Uu3: nat] : one_one_nat
% 11.11/6.22          @ A2 )
% 11.11/6.22        = one_one_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9364_prod_Oneutral__const,axiom,
% 11.11/6.22      ! [A2: set_nat] :
% 11.11/6.22        ( ( groups705719431365010083at_int
% 11.11/6.22          @ ^ [Uu3: nat] : one_one_int
% 11.11/6.22          @ A2 )
% 11.11/6.22        = one_one_int ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9365_prod_Oneutral__const,axiom,
% 11.11/6.22      ! [A2: set_int] :
% 11.11/6.22        ( ( groups1705073143266064639nt_int
% 11.11/6.22          @ ^ [Uu3: int] : one_one_int
% 11.11/6.22          @ A2 )
% 11.11/6.22        = one_one_int ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9366_prod_OlessThan__Suc,axiom,
% 11.11/6.22      ! [G: nat > complex,N2: nat] :
% 11.11/6.22        ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9367_prod_OlessThan__Suc,axiom,
% 11.11/6.22      ! [G: nat > real,N2: nat] :
% 11.11/6.22        ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9368_prod_OlessThan__Suc,axiom,
% 11.11/6.22      ! [G: nat > nat,N2: nat] :
% 11.11/6.22        ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9369_prod_OlessThan__Suc,axiom,
% 11.11/6.22      ! [G: nat > int,N2: nat] :
% 11.11/6.22        ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9370_prod_OatMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > complex,N2: nat] :
% 11.11/6.22        ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9371_prod_OatMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > real,N2: nat] :
% 11.11/6.22        ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9372_prod_OatMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > nat,N2: nat] :
% 11.11/6.22        ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9373_prod_OatMost__Suc,axiom,
% 11.11/6.22      ! [G: nat > int,N2: nat] :
% 11.11/6.22        ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 11.11/6.22        = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9374_prod_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > rat] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = one_one_rat ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9375_prod_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > complex] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = one_one_complex ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9376_prod_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > real] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = one_one_real ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9377_prod_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > nat] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = one_one_nat ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9378_prod_Ocl__ivl__Suc,axiom,
% 11.11/6.22      ! [N2: nat,M: nat,G: nat > int] :
% 11.11/6.22        ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = one_one_int ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22         => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 11.11/6.22            = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9379_divmod__algorithm__code_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc4245557441103728435nt_int
% 11.11/6.22          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 11.11/6.22          @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9380_divmod__algorithm__code_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc2626176000494625587at_nat
% 11.11/6.22          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 11.11/6.22          @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9381_divmod__algorithm__code_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( produc6916734918728496179nteger
% 11.11/6.22          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 11.11/6.22          @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9382_mod__prod__eq,axiom,
% 11.11/6.22      ! [F: nat > nat,A: nat,A2: set_nat] :
% 11.11/6.22        ( ( modulo_modulo_nat
% 11.11/6.22          @ ( groups708209901874060359at_nat
% 11.11/6.22            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 11.11/6.22            @ A2 )
% 11.11/6.22          @ A )
% 11.11/6.22        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9383_mod__prod__eq,axiom,
% 11.11/6.22      ! [F: nat > int,A: int,A2: set_nat] :
% 11.11/6.22        ( ( modulo_modulo_int
% 11.11/6.22          @ ( groups705719431365010083at_int
% 11.11/6.22            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 11.11/6.22            @ A2 )
% 11.11/6.22          @ A )
% 11.11/6.22        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9384_mod__prod__eq,axiom,
% 11.11/6.22      ! [F: int > int,A: int,A2: set_int] :
% 11.11/6.22        ( ( modulo_modulo_int
% 11.11/6.22          @ ( groups1705073143266064639nt_int
% 11.11/6.22            @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 11.11/6.22            @ A2 )
% 11.11/6.22          @ A )
% 11.11/6.22        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9385_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: real > complex,A2: set_real] :
% 11.11/6.22        ( ( ( groups713298508707869441omplex @ G @ A2 )
% 11.11/6.22         != one_one_complex )
% 11.11/6.22       => ~ ! [A5: real] :
% 11.11/6.22              ( ( member_real @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9386_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: nat > complex,A2: set_nat] :
% 11.11/6.22        ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 11.11/6.22         != one_one_complex )
% 11.11/6.22       => ~ ! [A5: nat] :
% 11.11/6.22              ( ( member_nat @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9387_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: complex > complex,A2: set_complex] :
% 11.11/6.22        ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 11.11/6.22         != one_one_complex )
% 11.11/6.22       => ~ ! [A5: complex] :
% 11.11/6.22              ( ( member_complex @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9388_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: int > complex,A2: set_int] :
% 11.11/6.22        ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 11.11/6.22         != one_one_complex )
% 11.11/6.22       => ~ ! [A5: int] :
% 11.11/6.22              ( ( member_int @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_complex ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9389_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: real > real,A2: set_real] :
% 11.11/6.22        ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 11.11/6.22         != one_one_real )
% 11.11/6.22       => ~ ! [A5: real] :
% 11.11/6.22              ( ( member_real @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9390_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: nat > real,A2: set_nat] :
% 11.11/6.22        ( ( ( groups129246275422532515t_real @ G @ A2 )
% 11.11/6.22         != one_one_real )
% 11.11/6.22       => ~ ! [A5: nat] :
% 11.11/6.22              ( ( member_nat @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9391_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: complex > real,A2: set_complex] :
% 11.11/6.22        ( ( ( groups766887009212190081x_real @ G @ A2 )
% 11.11/6.22         != one_one_real )
% 11.11/6.22       => ~ ! [A5: complex] :
% 11.11/6.22              ( ( member_complex @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9392_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: int > real,A2: set_int] :
% 11.11/6.22        ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 11.11/6.22         != one_one_real )
% 11.11/6.22       => ~ ! [A5: int] :
% 11.11/6.22              ( ( member_int @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9393_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: real > rat,A2: set_real] :
% 11.11/6.22        ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 11.11/6.22         != one_one_rat )
% 11.11/6.22       => ~ ! [A5: real] :
% 11.11/6.22              ( ( member_real @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_rat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9394_prod_Onot__neutral__contains__not__neutral,axiom,
% 11.11/6.22      ! [G: nat > rat,A2: set_nat] :
% 11.11/6.22        ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 11.11/6.22         != one_one_rat )
% 11.11/6.22       => ~ ! [A5: nat] :
% 11.11/6.22              ( ( member_nat @ A5 @ A2 )
% 11.11/6.22             => ( ( G @ A5 )
% 11.11/6.22                = one_one_rat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9395_prod_Oneutral,axiom,
% 11.11/6.22      ! [A2: set_nat,G: nat > nat] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ( G @ X5 )
% 11.11/6.22              = one_one_nat ) )
% 11.11/6.22       => ( ( groups708209901874060359at_nat @ G @ A2 )
% 11.11/6.22          = one_one_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9396_prod_Oneutral,axiom,
% 11.11/6.22      ! [A2: set_nat,G: nat > int] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ( G @ X5 )
% 11.11/6.22              = one_one_int ) )
% 11.11/6.22       => ( ( groups705719431365010083at_int @ G @ A2 )
% 11.11/6.22          = one_one_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9397_prod_Oneutral,axiom,
% 11.11/6.22      ! [A2: set_int,G: int > int] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ( G @ X5 )
% 11.11/6.22              = one_one_int ) )
% 11.11/6.22       => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 11.11/6.22          = one_one_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9398_prod__power__distrib,axiom,
% 11.11/6.22      ! [F: nat > nat,A2: set_nat,N2: nat] :
% 11.11/6.22        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
% 11.11/6.22        = ( groups708209901874060359at_nat
% 11.11/6.22          @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N2 )
% 11.11/6.22          @ A2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9399_prod__power__distrib,axiom,
% 11.11/6.22      ! [F: nat > int,A2: set_nat,N2: nat] :
% 11.11/6.22        ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N2 )
% 11.11/6.22        = ( groups705719431365010083at_int
% 11.11/6.22          @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N2 )
% 11.11/6.22          @ A2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9400_prod__power__distrib,axiom,
% 11.11/6.22      ! [F: int > int,A2: set_int,N2: nat] :
% 11.11/6.22        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N2 )
% 11.11/6.22        = ( groups1705073143266064639nt_int
% 11.11/6.22          @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N2 )
% 11.11/6.22          @ A2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9401_prod__nonneg,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > nat] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9402_prod__nonneg,axiom,
% 11.11/6.22      ! [A2: set_nat,F: nat > int] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9403_prod__nonneg,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > int] :
% 11.11/6.22        ( ! [X5: int] :
% 11.11/6.22            ( ( member_int @ X5 @ A2 )
% 11.11/6.22           => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9404_prod__mono,axiom,
% 11.11/6.22      ! [A2: set_int,F: int > int,G: int > int] :
% 11.11/6.22        ( ! [I4: int] :
% 11.11/6.22            ( ( member_int @ I4 @ A2 )
% 11.11/6.22           => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 11.11/6.22              & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 11.11/6.22       => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ A2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9405_ln__neg__is__const,axiom,
% 11.11/6.22      ! [X4: real] :
% 11.11/6.22        ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 11.11/6.22       => ( ( ln_ln_real @ X4 )
% 11.11/6.22          = ( the_real
% 11.11/6.22            @ ^ [X: real] : $false ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9406_periodic__finite__ex,axiom,
% 11.11/6.22      ! [D: int,P: int > $o] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D )
% 11.11/6.22       => ( ! [X5: int,K2: int] :
% 11.11/6.22              ( ( P @ X5 )
% 11.11/6.22              = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 11.11/6.22         => ( ( ? [X3: int] : ( P @ X3 ) )
% 11.11/6.22            = ( ? [X: int] :
% 11.11/6.22                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 11.11/6.22                  & ( P @ X ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9407_bset_I3_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,B3: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( X2 = T2 )
% 11.11/6.22               => ( ( minus_minus_int @ X2 @ D4 )
% 11.11/6.22                  = T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9408_bset_I4_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,B3: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ T2 @ B3 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( X2 != T2 )
% 11.11/6.22               => ( ( minus_minus_int @ X2 @ D4 )
% 11.11/6.22                 != T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9409_bset_I5_J,axiom,
% 11.11/6.22      ! [D4: int,B3: set_int,T2: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ! [X2: int] :
% 11.11/6.22            ( ! [Xa2: int] :
% 11.11/6.22                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22               => ! [Xb2: int] :
% 11.11/6.22                    ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                   => ( X2
% 11.11/6.22                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22           => ( ( ord_less_int @ X2 @ T2 )
% 11.11/6.22             => ( ord_less_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9410_bset_I7_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,B3: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ T2 @ B3 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( ord_less_int @ T2 @ X2 )
% 11.11/6.22               => ( ord_less_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9411_aset_I3_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,A2: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( X2 = T2 )
% 11.11/6.22               => ( ( plus_plus_int @ X2 @ D4 )
% 11.11/6.22                  = T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9412_aset_I4_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,A2: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ T2 @ A2 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( X2 != T2 )
% 11.11/6.22               => ( ( plus_plus_int @ X2 @ D4 )
% 11.11/6.22                 != T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9413_aset_I5_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,A2: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ T2 @ A2 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( ord_less_int @ X2 @ T2 )
% 11.11/6.22               => ( ord_less_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9414_aset_I7_J,axiom,
% 11.11/6.22      ! [D4: int,A2: set_int,T2: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ! [X2: int] :
% 11.11/6.22            ( ! [Xa2: int] :
% 11.11/6.22                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22               => ! [Xb2: int] :
% 11.11/6.22                    ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                   => ( X2
% 11.11/6.22                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22           => ( ( ord_less_int @ T2 @ X2 )
% 11.11/6.22             => ( ord_less_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9415_fact__eq__fact__times,axiom,
% 11.11/6.22      ! [N2: nat,M: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.22       => ( ( semiri1408675320244567234ct_nat @ M )
% 11.11/6.22          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 11.11/6.22            @ ( groups708209901874060359at_nat
% 11.11/6.22              @ ^ [X: nat] : X
% 11.11/6.22              @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9416_bset_I6_J,axiom,
% 11.11/6.22      ! [D4: int,B3: set_int,T2: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ! [X2: int] :
% 11.11/6.22            ( ! [Xa2: int] :
% 11.11/6.22                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22               => ! [Xb2: int] :
% 11.11/6.22                    ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                   => ( X2
% 11.11/6.22                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22           => ( ( ord_less_eq_int @ X2 @ T2 )
% 11.11/6.22             => ( ord_less_eq_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9417_bset_I8_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,B3: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ B3 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( ord_less_eq_int @ T2 @ X2 )
% 11.11/6.22               => ( ord_less_eq_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9418_aset_I6_J,axiom,
% 11.11/6.22      ! [D4: int,T2: int,A2: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 11.11/6.22         => ! [X2: int] :
% 11.11/6.22              ( ! [Xa2: int] :
% 11.11/6.22                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                 => ! [Xb2: int] :
% 11.11/6.22                      ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                     => ( X2
% 11.11/6.22                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22             => ( ( ord_less_eq_int @ X2 @ T2 )
% 11.11/6.22               => ( ord_less_eq_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9419_aset_I8_J,axiom,
% 11.11/6.22      ! [D4: int,A2: set_int,T2: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ! [X2: int] :
% 11.11/6.22            ( ! [Xa2: int] :
% 11.11/6.22                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22               => ! [Xb2: int] :
% 11.11/6.22                    ( ( member_int @ Xb2 @ A2 )
% 11.11/6.22                   => ( X2
% 11.11/6.22                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 11.11/6.22           => ( ( ord_less_eq_int @ T2 @ X2 )
% 11.11/6.22             => ( ord_less_eq_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9420_cppi,axiom,
% 11.11/6.22      ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ? [Z3: int] :
% 11.11/6.22            ! [X5: int] :
% 11.11/6.22              ( ( ord_less_int @ Z3 @ X5 )
% 11.11/6.22             => ( ( P @ X5 )
% 11.11/6.22                = ( P6 @ X5 ) ) )
% 11.11/6.22         => ( ! [X5: int] :
% 11.11/6.22                ( ! [Xa3: int] :
% 11.11/6.22                    ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                   => ! [Xb3: int] :
% 11.11/6.22                        ( ( member_int @ Xb3 @ A2 )
% 11.11/6.22                       => ( X5
% 11.11/6.22                         != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 11.11/6.22               => ( ( P @ X5 )
% 11.11/6.22                 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 11.11/6.22           => ( ! [X5: int,K2: int] :
% 11.11/6.22                  ( ( P6 @ X5 )
% 11.11/6.22                  = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 11.11/6.22             => ( ( ? [X3: int] : ( P @ X3 ) )
% 11.11/6.22                = ( ? [X: int] :
% 11.11/6.22                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                      & ( P6 @ X ) )
% 11.11/6.22                  | ? [X: int] :
% 11.11/6.22                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                      & ? [Y5: int] :
% 11.11/6.22                          ( ( member_int @ Y5 @ A2 )
% 11.11/6.22                          & ( P @ ( minus_minus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9421_cpmi,axiom,
% 11.11/6.22      ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ D4 )
% 11.11/6.22       => ( ? [Z3: int] :
% 11.11/6.22            ! [X5: int] :
% 11.11/6.22              ( ( ord_less_int @ X5 @ Z3 )
% 11.11/6.22             => ( ( P @ X5 )
% 11.11/6.22                = ( P6 @ X5 ) ) )
% 11.11/6.22         => ( ! [X5: int] :
% 11.11/6.22                ( ! [Xa3: int] :
% 11.11/6.22                    ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                   => ! [Xb3: int] :
% 11.11/6.22                        ( ( member_int @ Xb3 @ B3 )
% 11.11/6.22                       => ( X5
% 11.11/6.22                         != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 11.11/6.22               => ( ( P @ X5 )
% 11.11/6.22                 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 11.11/6.22           => ( ! [X5: int,K2: int] :
% 11.11/6.22                  ( ( P6 @ X5 )
% 11.11/6.22                  = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 11.11/6.22             => ( ( ? [X3: int] : ( P @ X3 ) )
% 11.11/6.22                = ( ? [X: int] :
% 11.11/6.22                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                      & ( P6 @ X ) )
% 11.11/6.22                  | ? [X: int] :
% 11.11/6.22                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 11.11/6.22                      & ? [Y5: int] :
% 11.11/6.22                          ( ( member_int @ Y5 @ B3 )
% 11.11/6.22                          & ( P @ ( plus_plus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9422_arccos__def,axiom,
% 11.11/6.22      ( arccos
% 11.11/6.22      = ( ^ [Y5: real] :
% 11.11/6.22            ( the_real
% 11.11/6.22            @ ^ [X: real] :
% 11.11/6.22                ( ( ord_less_eq_real @ zero_zero_real @ X )
% 11.11/6.22                & ( ord_less_eq_real @ X @ pi )
% 11.11/6.22                & ( ( cos_real @ X )
% 11.11/6.22                  = Y5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9423_fact__div__fact,axiom,
% 11.11/6.22      ! [N2: nat,M: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.22       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 11.11/6.22          = ( groups708209901874060359at_nat
% 11.11/6.22            @ ^ [X: nat] : X
% 11.11/6.22            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9424_divmod__step__nat__def,axiom,
% 11.11/6.22      ( unique5026877609467782581ep_nat
% 11.11/6.22      = ( ^ [L2: num] :
% 11.11/6.22            ( produc2626176000494625587at_nat
% 11.11/6.22            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9425_divmod__step__int__def,axiom,
% 11.11/6.22      ( unique5024387138958732305ep_int
% 11.11/6.22      = ( ^ [L2: num] :
% 11.11/6.22            ( produc4245557441103728435nt_int
% 11.11/6.22            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9426_pi__half,axiom,
% 11.11/6.22      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.22      = ( the_real
% 11.11/6.22        @ ^ [X: real] :
% 11.11/6.22            ( ( ord_less_eq_real @ zero_zero_real @ X )
% 11.11/6.22            & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.22            & ( ( cos_real @ X )
% 11.11/6.22              = zero_zero_real ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9427_pi__def,axiom,
% 11.11/6.22      ( pi
% 11.11/6.22      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 11.11/6.22        @ ( the_real
% 11.11/6.22          @ ^ [X: real] :
% 11.11/6.22              ( ( ord_less_eq_real @ zero_zero_real @ X )
% 11.11/6.22              & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 11.11/6.22              & ( ( cos_real @ X )
% 11.11/6.22                = zero_zero_real ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9428_Sum__Icc__int,axiom,
% 11.11/6.22      ! [M: int,N2: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ M @ N2 )
% 11.11/6.22       => ( ( groups4538972089207619220nt_int
% 11.11/6.22            @ ^ [X: int] : X
% 11.11/6.22            @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 11.11/6.22          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9429_arcsin__def,axiom,
% 11.11/6.22      ( arcsin
% 11.11/6.22      = ( ^ [Y5: real] :
% 11.11/6.22            ( the_real
% 11.11/6.22            @ ^ [X: real] :
% 11.11/6.22                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 11.11/6.22                & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.22                & ( ( sin_real @ X )
% 11.11/6.22                  = Y5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9430_divmod__nat__if,axiom,
% 11.11/6.22      ( divmod_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] :
% 11.11/6.22            ( if_Pro6206227464963214023at_nat
% 11.11/6.22            @ ( ( N = zero_zero_nat )
% 11.11/6.22              | ( ord_less_nat @ M6 @ N ) )
% 11.11/6.22            @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 11.11/6.22            @ ( produc2626176000494625587at_nat
% 11.11/6.22              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 11.11/6.22              @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9431_complex__mult__cnj,axiom,
% 11.11/6.22      ! [Z: complex] :
% 11.11/6.22        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 11.11/6.22        = ( 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 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9432_prod__int__eq,axiom,
% 11.11/6.22      ! [I2: nat,J: nat] :
% 11.11/6.22        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 11.11/6.22        = ( groups1705073143266064639nt_int
% 11.11/6.22          @ ^ [X: int] : X
% 11.11/6.22          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9433_prod__int__plus__eq,axiom,
% 11.11/6.22      ! [I2: nat,J: nat] :
% 11.11/6.22        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 11.11/6.22        = ( groups1705073143266064639nt_int
% 11.11/6.22          @ ^ [X: int] : X
% 11.11/6.22          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9434_Re__complex__div__gt__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9435_Re__complex__div__lt__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 11.11/6.22        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9436_Re__complex__div__ge__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9437_Re__complex__div__le__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 11.11/6.22        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9438_Im__complex__div__gt__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9439_Im__complex__div__lt__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 11.11/6.22        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9440_Im__complex__div__ge__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9441_Im__complex__div__le__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 11.11/6.22        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9442_complex__mod__mult__cnj,axiom,
% 11.11/6.22      ! [Z: complex] :
% 11.11/6.22        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 11.11/6.22        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9443_complex__div__gt__0,axiom,
% 11.11/6.22      ! [A: complex,B: complex] :
% 11.11/6.22        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 11.11/6.22        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 11.11/6.22          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9444_complex__norm__square,axiom,
% 11.11/6.22      ! [Z: complex] :
% 11.11/6.22        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 11.11/6.22        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9445_divmod__nat__def,axiom,
% 11.11/6.22      ( divmod_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N ) @ ( modulo_modulo_nat @ M6 @ N ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9446_complex__add__cnj,axiom,
% 11.11/6.22      ! [Z: complex] :
% 11.11/6.22        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 11.11/6.22        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9447_complex__diff__cnj,axiom,
% 11.11/6.22      ! [Z: complex] :
% 11.11/6.22        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 11.11/6.22        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9448_complex__div__cnj,axiom,
% 11.11/6.22      ( divide1717551699836669952omplex
% 11.11/6.22      = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9449_cnj__add__mult__eq__Re,axiom,
% 11.11/6.22      ! [Z: complex,W: complex] :
% 11.11/6.22        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 11.11/6.22        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9450_set__encode__def,axiom,
% 11.11/6.22      ( nat_set_encode
% 11.11/6.22      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9451_VEBT_Osize_I3_J,axiom,
% 11.11/6.22      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 11.11/6.22        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 11.11/6.22        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9452_VEBT_Osize__gen_I1_J,axiom,
% 11.11/6.22      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 11.11/6.22        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 11.11/6.22        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9453_Sum__Ico__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : X
% 11.11/6.22          @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9454_ex__nat__less__eq,axiom,
% 11.11/6.22      ! [N2: nat,P: nat > $o] :
% 11.11/6.22        ( ( ? [M6: nat] :
% 11.11/6.22              ( ( ord_less_nat @ M6 @ N2 )
% 11.11/6.22              & ( P @ M6 ) ) )
% 11.11/6.22        = ( ? [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22              & ( P @ X ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9455_all__nat__less__eq,axiom,
% 11.11/6.22      ! [N2: nat,P: nat > $o] :
% 11.11/6.22        ( ( ! [M6: nat] :
% 11.11/6.22              ( ( ord_less_nat @ M6 @ N2 )
% 11.11/6.22             => ( P @ M6 ) ) )
% 11.11/6.22        = ( ! [X: nat] :
% 11.11/6.22              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22             => ( P @ X ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9456_atLeastLessThanSuc__atLeastAtMost,axiom,
% 11.11/6.22      ! [L: nat,U: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 11.11/6.22        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9457_lessThan__atLeast0,axiom,
% 11.11/6.22      ( set_ord_lessThan_nat
% 11.11/6.22      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9458_prod__Suc__fact,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9459_prod__Suc__Suc__fact,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 11.11/6.22        = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9460_VEBT_Osize__gen_I2_J,axiom,
% 11.11/6.22      ! [X21: $o,X222: $o] :
% 11.11/6.22        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 11.11/6.22        = zero_zero_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9461_sum__power2,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 11.11/6.22        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9462_Chebyshev__sum__upper__nat,axiom,
% 11.11/6.22      ! [N2: nat,A: nat > nat,B: nat > nat] :
% 11.11/6.22        ( ! [I4: nat,J2: nat] :
% 11.11/6.22            ( ( ord_less_eq_nat @ I4 @ J2 )
% 11.11/6.22           => ( ( ord_less_nat @ J2 @ N2 )
% 11.11/6.22             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 11.11/6.22       => ( ! [I4: nat,J2: nat] :
% 11.11/6.22              ( ( ord_less_eq_nat @ I4 @ J2 )
% 11.11/6.22             => ( ( ord_less_nat @ J2 @ N2 )
% 11.11/6.22               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 11.11/6.22         => ( ord_less_eq_nat
% 11.11/6.22            @ ( times_times_nat @ N2
% 11.11/6.22              @ ( groups3542108847815614940at_nat
% 11.11/6.22                @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 11.11/6.22                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 11.11/6.22            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9463_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 11.11/6.22      ! [L: int,U: int] :
% 11.11/6.22        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 11.11/6.22        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9464_int__ge__less__than2__def,axiom,
% 11.11/6.22      ( int_ge_less_than2
% 11.11/6.22      = ( ^ [D5: int] :
% 11.11/6.22            ( collec213857154873943460nt_int
% 11.11/6.22            @ ( produc4947309494688390418_int_o
% 11.11/6.22              @ ^ [Z7: int,Z5: int] :
% 11.11/6.22                  ( ( ord_less_eq_int @ D5 @ Z5 )
% 11.11/6.22                  & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9465_int__ge__less__than__def,axiom,
% 11.11/6.22      ( int_ge_less_than
% 11.11/6.22      = ( ^ [D5: int] :
% 11.11/6.22            ( collec213857154873943460nt_int
% 11.11/6.22            @ ( produc4947309494688390418_int_o
% 11.11/6.22              @ ^ [Z7: int,Z5: int] :
% 11.11/6.22                  ( ( ord_less_eq_int @ D5 @ Z7 )
% 11.11/6.22                  & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9466_upto_Opinduct,axiom,
% 11.11/6.22      ! [A0: int,A12: int,P: int > int > $o] :
% 11.11/6.22        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 11.11/6.22       => ( ! [I4: int,J2: int] :
% 11.11/6.22              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 11.11/6.22             => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 11.11/6.22                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 11.11/6.22               => ( P @ I4 @ J2 ) ) )
% 11.11/6.22         => ( P @ A0 @ A12 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9467_divmod__step__integer__def,axiom,
% 11.11/6.22      ( unique4921790084139445826nteger
% 11.11/6.22      = ( ^ [L2: num] :
% 11.11/6.22            ( produc6916734918728496179nteger
% 11.11/6.22            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9468_or__int__rec,axiom,
% 11.11/6.22      ( bit_se1409905431419307370or_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] :
% 11.11/6.22            ( plus_plus_int
% 11.11/6.22            @ ( zero_n2684676970156552555ol_int
% 11.11/6.22              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 11.11/6.22                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 11.11/6.22            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9469_or__nonnegative__int__iff,axiom,
% 11.11/6.22      ! [K: int,L: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 11.11/6.22        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 11.11/6.22          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9470_or__negative__int__iff,axiom,
% 11.11/6.22      ! [K: int,L: int] :
% 11.11/6.22        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 11.11/6.22        = ( ( ord_less_int @ K @ zero_zero_int )
% 11.11/6.22          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9471_or__minus__numerals_I6_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9472_or__minus__numerals_I2_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9473_or__minus__minus__numerals,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9474_and__minus__minus__numerals,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9475_divmod__integer_H__def,axiom,
% 11.11/6.22      ( unique3479559517661332726nteger
% 11.11/6.22      = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9476_bit__or__int__iff,axiom,
% 11.11/6.22      ! [K: int,L: int,N2: nat] :
% 11.11/6.22        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N2 )
% 11.11/6.22        = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 11.11/6.22          | ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9477_sgn__integer__code,axiom,
% 11.11/6.22      ( sgn_sgn_Code_integer
% 11.11/6.22      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9478_less__eq__integer__code_I1_J,axiom,
% 11.11/6.22      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9479_OR__lower,axiom,
% 11.11/6.22      ! [X4: int,Y: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.22       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.22         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9480_or__greater__eq,axiom,
% 11.11/6.22      ! [L: int,K: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 11.11/6.22       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9481_plus__and__or,axiom,
% 11.11/6.22      ! [X4: int,Y: int] :
% 11.11/6.22        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se1409905431419307370or_int @ X4 @ Y ) )
% 11.11/6.22        = ( plus_plus_int @ X4 @ Y ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9482_nat_Odisc__eq__case_I1_J,axiom,
% 11.11/6.22      ! [Nat: nat] :
% 11.11/6.22        ( ( Nat = zero_zero_nat )
% 11.11/6.22        = ( case_nat_o @ $true
% 11.11/6.22          @ ^ [Uu3: nat] : $false
% 11.11/6.22          @ Nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9483_nat_Odisc__eq__case_I2_J,axiom,
% 11.11/6.22      ! [Nat: nat] :
% 11.11/6.22        ( ( Nat != zero_zero_nat )
% 11.11/6.22        = ( case_nat_o @ $false
% 11.11/6.22          @ ^ [Uu3: nat] : $true
% 11.11/6.22          @ Nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9484_or__int__def,axiom,
% 11.11/6.22      ( bit_se1409905431419307370or_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9485_or__not__numerals_I1_J,axiom,
% 11.11/6.22      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.22      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9486_xor__int__def,axiom,
% 11.11/6.22      ( bit_se6526347334894502574or_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9487_concat__bit__def,axiom,
% 11.11/6.22      ( bit_concat_bit
% 11.11/6.22      = ( ^ [N: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9488_set__bit__int__def,axiom,
% 11.11/6.22      ( bit_se7879613467334960850it_int
% 11.11/6.22      = ( ^ [N: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9489_one__natural_Orsp,axiom,
% 11.11/6.22      one_one_nat = one_one_nat ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9490_less__eq__nat_Osimps_I2_J,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 11.11/6.22        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9491_or__not__numerals_I4_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9492_or__not__numerals_I2_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9493_diff__Suc,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22        = ( case_nat_nat @ zero_zero_nat
% 11.11/6.22          @ ^ [K3: nat] : K3
% 11.11/6.22          @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9494_or__not__numerals_I3_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9495_or__not__numerals_I7_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9496_or__not__numerals_I6_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9497_OR__upper,axiom,
% 11.11/6.22      ! [X4: int,N2: nat,Y: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.22       => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.22         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 11.11/6.22           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9498_or__not__numerals_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( 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 @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9499_or__not__numerals_I9_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( 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 @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9500_or__not__numerals_I8_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( 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 @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9501_integer__of__int__code,axiom,
% 11.11/6.22      ( code_integer_of_int
% 11.11/6.22      = ( ^ [K3: int] :
% 11.11/6.22            ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 11.11/6.22            @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 11.11/6.22              @ ( if_Code_integer
% 11.11/6.22                @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 11.11/6.22                  = zero_zero_int )
% 11.11/6.22                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9502_or__minus__numerals_I1_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9503_or__minus__numerals_I5_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9504_or__nat__numerals_I4_J,axiom,
% 11.11/6.22      ! [X4: num] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.22        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9505_or__nat__numerals_I2_J,axiom,
% 11.11/6.22      ! [Y: num] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 11.11/6.22        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9506_or__nat__numerals_I3_J,axiom,
% 11.11/6.22      ! [X4: num] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 11.11/6.22        = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9507_or__nat__numerals_I1_J,axiom,
% 11.11/6.22      ! [Y: num] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 11.11/6.22        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9508_or__minus__numerals_I8_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9509_or__minus__numerals_I4_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9510_or__minus__numerals_I3_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9511_or__minus__numerals_I7_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9512_modulo__integer_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: int,X4: int] :
% 11.11/6.22        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 11.11/6.22        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9513_abs__integer__code,axiom,
% 11.11/6.22      ( abs_abs_Code_integer
% 11.11/6.22      = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9514_less__integer__code_I1_J,axiom,
% 11.11/6.22      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9515_less__integer_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: int,X4: int] :
% 11.11/6.22        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 11.11/6.22        = ( ord_less_int @ Xa @ X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9516_or__not__num__neg_Osimps_I1_J,axiom,
% 11.11/6.22      ( ( bit_or_not_num_neg @ one @ one )
% 11.11/6.22      = one ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9517_less__eq__integer_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: int,X4: int] :
% 11.11/6.22        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 11.11/6.22        = ( ord_less_eq_int @ Xa @ X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9518_set__bit__nat__def,axiom,
% 11.11/6.22      ( bit_se7882103937844011126it_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] : ( bit_se1412395901928357646or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9519_or__not__num__neg_Osimps_I4_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 11.11/6.22        = ( bit0 @ one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9520_or__not__num__neg_Osimps_I6_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 11.11/6.22        = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9521_or__not__num__neg_Osimps_I3_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 11.11/6.22        = ( bit1 @ M ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9522_or__not__num__neg_Osimps_I7_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 11.11/6.22        = one ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9523_or__not__num__neg_Osimps_I5_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 11.11/6.22        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9524_or__not__num__neg_Osimps_I9_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 11.11/6.22        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9525_or__nat__def,axiom,
% 11.11/6.22      ( bit_se1412395901928357646or_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9526_or__not__num__neg_Osimps_I2_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 11.11/6.22        = ( bit1 @ M ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9527_or__not__num__neg_Osimps_I8_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 11.11/6.22        = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9528_or__not__num__neg_Oelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: num] :
% 11.11/6.22        ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( X4 = one )
% 11.11/6.22           => ( ( Xa = one )
% 11.11/6.22             => ( Y != one ) ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ! [M5: num] :
% 11.11/6.22                  ( ( Xa
% 11.11/6.22                    = ( bit0 @ M5 ) )
% 11.11/6.22                 => ( Y
% 11.11/6.22                   != ( bit1 @ M5 ) ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ! [M5: num] :
% 11.11/6.22                    ( ( Xa
% 11.11/6.22                      = ( bit1 @ M5 ) )
% 11.11/6.22                   => ( Y
% 11.11/6.22                     != ( bit1 @ M5 ) ) ) )
% 11.11/6.22             => ( ( ? [N3: num] :
% 11.11/6.22                      ( X4
% 11.11/6.22                      = ( bit0 @ N3 ) )
% 11.11/6.22                 => ( ( Xa = one )
% 11.11/6.22                   => ( Y
% 11.11/6.22                     != ( bit0 @ one ) ) ) )
% 11.11/6.22               => ( ! [N3: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ N3 ) )
% 11.11/6.22                     => ! [M5: num] :
% 11.11/6.22                          ( ( Xa
% 11.11/6.22                            = ( bit0 @ M5 ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 11.11/6.22                 => ( ! [N3: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ N3 ) )
% 11.11/6.22                       => ! [M5: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit1 @ M5 ) )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 11.11/6.22                   => ( ( ? [N3: num] :
% 11.11/6.22                            ( X4
% 11.11/6.22                            = ( bit1 @ N3 ) )
% 11.11/6.22                       => ( ( Xa = one )
% 11.11/6.22                         => ( Y != one ) ) )
% 11.11/6.22                     => ( ! [N3: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ N3 ) )
% 11.11/6.22                           => ! [M5: num] :
% 11.11/6.22                                ( ( Xa
% 11.11/6.22                                  = ( bit0 @ M5 ) )
% 11.11/6.22                               => ( Y
% 11.11/6.22                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 11.11/6.22                       => ~ ! [N3: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ N3 ) )
% 11.11/6.22                             => ! [M5: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit1 @ M5 ) )
% 11.11/6.22                                 => ( Y
% 11.11/6.22                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9529_numeral__or__not__num__eq,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9530_int__numeral__not__or__num__neg,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9531_int__numeral__or__not__num__neg,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9532_floor__real__def,axiom,
% 11.11/6.22      ( archim6058952711729229775r_real
% 11.11/6.22      = ( ^ [X: real] :
% 11.11/6.22            ( the_int
% 11.11/6.22            @ ^ [Z5: int] :
% 11.11/6.22                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 11.11/6.22                & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9533_or__Suc__0__eq,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.22        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9534_Suc__0__or__eq,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.22        = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9535_or__nat__rec,axiom,
% 11.11/6.22      ( bit_se1412395901928357646or_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] :
% 11.11/6.22            ( plus_plus_nat
% 11.11/6.22            @ ( zero_n2687167440665602831ol_nat
% 11.11/6.22              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 11.11/6.22                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.22            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9536_or__not__num__neg_Opelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: num] :
% 11.11/6.22        ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ( ( Xa = one )
% 11.11/6.22               => ( ( Y = one )
% 11.11/6.22                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ! [M5: num] :
% 11.11/6.22                    ( ( Xa
% 11.11/6.22                      = ( bit0 @ M5 ) )
% 11.11/6.22                   => ( ( Y
% 11.11/6.22                        = ( bit1 @ M5 ) )
% 11.11/6.22                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 11.11/6.22             => ( ( ( X4 = one )
% 11.11/6.22                 => ! [M5: num] :
% 11.11/6.22                      ( ( Xa
% 11.11/6.22                        = ( bit1 @ M5 ) )
% 11.11/6.22                     => ( ( Y
% 11.11/6.22                          = ( bit1 @ M5 ) )
% 11.11/6.22                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 11.11/6.22               => ( ! [N3: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ N3 ) )
% 11.11/6.22                     => ( ( Xa = one )
% 11.11/6.22                       => ( ( Y
% 11.11/6.22                            = ( bit0 @ one ) )
% 11.11/6.22                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 11.11/6.22                 => ( ! [N3: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ N3 ) )
% 11.11/6.22                       => ! [M5: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit0 @ M5 ) )
% 11.11/6.22                           => ( ( Y
% 11.11/6.22                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 11.11/6.22                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 11.11/6.22                   => ( ! [N3: num] :
% 11.11/6.22                          ( ( X4
% 11.11/6.22                            = ( bit0 @ N3 ) )
% 11.11/6.22                         => ! [M5: num] :
% 11.11/6.22                              ( ( Xa
% 11.11/6.22                                = ( bit1 @ M5 ) )
% 11.11/6.22                             => ( ( Y
% 11.11/6.22                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 11.11/6.22                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 11.11/6.22                     => ( ! [N3: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ N3 ) )
% 11.11/6.22                           => ( ( Xa = one )
% 11.11/6.22                             => ( ( Y = one )
% 11.11/6.22                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 11.11/6.22                       => ( ! [N3: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ N3 ) )
% 11.11/6.22                             => ! [M5: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit0 @ M5 ) )
% 11.11/6.22                                 => ( ( Y
% 11.11/6.22                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 11.11/6.22                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 11.11/6.22                         => ~ ! [N3: num] :
% 11.11/6.22                                ( ( X4
% 11.11/6.22                                  = ( bit1 @ N3 ) )
% 11.11/6.22                               => ! [M5: num] :
% 11.11/6.22                                    ( ( Xa
% 11.11/6.22                                      = ( bit1 @ M5 ) )
% 11.11/6.22                                   => ( ( Y
% 11.11/6.22                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 11.11/6.22                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9537_or__int__unfold,axiom,
% 11.11/6.22      ( bit_se1409905431419307370or_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] :
% 11.11/6.22            ( if_int
% 11.11/6.22            @ ( ( K3
% 11.11/6.22                = ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.22              | ( L2
% 11.11/6.22                = ( uminus_uminus_int @ one_one_int ) ) )
% 11.11/6.22            @ ( uminus_uminus_int @ one_one_int )
% 11.11/6.22            @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9538_max__enat__simps_I2_J,axiom,
% 11.11/6.22      ! [Q3: extended_enat] :
% 11.11/6.22        ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 11.11/6.22        = Q3 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9539_max__enat__simps_I3_J,axiom,
% 11.11/6.22      ! [Q3: extended_enat] :
% 11.11/6.22        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 11.11/6.22        = Q3 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9540_max__Suc__Suc,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 11.11/6.22        = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9541_max__0R,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 11.11/6.22        = N2 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9542_max__0L,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 11.11/6.22        = N2 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9543_max__nat_Oright__neutral,axiom,
% 11.11/6.22      ! [A: nat] :
% 11.11/6.22        ( ( ord_max_nat @ A @ zero_zero_nat )
% 11.11/6.22        = A ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9544_max__nat_Oneutr__eq__iff,axiom,
% 11.11/6.22      ! [A: nat,B: nat] :
% 11.11/6.22        ( ( zero_zero_nat
% 11.11/6.22          = ( ord_max_nat @ A @ B ) )
% 11.11/6.22        = ( ( A = zero_zero_nat )
% 11.11/6.22          & ( B = zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9545_max__nat_Oleft__neutral,axiom,
% 11.11/6.22      ! [A: nat] :
% 11.11/6.22        ( ( ord_max_nat @ zero_zero_nat @ A )
% 11.11/6.22        = A ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9546_max__nat_Oeq__neutr__iff,axiom,
% 11.11/6.22      ! [A: nat,B: nat] :
% 11.11/6.22        ( ( ( ord_max_nat @ A @ B )
% 11.11/6.22          = zero_zero_nat )
% 11.11/6.22        = ( ( A = zero_zero_nat )
% 11.11/6.22          & ( B = zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9547_max__Suc__numeral,axiom,
% 11.11/6.22      ! [N2: nat,K: num] :
% 11.11/6.22        ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22        = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9548_max__numeral__Suc,axiom,
% 11.11/6.22      ! [K: num,N2: nat] :
% 11.11/6.22        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 11.11/6.22        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9549_nat__add__max__left,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.22        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 11.11/6.22        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9550_nat__add__max__right,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.22        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 11.11/6.22        = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9551_nat__mult__max__right,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.22        ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 11.11/6.22        = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9552_nat__mult__max__left,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.22        ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 11.11/6.22        = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9553_nat__minus__add__max,axiom,
% 11.11/6.22      ! [N2: nat,M: nat] :
% 11.11/6.22        ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 11.11/6.22        = ( ord_max_nat @ N2 @ M ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9554_max__Suc2,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22        = ( case_nat_nat @ ( suc @ N2 )
% 11.11/6.22          @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N2 ) )
% 11.11/6.22          @ M ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9555_max__Suc1,axiom,
% 11.11/6.22      ! [N2: nat,M: nat] :
% 11.11/6.22        ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 11.11/6.22        = ( case_nat_nat @ ( suc @ N2 )
% 11.11/6.22          @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N2 @ M3 ) )
% 11.11/6.22          @ M ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9556_or__nat__unfold,axiom,
% 11.11/6.22      ( bit_se1412395901928357646or_nat
% 11.11/6.22      = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( 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 @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9557_floor__rat__def,axiom,
% 11.11/6.22      ( archim3151403230148437115or_rat
% 11.11/6.22      = ( ^ [X: rat] :
% 11.11/6.22            ( the_int
% 11.11/6.22            @ ^ [Z5: int] :
% 11.11/6.22                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 11.11/6.22                & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9558_bit__cut__integer__def,axiom,
% 11.11/6.22      ( code_bit_cut_integer
% 11.11/6.22      = ( ^ [K3: code_integer] :
% 11.11/6.22            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 11.11/6.22            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9559_divmod__integer__def,axiom,
% 11.11/6.22      ( code_divmod_integer
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L2 ) @ ( modulo364778990260209775nteger @ K3 @ L2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9560_sgn__rat__def,axiom,
% 11.11/6.22      ( sgn_sgn_rat
% 11.11/6.22      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9561_obtain__pos__sum,axiom,
% 11.11/6.22      ! [R3: rat] :
% 11.11/6.22        ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 11.11/6.22       => ~ ! [S3: rat] :
% 11.11/6.22              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 11.11/6.22             => ! [T3: rat] :
% 11.11/6.22                  ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 11.11/6.22                 => ( R3
% 11.11/6.22                   != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9562_less__eq__rat__def,axiom,
% 11.11/6.22      ( ord_less_eq_rat
% 11.11/6.22      = ( ^ [X: rat,Y5: rat] :
% 11.11/6.22            ( ( ord_less_rat @ X @ Y5 )
% 11.11/6.22            | ( X = Y5 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9563_abs__rat__def,axiom,
% 11.11/6.22      ( abs_abs_rat
% 11.11/6.22      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9564_pred__def,axiom,
% 11.11/6.22      ( pred
% 11.11/6.22      = ( case_nat_nat @ zero_zero_nat
% 11.11/6.22        @ ^ [X24: nat] : X24 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9565_bit__cut__integer__code,axiom,
% 11.11/6.22      ( code_bit_cut_integer
% 11.11/6.22      = ( ^ [K3: code_integer] :
% 11.11/6.22            ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 11.11/6.22            @ ( produc9125791028180074456eger_o
% 11.11/6.22              @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 11.11/6.22              @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9566_normalize__negative,axiom,
% 11.11/6.22      ! [Q3: int,P2: int] :
% 11.11/6.22        ( ( ord_less_int @ Q3 @ zero_zero_int )
% 11.11/6.22       => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 11.11/6.22          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9567_divmod__abs__def,axiom,
% 11.11/6.22      ( code_divmod_abs
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9568_prod__decode__aux_Oelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 11.11/6.22        ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 11.11/6.22          & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9569_normalize__denom__pos,axiom,
% 11.11/6.22      ! [R3: product_prod_int_int,P2: int,Q3: int] :
% 11.11/6.22        ( ( ( normalize @ R3 )
% 11.11/6.22          = ( product_Pair_int_int @ P2 @ Q3 ) )
% 11.11/6.22       => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9570_prod__decode__aux_Osimps,axiom,
% 11.11/6.22      ( nat_prod_decode_aux
% 11.11/6.22      = ( ^ [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 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9571_prod__decode__aux_Opelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 11.11/6.22        ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 11.11/6.22         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 11.11/6.22                & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) )
% 11.11/6.22             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9572_divmod__integer__code,axiom,
% 11.11/6.22      ( code_divmod_integer
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] :
% 11.11/6.22            ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 11.11/6.22            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 11.11/6.22              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 11.11/6.22                @ ( produc6916734918728496179nteger
% 11.11/6.22                  @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 11.11/6.22                  @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 11.11/6.22              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 11.11/6.22                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 11.11/6.22                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 11.11/6.22                    @ ( produc6916734918728496179nteger
% 11.11/6.22                      @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 11.11/6.22                      @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9573_Suc__0__div__numeral,axiom,
% 11.11/6.22      ! [K: num] :
% 11.11/6.22        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9574_finite__atLeastAtMost,axiom,
% 11.11/6.22      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9575_finite__atLeastLessThan,axiom,
% 11.11/6.22      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9576_finite__lessThan,axiom,
% 11.11/6.22      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9577_finite__atMost,axiom,
% 11.11/6.22      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9578_fst__divmod__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 11.11/6.22        = ( divide_divide_nat @ M @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9579_finite__nat__set__iff__bounded__le,axiom,
% 11.11/6.22      ( finite_finite_nat
% 11.11/6.22      = ( ^ [N9: set_nat] :
% 11.11/6.22          ? [M6: nat] :
% 11.11/6.22          ! [X: nat] :
% 11.11/6.22            ( ( member_nat @ X @ N9 )
% 11.11/6.22           => ( ord_less_eq_nat @ X @ M6 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9580_finite__less__ub,axiom,
% 11.11/6.22      ! [F: nat > nat,U: nat] :
% 11.11/6.22        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 11.11/6.22       => ( finite_finite_nat
% 11.11/6.22          @ ( collect_nat
% 11.11/6.22            @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9581_finite__M__bounded__by__nat,axiom,
% 11.11/6.22      ! [P: nat > $o,I2: nat] :
% 11.11/6.22        ( finite_finite_nat
% 11.11/6.22        @ ( collect_nat
% 11.11/6.22          @ ^ [K3: nat] :
% 11.11/6.22              ( ( P @ K3 )
% 11.11/6.22              & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9582_bounded__nat__set__is__finite,axiom,
% 11.11/6.22      ! [N4: set_nat,N2: nat] :
% 11.11/6.22        ( ! [X5: nat] :
% 11.11/6.22            ( ( member_nat @ X5 @ N4 )
% 11.11/6.22           => ( ord_less_nat @ X5 @ N2 ) )
% 11.11/6.22       => ( finite_finite_nat @ N4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9583_finite__nat__set__iff__bounded,axiom,
% 11.11/6.22      ( finite_finite_nat
% 11.11/6.22      = ( ^ [N9: set_nat] :
% 11.11/6.22          ? [M6: nat] :
% 11.11/6.22          ! [X: nat] :
% 11.11/6.22            ( ( member_nat @ X @ N9 )
% 11.11/6.22           => ( ord_less_nat @ X @ M6 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9584_finite__divisors__nat,axiom,
% 11.11/6.22      ! [M: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.22       => ( finite_finite_nat
% 11.11/6.22          @ ( collect_nat
% 11.11/6.22            @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9585_subset__eq__atLeast0__atMost__finite,axiom,
% 11.11/6.22      ! [N4: set_nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22       => ( finite_finite_nat @ N4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9586_subset__eq__atLeast0__lessThan__finite,axiom,
% 11.11/6.22      ! [N4: set_nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22       => ( finite_finite_nat @ N4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9587_even__set__encode__iff,axiom,
% 11.11/6.22      ! [A2: set_nat] :
% 11.11/6.22        ( ( finite_finite_nat @ A2 )
% 11.11/6.22       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 11.11/6.22          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9588_finite__Collect__le__nat,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( finite_finite_nat
% 11.11/6.22        @ ( collect_nat
% 11.11/6.22          @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9589_finite__Collect__less__nat,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( finite_finite_nat
% 11.11/6.22        @ ( collect_nat
% 11.11/6.22          @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9590_finite__atLeastAtMost__int,axiom,
% 11.11/6.22      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9591_finite__atLeastLessThan__int,axiom,
% 11.11/6.22      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9592_finite__interval__int1,axiom,
% 11.11/6.22      ! [A: int,B: int] :
% 11.11/6.22        ( finite_finite_int
% 11.11/6.22        @ ( collect_int
% 11.11/6.22          @ ^ [I3: int] :
% 11.11/6.22              ( ( ord_less_eq_int @ A @ I3 )
% 11.11/6.22              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9593_finite__interval__int4,axiom,
% 11.11/6.22      ! [A: int,B: int] :
% 11.11/6.22        ( finite_finite_int
% 11.11/6.22        @ ( collect_int
% 11.11/6.22          @ ^ [I3: int] :
% 11.11/6.22              ( ( ord_less_int @ A @ I3 )
% 11.11/6.22              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9594_finite__interval__int2,axiom,
% 11.11/6.22      ! [A: int,B: int] :
% 11.11/6.22        ( finite_finite_int
% 11.11/6.22        @ ( collect_int
% 11.11/6.22          @ ^ [I3: int] :
% 11.11/6.22              ( ( ord_less_eq_int @ A @ I3 )
% 11.11/6.22              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9595_finite__interval__int3,axiom,
% 11.11/6.22      ! [A: int,B: int] :
% 11.11/6.22        ( finite_finite_int
% 11.11/6.22        @ ( collect_int
% 11.11/6.22          @ ^ [I3: int] :
% 11.11/6.22              ( ( ord_less_int @ A @ I3 )
% 11.11/6.22              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9596_finite__nth__roots,axiom,
% 11.11/6.22      ! [N2: nat,C: complex] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( finite3207457112153483333omplex
% 11.11/6.22          @ ( collect_complex
% 11.11/6.22            @ ^ [Z5: complex] :
% 11.11/6.22                ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                = C ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9597_finite__atLeastZeroLessThan__int,axiom,
% 11.11/6.22      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9598_finite__nat__iff__bounded__le,axiom,
% 11.11/6.22      ( finite_finite_nat
% 11.11/6.22      = ( ^ [S5: set_nat] :
% 11.11/6.22          ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9599_finite__nat__iff__bounded,axiom,
% 11.11/6.22      ( finite_finite_nat
% 11.11/6.22      = ( ^ [S5: set_nat] :
% 11.11/6.22          ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9600_finite__nat__bounded,axiom,
% 11.11/6.22      ! [S2: set_nat] :
% 11.11/6.22        ( ( finite_finite_nat @ S2 )
% 11.11/6.22       => ? [K2: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9601_infinite__int__iff__unbounded__le,axiom,
% 11.11/6.22      ! [S2: set_int] :
% 11.11/6.22        ( ( ~ ( finite_finite_int @ S2 ) )
% 11.11/6.22        = ( ! [M6: int] :
% 11.11/6.22            ? [N: int] :
% 11.11/6.22              ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N ) )
% 11.11/6.22              & ( member_int @ N @ S2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9602_infinite__int__iff__unbounded,axiom,
% 11.11/6.22      ! [S2: set_int] :
% 11.11/6.22        ( ( ~ ( finite_finite_int @ S2 ) )
% 11.11/6.22        = ( ! [M6: int] :
% 11.11/6.22            ? [N: int] :
% 11.11/6.22              ( ( ord_less_int @ M6 @ ( abs_abs_int @ N ) )
% 11.11/6.22              & ( member_int @ N @ S2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9603_unbounded__k__infinite,axiom,
% 11.11/6.22      ! [K: nat,S2: set_nat] :
% 11.11/6.22        ( ! [M5: nat] :
% 11.11/6.22            ( ( ord_less_nat @ K @ M5 )
% 11.11/6.22           => ? [N6: nat] :
% 11.11/6.22                ( ( ord_less_nat @ M5 @ N6 )
% 11.11/6.22                & ( member_nat @ N6 @ S2 ) ) )
% 11.11/6.22       => ~ ( finite_finite_nat @ S2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9604_infinite__nat__iff__unbounded,axiom,
% 11.11/6.22      ! [S2: set_nat] :
% 11.11/6.22        ( ( ~ ( finite_finite_nat @ S2 ) )
% 11.11/6.22        = ( ! [M6: nat] :
% 11.11/6.22            ? [N: nat] :
% 11.11/6.22              ( ( ord_less_nat @ M6 @ N )
% 11.11/6.22              & ( member_nat @ N @ S2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9605_infinite__nat__iff__unbounded__le,axiom,
% 11.11/6.22      ! [S2: set_nat] :
% 11.11/6.22        ( ( ~ ( finite_finite_nat @ S2 ) )
% 11.11/6.22        = ( ! [M6: nat] :
% 11.11/6.22            ? [N: nat] :
% 11.11/6.22              ( ( ord_less_eq_nat @ M6 @ N )
% 11.11/6.22              & ( member_nat @ N @ S2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9606_bij__betw__nth__root__unity,axiom,
% 11.11/6.22      ! [C: complex,N2: nat] :
% 11.11/6.22        ( ( C != zero_zero_complex )
% 11.11/6.22       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 11.11/6.22            @ ( collect_complex
% 11.11/6.22              @ ^ [Z5: complex] :
% 11.11/6.22                  ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                  = one_one_complex ) )
% 11.11/6.22            @ ( collect_complex
% 11.11/6.22              @ ^ [Z5: complex] :
% 11.11/6.22                  ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                  = C ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9607_real__root__Suc__0,axiom,
% 11.11/6.22      ! [X4: real] :
% 11.11/6.22        ( ( root @ ( suc @ zero_zero_nat ) @ X4 )
% 11.11/6.22        = X4 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9608_real__root__eq__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ( root @ N2 @ X4 )
% 11.11/6.22            = ( root @ N2 @ Y ) )
% 11.11/6.22          = ( X4 = Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9609_real__root__eq__0__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ( root @ N2 @ X4 )
% 11.11/6.22            = zero_zero_real )
% 11.11/6.22          = ( X4 = zero_zero_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9610_real__root__less__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_real @ X4 @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9611_real__root__le__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9612_real__root__one,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( root @ N2 @ one_one_real )
% 11.11/6.22          = one_one_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9613_real__root__eq__1__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ( root @ N2 @ X4 )
% 11.11/6.22            = one_one_real )
% 11.11/6.22          = ( X4 = one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9614_real__root__gt__0__iff,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9615_real__root__lt__0__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 11.11/6.22          = ( ord_less_real @ X4 @ zero_zero_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9616_real__root__ge__0__iff,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9617_real__root__le__0__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 11.11/6.22          = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9618_real__root__gt__1__iff,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9619_real__root__lt__1__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 11.11/6.22          = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9620_real__root__ge__1__iff,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 11.11/6.22          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9621_real__root__le__1__iff,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 11.11/6.22          = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9622_real__root__pow__pos2,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 11.11/6.22            = X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9623_real__root__pos__pos__le,axiom,
% 11.11/6.22      ! [X4: real,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.22       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9624_real__root__less__mono,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ X4 @ Y )
% 11.11/6.22         => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9625_real__root__le__mono,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ X4 @ Y )
% 11.11/6.22         => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9626_real__root__power,axiom,
% 11.11/6.22      ! [N2: nat,X4: real,K: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( root @ N2 @ ( power_power_real @ X4 @ K ) )
% 11.11/6.22          = ( power_power_real @ ( root @ N2 @ X4 ) @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9627_real__root__abs,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( root @ N2 @ ( abs_abs_real @ X4 ) )
% 11.11/6.22          = ( abs_abs_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9628_sgn__root,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( sgn_sgn_real @ ( root @ N2 @ X4 ) )
% 11.11/6.22          = ( sgn_sgn_real @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9629_real__root__gt__zero,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9630_real__root__strict__decreasing,axiom,
% 11.11/6.22      ! [N2: nat,N4: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.22         => ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.22           => ( ord_less_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9631_sqrt__def,axiom,
% 11.11/6.22      ( sqrt
% 11.11/6.22      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9632_root__abs__power,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 11.11/6.22          = ( abs_abs_real @ Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9633_real__root__pos__pos,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9634_real__root__strict__increasing,axiom,
% 11.11/6.22      ! [N2: nat,N4: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_nat @ N2 @ N4 )
% 11.11/6.22         => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22           => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.22             => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9635_real__root__decreasing,axiom,
% 11.11/6.22      ! [N2: nat,N4: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.22         => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 11.11/6.22           => ( ord_less_eq_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9636_real__root__pow__pos,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 11.11/6.22            = X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9637_real__root__pos__unique,axiom,
% 11.11/6.22      ! [N2: nat,Y: real,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 11.11/6.22         => ( ( ( power_power_real @ Y @ N2 )
% 11.11/6.22              = X4 )
% 11.11/6.22           => ( ( root @ N2 @ X4 )
% 11.11/6.22              = Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9638_real__root__power__cancel,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.22            = X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9639_odd__real__root__power__cancel,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.22       => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 11.11/6.22          = X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9640_odd__real__root__unique,axiom,
% 11.11/6.22      ! [N2: nat,Y: real,X4: real] :
% 11.11/6.22        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.22       => ( ( ( power_power_real @ Y @ N2 )
% 11.11/6.22            = X4 )
% 11.11/6.22         => ( ( root @ N2 @ X4 )
% 11.11/6.22            = Y ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9641_odd__real__root__pow,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.22       => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 11.11/6.22          = X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9642_real__root__increasing,axiom,
% 11.11/6.22      ! [N2: nat,N4: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_eq_nat @ N2 @ N4 )
% 11.11/6.22         => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.22           => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.22             => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9643_root__sgn__power,axiom,
% 11.11/6.22      ! [N2: nat,Y: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 11.11/6.22          = Y ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9644_sgn__power__root,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X4 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X4 ) ) @ N2 ) )
% 11.11/6.22          = X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9645_ln__root,axiom,
% 11.11/6.22      ! [N2: nat,B: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.22         => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 11.11/6.22            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9646_log__root,axiom,
% 11.11/6.22      ! [N2: nat,A: real,B: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ A )
% 11.11/6.22         => ( ( log @ B @ ( root @ N2 @ A ) )
% 11.11/6.22            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9647_log__base__root,axiom,
% 11.11/6.22      ! [N2: nat,B: real,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ B )
% 11.11/6.22         => ( ( log @ ( root @ N2 @ B ) @ X4 )
% 11.11/6.22            = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9648_split__root,axiom,
% 11.11/6.22      ! [P: real > $o,N2: nat,X4: real] :
% 11.11/6.22        ( ( P @ ( root @ N2 @ X4 ) )
% 11.11/6.22        = ( ( ( N2 = zero_zero_nat )
% 11.11/6.22           => ( P @ zero_zero_real ) )
% 11.11/6.22          & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22           => ! [Y5: real] :
% 11.11/6.22                ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 11.11/6.22                  = X4 )
% 11.11/6.22               => ( P @ Y5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9649_root__powr__inverse,axiom,
% 11.11/6.22      ! [N2: nat,X4: real] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.22         => ( ( root @ N2 @ X4 )
% 11.11/6.22            = ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9650_set__encode__insert,axiom,
% 11.11/6.22      ! [A2: set_nat,N2: nat] :
% 11.11/6.22        ( ( finite_finite_nat @ A2 )
% 11.11/6.22       => ( ~ ( member_nat @ N2 @ A2 )
% 11.11/6.22         => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 11.11/6.22            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9651_Suc__0__mod__numeral,axiom,
% 11.11/6.22      ! [K: num] :
% 11.11/6.22        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9652_card__lessThan,axiom,
% 11.11/6.22      ! [U: nat] :
% 11.11/6.22        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 11.11/6.22        = U ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9653_card__Collect__less__nat,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( finite_card_nat
% 11.11/6.22          @ ( collect_nat
% 11.11/6.22            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N2 ) ) )
% 11.11/6.22        = N2 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9654_card__atMost,axiom,
% 11.11/6.22      ! [U: nat] :
% 11.11/6.22        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 11.11/6.22        = ( suc @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9655_card__atLeastLessThan,axiom,
% 11.11/6.22      ! [L: nat,U: nat] :
% 11.11/6.22        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 11.11/6.22        = ( minus_minus_nat @ U @ L ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9656_card__Collect__le__nat,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( finite_card_nat
% 11.11/6.22          @ ( collect_nat
% 11.11/6.22            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N2 ) ) )
% 11.11/6.22        = ( suc @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9657_card__atLeastAtMost,axiom,
% 11.11/6.22      ! [L: nat,U: nat] :
% 11.11/6.22        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 11.11/6.22        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9658_card__atLeastLessThan__int,axiom,
% 11.11/6.22      ! [L: int,U: int] :
% 11.11/6.22        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 11.11/6.22        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9659_snd__divmod__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 11.11/6.22        = ( modulo_modulo_nat @ M @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9660_card__atLeastAtMost__int,axiom,
% 11.11/6.22      ! [L: int,U: int] :
% 11.11/6.22        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 11.11/6.22        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9661_lessThan__Suc,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 11.11/6.22        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9662_atMost__Suc,axiom,
% 11.11/6.22      ! [K: nat] :
% 11.11/6.22        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 11.11/6.22        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9663_atLeast0__atMost__Suc,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 11.11/6.22        = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9664_atLeast0__lessThan__Suc,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 11.11/6.22        = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9665_Icc__eq__insert__lb__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 11.11/6.22          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9666_atLeastAtMostSuc__conv,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22          = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9667_atLeastAtMost__insertL,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 11.11/6.22          = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9668_lessThan__nat__numeral,axiom,
% 11.11/6.22      ! [K: num] :
% 11.11/6.22        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9669_card__less,axiom,
% 11.11/6.22      ! [M7: set_nat,I2: nat] :
% 11.11/6.22        ( ( member_nat @ zero_zero_nat @ M7 )
% 11.11/6.22       => ( ( finite_card_nat
% 11.11/6.22            @ ( collect_nat
% 11.11/6.22              @ ^ [K3: nat] :
% 11.11/6.22                  ( ( member_nat @ K3 @ M7 )
% 11.11/6.22                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 11.11/6.22         != zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9670_card__less__Suc,axiom,
% 11.11/6.22      ! [M7: set_nat,I2: nat] :
% 11.11/6.22        ( ( member_nat @ zero_zero_nat @ M7 )
% 11.11/6.22       => ( ( suc
% 11.11/6.22            @ ( finite_card_nat
% 11.11/6.22              @ ( collect_nat
% 11.11/6.22                @ ^ [K3: nat] :
% 11.11/6.22                    ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 11.11/6.22                    & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 11.11/6.22          = ( finite_card_nat
% 11.11/6.22            @ ( collect_nat
% 11.11/6.22              @ ^ [K3: nat] :
% 11.11/6.22                  ( ( member_nat @ K3 @ M7 )
% 11.11/6.22                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9671_card__less__Suc2,axiom,
% 11.11/6.22      ! [M7: set_nat,I2: nat] :
% 11.11/6.22        ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 11.11/6.22       => ( ( finite_card_nat
% 11.11/6.22            @ ( collect_nat
% 11.11/6.22              @ ^ [K3: nat] :
% 11.11/6.22                  ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 11.11/6.22                  & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 11.11/6.22          = ( finite_card_nat
% 11.11/6.22            @ ( collect_nat
% 11.11/6.22              @ ^ [K3: nat] :
% 11.11/6.22                  ( ( member_nat @ K3 @ M7 )
% 11.11/6.22                  & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9672_atMost__nat__numeral,axiom,
% 11.11/6.22      ! [K: num] :
% 11.11/6.22        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9673_card__atLeastZeroLessThan__int,axiom,
% 11.11/6.22      ! [U: int] :
% 11.11/6.22        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 11.11/6.22        = ( nat2 @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9674_subset__card__intvl__is__intvl,axiom,
% 11.11/6.22      ! [A2: set_nat,K: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 11.11/6.22       => ( A2
% 11.11/6.22          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9675_subset__eq__atLeast0__lessThan__card,axiom,
% 11.11/6.22      ! [N4: set_nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 11.11/6.22       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9676_card__sum__le__nat__sum,axiom,
% 11.11/6.22      ! [S2: set_nat] :
% 11.11/6.22        ( ord_less_eq_nat
% 11.11/6.22        @ ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : X
% 11.11/6.22          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 11.11/6.22        @ ( groups3542108847815614940at_nat
% 11.11/6.22          @ ^ [X: nat] : X
% 11.11/6.22          @ S2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9677_card__nth__roots,axiom,
% 11.11/6.22      ! [C: complex,N2: nat] :
% 11.11/6.22        ( ( C != zero_zero_complex )
% 11.11/6.22       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ( ( finite_card_complex
% 11.11/6.22              @ ( collect_complex
% 11.11/6.22                @ ^ [Z5: complex] :
% 11.11/6.22                    ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                    = C ) ) )
% 11.11/6.22            = N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9678_card__roots__unity__eq,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( finite_card_complex
% 11.11/6.22            @ ( collect_complex
% 11.11/6.22              @ ^ [Z5: complex] :
% 11.11/6.22                  ( ( power_power_complex @ Z5 @ N2 )
% 11.11/6.22                  = one_one_complex ) ) )
% 11.11/6.22          = N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9679_set__decode__plus__power__2,axiom,
% 11.11/6.22      ! [N2: nat,Z: nat] :
% 11.11/6.22        ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 11.11/6.22       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 11.11/6.22          = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9680_snd__divmod__integer,axiom,
% 11.11/6.22      ! [K: code_integer,L: code_integer] :
% 11.11/6.22        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 11.11/6.22        = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9681_snd__divmod__abs,axiom,
% 11.11/6.22      ! [K: code_integer,L: code_integer] :
% 11.11/6.22        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 11.11/6.22        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9682_atLeastAtMostPlus1__int__conv,axiom,
% 11.11/6.22      ! [M: int,N2: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 11.11/6.22       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 11.11/6.22          = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9683_minus__one__mod__numeral,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.22        = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9684_one__mod__minus__numeral,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9685_minus__numeral__mod__numeral,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.22        = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9686_numeral__mod__minus__numeral,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9687_Divides_Oadjust__mod__def,axiom,
% 11.11/6.22      ( adjust_mod
% 11.11/6.22      = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9688_and__int_Oelims,axiom,
% 11.11/6.22      ! [X4: int,Xa: int,Y: int] :
% 11.11/6.22        ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( uminus_uminus_int
% 11.11/6.22                @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.22                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 11.11/6.22          & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( plus_plus_int
% 11.11/6.22                @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.22                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 11.11/6.22                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9689_and__int_Osimps,axiom,
% 11.11/6.22      ( bit_se725231765392027082nd_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] :
% 11.11/6.22            ( if_int
% 11.11/6.22            @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22            @ ( uminus_uminus_int
% 11.11/6.22              @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 11.11/6.22                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 11.11/6.22            @ ( plus_plus_int
% 11.11/6.22              @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 11.11/6.22                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 11.11/6.22              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9690_bezw_Oelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 11.11/6.22        ( ( ( bezw @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( Xa = zero_zero_nat )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 11.11/6.22          & ( ( Xa != zero_zero_nat )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9691_simp__from__to,axiom,
% 11.11/6.22      ( set_or1266510415728281911st_int
% 11.11/6.22      = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9692_bezw__non__0,axiom,
% 11.11/6.22      ! [Y: nat,X4: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 11.11/6.22       => ( ( bezw @ X4 @ Y )
% 11.11/6.22          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9693_bezw_Osimps,axiom,
% 11.11/6.22      ( bezw
% 11.11/6.22      = ( ^ [X: nat,Y5: nat] : ( if_Pro3027730157355071871nt_int @ ( Y5 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y5 ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9694_bezw_Opelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 11.11/6.22        ( ( ( bezw @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 11.11/6.22         => ~ ( ( ( ( Xa = zero_zero_nat )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 11.11/6.22                & ( ( Xa != zero_zero_nat )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) )
% 11.11/6.22             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9695_and__int_Opsimps,axiom,
% 11.11/6.22      ! [K: int,L: int] :
% 11.11/6.22        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 11.11/6.22       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 11.11/6.22              = ( uminus_uminus_int
% 11.11/6.22                @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 11.11/6.22                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 11.11/6.22          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 11.11/6.22              = ( plus_plus_int
% 11.11/6.22                @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 11.11/6.22                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 11.11/6.22                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9696_and__int_Opelims,axiom,
% 11.11/6.22      ! [X4: int,Xa: int,Y: int] :
% 11.11/6.22        ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 11.11/6.22         => ~ ( ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( uminus_uminus_int
% 11.11/6.22                      @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.22                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 11.11/6.22                & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( plus_plus_int
% 11.11/6.22                      @ ( zero_n2684676970156552555ol_int
% 11.11/6.22                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 11.11/6.22                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 11.11/6.22                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 11.11/6.22             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9697_lessThan__0,axiom,
% 11.11/6.22      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 11.11/6.22      = bot_bot_set_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9698_atLeastLessThan__singleton,axiom,
% 11.11/6.22      ! [M: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 11.11/6.22        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9699_atMost__0,axiom,
% 11.11/6.22      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 11.11/6.22      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9700_bot__enat__def,axiom,
% 11.11/6.22      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9701_bot__nat__def,axiom,
% 11.11/6.22      bot_bot_nat = zero_zero_nat ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9702_atLeastLessThan0,axiom,
% 11.11/6.22      ! [M: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 11.11/6.22        = bot_bot_set_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9703_lessThan__empty__iff,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ( set_ord_lessThan_nat @ N2 )
% 11.11/6.22          = bot_bot_set_nat )
% 11.11/6.22        = ( N2 = zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9704_atLeastLessThanSuc,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22            = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 11.11/6.22            = bot_bot_set_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9705_atLeast1__lessThan__eq__remove0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.22        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9706_atLeast1__atMost__eq__remove0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 11.11/6.22        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9707_atLeastLessThan__nat__numeral,axiom,
% 11.11/6.22      ! [M: nat,K: num] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 11.11/6.22         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 11.11/6.22         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 11.11/6.22            = bot_bot_set_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9708_and__int_Opinduct,axiom,
% 11.11/6.22      ! [A0: int,A12: int,P: int > int > $o] :
% 11.11/6.22        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 11.11/6.22       => ( ! [K2: int,L4: int] :
% 11.11/6.22              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 11.11/6.22             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 11.11/6.22                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 11.11/6.22                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22               => ( P @ K2 @ L4 ) ) )
% 11.11/6.22         => ( P @ A0 @ A12 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9709_normalize__def,axiom,
% 11.11/6.22      ( normalize
% 11.11/6.22      = ( ^ [P5: product_prod_int_int] :
% 11.11/6.22            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 11.11/6.22            @ ( if_Pro3027730157355071871nt_int
% 11.11/6.22              @ ( ( product_snd_int_int @ P5 )
% 11.11/6.22                = zero_zero_int )
% 11.11/6.22              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 11.11/6.22              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9710_gcd__pos__int,axiom,
% 11.11/6.22      ! [M: int,N2: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 11.11/6.22        = ( ( M != zero_zero_int )
% 11.11/6.22          | ( N2 != zero_zero_int ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9711_gcd__red__int,axiom,
% 11.11/6.22      ( gcd_gcd_int
% 11.11/6.22      = ( ^ [X: int,Y5: int] : ( gcd_gcd_int @ Y5 @ ( modulo_modulo_int @ X @ Y5 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9712_gcd__ge__0__int,axiom,
% 11.11/6.22      ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X4 @ Y ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9713_gcd__le1__int,axiom,
% 11.11/6.22      ! [A: int,B: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ A )
% 11.11/6.22       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9714_gcd__le2__int,axiom,
% 11.11/6.22      ! [B: int,A: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.22       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9715_gcd__cases__int,axiom,
% 11.11/6.22      ! [X4: int,Y: int,P: int > $o] :
% 11.11/6.22        ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.22         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.22           => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) )
% 11.11/6.22       => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 11.11/6.22           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 11.11/6.22             => ( P @ ( gcd_gcd_int @ X4 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 11.11/6.22         => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 11.11/6.22             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 11.11/6.22               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ Y ) ) ) )
% 11.11/6.22           => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 11.11/6.22               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 11.11/6.22                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 11.11/6.22             => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9716_gcd__unique__int,axiom,
% 11.11/6.22      ! [D: int,A: int,B: int] :
% 11.11/6.22        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 11.11/6.22          & ( dvd_dvd_int @ D @ A )
% 11.11/6.22          & ( dvd_dvd_int @ D @ B )
% 11.11/6.22          & ! [E3: int] :
% 11.11/6.22              ( ( ( dvd_dvd_int @ E3 @ A )
% 11.11/6.22                & ( dvd_dvd_int @ E3 @ B ) )
% 11.11/6.22             => ( dvd_dvd_int @ E3 @ D ) ) )
% 11.11/6.22        = ( D
% 11.11/6.22          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9717_gcd__non__0__int,axiom,
% 11.11/6.22      ! [Y: int,X4: int] :
% 11.11/6.22        ( ( ord_less_int @ zero_zero_int @ Y )
% 11.11/6.22       => ( ( gcd_gcd_int @ X4 @ Y )
% 11.11/6.22          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X4 @ Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9718_gcd__code__int,axiom,
% 11.11/6.22      ( gcd_gcd_int
% 11.11/6.22      = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9719_gcd__1__nat,axiom,
% 11.11/6.22      ! [M: nat] :
% 11.11/6.22        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 11.11/6.22        = one_one_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9720_gcd__Suc__0,axiom,
% 11.11/6.22      ! [M: nat] :
% 11.11/6.22        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 11.11/6.22        = ( suc @ zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9721_gcd__pos__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 11.11/6.22        = ( ( M != zero_zero_nat )
% 11.11/6.22          | ( N2 != zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9722_gcd__red__nat,axiom,
% 11.11/6.22      ( gcd_gcd_nat
% 11.11/6.22      = ( ^ [X: nat,Y5: nat] : ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9723_gcd__le1__nat,axiom,
% 11.11/6.22      ! [A: nat,B: nat] :
% 11.11/6.22        ( ( A != zero_zero_nat )
% 11.11/6.22       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9724_gcd__le2__nat,axiom,
% 11.11/6.22      ! [B: nat,A: nat] :
% 11.11/6.22        ( ( B != zero_zero_nat )
% 11.11/6.22       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9725_gcd__diff1__nat,axiom,
% 11.11/6.22      ! [N2: nat,M: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ N2 @ M )
% 11.11/6.22       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 11.11/6.22          = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9726_gcd__diff2__nat,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.22       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 11.11/6.22          = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9727_gcd__non__0__nat,axiom,
% 11.11/6.22      ! [Y: nat,X4: nat] :
% 11.11/6.22        ( ( Y != zero_zero_nat )
% 11.11/6.22       => ( ( gcd_gcd_nat @ X4 @ Y )
% 11.11/6.22          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9728_gcd__nat_Osimps,axiom,
% 11.11/6.22      ( gcd_gcd_nat
% 11.11/6.22      = ( ^ [X: nat,Y5: nat] : ( if_nat @ ( Y5 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9729_gcd__nat_Oelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: nat] :
% 11.11/6.22        ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( Xa = zero_zero_nat )
% 11.11/6.22           => ( Y = X4 ) )
% 11.11/6.22          & ( ( Xa != zero_zero_nat )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9730_bezout__nat,axiom,
% 11.11/6.22      ! [A: nat,B: nat] :
% 11.11/6.22        ( ( A != zero_zero_nat )
% 11.11/6.22       => ? [X5: nat,Y3: nat] :
% 11.11/6.22            ( ( times_times_nat @ A @ X5 )
% 11.11/6.22            = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9731_bezout__gcd__nat_H,axiom,
% 11.11/6.22      ! [B: nat,A: nat] :
% 11.11/6.22      ? [X5: nat,Y3: nat] :
% 11.11/6.22        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 11.11/6.22          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 11.11/6.22            = ( gcd_gcd_nat @ A @ B ) ) )
% 11.11/6.22        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 11.11/6.22          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 11.11/6.22            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9732_gcd__code__integer,axiom,
% 11.11/6.22      ( gcd_gcd_Code_integer
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9733_nat__descend__induct,axiom,
% 11.11/6.22      ! [N2: nat,P: nat > $o,M: nat] :
% 11.11/6.22        ( ! [K2: nat] :
% 11.11/6.22            ( ( ord_less_nat @ N2 @ K2 )
% 11.11/6.22           => ( P @ K2 ) )
% 11.11/6.22       => ( ! [K2: nat] :
% 11.11/6.22              ( ( ord_less_eq_nat @ K2 @ N2 )
% 11.11/6.22             => ( ! [I: nat] :
% 11.11/6.22                    ( ( ord_less_nat @ K2 @ I )
% 11.11/6.22                   => ( P @ I ) )
% 11.11/6.22               => ( P @ K2 ) ) )
% 11.11/6.22         => ( P @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9734_gcd__nat_Opelims,axiom,
% 11.11/6.22      ! [X4: nat,Xa: nat,Y: nat] :
% 11.11/6.22        ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 11.11/6.22         => ~ ( ( ( ( Xa = zero_zero_nat )
% 11.11/6.22                 => ( Y = X4 ) )
% 11.11/6.22                & ( ( Xa != zero_zero_nat )
% 11.11/6.22                 => ( Y
% 11.11/6.22                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) )
% 11.11/6.22             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9735_drop__bit__numeral__minus__bit1,axiom,
% 11.11/6.22      ! [L: num,K: num] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.22        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9736_finite__enumerate,axiom,
% 11.11/6.22      ! [S2: set_nat] :
% 11.11/6.22        ( ( finite_finite_nat @ S2 )
% 11.11/6.22       => ? [R2: nat > nat] :
% 11.11/6.22            ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 11.11/6.22            & ! [N6: nat] :
% 11.11/6.22                ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 11.11/6.22               => ( member_nat @ ( R2 @ N6 ) @ S2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9737_drop__bit__nonnegative__int__iff,axiom,
% 11.11/6.22      ! [N2: nat,K: int] :
% 11.11/6.22        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 11.11/6.22        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9738_drop__bit__negative__int__iff,axiom,
% 11.11/6.22      ! [N2: nat,K: int] :
% 11.11/6.22        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 11.11/6.22        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9739_drop__bit__minus__one,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 11.11/6.22        = ( uminus_uminus_int @ one_one_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9740_drop__bit__Suc__minus__bit0,axiom,
% 11.11/6.22      ! [N2: nat,K: num] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.22        = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9741_drop__bit__numeral__minus__bit0,axiom,
% 11.11/6.22      ! [L: num,K: num] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 11.11/6.22        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9742_drop__bit__Suc__minus__bit1,axiom,
% 11.11/6.22      ! [N2: nat,K: num] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 11.11/6.22        = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9743_drop__bit__push__bit__int,axiom,
% 11.11/6.22      ! [M: nat,N2: nat,K: int] :
% 11.11/6.22        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 11.11/6.22        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9744_drop__bit__int__def,axiom,
% 11.11/6.22      ( bit_se8568078237143864401it_int
% 11.11/6.22      = ( ^ [N: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9745_drop__bit__of__Suc__0,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 11.11/6.22        = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9746_drop__bit__nat__eq,axiom,
% 11.11/6.22      ! [N2: nat,K: int] :
% 11.11/6.22        ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 11.11/6.22        = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9747_drop__bit__nat__def,axiom,
% 11.11/6.22      ( bit_se8570568707652914677it_nat
% 11.11/6.22      = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9748_card__greaterThanLessThan__int,axiom,
% 11.11/6.22      ! [L: int,U: int] :
% 11.11/6.22        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 11.11/6.22        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9749_finite__greaterThanLessThan__int,axiom,
% 11.11/6.22      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9750_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 11.11/6.22      ! [L: int,U: int] :
% 11.11/6.22        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 11.11/6.22        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9751_xor__minus__numerals_I1_J,axiom,
% 11.11/6.22      ! [N2: num,K: int] :
% 11.11/6.22        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9752_xor__minus__numerals_I2_J,axiom,
% 11.11/6.22      ! [K: int,N2: num] :
% 11.11/6.22        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9753_finite__greaterThanLessThan,axiom,
% 11.11/6.22      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9754_card__greaterThanLessThan,axiom,
% 11.11/6.22      ! [L: nat,U: nat] :
% 11.11/6.22        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 11.11/6.22        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9755_atLeastSucLessThan__greaterThanLessThan,axiom,
% 11.11/6.22      ! [L: nat,U: nat] :
% 11.11/6.22        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 11.11/6.22        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9756_tanh__real__bounds,axiom,
% 11.11/6.22      ! [X4: real] : ( member_real @ ( tanh_real @ X4 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9757_sub__BitM__One__eq,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 11.11/6.22        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9758_Suc__funpow,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( compow_nat_nat @ N2 @ suc )
% 11.11/6.22        = ( plus_plus_nat @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9759_nat__of__integer__non__positive,axiom,
% 11.11/6.22      ! [K: code_integer] :
% 11.11/6.22        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 11.11/6.22       => ( ( code_nat_of_integer @ K )
% 11.11/6.22          = zero_zero_nat ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9760_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 11.11/6.22      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 11.11/6.22      @ ^ [X: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X )
% 11.11/6.22      @ ^ [X: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9761_nat__of__integer__code__post_I3_J,axiom,
% 11.11/6.22      ! [K: num] :
% 11.11/6.22        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 11.11/6.22        = ( numeral_numeral_nat @ K ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9762_nat__of__integer__code__post_I2_J,axiom,
% 11.11/6.22      ( ( code_nat_of_integer @ one_one_Code_integer )
% 11.11/6.22      = one_one_nat ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9763_nat__of__integer__code,axiom,
% 11.11/6.22      ( code_nat_of_integer
% 11.11/6.22      = ( ^ [K3: code_integer] :
% 11.11/6.22            ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 11.11/6.22            @ ( produc1555791787009142072er_nat
% 11.11/6.22              @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 11.11/6.22              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9764_int__of__integer__code,axiom,
% 11.11/6.22      ( code_int_of_integer
% 11.11/6.22      = ( ^ [K3: code_integer] :
% 11.11/6.22            ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 11.11/6.22            @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 11.11/6.22              @ ( produc1553301316500091796er_int
% 11.11/6.22                @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 11.11/6.22                @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9765_modulo__integer_Orep__eq,axiom,
% 11.11/6.22      ! [X4: code_integer,Xa: code_integer] :
% 11.11/6.22        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X4 @ Xa ) )
% 11.11/6.22        = ( modulo_modulo_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9766_integer__less__iff,axiom,
% 11.11/6.22      ( ord_le6747313008572928689nteger
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9767_less__integer_Orep__eq,axiom,
% 11.11/6.22      ( ord_le6747313008572928689nteger
% 11.11/6.22      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9768_less__eq__integer_Orep__eq,axiom,
% 11.11/6.22      ( ord_le3102999989581377725nteger
% 11.11/6.22      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9769_integer__less__eq__iff,axiom,
% 11.11/6.22      ( ord_le3102999989581377725nteger
% 11.11/6.22      = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9770_times__int_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 11.11/6.22        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 11.11/6.22        = ( abs_Integ
% 11.11/6.22          @ ( produc27273713700761075at_nat
% 11.11/6.22            @ ^ [X: nat,Y5: nat] :
% 11.11/6.22                ( produc2626176000494625587at_nat
% 11.11/6.22                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 11.11/6.22            @ Xa
% 11.11/6.22            @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9771_one__int__def,axiom,
% 11.11/6.22      ( one_one_int
% 11.11/6.22      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9772_less__int_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 11.11/6.22        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 11.11/6.22        = ( produc8739625826339149834_nat_o
% 11.11/6.22          @ ^ [X: nat,Y5: nat] :
% 11.11/6.22              ( produc6081775807080527818_nat_o
% 11.11/6.22              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 11.11/6.22          @ Xa
% 11.11/6.22          @ X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9773_less__eq__int_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 11.11/6.22        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 11.11/6.22        = ( produc8739625826339149834_nat_o
% 11.11/6.22          @ ^ [X: nat,Y5: nat] :
% 11.11/6.22              ( produc6081775807080527818_nat_o
% 11.11/6.22              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 11.11/6.22          @ Xa
% 11.11/6.22          @ X4 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9774_plus__int_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 11.11/6.22        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 11.11/6.22        = ( abs_Integ
% 11.11/6.22          @ ( produc27273713700761075at_nat
% 11.11/6.22            @ ^ [X: nat,Y5: nat] :
% 11.11/6.22                ( produc2626176000494625587at_nat
% 11.11/6.22                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 11.11/6.22            @ Xa
% 11.11/6.22            @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9775_minus__int_Oabs__eq,axiom,
% 11.11/6.22      ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 11.11/6.22        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 11.11/6.22        = ( abs_Integ
% 11.11/6.22          @ ( produc27273713700761075at_nat
% 11.11/6.22            @ ^ [X: nat,Y5: nat] :
% 11.11/6.22                ( produc2626176000494625587at_nat
% 11.11/6.22                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 11.11/6.22            @ Xa
% 11.11/6.22            @ X4 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9776_num__of__nat_Osimps_I2_J,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ( ( num_of_nat @ ( suc @ N2 ) )
% 11.11/6.22            = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 11.11/6.22        & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ( ( num_of_nat @ ( suc @ N2 ) )
% 11.11/6.22            = one ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9777_pred__nat__def,axiom,
% 11.11/6.22      ( pred_nat
% 11.11/6.22      = ( collec3392354462482085612at_nat
% 11.11/6.22        @ ( produc6081775807080527818_nat_o
% 11.11/6.22          @ ^ [M6: nat,N: nat] :
% 11.11/6.22              ( N
% 11.11/6.22              = ( suc @ M6 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9778_num__of__nat__numeral__eq,axiom,
% 11.11/6.22      ! [Q3: num] :
% 11.11/6.22        ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 11.11/6.22        = Q3 ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9779_num__of__nat_Osimps_I1_J,axiom,
% 11.11/6.22      ( ( num_of_nat @ zero_zero_nat )
% 11.11/6.22      = one ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9780_numeral__num__of__nat,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 11.11/6.22          = N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9781_num__of__nat__One,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 11.11/6.22       => ( ( num_of_nat @ N2 )
% 11.11/6.22          = one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9782_num__of__nat__double,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22       => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 11.11/6.22          = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9783_num__of__nat__plus__distrib,axiom,
% 11.11/6.22      ! [M: nat,N2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ zero_zero_nat @ M )
% 11.11/6.22       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.22         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 11.11/6.22            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9784_less__eq__int_Orep__eq,axiom,
% 11.11/6.22      ( ord_less_eq_int
% 11.11/6.22      = ( ^ [X: int,Xa4: int] :
% 11.11/6.22            ( produc8739625826339149834_nat_o
% 11.11/6.22            @ ^ [Y5: nat,Z5: nat] :
% 11.11/6.22                ( produc6081775807080527818_nat_o
% 11.11/6.22                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 11.11/6.22            @ ( rep_Integ @ X )
% 11.11/6.22            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9785_less__int_Orep__eq,axiom,
% 11.11/6.22      ( ord_less_int
% 11.11/6.22      = ( ^ [X: int,Xa4: int] :
% 11.11/6.22            ( produc8739625826339149834_nat_o
% 11.11/6.22            @ ^ [Y5: nat,Z5: nat] :
% 11.11/6.22                ( produc6081775807080527818_nat_o
% 11.11/6.22                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 11.11/6.22            @ ( rep_Integ @ X )
% 11.11/6.22            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9786_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.22        ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22       => ( ( ? [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( X4
% 11.11/6.22                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22           => ( Xa = one_one_nat ) )
% 11.11/6.22         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22               => ( ( Deg2 = Xa )
% 11.11/6.22                  & ! [X5: vEBT_VEBT] :
% 11.11/6.22                      ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                     => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                  & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                  & ( case_o184042715313410164at_nat
% 11.11/6.22                    @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                      & ! [X: vEBT_VEBT] :
% 11.11/6.22                          ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                         => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                    @ ( produc6081775807080527818_nat_o
% 11.11/6.22                      @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                          ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                          & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                          & ! [I3: nat] :
% 11.11/6.22                              ( ( 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 ) ) ) ) ) )
% 11.11/6.22                             => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                          & ( ( Mi2 = Ma2 )
% 11.11/6.22                           => ! [X: vEBT_VEBT] :
% 11.11/6.22                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                          & ( ( Mi2 != Ma2 )
% 11.11/6.22                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                              & ! [X: nat] :
% 11.11/6.22                                  ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                   => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                      & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                    @ Mima ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9787_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.22        ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22       => ( ( ? [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( X4
% 11.11/6.22                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22           => ( Xa != one_one_nat ) )
% 11.11/6.22         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22               => ~ ( ( Deg2 = Xa )
% 11.11/6.22                    & ! [X2: vEBT_VEBT] :
% 11.11/6.22                        ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                       => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                    & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                    & ( case_o184042715313410164at_nat
% 11.11/6.22                      @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                        & ! [X: vEBT_VEBT] :
% 11.11/6.22                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                           => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                      @ ( produc6081775807080527818_nat_o
% 11.11/6.22                        @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                            ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                            & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                            & ! [I3: nat] :
% 11.11/6.22                                ( ( 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 ) ) ) ) ) )
% 11.11/6.22                               => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                  = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                            & ( ( Mi2 = Ma2 )
% 11.11/6.22                             => ! [X: vEBT_VEBT] :
% 11.11/6.22                                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                                 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                            & ( ( Mi2 != Ma2 )
% 11.11/6.22                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                                & ! [X: nat] :
% 11.11/6.22                                    ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                     => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                        & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                      @ Mima ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9788_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.22        ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ? [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( X4
% 11.11/6.22                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22           => ( Y
% 11.11/6.22              = ( Xa != one_one_nat ) ) )
% 11.11/6.22         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22               => ( Y
% 11.11/6.22                  = ( ~ ( ( Deg2 = Xa )
% 11.11/6.22                        & ! [X: vEBT_VEBT] :
% 11.11/6.22                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                        & ( case_o184042715313410164at_nat
% 11.11/6.22                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                            & ! [X: vEBT_VEBT] :
% 11.11/6.22                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                          @ ( produc6081775807080527818_nat_o
% 11.11/6.22                            @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                & ! [I3: nat] :
% 11.11/6.22                                    ( ( 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 ) ) ) ) ) )
% 11.11/6.22                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                                & ( ( Mi2 = Ma2 )
% 11.11/6.22                                 => ! [X: vEBT_VEBT] :
% 11.11/6.22                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                                & ( ( Mi2 != Ma2 )
% 11.11/6.22                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                                    & ! [X: nat] :
% 11.11/6.22                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                         => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                          @ Mima ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9789_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 11.11/6.22      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 11.11/6.22        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 11.11/6.22        = ( ( Deg = Deg4 )
% 11.11/6.22          & ! [X: vEBT_VEBT] :
% 11.11/6.22              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.22             => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 11.11/6.22            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22          & ( case_o184042715313410164at_nat
% 11.11/6.22            @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X3 )
% 11.11/6.22              & ! [X: vEBT_VEBT] :
% 11.11/6.22                  ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.22                 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22            @ ( produc6081775807080527818_nat_o
% 11.11/6.22              @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                  ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                  & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 11.11/6.22                  & ! [I3: nat] :
% 11.11/6.22                      ( ( 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 ) ) ) ) ) )
% 11.11/6.22                     => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X3 ) )
% 11.11/6.22                        = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 11.11/6.22                  & ( ( Mi2 = Ma2 )
% 11.11/6.22                   => ! [X: vEBT_VEBT] :
% 11.11/6.22                        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 11.11/6.22                       => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                  & ( ( Mi2 != Ma2 )
% 11.11/6.22                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma2 )
% 11.11/6.22                      & ! [X: nat] :
% 11.11/6.22                          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 11.11/6.22                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 11.11/6.22                           => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                              & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22            @ Mima2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9790_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 11.11/6.22        ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.22         => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22               => ( ( Y
% 11.11/6.22                    = ( Xa = one_one_nat ) )
% 11.11/6.22                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 11.11/6.22           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                  ( ( X4
% 11.11/6.22                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22                 => ( ( Y
% 11.11/6.22                      = ( ( Deg2 = Xa )
% 11.11/6.22                        & ! [X: vEBT_VEBT] :
% 11.11/6.22                            ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                           => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                        & ( case_o184042715313410164at_nat
% 11.11/6.22                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                            & ! [X: vEBT_VEBT] :
% 11.11/6.22                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                          @ ( produc6081775807080527818_nat_o
% 11.11/6.22                            @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                & ! [I3: nat] :
% 11.11/6.22                                    ( ( 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 ) ) ) ) ) )
% 11.11/6.22                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                                & ( ( Mi2 = Ma2 )
% 11.11/6.22                                 => ! [X: vEBT_VEBT] :
% 11.11/6.22                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                                & ( ( Mi2 != Ma2 )
% 11.11/6.22                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                                    & ! [X: nat] :
% 11.11/6.22                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                         => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                          @ Mima ) ) )
% 11.11/6.22                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9791_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.22        ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.22         => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 11.11/6.22                 => ( Xa != one_one_nat ) ) )
% 11.11/6.22           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                  ( ( X4
% 11.11/6.22                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 11.11/6.22                   => ~ ( ( Deg2 = Xa )
% 11.11/6.22                        & ! [X2: vEBT_VEBT] :
% 11.11/6.22                            ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                           => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                        & ( case_o184042715313410164at_nat
% 11.11/6.22                          @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                            & ! [X: vEBT_VEBT] :
% 11.11/6.22                                ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                               => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                          @ ( produc6081775807080527818_nat_o
% 11.11/6.22                            @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                                ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                                & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                & ! [I3: nat] :
% 11.11/6.22                                    ( ( 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 ) ) ) ) ) )
% 11.11/6.22                                   => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                                & ( ( Mi2 = Ma2 )
% 11.11/6.22                                 => ! [X: vEBT_VEBT] :
% 11.11/6.22                                      ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                                     => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                                & ( ( Mi2 != Ma2 )
% 11.11/6.22                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                                    & ! [X: nat] :
% 11.11/6.22                                        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                         => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                            & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                          @ Mima ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9792_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 11.11/6.22      ! [X4: vEBT_VEBT,Xa: nat] :
% 11.11/6.22        ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 11.11/6.22       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 11.11/6.22         => ( ! [Uu2: $o,Uv2: $o] :
% 11.11/6.22                ( ( X4
% 11.11/6.22                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 11.11/6.22               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 11.11/6.22                 => ( Xa = one_one_nat ) ) )
% 11.11/6.22           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 11.11/6.22                  ( ( X4
% 11.11/6.22                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 11.11/6.22                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 11.11/6.22                   => ( ( Deg2 = Xa )
% 11.11/6.22                      & ! [X5: vEBT_VEBT] :
% 11.11/6.22                          ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                         => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                      & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 11.11/6.22                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 11.11/6.22                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.22                      & ( case_o184042715313410164at_nat
% 11.11/6.22                        @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 11.11/6.22                          & ! [X: vEBT_VEBT] :
% 11.11/6.22                              ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                             => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                        @ ( produc6081775807080527818_nat_o
% 11.11/6.22                          @ ^ [Mi2: nat,Ma2: nat] :
% 11.11/6.22                              ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 11.11/6.22                              & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                              & ! [I3: nat] :
% 11.11/6.22                                  ( ( 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 ) ) ) ) ) )
% 11.11/6.22                                 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 11.11/6.22                                    = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 11.11/6.22                              & ( ( Mi2 = Ma2 )
% 11.11/6.22                               => ! [X: vEBT_VEBT] :
% 11.11/6.22                                    ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 11.11/6.22                                   => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 11.11/6.22                              & ( ( Mi2 != Ma2 )
% 11.11/6.22                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 11.11/6.22                                  & ! [X: nat] :
% 11.11/6.22                                      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 11.11/6.22                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 11.11/6.22                                       => ( ( ord_less_nat @ Mi2 @ X )
% 11.11/6.22                                          & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 11.11/6.22                        @ Mima ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9793_Sup__int__def,axiom,
% 11.11/6.22      ( complete_Sup_Sup_int
% 11.11/6.22      = ( ^ [X3: set_int] :
% 11.11/6.22            ( the_int
% 11.11/6.22            @ ^ [X: int] :
% 11.11/6.22                ( ( member_int @ X @ X3 )
% 11.11/6.22                & ! [Y5: int] :
% 11.11/6.22                    ( ( member_int @ Y5 @ X3 )
% 11.11/6.22                   => ( ord_less_eq_int @ Y5 @ X ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9794_take__bit__numeral__minus__numeral__int,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int
% 11.11/6.22          @ ^ [Q5: 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 @ Q5 ) ) )
% 11.11/6.22          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9795_and__minus__numerals_I7_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9796_take__bit__num__simps_I1_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 11.11/6.22        = none_num ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9797_take__bit__num__simps_I2_J,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 11.11/6.22        = ( some_num @ one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9798_take__bit__num__simps_I5_J,axiom,
% 11.11/6.22      ! [R3: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ one )
% 11.11/6.22        = ( some_num @ one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9799_take__bit__num__simps_I3_J,axiom,
% 11.11/6.22      ! [N2: nat,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 11.11/6.22        = ( case_o6005452278849405969um_num @ none_num
% 11.11/6.22          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 11.11/6.22          @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9800_take__bit__num__simps_I4_J,axiom,
% 11.11/6.22      ! [N2: nat,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 11.11/6.22        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9801_take__bit__num__simps_I6_J,axiom,
% 11.11/6.22      ! [R3: num,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 11.11/6.22        = ( case_o6005452278849405969um_num @ none_num
% 11.11/6.22          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 11.11/6.22          @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9802_take__bit__num__simps_I7_J,axiom,
% 11.11/6.22      ! [R3: num,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 11.11/6.22        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9803_and__minus__numerals_I8_J,axiom,
% 11.11/6.22      ! [N2: num,M: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9804_and__minus__numerals_I4_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9805_and__minus__numerals_I3_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9806_and__not__num_Osimps_I1_J,axiom,
% 11.11/6.22      ( ( bit_and_not_num @ one @ one )
% 11.11/6.22      = none_num ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9807_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 11.11/6.22      ! [N2: nat,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 11.11/6.22        = ( case_nat_option_num @ none_num
% 11.11/6.22          @ ^ [N: nat] :
% 11.11/6.22              ( case_o6005452278849405969um_num @ none_num
% 11.11/6.22              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 11.11/6.22              @ ( bit_take_bit_num @ N @ M ) )
% 11.11/6.22          @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9808_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 11.11/6.22      ! [N2: nat] :
% 11.11/6.22        ( ( bit_take_bit_num @ N2 @ one )
% 11.11/6.22        = ( case_nat_option_num @ none_num
% 11.11/6.22          @ ^ [N: nat] : ( some_num @ one )
% 11.11/6.22          @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9809_and__not__num_Osimps_I2_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( some_num @ one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9810_and__not__num_Osimps_I4_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 11.11/6.22        = ( some_num @ ( bit0 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9811_GreatestI__ex__nat,axiom,
% 11.11/6.22      ! [P: nat > $o,B: nat] :
% 11.11/6.22        ( ? [X_1: nat] : ( P @ X_1 )
% 11.11/6.22       => ( ! [Y3: nat] :
% 11.11/6.22              ( ( P @ Y3 )
% 11.11/6.22             => ( ord_less_eq_nat @ Y3 @ B ) )
% 11.11/6.22         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9812_Greatest__le__nat,axiom,
% 11.11/6.22      ! [P: nat > $o,K: nat,B: nat] :
% 11.11/6.22        ( ( P @ K )
% 11.11/6.22       => ( ! [Y3: nat] :
% 11.11/6.22              ( ( P @ Y3 )
% 11.11/6.22             => ( ord_less_eq_nat @ Y3 @ B ) )
% 11.11/6.22         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9813_GreatestI__nat,axiom,
% 11.11/6.22      ! [P: nat > $o,K: nat,B: nat] :
% 11.11/6.22        ( ( P @ K )
% 11.11/6.22       => ( ! [Y3: nat] :
% 11.11/6.22              ( ( P @ Y3 )
% 11.11/6.22             => ( ord_less_eq_nat @ Y3 @ B ) )
% 11.11/6.22         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9814_and__not__num_Osimps_I3_J,axiom,
% 11.11/6.22      ! [N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 11.11/6.22        = none_num ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9815_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 11.11/6.22      ! [N2: nat,M: num] :
% 11.11/6.22        ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 11.11/6.22        = ( case_nat_option_num @ none_num
% 11.11/6.22          @ ^ [N: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) )
% 11.11/6.22          @ N2 ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9816_and__not__num_Osimps_I7_J,axiom,
% 11.11/6.22      ! [M: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 11.11/6.22        = ( some_num @ ( bit0 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9817_and__not__num__eq__Some__iff,axiom,
% 11.11/6.22      ! [M: num,N2: num,Q3: num] :
% 11.11/6.22        ( ( ( bit_and_not_num @ M @ N2 )
% 11.11/6.22          = ( some_num @ Q3 ) )
% 11.11/6.22        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22          = ( numeral_numeral_int @ Q3 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9818_and__not__num_Osimps_I8_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.22          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.22          @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9819_and__not__num__eq__None__iff,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( ( bit_and_not_num @ M @ N2 )
% 11.11/6.22          = none_num )
% 11.11/6.22        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22          = zero_zero_int ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9820_int__numeral__not__and__num,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9821_int__numeral__and__not__num,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.22        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9822_take__bit__num__def,axiom,
% 11.11/6.22      ( bit_take_bit_num
% 11.11/6.22      = ( ^ [N: nat,M6: num] :
% 11.11/6.22            ( if_option_num
% 11.11/6.22            @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) )
% 11.11/6.22              = zero_zero_nat )
% 11.11/6.22            @ none_num
% 11.11/6.22            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9823_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 11.11/6.22      ! [N2: nat,J: nat,I2: nat] :
% 11.11/6.22        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 11.11/6.22       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 11.11/6.22          = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9824_and__not__num_Oelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.22        ( ( ( bit_and_not_num @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( X4 = one )
% 11.11/6.22           => ( ( Xa = one )
% 11.11/6.22             => ( Y != none_num ) ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ( ? [N3: num] :
% 11.11/6.22                    ( Xa
% 11.11/6.22                    = ( bit0 @ N3 ) )
% 11.11/6.22               => ( Y
% 11.11/6.22                 != ( some_num @ one ) ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ( ? [N3: num] :
% 11.11/6.22                      ( Xa
% 11.11/6.22                      = ( bit1 @ N3 ) )
% 11.11/6.22                 => ( Y != none_num ) ) )
% 11.11/6.22             => ( ! [M5: num] :
% 11.11/6.22                    ( ( X4
% 11.11/6.22                      = ( bit0 @ M5 ) )
% 11.11/6.22                   => ( ( Xa = one )
% 11.11/6.22                     => ( Y
% 11.11/6.22                       != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 11.11/6.22               => ( ! [M5: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ M5 ) )
% 11.11/6.22                     => ! [N3: num] :
% 11.11/6.22                          ( ( Xa
% 11.11/6.22                            = ( bit0 @ N3 ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                 => ( ! [M5: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ M5 ) )
% 11.11/6.22                       => ! [N3: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit1 @ N3 ) )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                   => ( ! [M5: num] :
% 11.11/6.22                          ( ( X4
% 11.11/6.22                            = ( bit1 @ M5 ) )
% 11.11/6.22                         => ( ( Xa = one )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 11.11/6.22                     => ( ! [M5: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ M5 ) )
% 11.11/6.22                           => ! [N3: num] :
% 11.11/6.22                                ( ( Xa
% 11.11/6.22                                  = ( bit0 @ N3 ) )
% 11.11/6.22                               => ( Y
% 11.11/6.22                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.22                                    @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.22                                    @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                       => ~ ! [M5: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ M5 ) )
% 11.11/6.22                             => ! [N3: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit1 @ N3 ) )
% 11.11/6.22                                 => ( Y
% 11.11/6.22                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9825_Bit__Operations_Otake__bit__num__code,axiom,
% 11.11/6.22      ( bit_take_bit_num
% 11.11/6.22      = ( ^ [N: nat,M6: num] :
% 11.11/6.22            ( produc478579273971653890on_num
% 11.11/6.22            @ ^ [A3: nat,X: num] :
% 11.11/6.22                ( case_nat_option_num @ none_num
% 11.11/6.22                @ ^ [O: nat] :
% 11.11/6.22                    ( case_num_option_num @ ( some_num @ one )
% 11.11/6.22                    @ ^ [P5: num] :
% 11.11/6.22                        ( case_o6005452278849405969um_num @ none_num
% 11.11/6.22                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 11.11/6.22                        @ ( bit_take_bit_num @ O @ P5 ) )
% 11.11/6.22                    @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 11.11/6.22                    @ X )
% 11.11/6.22                @ A3 )
% 11.11/6.22            @ ( product_Pair_nat_num @ N @ M6 ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9826_and__not__num_Osimps_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9827_and__not__num_Osimps_I9_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.22        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9828_and__not__num_Osimps_I6_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.22        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9829_and__not__num_Opelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.22        ( ( ( bit_and_not_num @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ( ( Xa = one )
% 11.11/6.22               => ( ( Y = none_num )
% 11.11/6.22                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ! [N3: num] :
% 11.11/6.22                    ( ( Xa
% 11.11/6.22                      = ( bit0 @ N3 ) )
% 11.11/6.22                   => ( ( Y
% 11.11/6.22                        = ( some_num @ one ) )
% 11.11/6.22                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.22             => ( ( ( X4 = one )
% 11.11/6.22                 => ! [N3: num] :
% 11.11/6.22                      ( ( Xa
% 11.11/6.22                        = ( bit1 @ N3 ) )
% 11.11/6.22                     => ( ( Y = none_num )
% 11.11/6.22                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.22               => ( ! [M5: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ M5 ) )
% 11.11/6.22                     => ( ( Xa = one )
% 11.11/6.22                       => ( ( Y
% 11.11/6.22                            = ( some_num @ ( bit0 @ M5 ) ) )
% 11.11/6.22                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 11.11/6.22                 => ( ! [M5: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ M5 ) )
% 11.11/6.22                       => ! [N3: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit0 @ N3 ) )
% 11.11/6.22                           => ( ( Y
% 11.11/6.22                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 11.11/6.22                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.22                   => ( ! [M5: num] :
% 11.11/6.22                          ( ( X4
% 11.11/6.22                            = ( bit0 @ M5 ) )
% 11.11/6.22                         => ! [N3: num] :
% 11.11/6.22                              ( ( Xa
% 11.11/6.22                                = ( bit1 @ N3 ) )
% 11.11/6.22                             => ( ( Y
% 11.11/6.22                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 11.11/6.22                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.22                     => ( ! [M5: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ M5 ) )
% 11.11/6.22                           => ( ( Xa = one )
% 11.11/6.22                             => ( ( Y
% 11.11/6.22                                  = ( some_num @ ( bit0 @ M5 ) ) )
% 11.11/6.22                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 11.11/6.22                       => ( ! [M5: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ M5 ) )
% 11.11/6.22                             => ! [N3: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit0 @ N3 ) )
% 11.11/6.22                                 => ( ( Y
% 11.11/6.22                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.22                                        @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.22                                        @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 11.11/6.22                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.22                         => ~ ! [M5: num] :
% 11.11/6.22                                ( ( X4
% 11.11/6.22                                  = ( bit1 @ M5 ) )
% 11.11/6.22                               => ! [N3: num] :
% 11.11/6.22                                    ( ( Xa
% 11.11/6.22                                      = ( bit1 @ N3 ) )
% 11.11/6.22                                   => ( ( Y
% 11.11/6.22                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 11.11/6.22                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9830_and__num_Oelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.22        ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( X4 = one )
% 11.11/6.22           => ( ( Xa = one )
% 11.11/6.22             => ( Y
% 11.11/6.22               != ( some_num @ one ) ) ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ( ? [N3: num] :
% 11.11/6.22                    ( Xa
% 11.11/6.22                    = ( bit0 @ N3 ) )
% 11.11/6.22               => ( Y != none_num ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ( ? [N3: num] :
% 11.11/6.22                      ( Xa
% 11.11/6.22                      = ( bit1 @ N3 ) )
% 11.11/6.22                 => ( Y
% 11.11/6.22                   != ( some_num @ one ) ) ) )
% 11.11/6.22             => ( ( ? [M5: num] :
% 11.11/6.22                      ( X4
% 11.11/6.22                      = ( bit0 @ M5 ) )
% 11.11/6.22                 => ( ( Xa = one )
% 11.11/6.22                   => ( Y != none_num ) ) )
% 11.11/6.22               => ( ! [M5: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ M5 ) )
% 11.11/6.22                     => ! [N3: num] :
% 11.11/6.22                          ( ( Xa
% 11.11/6.22                            = ( bit0 @ N3 ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                 => ( ! [M5: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ M5 ) )
% 11.11/6.22                       => ! [N3: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit1 @ N3 ) )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                   => ( ( ? [M5: num] :
% 11.11/6.22                            ( X4
% 11.11/6.22                            = ( bit1 @ M5 ) )
% 11.11/6.22                       => ( ( Xa = one )
% 11.11/6.22                         => ( Y
% 11.11/6.22                           != ( some_num @ one ) ) ) )
% 11.11/6.22                     => ( ! [M5: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ M5 ) )
% 11.11/6.22                           => ! [N3: num] :
% 11.11/6.22                                ( ( Xa
% 11.11/6.22                                  = ( bit0 @ N3 ) )
% 11.11/6.22                               => ( Y
% 11.11/6.22                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                       => ~ ! [M5: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ M5 ) )
% 11.11/6.22                             => ! [N3: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit1 @ N3 ) )
% 11.11/6.22                                 => ( Y
% 11.11/6.22                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.22                                      @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.22                                      @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9831_xor__num_Oelims,axiom,
% 11.11/6.22      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.22        ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 11.11/6.22          = Y )
% 11.11/6.22       => ( ( ( X4 = one )
% 11.11/6.22           => ( ( Xa = one )
% 11.11/6.22             => ( Y != none_num ) ) )
% 11.11/6.22         => ( ( ( X4 = one )
% 11.11/6.22             => ! [N3: num] :
% 11.11/6.22                  ( ( Xa
% 11.11/6.22                    = ( bit0 @ N3 ) )
% 11.11/6.22                 => ( Y
% 11.11/6.22                   != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 11.11/6.22           => ( ( ( X4 = one )
% 11.11/6.22               => ! [N3: num] :
% 11.11/6.22                    ( ( Xa
% 11.11/6.22                      = ( bit1 @ N3 ) )
% 11.11/6.22                   => ( Y
% 11.11/6.22                     != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 11.11/6.22             => ( ! [M5: num] :
% 11.11/6.22                    ( ( X4
% 11.11/6.22                      = ( bit0 @ M5 ) )
% 11.11/6.22                   => ( ( Xa = one )
% 11.11/6.22                     => ( Y
% 11.11/6.22                       != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 11.11/6.22               => ( ! [M5: num] :
% 11.11/6.22                      ( ( X4
% 11.11/6.22                        = ( bit0 @ M5 ) )
% 11.11/6.22                     => ! [N3: num] :
% 11.11/6.22                          ( ( Xa
% 11.11/6.22                            = ( bit0 @ N3 ) )
% 11.11/6.22                         => ( Y
% 11.11/6.22                           != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) )
% 11.11/6.22                 => ( ! [M5: num] :
% 11.11/6.22                        ( ( X4
% 11.11/6.22                          = ( bit0 @ M5 ) )
% 11.11/6.22                       => ! [N3: num] :
% 11.11/6.22                            ( ( Xa
% 11.11/6.22                              = ( bit1 @ N3 ) )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 11.11/6.22                   => ( ! [M5: num] :
% 11.11/6.22                          ( ( X4
% 11.11/6.22                            = ( bit1 @ M5 ) )
% 11.11/6.22                         => ( ( Xa = one )
% 11.11/6.22                           => ( Y
% 11.11/6.22                             != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 11.11/6.22                     => ( ! [M5: num] :
% 11.11/6.22                            ( ( X4
% 11.11/6.22                              = ( bit1 @ M5 ) )
% 11.11/6.22                           => ! [N3: num] :
% 11.11/6.22                                ( ( Xa
% 11.11/6.22                                  = ( bit0 @ N3 ) )
% 11.11/6.22                               => ( Y
% 11.11/6.22                                 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 11.11/6.22                       => ~ ! [M5: num] :
% 11.11/6.22                              ( ( X4
% 11.11/6.22                                = ( bit1 @ M5 ) )
% 11.11/6.22                             => ! [N3: num] :
% 11.11/6.22                                  ( ( Xa
% 11.11/6.22                                    = ( bit1 @ N3 ) )
% 11.11/6.22                                 => ( Y
% 11.11/6.22                                   != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9832_and__num_Osimps_I1_J,axiom,
% 11.11/6.22      ( ( bit_un7362597486090784418nd_num @ one @ one )
% 11.11/6.22      = ( some_num @ one ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9833_xor__num_Osimps_I1_J,axiom,
% 11.11/6.22      ( ( bit_un2480387367778600638or_num @ one @ one )
% 11.11/6.22      = none_num ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9834_and__num_Osimps_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.22        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 11.11/6.22  
% 11.11/6.22  thf(fact_9835_xor__num_Osimps_I5_J,axiom,
% 11.11/6.22      ! [M: num,N2: num] :
% 11.11/6.22        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9836_and__num_Osimps_I7_J,axiom,
% 11.11/6.23      ! [M: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 11.11/6.23        = ( some_num @ one ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9837_and__num_Osimps_I3_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( some_num @ one ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9838_and__num_Osimps_I4_J,axiom,
% 11.11/6.23      ! [M: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 11.11/6.23        = none_num ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9839_and__num_Osimps_I2_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 11.11/6.23        = none_num ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9840_xor__num_Osimps_I9_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9841_and__num_Osimps_I6_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9842_and__num_Osimps_I8_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9843_xor__num_Osimps_I7_J,axiom,
% 11.11/6.23      ! [M: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 11.11/6.23        = ( some_num @ ( bit0 @ M ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9844_xor__num_Osimps_I4_J,axiom,
% 11.11/6.23      ! [M: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 11.11/6.23        = ( some_num @ ( bit1 @ M ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9845_xor__num_Osimps_I3_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9846_xor__num_Osimps_I2_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9847_and__num_Osimps_I9_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.23          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.23          @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9848_xor__num_Osimps_I8_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9849_xor__num_Osimps_I6_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9850_and__num_Opelims,axiom,
% 11.11/6.23      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.23        ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 11.11/6.23         => ( ( ( X4 = one )
% 11.11/6.23             => ( ( Xa = one )
% 11.11/6.23               => ( ( Y
% 11.11/6.23                    = ( some_num @ one ) )
% 11.11/6.23                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 11.11/6.23           => ( ( ( X4 = one )
% 11.11/6.23               => ! [N3: num] :
% 11.11/6.23                    ( ( Xa
% 11.11/6.23                      = ( bit0 @ N3 ) )
% 11.11/6.23                   => ( ( Y = none_num )
% 11.11/6.23                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23             => ( ( ( X4 = one )
% 11.11/6.23                 => ! [N3: num] :
% 11.11/6.23                      ( ( Xa
% 11.11/6.23                        = ( bit1 @ N3 ) )
% 11.11/6.23                     => ( ( Y
% 11.11/6.23                          = ( some_num @ one ) )
% 11.11/6.23                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.23               => ( ! [M5: num] :
% 11.11/6.23                      ( ( X4
% 11.11/6.23                        = ( bit0 @ M5 ) )
% 11.11/6.23                     => ( ( Xa = one )
% 11.11/6.23                       => ( ( Y = none_num )
% 11.11/6.23                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 11.11/6.23                 => ( ! [M5: num] :
% 11.11/6.23                        ( ( X4
% 11.11/6.23                          = ( bit0 @ M5 ) )
% 11.11/6.23                       => ! [N3: num] :
% 11.11/6.23                            ( ( Xa
% 11.11/6.23                              = ( bit0 @ N3 ) )
% 11.11/6.23                           => ( ( Y
% 11.11/6.23                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 11.11/6.23                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23                   => ( ! [M5: num] :
% 11.11/6.23                          ( ( X4
% 11.11/6.23                            = ( bit0 @ M5 ) )
% 11.11/6.23                         => ! [N3: num] :
% 11.11/6.23                              ( ( Xa
% 11.11/6.23                                = ( bit1 @ N3 ) )
% 11.11/6.23                             => ( ( Y
% 11.11/6.23                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 11.11/6.23                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.23                     => ( ! [M5: num] :
% 11.11/6.23                            ( ( X4
% 11.11/6.23                              = ( bit1 @ M5 ) )
% 11.11/6.23                           => ( ( Xa = one )
% 11.11/6.23                             => ( ( Y
% 11.11/6.23                                  = ( some_num @ one ) )
% 11.11/6.23                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 11.11/6.23                       => ( ! [M5: num] :
% 11.11/6.23                              ( ( X4
% 11.11/6.23                                = ( bit1 @ M5 ) )
% 11.11/6.23                             => ! [N3: num] :
% 11.11/6.23                                  ( ( Xa
% 11.11/6.23                                    = ( bit0 @ N3 ) )
% 11.11/6.23                                 => ( ( Y
% 11.11/6.23                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 11.11/6.23                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23                         => ~ ! [M5: num] :
% 11.11/6.23                                ( ( X4
% 11.11/6.23                                  = ( bit1 @ M5 ) )
% 11.11/6.23                               => ! [N3: num] :
% 11.11/6.23                                    ( ( Xa
% 11.11/6.23                                      = ( bit1 @ N3 ) )
% 11.11/6.23                                   => ( ( Y
% 11.11/6.23                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 11.11/6.23                                          @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 11.11/6.23                                          @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 11.11/6.23                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9851_xor__num_Opelims,axiom,
% 11.11/6.23      ! [X4: num,Xa: num,Y: option_num] :
% 11.11/6.23        ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 11.11/6.23         => ( ( ( X4 = one )
% 11.11/6.23             => ( ( Xa = one )
% 11.11/6.23               => ( ( Y = none_num )
% 11.11/6.23                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 11.11/6.23           => ( ( ( X4 = one )
% 11.11/6.23               => ! [N3: num] :
% 11.11/6.23                    ( ( Xa
% 11.11/6.23                      = ( bit0 @ N3 ) )
% 11.11/6.23                   => ( ( Y
% 11.11/6.23                        = ( some_num @ ( bit1 @ N3 ) ) )
% 11.11/6.23                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23             => ( ( ( X4 = one )
% 11.11/6.23                 => ! [N3: num] :
% 11.11/6.23                      ( ( Xa
% 11.11/6.23                        = ( bit1 @ N3 ) )
% 11.11/6.23                     => ( ( Y
% 11.11/6.23                          = ( some_num @ ( bit0 @ N3 ) ) )
% 11.11/6.23                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.23               => ( ! [M5: num] :
% 11.11/6.23                      ( ( X4
% 11.11/6.23                        = ( bit0 @ M5 ) )
% 11.11/6.23                     => ( ( Xa = one )
% 11.11/6.23                       => ( ( Y
% 11.11/6.23                            = ( some_num @ ( bit1 @ M5 ) ) )
% 11.11/6.23                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 11.11/6.23                 => ( ! [M5: num] :
% 11.11/6.23                        ( ( X4
% 11.11/6.23                          = ( bit0 @ M5 ) )
% 11.11/6.23                       => ! [N3: num] :
% 11.11/6.23                            ( ( Xa
% 11.11/6.23                              = ( bit0 @ N3 ) )
% 11.11/6.23                           => ( ( Y
% 11.11/6.23                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 11.11/6.23                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23                   => ( ! [M5: num] :
% 11.11/6.23                          ( ( X4
% 11.11/6.23                            = ( bit0 @ M5 ) )
% 11.11/6.23                         => ! [N3: num] :
% 11.11/6.23                              ( ( Xa
% 11.11/6.23                                = ( bit1 @ N3 ) )
% 11.11/6.23                             => ( ( Y
% 11.11/6.23                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 11.11/6.23                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 11.11/6.23                     => ( ! [M5: num] :
% 11.11/6.23                            ( ( X4
% 11.11/6.23                              = ( bit1 @ M5 ) )
% 11.11/6.23                           => ( ( Xa = one )
% 11.11/6.23                             => ( ( Y
% 11.11/6.23                                  = ( some_num @ ( bit0 @ M5 ) ) )
% 11.11/6.23                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 11.11/6.23                       => ( ! [M5: num] :
% 11.11/6.23                              ( ( X4
% 11.11/6.23                                = ( bit1 @ M5 ) )
% 11.11/6.23                             => ! [N3: num] :
% 11.11/6.23                                  ( ( Xa
% 11.11/6.23                                    = ( bit0 @ N3 ) )
% 11.11/6.23                                 => ( ( Y
% 11.11/6.23                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 11.11/6.23                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 11.11/6.23                         => ~ ! [M5: num] :
% 11.11/6.23                                ( ( X4
% 11.11/6.23                                  = ( bit1 @ M5 ) )
% 11.11/6.23                               => ! [N3: num] :
% 11.11/6.23                                    ( ( Xa
% 11.11/6.23                                      = ( bit1 @ N3 ) )
% 11.11/6.23                                   => ( ( Y
% 11.11/6.23                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 11.11/6.23                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9852_xor__num__dict,axiom,
% 11.11/6.23      bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9853_and__num__rel__dict,axiom,
% 11.11/6.23      bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9854_xor__num__rel__dict,axiom,
% 11.11/6.23      bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9855_and__num__dict,axiom,
% 11.11/6.23      bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9856_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 11.11/6.23      ! [N2: nat,J: nat,I2: nat] :
% 11.11/6.23        ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 11.11/6.23       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 11.11/6.23          = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9857_pow_Osimps_I3_J,axiom,
% 11.11/6.23      ! [X4: num,Y: num] :
% 11.11/6.23        ( ( pow @ X4 @ ( bit1 @ Y ) )
% 11.11/6.23        = ( times_times_num @ ( sqr @ ( pow @ X4 @ Y ) ) @ X4 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9858_finite__greaterThanAtMost,axiom,
% 11.11/6.23      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9859_card__greaterThanAtMost,axiom,
% 11.11/6.23      ! [L: nat,U: nat] :
% 11.11/6.23        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 11.11/6.23        = ( minus_minus_nat @ U @ L ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9860_sqr_Osimps_I2_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( sqr @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9861_sqr_Osimps_I1_J,axiom,
% 11.11/6.23      ( ( sqr @ one )
% 11.11/6.23      = one ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9862_atLeastSucAtMost__greaterThanAtMost,axiom,
% 11.11/6.23      ! [L: nat,U: nat] :
% 11.11/6.23        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 11.11/6.23        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9863_sqr__conv__mult,axiom,
% 11.11/6.23      ( sqr
% 11.11/6.23      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9864_pow_Osimps_I2_J,axiom,
% 11.11/6.23      ! [X4: num,Y: num] :
% 11.11/6.23        ( ( pow @ X4 @ ( bit0 @ Y ) )
% 11.11/6.23        = ( sqr @ ( pow @ X4 @ Y ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9865_sqr_Osimps_I3_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( sqr @ ( bit1 @ N2 ) )
% 11.11/6.23        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9866_integer__of__num__triv_I2_J,axiom,
% 11.11/6.23      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 11.11/6.23      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9867_finite__greaterThanAtMost__int,axiom,
% 11.11/6.23      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9868_card__greaterThanAtMost__int,axiom,
% 11.11/6.23      ! [L: int,U: int] :
% 11.11/6.23        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 11.11/6.23        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9869_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 11.11/6.23      ! [L: int,U: int] :
% 11.11/6.23        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 11.11/6.23        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9870_integer__of__num__triv_I1_J,axiom,
% 11.11/6.23      ( ( code_integer_of_num @ one )
% 11.11/6.23      = one_one_Code_integer ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9871_integer__of__num_I2_J,axiom,
% 11.11/6.23      ! [N2: num] :
% 11.11/6.23        ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 11.11/6.23        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9872_Rats__eq__int__div__nat,axiom,
% 11.11/6.23      ( field_5140801741446780682s_real
% 11.11/6.23      = ( collect_real
% 11.11/6.23        @ ^ [Uu3: real] :
% 11.11/6.23          ? [I3: int,N: nat] :
% 11.11/6.23            ( ( Uu3
% 11.11/6.23              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 11.11/6.23            & ( N != zero_zero_nat ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9873_image__minus__const__atLeastLessThan__nat,axiom,
% 11.11/6.23      ! [C: nat,Y: nat,X4: nat] :
% 11.11/6.23        ( ( ( ord_less_nat @ C @ Y )
% 11.11/6.23         => ( ( image_nat_nat
% 11.11/6.23              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 11.11/6.23              @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 11.11/6.23            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X4 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_nat @ C @ Y )
% 11.11/6.23         => ( ( ( ord_less_nat @ X4 @ Y )
% 11.11/6.23             => ( ( image_nat_nat
% 11.11/6.23                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 11.11/6.23                  @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 11.11/6.23                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 11.11/6.23            & ( ~ ( ord_less_nat @ X4 @ Y )
% 11.11/6.23             => ( ( image_nat_nat
% 11.11/6.23                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 11.11/6.23                  @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 11.11/6.23                = bot_bot_set_nat ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9874_bij__betw__Suc,axiom,
% 11.11/6.23      ! [M7: set_nat,N4: set_nat] :
% 11.11/6.23        ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 11.11/6.23        = ( ( image_nat_nat @ suc @ M7 )
% 11.11/6.23          = N4 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9875_Rats__abs__iff,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( member_real @ ( abs_abs_real @ X4 ) @ field_5140801741446780682s_real )
% 11.11/6.23        = ( member_real @ X4 @ field_5140801741446780682s_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9876_image__Suc__atLeastAtMost,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 11.11/6.23        = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9877_image__Suc__atLeastLessThan,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 11.11/6.23        = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9878_Rats__dense__in__real,axiom,
% 11.11/6.23      ! [X4: real,Y: real] :
% 11.11/6.23        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.23       => ? [X5: real] :
% 11.11/6.23            ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 11.11/6.23            & ( ord_less_real @ X4 @ X5 )
% 11.11/6.23            & ( ord_less_real @ X5 @ Y ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9879_Rats__no__bot__less,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23      ? [X5: real] :
% 11.11/6.23        ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 11.11/6.23        & ( ord_less_real @ X5 @ X4 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9880_Rats__no__top__le,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23      ? [X5: real] :
% 11.11/6.23        ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 11.11/6.23        & ( ord_less_eq_real @ X4 @ X5 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9881_zero__notin__Suc__image,axiom,
% 11.11/6.23      ! [A2: set_nat] :
% 11.11/6.23        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9882_image__Suc__lessThan,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23        = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9883_image__Suc__atMost,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 11.11/6.23        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9884_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 11.11/6.23        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9885_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 11.11/6.23        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9886_lessThan__Suc__eq__insert__0,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 11.11/6.23        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9887_atMost__Suc__eq__insert__0,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 11.11/6.23        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9888_Rats__eq__int__div__int,axiom,
% 11.11/6.23      ( field_5140801741446780682s_real
% 11.11/6.23      = ( collect_real
% 11.11/6.23        @ ^ [Uu3: real] :
% 11.11/6.23          ? [I3: int,J3: int] :
% 11.11/6.23            ( ( Uu3
% 11.11/6.23              = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 11.11/6.23            & ( J3 != zero_zero_int ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9889_Inf__real__def,axiom,
% 11.11/6.23      ( comple4887499456419720421f_real
% 11.11/6.23      = ( ^ [X3: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X3 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9890_finite__int__iff__bounded__le,axiom,
% 11.11/6.23      ( finite_finite_int
% 11.11/6.23      = ( ^ [S5: set_int] :
% 11.11/6.23          ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9891_finite__int__iff__bounded,axiom,
% 11.11/6.23      ( finite_finite_int
% 11.11/6.23      = ( ^ [S5: set_int] :
% 11.11/6.23          ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9892_image__int__atLeastAtMost,axiom,
% 11.11/6.23      ! [A: nat,B: nat] :
% 11.11/6.23        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 11.11/6.23        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9893_image__int__atLeastLessThan,axiom,
% 11.11/6.23      ! [A: nat,B: nat] :
% 11.11/6.23        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 11.11/6.23        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9894_image__add__int__atLeastLessThan,axiom,
% 11.11/6.23      ! [L: int,U: int] :
% 11.11/6.23        ( ( image_int_int
% 11.11/6.23          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 11.11/6.23          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 11.11/6.23        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9895_image__atLeastZeroLessThan__int,axiom,
% 11.11/6.23      ! [U: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 11.11/6.23       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 11.11/6.23          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9896_suminf__eq__SUP__real,axiom,
% 11.11/6.23      ! [X8: nat > real] :
% 11.11/6.23        ( ( summable_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 11.11/6.23         => ( ( suminf_real @ X8 )
% 11.11/6.23            = ( comple1385675409528146559p_real
% 11.11/6.23              @ ( image_nat_real
% 11.11/6.23                @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 11.11/6.23                @ top_top_set_nat ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9897_UN__atMost__UNIV,axiom,
% 11.11/6.23      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 11.11/6.23      = top_top_set_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9898_UN__lessThan__UNIV,axiom,
% 11.11/6.23      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 11.11/6.23      = top_top_set_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9899_range__mod,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( image_nat_nat
% 11.11/6.23            @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 11.11/6.23            @ top_top_set_nat )
% 11.11/6.23          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9900_UNIV__nat__eq,axiom,
% 11.11/6.23      ( top_top_set_nat
% 11.11/6.23      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9901_card__UNIV__unit,axiom,
% 11.11/6.23      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 11.11/6.23      = one_one_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9902_card__UNIV__bool,axiom,
% 11.11/6.23      ( ( finite_card_o @ top_top_set_o )
% 11.11/6.23      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9903_root__def,axiom,
% 11.11/6.23      ( root
% 11.11/6.23      = ( ^ [N: nat,X: real] :
% 11.11/6.23            ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 11.11/6.23            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 11.11/6.23              @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 11.11/6.23              @ X ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9904_card__UNIV__char,axiom,
% 11.11/6.23      ( ( finite_card_char @ top_top_set_char )
% 11.11/6.23      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9905_DERIV__even__real__root,axiom,
% 11.11/6.23      ! [N2: nat,X4: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23         => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.23           => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9906_MVT2,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,F4: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23         => ? [Z2: real] :
% 11.11/6.23              ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23              & ( ord_less_real @ Z2 @ B )
% 11.11/6.23              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 11.11/6.23                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9907_DERIV__nonneg__imp__nondecreasing,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 11.11/6.23         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9908_DERIV__nonpos__imp__nonincreasing,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 11.11/6.23         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9909_DERIV__neg__imp__decreasing,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 11.11/6.23         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9910_DERIV__pos__imp__increasing,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 11.11/6.23         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9911_deriv__nonneg__imp__mono,axiom,
% 11.11/6.23      ! [A: real,B: real,G: real > real,G2: real > real] :
% 11.11/6.23        ( ! [X5: real] :
% 11.11/6.23            ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 11.11/6.23           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 11.11/6.23             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 11.11/6.23         => ( ( ord_less_eq_real @ A @ B )
% 11.11/6.23           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9912_DERIV__isconst3,axiom,
% 11.11/6.23      ! [A: real,B: real,X4: real,Y: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23           => ( ! [X5: real] :
% 11.11/6.23                  ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 11.11/6.23             => ( ( F @ X4 )
% 11.11/6.23                = ( F @ Y ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9913_DERIV__local__const,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,D: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ D )
% 11.11/6.23         => ( ! [Y3: real] :
% 11.11/6.23                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 11.11/6.23               => ( ( F @ X4 )
% 11.11/6.23                  = ( F @ Y3 ) ) )
% 11.11/6.23           => ( L = zero_zero_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9914_DERIV__neg__dec__left,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ L @ zero_zero_real )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                   => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9915_DERIV__pos__inc__left,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ L )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9916_DERIV__neg__dec__right,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ L @ zero_zero_real )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9917_DERIV__pos__inc__right,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ L )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                   => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9918_DERIV__ln,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9919_has__real__derivative__neg__dec__right,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 11.11/6.23       => ( ( ord_less_real @ L @ zero_zero_real )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 11.11/6.23                   => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9920_has__real__derivative__pos__inc__right,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ L )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 11.11/6.23                   => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                     => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9921_has__real__derivative__pos__inc__left,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ L )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 11.11/6.23                   => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9922_has__real__derivative__neg__dec__left,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,S2: set_real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 11.11/6.23       => ( ( ord_less_real @ L @ zero_zero_real )
% 11.11/6.23         => ? [D3: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ D3 )
% 11.11/6.23              & ! [H4: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 11.11/6.23                 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 11.11/6.23                   => ( ( ord_less_real @ H4 @ D3 )
% 11.11/6.23                     => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9923_DERIV__const__average,axiom,
% 11.11/6.23      ! [A: real,B: real,V: real > real,K: real] :
% 11.11/6.23        ( ( A != B )
% 11.11/6.23       => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 11.11/6.23            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9924_DERIV__local__max,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,D: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ D )
% 11.11/6.23         => ( ! [Y3: real] :
% 11.11/6.23                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 11.11/6.23               => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 11.11/6.23           => ( L = zero_zero_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9925_DERIV__local__min,axiom,
% 11.11/6.23      ! [F: real > real,L: real,X4: real,D: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ D )
% 11.11/6.23         => ( ! [Y3: real] :
% 11.11/6.23                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 11.11/6.23               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 11.11/6.23           => ( L = zero_zero_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9926_DERIV__ln__divide,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9927_DERIV__fun__pow,axiom,
% 11.11/6.23      ! [G: real > real,M: real,X4: real,N2: nat] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( has_fi5821293074295781190e_real
% 11.11/6.23          @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N2 )
% 11.11/6.23          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X4 ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 11.11/6.23          @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9928_DERIV__pow,axiom,
% 11.11/6.23      ! [N2: nat,X4: real,S: set_real] :
% 11.11/6.23        ( has_fi5821293074295781190e_real
% 11.11/6.23        @ ^ [X: real] : ( power_power_real @ X @ N2 )
% 11.11/6.23        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 11.11/6.23        @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9929_has__real__derivative__powr,axiom,
% 11.11/6.23      ! [Z: real,R3: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ Z )
% 11.11/6.23       => ( has_fi5821293074295781190e_real
% 11.11/6.23          @ ^ [Z5: real] : ( powr_real @ Z5 @ R3 )
% 11.11/6.23          @ ( times_times_real @ R3 @ ( powr_real @ Z @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 11.11/6.23          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9930_DERIV__log,axiom,
% 11.11/6.23      ! [X4: real,B: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X4 ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9931_DERIV__fun__powr,axiom,
% 11.11/6.23      ! [G: real > real,M: real,X4: real,R3: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 11.11/6.23         => ( has_fi5821293074295781190e_real
% 11.11/6.23            @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R3 )
% 11.11/6.23            @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G @ X4 ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 11.11/6.23            @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9932_DERIV__powr,axiom,
% 11.11/6.23      ! [G: real > real,M: real,X4: real,F: real > real,R3: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 11.11/6.23         => ( ( has_fi5821293074295781190e_real @ F @ R3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 11.11/6.23           => ( has_fi5821293074295781190e_real
% 11.11/6.23              @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 11.11/6.23              @ ( times_times_real @ ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G @ X4 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X4 ) ) @ ( G @ X4 ) ) ) )
% 11.11/6.23              @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9933_DERIV__real__sqrt,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9934_DERIV__series_H,axiom,
% 11.11/6.23      ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 11.11/6.23        ( ! [N3: nat] :
% 11.11/6.23            ( has_fi5821293074295781190e_real
% 11.11/6.23            @ ^ [X: real] : ( F @ X @ N3 )
% 11.11/6.23            @ ( F4 @ X0 @ N3 )
% 11.11/6.23            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23             => ( summable_real @ ( F @ X5 ) ) )
% 11.11/6.23         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23           => ( ( summable_real @ ( F4 @ X0 ) )
% 11.11/6.23             => ( ( summable_real @ L5 )
% 11.11/6.23               => ( ! [N3: nat,X5: real,Y3: real] :
% 11.11/6.23                      ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23                     => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y3 ) ) ) ) ) )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real
% 11.11/6.23                    @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 11.11/6.23                    @ ( suminf_real @ ( F4 @ X0 ) )
% 11.11/6.23                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9935_DERIV__arctan,axiom,
% 11.11/6.23      ! [X4: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9936_DERIV__real__sqrt__generic,axiom,
% 11.11/6.23      ! [X4: real,D4: real] :
% 11.11/6.23        ( ( X4 != zero_zero_real )
% 11.11/6.23       => ( ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23           => ( D4
% 11.11/6.23              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.23         => ( ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.23             => ( D4
% 11.11/6.23                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 11.11/6.23           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9937_arsinh__real__has__field__derivative,axiom,
% 11.11/6.23      ! [X4: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9938_arcosh__real__has__field__derivative,axiom,
% 11.11/6.23      ! [X4: real,A2: set_real] :
% 11.11/6.23        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9939_artanh__real__has__field__derivative,axiom,
% 11.11/6.23      ! [X4: real,A2: set_real] :
% 11.11/6.23        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.23       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9940_DERIV__power__series_H,axiom,
% 11.11/6.23      ! [R: real,F: nat > real,X0: real] :
% 11.11/6.23        ( ! [X5: real] :
% 11.11/6.23            ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 11.11/6.23           => ( summable_real
% 11.11/6.23              @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X5 @ N ) ) ) )
% 11.11/6.23       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 11.11/6.23         => ( ( ord_less_real @ zero_zero_real @ R )
% 11.11/6.23           => ( has_fi5821293074295781190e_real
% 11.11/6.23              @ ^ [X: real] :
% 11.11/6.23                  ( suminf_real
% 11.11/6.23                  @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ ( suc @ N ) ) ) )
% 11.11/6.23              @ ( suminf_real
% 11.11/6.23                @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 11.11/6.23              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9941_DERIV__real__root,axiom,
% 11.11/6.23      ! [N2: nat,X4: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9942_DERIV__arccos,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9943_DERIV__arcsin,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9944_Maclaurin__all__le__objl,axiom,
% 11.11/6.23      ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 11.11/6.23        ( ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23            = F )
% 11.11/6.23          & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 11.11/6.23       => ? [T3: real] :
% 11.11/6.23            ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.23            & ( ( F @ X4 )
% 11.11/6.23              = ( plus_plus_real
% 11.11/6.23                @ ( groups6591440286371151544t_real
% 11.11/6.23                  @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.23                  @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9945_Maclaurin__all__le,axiom,
% 11.11/6.23      ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 11.11/6.23        ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23          = F )
% 11.11/6.23       => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23         => ? [T3: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.23              & ( ( F @ X4 )
% 11.11/6.23                = ( plus_plus_real
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9946_DERIV__odd__real__root,axiom,
% 11.11/6.23      ! [N2: nat,X4: real] :
% 11.11/6.23        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23       => ( ( X4 != zero_zero_real )
% 11.11/6.23         => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9947_Maclaurin__minus,axiom,
% 11.11/6.23      ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ H @ zero_zero_real )
% 11.11/6.23       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23         => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23              = F )
% 11.11/6.23           => ( ! [M5: nat,T3: real] :
% 11.11/6.23                  ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                    & ( ord_less_eq_real @ H @ T3 )
% 11.11/6.23                    & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23             => ? [T3: real] :
% 11.11/6.23                  ( ( ord_less_real @ H @ T3 )
% 11.11/6.23                  & ( ord_less_real @ T3 @ zero_zero_real )
% 11.11/6.23                  & ( ( F @ H )
% 11.11/6.23                    = ( plus_plus_real
% 11.11/6.23                      @ ( groups6591440286371151544t_real
% 11.11/6.23                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 11.11/6.23                        @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9948_Maclaurin2,axiom,
% 11.11/6.23      ! [H: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ H )
% 11.11/6.23       => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23            = F )
% 11.11/6.23         => ( ! [M5: nat,T3: real] :
% 11.11/6.23                ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                  & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.23                  & ( ord_less_eq_real @ T3 @ H ) )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23           => ? [T3: real] :
% 11.11/6.23                ( ( ord_less_real @ zero_zero_real @ T3 )
% 11.11/6.23                & ( ord_less_eq_real @ T3 @ H )
% 11.11/6.23                & ( ( F @ H )
% 11.11/6.23                  = ( plus_plus_real
% 11.11/6.23                    @ ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9949_Maclaurin,axiom,
% 11.11/6.23      ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ H )
% 11.11/6.23       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23         => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23              = F )
% 11.11/6.23           => ( ! [M5: nat,T3: real] :
% 11.11/6.23                  ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                    & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.23                    & ( ord_less_eq_real @ T3 @ H ) )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23             => ? [T3: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ T3 )
% 11.11/6.23                  & ( ord_less_real @ T3 @ H )
% 11.11/6.23                  & ( ( F @ H )
% 11.11/6.23                    = ( plus_plus_real
% 11.11/6.23                      @ ( groups6591440286371151544t_real
% 11.11/6.23                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 11.11/6.23                        @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9950_Maclaurin__all__lt,axiom,
% 11.11/6.23      ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 11.11/6.23        ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23          = F )
% 11.11/6.23       => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23         => ( ( X4 != zero_zero_real )
% 11.11/6.23           => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23             => ? [T3: real] :
% 11.11/6.23                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 11.11/6.23                  & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.23                  & ( ( F @ X4 )
% 11.11/6.23                    = ( plus_plus_real
% 11.11/6.23                      @ ( groups6591440286371151544t_real
% 11.11/6.23                        @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.23                        @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9951_Maclaurin__bi__le,axiom,
% 11.11/6.23      ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 11.11/6.23        ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23          = F )
% 11.11/6.23       => ( ! [M5: nat,T3: real] :
% 11.11/6.23              ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) ) )
% 11.11/6.23             => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23         => ? [T3: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 11.11/6.23              & ( ( F @ X4 )
% 11.11/6.23                = ( plus_plus_real
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9952_Taylor__down,axiom,
% 11.11/6.23      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23            = F )
% 11.11/6.23         => ( ! [M5: nat,T3: real] :
% 11.11/6.23                ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                  & ( ord_less_eq_real @ A @ T3 )
% 11.11/6.23                  & ( ord_less_eq_real @ T3 @ B ) )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23           => ( ( ord_less_real @ A @ C )
% 11.11/6.23             => ( ( ord_less_eq_real @ C @ B )
% 11.11/6.23               => ? [T3: real] :
% 11.11/6.23                    ( ( ord_less_real @ A @ T3 )
% 11.11/6.23                    & ( ord_less_real @ T3 @ C )
% 11.11/6.23                    & ( ( F @ A )
% 11.11/6.23                      = ( plus_plus_real
% 11.11/6.23                        @ ( groups6591440286371151544t_real
% 11.11/6.23                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 11.11/6.23                          @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9953_Taylor__up,axiom,
% 11.11/6.23      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23            = F )
% 11.11/6.23         => ( ! [M5: nat,T3: real] :
% 11.11/6.23                ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                  & ( ord_less_eq_real @ A @ T3 )
% 11.11/6.23                  & ( ord_less_eq_real @ T3 @ B ) )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23           => ( ( ord_less_eq_real @ A @ C )
% 11.11/6.23             => ( ( ord_less_real @ C @ B )
% 11.11/6.23               => ? [T3: real] :
% 11.11/6.23                    ( ( ord_less_real @ C @ T3 )
% 11.11/6.23                    & ( ord_less_real @ T3 @ B )
% 11.11/6.23                    & ( ( F @ B )
% 11.11/6.23                      = ( plus_plus_real
% 11.11/6.23                        @ ( groups6591440286371151544t_real
% 11.11/6.23                          @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 11.11/6.23                          @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9954_Taylor,axiom,
% 11.11/6.23      ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X4: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( ( Diff @ zero_zero_nat )
% 11.11/6.23            = F )
% 11.11/6.23         => ( ! [M5: nat,T3: real] :
% 11.11/6.23                ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23                  & ( ord_less_eq_real @ A @ T3 )
% 11.11/6.23                  & ( ord_less_eq_real @ T3 @ B ) )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23           => ( ( ord_less_eq_real @ A @ C )
% 11.11/6.23             => ( ( ord_less_eq_real @ C @ B )
% 11.11/6.23               => ( ( ord_less_eq_real @ A @ X4 )
% 11.11/6.23                 => ( ( ord_less_eq_real @ X4 @ B )
% 11.11/6.23                   => ( ( X4 != C )
% 11.11/6.23                     => ? [T3: real] :
% 11.11/6.23                          ( ( ( ord_less_real @ X4 @ C )
% 11.11/6.23                           => ( ( ord_less_real @ X4 @ T3 )
% 11.11/6.23                              & ( ord_less_real @ T3 @ C ) ) )
% 11.11/6.23                          & ( ~ ( ord_less_real @ X4 @ C )
% 11.11/6.23                           => ( ( ord_less_real @ C @ T3 )
% 11.11/6.23                              & ( ord_less_real @ T3 @ X4 ) ) )
% 11.11/6.23                          & ( ( F @ X4 )
% 11.11/6.23                            = ( plus_plus_real
% 11.11/6.23                              @ ( groups6591440286371151544t_real
% 11.11/6.23                                @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ M6 ) )
% 11.11/6.23                                @ ( set_ord_lessThan_nat @ N2 ) )
% 11.11/6.23                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9955_Maclaurin__lemma2,axiom,
% 11.11/6.23      ! [N2: nat,H: real,Diff: nat > real > real,K: nat,B3: real] :
% 11.11/6.23        ( ! [M5: nat,T3: real] :
% 11.11/6.23            ( ( ( ord_less_nat @ M5 @ N2 )
% 11.11/6.23              & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 11.11/6.23              & ( ord_less_eq_real @ T3 @ H ) )
% 11.11/6.23           => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 11.11/6.23       => ( ( N2
% 11.11/6.23            = ( suc @ K ) )
% 11.11/6.23         => ! [M2: nat,T4: real] :
% 11.11/6.23              ( ( ( ord_less_nat @ M2 @ N2 )
% 11.11/6.23                & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 11.11/6.23                & ( ord_less_eq_real @ T4 @ H ) )
% 11.11/6.23             => ( has_fi5821293074295781190e_real
% 11.11/6.23                @ ^ [U2: real] :
% 11.11/6.23                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 11.11/6.23                    @ ( plus_plus_real
% 11.11/6.23                      @ ( groups6591440286371151544t_real
% 11.11/6.23                        @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 11.11/6.23                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 11.11/6.23                      @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 11.11/6.23                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 11.11/6.23                  @ ( plus_plus_real
% 11.11/6.23                    @ ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T4 @ P5 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 11.11/6.23                    @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 11.11/6.23                @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9956_DERIV__arctan__series,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.23       => ( has_fi5821293074295781190e_real
% 11.11/6.23          @ ^ [X9: real] :
% 11.11/6.23              ( suminf_real
% 11.11/6.23              @ ^ [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 ) ) ) ) )
% 11.11/6.23          @ ( suminf_real
% 11.11/6.23            @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 11.11/6.23          @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9957_DERIV__real__root__generic,axiom,
% 11.11/6.23      ! [N2: nat,X4: real,D4: real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( X4 != zero_zero_real )
% 11.11/6.23         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23             => ( ( ord_less_real @ zero_zero_real @ X4 )
% 11.11/6.23               => ( D4
% 11.11/6.23                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 11.11/6.23           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23               => ( ( ord_less_real @ X4 @ zero_zero_real )
% 11.11/6.23                 => ( D4
% 11.11/6.23                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 11.11/6.23             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23                 => ( D4
% 11.11/6.23                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 11.11/6.23               => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9958_UNIV__char__of__nat,axiom,
% 11.11/6.23      ( top_top_set_char
% 11.11/6.23      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9959_nat__of__char__less__256,axiom,
% 11.11/6.23      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9960_range__nat__of__char,axiom,
% 11.11/6.23      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 11.11/6.23      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9961_integer__of__char__code,axiom,
% 11.11/6.23      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 11.11/6.23        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 11.11/6.23        = ( 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 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9962_String_Ochar__of__ascii__of,axiom,
% 11.11/6.23      ! [C: char] :
% 11.11/6.23        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 11.11/6.23        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9963_sorted__list__of__set__lessThan__Suc,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 11.11/6.23        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9964_sorted__list__of__set__atMost__Suc,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 11.11/6.23        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9965_sorted__list__of__set__greaterThanAtMost,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 11.11/6.23       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 11.11/6.23          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9966_sorted__list__of__set__greaterThanLessThan,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 11.11/6.23       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 11.11/6.23          = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9967_upto__aux__rec,axiom,
% 11.11/6.23      ( upto_aux
% 11.11/6.23      = ( ^ [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 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9968_upto_Opelims,axiom,
% 11.11/6.23      ! [X4: int,Xa: int,Y: list_int] :
% 11.11/6.23        ( ( ( upto @ X4 @ Xa )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 11.11/6.23         => ~ ( ( ( ( ord_less_eq_int @ X4 @ Xa )
% 11.11/6.23                 => ( Y
% 11.11/6.23                    = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 11.11/6.23                & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 11.11/6.23                 => ( Y = nil_int ) ) )
% 11.11/6.23             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9969_upto__Nil,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( ( upto @ I2 @ J )
% 11.11/6.23          = nil_int )
% 11.11/6.23        = ( ord_less_int @ J @ I2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9970_upto__Nil2,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( nil_int
% 11.11/6.23          = ( upto @ I2 @ J ) )
% 11.11/6.23        = ( ord_less_int @ J @ I2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9971_upto__empty,axiom,
% 11.11/6.23      ! [J: int,I2: int] :
% 11.11/6.23        ( ( ord_less_int @ J @ I2 )
% 11.11/6.23       => ( ( upto @ I2 @ J )
% 11.11/6.23          = nil_int ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9972_upto__single,axiom,
% 11.11/6.23      ! [I2: int] :
% 11.11/6.23        ( ( upto @ I2 @ I2 )
% 11.11/6.23        = ( cons_int @ I2 @ nil_int ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9973_nth__upto,axiom,
% 11.11/6.23      ! [I2: int,K: nat,J: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 11.11/6.23       => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 11.11/6.23          = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9974_length__upto,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 11.11/6.23        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9975_upto__rec__numeral_I1_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23            = nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9976_upto__rec__numeral_I2_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23            = nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9977_upto__rec__numeral_I3_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23            = ( 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 @ N2 ) ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 11.11/6.23            = nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9978_upto__rec__numeral_I4_J,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23            = ( 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 @ N2 ) ) ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 11.11/6.23            = nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9979_upto__aux__def,axiom,
% 11.11/6.23      ( upto_aux
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( append_int @ ( upto @ I3 @ J3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9980_sup__enat__def,axiom,
% 11.11/6.23      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9981_sup__nat__def,axiom,
% 11.11/6.23      sup_sup_nat = ord_max_nat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9982_upto__code,axiom,
% 11.11/6.23      ( upto
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( upto_aux @ I3 @ J3 @ nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9983_atLeastAtMost__upto,axiom,
% 11.11/6.23      ( set_or1266510415728281911st_int
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9984_distinct__upto,axiom,
% 11.11/6.23      ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9985_atLeastLessThan__add__Un,axiom,
% 11.11/6.23      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.23       => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 11.11/6.23          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9986_upto__split2,axiom,
% 11.11/6.23      ! [I2: int,J: int,K: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23       => ( ( ord_less_eq_int @ J @ K )
% 11.11/6.23         => ( ( upto @ I2 @ K )
% 11.11/6.23            = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9987_upto__split1,axiom,
% 11.11/6.23      ! [I2: int,J: int,K: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23       => ( ( ord_less_eq_int @ J @ K )
% 11.11/6.23         => ( ( upto @ I2 @ K )
% 11.11/6.23            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9988_atLeastLessThan__upto,axiom,
% 11.11/6.23      ( set_or4662586982721622107an_int
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9989_greaterThanAtMost__upto,axiom,
% 11.11/6.23      ( set_or6656581121297822940st_int
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9990_upto_Osimps,axiom,
% 11.11/6.23      ( upto
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9991_upto_Oelims,axiom,
% 11.11/6.23      ! [X4: int,Xa: int,Y: list_int] :
% 11.11/6.23        ( ( ( upto @ X4 @ Xa )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( ( ord_less_eq_int @ X4 @ Xa )
% 11.11/6.23           => ( Y
% 11.11/6.23              = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 11.11/6.23          & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 11.11/6.23           => ( Y = nil_int ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9992_upto__rec1,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23       => ( ( upto @ I2 @ J )
% 11.11/6.23          = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9993_upto__rec2,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23       => ( ( upto @ I2 @ J )
% 11.11/6.23          = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9994_greaterThanLessThan__upto,axiom,
% 11.11/6.23      ( set_or5832277885323065728an_int
% 11.11/6.23      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9995_upto__split3,axiom,
% 11.11/6.23      ! [I2: int,J: int,K: int] :
% 11.11/6.23        ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23       => ( ( ord_less_eq_int @ J @ K )
% 11.11/6.23         => ( ( upto @ I2 @ K )
% 11.11/6.23            = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9996_upto_Opsimps,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 11.11/6.23       => ( ( ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23           => ( ( upto @ I2 @ J )
% 11.11/6.23              = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 11.11/6.23          & ( ~ ( ord_less_eq_int @ I2 @ J )
% 11.11/6.23           => ( ( upto @ I2 @ J )
% 11.11/6.23              = nil_int ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9997_LIM__fun__gt__zero,axiom,
% 11.11/6.23      ! [F: real > real,L: real,C: real] :
% 11.11/6.23        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ zero_zero_real @ L )
% 11.11/6.23         => ? [R2: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ R2 )
% 11.11/6.23              & ! [X2: real] :
% 11.11/6.23                  ( ( ( X2 != C )
% 11.11/6.23                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 11.11/6.23                 => ( ord_less_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9998_LIM__fun__not__zero,axiom,
% 11.11/6.23      ! [F: real > real,L: real,C: real] :
% 11.11/6.23        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 11.11/6.23       => ( ( L != zero_zero_real )
% 11.11/6.23         => ? [R2: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ R2 )
% 11.11/6.23              & ! [X2: real] :
% 11.11/6.23                  ( ( ( X2 != C )
% 11.11/6.23                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 11.11/6.23                 => ( ( F @ X2 )
% 11.11/6.23                   != zero_zero_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_9999_LIM__fun__less__zero,axiom,
% 11.11/6.23      ! [F: real > real,L: real,C: real] :
% 11.11/6.23        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 11.11/6.23       => ( ( ord_less_real @ L @ zero_zero_real )
% 11.11/6.23         => ? [R2: real] :
% 11.11/6.23              ( ( ord_less_real @ zero_zero_real @ R2 )
% 11.11/6.23              & ! [X2: real] :
% 11.11/6.23                  ( ( ( X2 != C )
% 11.11/6.23                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 11.11/6.23                 => ( ord_less_real @ ( F @ X2 ) @ zero_zero_real ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10000_LIM__cos__div__sin,axiom,
% 11.11/6.23      ( filterlim_real_real
% 11.11/6.23      @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 11.11/6.23      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10001_summable__Leibniz_I3_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ( topolo6980174941875973593q_real @ A )
% 11.11/6.23         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 11.11/6.23           => ! [N6: nat] :
% 11.11/6.23                ( member_real
% 11.11/6.23                @ ( suminf_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 11.11/6.23                @ ( set_or1222579329274155063t_real
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10002_summable__Leibniz_I2_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ( topolo6980174941875973593q_real @ A )
% 11.11/6.23         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 11.11/6.23           => ! [N6: nat] :
% 11.11/6.23                ( member_real
% 11.11/6.23                @ ( suminf_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 11.11/6.23                @ ( set_or1222579329274155063t_real
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 11.11/6.23                  @ ( groups6591440286371151544t_real
% 11.11/6.23                    @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10003_filterlim__Suc,axiom,
% 11.11/6.23      filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10004_mult__nat__left__at__top,axiom,
% 11.11/6.23      ! [C: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.23       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10005_mult__nat__right__at__top,axiom,
% 11.11/6.23      ! [C: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ C )
% 11.11/6.23       => ( filterlim_nat_nat
% 11.11/6.23          @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 11.11/6.23          @ at_top_nat
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10006_monoseq__convergent,axiom,
% 11.11/6.23      ! [X8: nat > real,B3: real] :
% 11.11/6.23        ( ( topolo6980174941875973593q_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 11.11/6.23         => ~ ! [L6: real] :
% 11.11/6.23                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10007_LIMSEQ__root,axiom,
% 11.11/6.23      ( filterlim_nat_real
% 11.11/6.23      @ ^ [N: nat] : ( root @ N @ ( semiri5074537144036343181t_real @ N ) )
% 11.11/6.23      @ ( topolo2815343760600316023s_real @ one_one_real )
% 11.11/6.23      @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10008_nested__sequence__unique,axiom,
% 11.11/6.23      ! [F: nat > real,G: nat > real] :
% 11.11/6.23        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 11.11/6.23           => ( ( filterlim_nat_real
% 11.11/6.23                @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 11.11/6.23                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23                @ at_top_nat )
% 11.11/6.23             => ? [L4: real] :
% 11.11/6.23                  ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L4 )
% 11.11/6.23                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 11.11/6.23                  & ! [N6: nat] : ( ord_less_eq_real @ L4 @ ( G @ N6 ) )
% 11.11/6.23                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10009_LIMSEQ__inverse__zero,axiom,
% 11.11/6.23      ! [X8: nat > real] :
% 11.11/6.23        ( ! [R2: real] :
% 11.11/6.23          ? [N7: nat] :
% 11.11/6.23          ! [N3: nat] :
% 11.11/6.23            ( ( ord_less_eq_nat @ N7 @ N3 )
% 11.11/6.23           => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 11.11/6.23       => ( filterlim_nat_real
% 11.11/6.23          @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10010_lim__inverse__n_H,axiom,
% 11.11/6.23      ( filterlim_nat_real
% 11.11/6.23      @ ^ [N: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 11.11/6.23      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23      @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10011_LIMSEQ__root__const,axiom,
% 11.11/6.23      ! [C: real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ C )
% 11.11/6.23       => ( filterlim_nat_real
% 11.11/6.23          @ ^ [N: nat] : ( root @ N @ C )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ one_one_real )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10012_LIMSEQ__inverse__real__of__nat,axiom,
% 11.11/6.23      ( filterlim_nat_real
% 11.11/6.23      @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 11.11/6.23      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23      @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10013_LIMSEQ__inverse__real__of__nat__add,axiom,
% 11.11/6.23      ! [R3: real] :
% 11.11/6.23        ( filterlim_nat_real
% 11.11/6.23        @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ R3 )
% 11.11/6.23        @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10014_increasing__LIMSEQ,axiom,
% 11.11/6.23      ! [F: nat > real,L: real] :
% 11.11/6.23        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 11.11/6.23         => ( ! [E: real] :
% 11.11/6.23                ( ( ord_less_real @ zero_zero_real @ E )
% 11.11/6.23               => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 11.11/6.23           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10015_LIMSEQ__realpow__zero,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( filterlim_nat_real @ ( power_power_real @ X4 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10016_LIMSEQ__divide__realpow__zero,axiom,
% 11.11/6.23      ! [X4: real,A: real] :
% 11.11/6.23        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.23       => ( filterlim_nat_real
% 11.11/6.23          @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X4 @ N ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10017_LIMSEQ__abs__realpow__zero2,axiom,
% 11.11/6.23      ! [C: real] :
% 11.11/6.23        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 11.11/6.23       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10018_LIMSEQ__abs__realpow__zero,axiom,
% 11.11/6.23      ! [C: real] :
% 11.11/6.23        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 11.11/6.23       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10019_LIMSEQ__inverse__realpow__zero,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.23       => ( filterlim_nat_real
% 11.11/6.23          @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X4 @ N ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10020_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 11.11/6.23      ! [R3: real] :
% 11.11/6.23        ( filterlim_nat_real
% 11.11/6.23        @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ R3 )
% 11.11/6.23        @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10021_tendsto__exp__limit__sequentially,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( filterlim_nat_real
% 11.11/6.23        @ ^ [N: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 11.11/6.23        @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10022_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 11.11/6.23      ! [R3: real] :
% 11.11/6.23        ( filterlim_nat_real
% 11.11/6.23        @ ^ [N: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ R3 )
% 11.11/6.23        @ at_top_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10023_summable__Leibniz_I1_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ( topolo6980174941875973593q_real @ A )
% 11.11/6.23         => ( summable_real
% 11.11/6.23            @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10024_summable,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23           => ( summable_real
% 11.11/6.23              @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10025_cos__diff__limit__1,axiom,
% 11.11/6.23      ! [Theta: nat > real,Theta2: real] :
% 11.11/6.23        ( ( filterlim_nat_real
% 11.11/6.23          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ one_one_real )
% 11.11/6.23          @ at_top_nat )
% 11.11/6.23       => ~ ! [K2: nat > int] :
% 11.11/6.23              ~ ( filterlim_nat_real
% 11.11/6.23                @ ^ [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 ) ) )
% 11.11/6.23                @ ( topolo2815343760600316023s_real @ Theta2 )
% 11.11/6.23                @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10026_cos__limit__1,axiom,
% 11.11/6.23      ! [Theta: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real
% 11.11/6.23          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ one_one_real )
% 11.11/6.23          @ at_top_nat )
% 11.11/6.23       => ? [K2: nat > int] :
% 11.11/6.23            ( filterlim_nat_real
% 11.11/6.23            @ ^ [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 ) ) )
% 11.11/6.23            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23            @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10027_summable__Leibniz_I4_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ( topolo6980174941875973593q_real @ A )
% 11.11/6.23         => ( filterlim_nat_real
% 11.11/6.23            @ ^ [N: nat] :
% 11.11/6.23                ( groups6591440286371151544t_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.23            @ ( topolo2815343760600316023s_real
% 11.11/6.23              @ ( suminf_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 11.11/6.23            @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10028_zeroseq__arctan__series,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 11.11/6.23       => ( filterlim_nat_real
% 11.11/6.23          @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 11.11/6.23          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10029_summable__Leibniz_H_I2_J,axiom,
% 11.11/6.23      ! [A: nat > real,N2: nat] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23           => ( ord_less_eq_real
% 11.11/6.23              @ ( groups6591440286371151544t_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 11.11/6.23              @ ( suminf_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10030_summable__Leibniz_H_I3_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23           => ( filterlim_nat_real
% 11.11/6.23              @ ^ [N: nat] :
% 11.11/6.23                  ( groups6591440286371151544t_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.23              @ ( topolo2815343760600316023s_real
% 11.11/6.23                @ ( suminf_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 11.11/6.23              @ at_top_nat ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10031_sums__alternating__upper__lower,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23           => ? [L4: real] :
% 11.11/6.23                ( ! [N6: nat] :
% 11.11/6.23                    ( ord_less_eq_real
% 11.11/6.23                    @ ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 11.11/6.23                    @ L4 )
% 11.11/6.23                & ( filterlim_nat_real
% 11.11/6.23                  @ ^ [N: nat] :
% 11.11/6.23                      ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 11.11/6.23                  @ ( topolo2815343760600316023s_real @ L4 )
% 11.11/6.23                  @ at_top_nat )
% 11.11/6.23                & ! [N6: nat] :
% 11.11/6.23                    ( ord_less_eq_real @ L4
% 11.11/6.23                    @ ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 11.11/6.23                & ( filterlim_nat_real
% 11.11/6.23                  @ ^ [N: nat] :
% 11.11/6.23                      ( groups6591440286371151544t_real
% 11.11/6.23                      @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 11.11/6.23                  @ ( topolo2815343760600316023s_real @ L4 )
% 11.11/6.23                  @ at_top_nat ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10032_summable__Leibniz_I5_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ( topolo6980174941875973593q_real @ A )
% 11.11/6.23         => ( filterlim_nat_real
% 11.11/6.23            @ ^ [N: nat] :
% 11.11/6.23                ( groups6591440286371151544t_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 11.11/6.23            @ ( topolo2815343760600316023s_real
% 11.11/6.23              @ ( suminf_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 11.11/6.23            @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10033_summable__Leibniz_H_I5_J,axiom,
% 11.11/6.23      ! [A: nat > real] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23           => ( filterlim_nat_real
% 11.11/6.23              @ ^ [N: nat] :
% 11.11/6.23                  ( groups6591440286371151544t_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 11.11/6.23              @ ( topolo2815343760600316023s_real
% 11.11/6.23                @ ( suminf_real
% 11.11/6.23                  @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 11.11/6.23              @ at_top_nat ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10034_summable__Leibniz_H_I4_J,axiom,
% 11.11/6.23      ! [A: nat > real,N2: nat] :
% 11.11/6.23        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 11.11/6.23       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 11.11/6.23         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 11.11/6.23           => ( ord_less_eq_real
% 11.11/6.23              @ ( suminf_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 11.11/6.23              @ ( groups6591440286371151544t_real
% 11.11/6.23                @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 11.11/6.23                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10035_eventually__sequentially__Suc,axiom,
% 11.11/6.23      ! [P: nat > $o] :
% 11.11/6.23        ( ( eventually_nat
% 11.11/6.23          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 11.11/6.23          @ at_top_nat )
% 11.11/6.23        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10036_eventually__sequentially__seg,axiom,
% 11.11/6.23      ! [P: nat > $o,K: nat] :
% 11.11/6.23        ( ( eventually_nat
% 11.11/6.23          @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 11.11/6.23          @ at_top_nat )
% 11.11/6.23        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10037_le__sequentially,axiom,
% 11.11/6.23      ! [F5: filter_nat] :
% 11.11/6.23        ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 11.11/6.23        = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F5 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10038_eventually__sequentially,axiom,
% 11.11/6.23      ! [P: nat > $o] :
% 11.11/6.23        ( ( eventually_nat @ P @ at_top_nat )
% 11.11/6.23        = ( ? [N9: nat] :
% 11.11/6.23            ! [N: nat] :
% 11.11/6.23              ( ( ord_less_eq_nat @ N9 @ N )
% 11.11/6.23             => ( P @ N ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10039_eventually__sequentiallyI,axiom,
% 11.11/6.23      ! [C: nat,P: nat > $o] :
% 11.11/6.23        ( ! [X5: nat] :
% 11.11/6.23            ( ( ord_less_eq_nat @ C @ X5 )
% 11.11/6.23           => ( P @ X5 ) )
% 11.11/6.23       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10040_sequentially__offset,axiom,
% 11.11/6.23      ! [P: nat > $o,K: nat] :
% 11.11/6.23        ( ( eventually_nat @ P @ at_top_nat )
% 11.11/6.23       => ( eventually_nat
% 11.11/6.23          @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 11.11/6.23          @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10041_eventually__at__left__real,axiom,
% 11.11/6.23      ! [B: real,A: real] :
% 11.11/6.23        ( ( ord_less_real @ B @ A )
% 11.11/6.23       => ( eventually_real
% 11.11/6.23          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 11.11/6.23          @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10042_tanh__real__at__top,axiom,
% 11.11/6.23      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10043_artanh__real__at__left__1,axiom,
% 11.11/6.23      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10044_tendsto__power__div__exp__0,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( filterlim_real_real
% 11.11/6.23        @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 11.11/6.23        @ at_top_real ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10045_tendsto__exp__limit__at__top,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( filterlim_real_real
% 11.11/6.23        @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ Y5 ) ) @ Y5 )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 11.11/6.23        @ at_top_real ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10046_filterlim__tan__at__left,axiom,
% 11.11/6.23      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 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10047_DERIV__neg__imp__decreasing__at__top,axiom,
% 11.11/6.23      ! [B: real,F: real > real,Flim: real] :
% 11.11/6.23        ( ! [X5: real] :
% 11.11/6.23            ( ( ord_less_eq_real @ B @ X5 )
% 11.11/6.23           => ? [Y4: real] :
% 11.11/6.23                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 11.11/6.23       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 11.11/6.23         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10048_tendsto__arctan__at__top,axiom,
% 11.11/6.23      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10049_at__top__le__at__infinity,axiom,
% 11.11/6.23      ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10050_Bseq__eq__bounded,axiom,
% 11.11/6.23      ! [F: nat > real,A: real,B: real] :
% 11.11/6.23        ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 11.11/6.23       => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10051_Bseq__realpow,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 11.11/6.23       => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 11.11/6.23         => ( bfun_nat_real @ ( power_power_real @ X4 ) @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10052_filterlim__pow__at__bot__even,axiom,
% 11.11/6.23      ! [N2: nat,F: real > real,F5: filter_real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 11.11/6.23         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23           => ( filterlim_real_real
% 11.11/6.23              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 11.11/6.23              @ at_top_real
% 11.11/6.23              @ F5 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10053_at__bot__le__at__infinity,axiom,
% 11.11/6.23      ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10054_tanh__real__at__bot,axiom,
% 11.11/6.23      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10055_DERIV__pos__imp__increasing__at__bot,axiom,
% 11.11/6.23      ! [B: real,F: real > real,Flim: real] :
% 11.11/6.23        ( ! [X5: real] :
% 11.11/6.23            ( ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23           => ? [Y4: real] :
% 11.11/6.23                ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 11.11/6.23       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 11.11/6.23         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10056_filterlim__pow__at__bot__odd,axiom,
% 11.11/6.23      ! [N2: nat,F: real > real,F5: filter_real] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 11.11/6.23         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 11.11/6.23           => ( filterlim_real_real
% 11.11/6.23              @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 11.11/6.23              @ at_bot_real
% 11.11/6.23              @ F5 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10057_tendsto__arctan__at__bot,axiom,
% 11.11/6.23      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10058_tendsto__exp__limit__at__right,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( filterlim_real_real
% 11.11/6.23        @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X4 @ Y5 ) ) @ ( divide_divide_real @ one_one_real @ Y5 ) )
% 11.11/6.23        @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 11.11/6.23        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10059_filterlim__tan__at__right,axiom,
% 11.11/6.23      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 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10060_eventually__at__right__real,axiom,
% 11.11/6.23      ! [A: real,B: real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( eventually_real
% 11.11/6.23          @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 11.11/6.23          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10061_tendsto__arcosh__at__left__1,axiom,
% 11.11/6.23      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10062_artanh__real__at__right__1,axiom,
% 11.11/6.23      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 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10063_atLeast__0,axiom,
% 11.11/6.23      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 11.11/6.23      = top_top_set_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10064_atLeast__Suc__greaterThan,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 11.11/6.23        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10065_decseq__bounded,axiom,
% 11.11/6.23      ! [X8: nat > real,B3: real] :
% 11.11/6.23        ( ( order_9091379641038594480t_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 11.11/6.23         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10066_INT__greaterThan__UNIV,axiom,
% 11.11/6.23      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 11.11/6.23      = bot_bot_set_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10067_greaterThan__0,axiom,
% 11.11/6.23      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 11.11/6.23      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10068_greaterThan__Suc,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 11.11/6.23        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10069_decseq__convergent,axiom,
% 11.11/6.23      ! [X8: nat > real,B3: real] :
% 11.11/6.23        ( ( order_9091379641038594480t_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 11.11/6.23         => ~ ! [L6: real] :
% 11.11/6.23                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 11.11/6.23               => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10070_UN__atLeast__UNIV,axiom,
% 11.11/6.23      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 11.11/6.23      = top_top_set_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10071_atLeast__Suc,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 11.11/6.23        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10072_isCont__Lb__Ub,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23                & ( ord_less_eq_real @ X5 @ B ) )
% 11.11/6.23             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 11.11/6.23         => ? [L6: real,M9: real] :
% 11.11/6.23              ( ! [X2: real] :
% 11.11/6.23                  ( ( ( ord_less_eq_real @ A @ X2 )
% 11.11/6.23                    & ( ord_less_eq_real @ X2 @ B ) )
% 11.11/6.23                 => ( ( ord_less_eq_real @ L6 @ ( F @ X2 ) )
% 11.11/6.23                    & ( ord_less_eq_real @ ( F @ X2 ) @ M9 ) ) )
% 11.11/6.23              & ! [Y4: real] :
% 11.11/6.23                  ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 11.11/6.23                    & ( ord_less_eq_real @ Y4 @ M9 ) )
% 11.11/6.23                 => ? [X5: real] :
% 11.11/6.23                      ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23                      & ( ord_less_eq_real @ X5 @ B )
% 11.11/6.23                      & ( ( F @ X5 )
% 11.11/6.23                        = Y4 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10073_less__eq,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 11.11/6.23        = ( ord_less_nat @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10074_isCont__inverse__function2,axiom,
% 11.11/6.23      ! [A: real,X4: real,B: real,G: real > real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ B )
% 11.11/6.23         => ( ! [Z2: real] :
% 11.11/6.23                ( ( ord_less_eq_real @ A @ Z2 )
% 11.11/6.23               => ( ( ord_less_eq_real @ Z2 @ B )
% 11.11/6.23                 => ( ( G @ ( F @ Z2 ) )
% 11.11/6.23                    = Z2 ) ) )
% 11.11/6.23           => ( ! [Z2: real] :
% 11.11/6.23                  ( ( ord_less_eq_real @ A @ Z2 )
% 11.11/6.23                 => ( ( ord_less_eq_real @ Z2 @ B )
% 11.11/6.23                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 11.11/6.23             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10075_isCont__arcosh,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ one_one_real @ X4 )
% 11.11/6.23       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcosh_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10076_DERIV__inverse__function,axiom,
% 11.11/6.23      ! [F: real > real,D4: real,G: real > real,X4: real,A: real,B: real] :
% 11.11/6.23        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X4 ) @ top_top_set_real ) )
% 11.11/6.23       => ( ( D4 != zero_zero_real )
% 11.11/6.23         => ( ( ord_less_real @ A @ X4 )
% 11.11/6.23           => ( ( ord_less_real @ X4 @ B )
% 11.11/6.23             => ( ! [Y3: real] :
% 11.11/6.23                    ( ( ord_less_real @ A @ Y3 )
% 11.11/6.23                   => ( ( ord_less_real @ Y3 @ B )
% 11.11/6.23                     => ( ( F @ ( G @ Y3 ) )
% 11.11/6.23                        = Y3 ) ) )
% 11.11/6.23               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10077_isCont__arccos,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arccos ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10078_isCont__arcsin,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcsin ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10079_LIM__less__bound,axiom,
% 11.11/6.23      ! [B: real,X4: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ B @ X4 )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X4 ) )
% 11.11/6.23             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 11.11/6.23         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F )
% 11.11/6.23           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10080_isCont__artanh,axiom,
% 11.11/6.23      ! [X4: real] :
% 11.11/6.23        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 11.11/6.23       => ( ( ord_less_real @ X4 @ one_one_real )
% 11.11/6.23         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10081_isCont__inverse__function,axiom,
% 11.11/6.23      ! [D: real,X4: real,G: real > real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ zero_zero_real @ D )
% 11.11/6.23       => ( ! [Z2: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 11.11/6.23             => ( ( G @ ( F @ Z2 ) )
% 11.11/6.23                = Z2 ) )
% 11.11/6.23         => ( ! [Z2: real] :
% 11.11/6.23                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 11.11/6.23               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 11.11/6.23           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10082_GMVT_H,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [Z2: real] :
% 11.11/6.23              ( ( ord_less_eq_real @ A @ Z2 )
% 11.11/6.23             => ( ( ord_less_eq_real @ Z2 @ B )
% 11.11/6.23               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 11.11/6.23         => ( ! [Z2: real] :
% 11.11/6.23                ( ( ord_less_eq_real @ A @ Z2 )
% 11.11/6.23               => ( ( ord_less_eq_real @ Z2 @ B )
% 11.11/6.23                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 11.11/6.23           => ( ! [Z2: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23                 => ( ( ord_less_real @ Z2 @ B )
% 11.11/6.23                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 11.11/6.23             => ( ! [Z2: real] :
% 11.11/6.23                    ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23                   => ( ( ord_less_real @ Z2 @ B )
% 11.11/6.23                     => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 11.11/6.23               => ? [C3: real] :
% 11.11/6.23                    ( ( ord_less_real @ A @ C3 )
% 11.11/6.23                    & ( ord_less_real @ C3 @ B )
% 11.11/6.23                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 11.11/6.23                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10083_GMVT,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,G: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23                & ( ord_less_eq_real @ X5 @ B ) )
% 11.11/6.23             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 11.11/6.23         => ( ! [X5: real] :
% 11.11/6.23                ( ( ( ord_less_real @ A @ X5 )
% 11.11/6.23                  & ( ord_less_real @ X5 @ B ) )
% 11.11/6.23               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 11.11/6.23           => ( ! [X5: real] :
% 11.11/6.23                  ( ( ( ord_less_eq_real @ A @ X5 )
% 11.11/6.23                    & ( ord_less_eq_real @ X5 @ B ) )
% 11.11/6.23                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 11.11/6.23             => ( ! [X5: real] :
% 11.11/6.23                    ( ( ( ord_less_real @ A @ X5 )
% 11.11/6.23                      & ( ord_less_real @ X5 @ B ) )
% 11.11/6.23                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 11.11/6.23               => ? [G_c: real,F_c: real,C3: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 11.11/6.23                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_real @ A @ C3 )
% 11.11/6.23                    & ( ord_less_real @ C3 @ B )
% 11.11/6.23                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 11.11/6.23                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10084_MVT,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23         => ( ! [X5: real] :
% 11.11/6.23                ( ( ord_less_real @ A @ X5 )
% 11.11/6.23               => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23           => ? [L4: real,Z2: real] :
% 11.11/6.23                ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23                & ( ord_less_real @ Z2 @ B )
% 11.11/6.23                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 11.11/6.23                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 11.11/6.23                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10085_continuous__on__arcosh_H,axiom,
% 11.11/6.23      ! [A2: set_real,F: real > real] :
% 11.11/6.23        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( member_real @ X5 @ A2 )
% 11.11/6.23             => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 11.11/6.23         => ( topolo5044208981011980120l_real @ A2
% 11.11/6.23            @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10086_continuous__image__closed__interval,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_eq_real @ A @ B )
% 11.11/6.23       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23         => ? [C3: real,D3: real] :
% 11.11/6.23              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 11.11/6.23                = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 11.11/6.23              & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10087_continuous__on__arcosh,axiom,
% 11.11/6.23      ! [A2: set_real] :
% 11.11/6.23        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 11.11/6.23       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10088_continuous__on__arccos_H,axiom,
% 11.11/6.23      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10089_continuous__on__arcsin_H,axiom,
% 11.11/6.23      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10090_continuous__on__artanh_H,axiom,
% 11.11/6.23      ! [A2: set_real,F: real > real] :
% 11.11/6.23        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( member_real @ X5 @ A2 )
% 11.11/6.23             => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 11.11/6.23         => ( topolo5044208981011980120l_real @ A2
% 11.11/6.23            @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10091_Rolle__deriv,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( ( F @ A )
% 11.11/6.23            = ( F @ B ) )
% 11.11/6.23         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23           => ( ! [X5: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ X5 )
% 11.11/6.23                 => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                   => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23             => ? [Z2: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23                  & ( ord_less_real @ Z2 @ B )
% 11.11/6.23                  & ( ( F4 @ Z2 )
% 11.11/6.23                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10092_mvt,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23         => ( ! [X5: real] :
% 11.11/6.23                ( ( ord_less_real @ A @ X5 )
% 11.11/6.23               => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23           => ~ ! [Xi: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ Xi )
% 11.11/6.23                 => ( ( ord_less_real @ Xi @ B )
% 11.11/6.23                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 11.11/6.23                     != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10093_DERIV__pos__imp__increasing__open,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 11.11/6.23         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10094_DERIV__neg__imp__decreasing__open,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ! [X5: real] :
% 11.11/6.23              ( ( ord_less_real @ A @ X5 )
% 11.11/6.23             => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23               => ? [Y4: real] :
% 11.11/6.23                    ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23                    & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 11.11/6.23         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10095_DERIV__isconst__end,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23         => ( ! [X5: real] :
% 11.11/6.23                ( ( ord_less_real @ A @ X5 )
% 11.11/6.23               => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23           => ( ( F @ B )
% 11.11/6.23              = ( F @ A ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10096_continuous__on__artanh,axiom,
% 11.11/6.23      ! [A2: set_real] :
% 11.11/6.23        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 11.11/6.23       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10097_DERIV__isconst2,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real,X4: real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23         => ( ! [X5: real] :
% 11.11/6.23                ( ( ord_less_real @ A @ X5 )
% 11.11/6.23               => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23           => ( ( ord_less_eq_real @ A @ X4 )
% 11.11/6.23             => ( ( ord_less_eq_real @ X4 @ B )
% 11.11/6.23               => ( ( F @ X4 )
% 11.11/6.23                  = ( F @ A ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10098_Rolle,axiom,
% 11.11/6.23      ! [A: real,B: real,F: real > real] :
% 11.11/6.23        ( ( ord_less_real @ A @ B )
% 11.11/6.23       => ( ( ( F @ A )
% 11.11/6.23            = ( F @ B ) )
% 11.11/6.23         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 11.11/6.23           => ( ! [X5: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ X5 )
% 11.11/6.23                 => ( ( ord_less_real @ X5 @ B )
% 11.11/6.23                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 11.11/6.23             => ? [Z2: real] :
% 11.11/6.23                  ( ( ord_less_real @ A @ Z2 )
% 11.11/6.23                  & ( ord_less_real @ Z2 @ B )
% 11.11/6.23                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10099_mono__Suc,axiom,
% 11.11/6.23      order_mono_nat_nat @ suc ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10100_mono__times__nat,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10101_incseq__bounded,axiom,
% 11.11/6.23      ! [X8: nat > real,B3: real] :
% 11.11/6.23        ( ( order_mono_nat_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 11.11/6.23         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10102_incseq__convergent,axiom,
% 11.11/6.23      ! [X8: nat > real,B3: real] :
% 11.11/6.23        ( ( order_mono_nat_real @ X8 )
% 11.11/6.23       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 11.11/6.23         => ~ ! [L6: real] :
% 11.11/6.23                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 11.11/6.23               => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10103_mono__ge2__power__minus__self,axiom,
% 11.11/6.23      ! [K: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 11.11/6.23       => ( order_mono_nat_nat
% 11.11/6.23          @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10104_nonneg__incseq__Bseq__subseq__iff,axiom,
% 11.11/6.23      ! [F: nat > real,G: nat > nat] :
% 11.11/6.23        ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 11.11/6.23       => ( ( order_mono_nat_real @ F )
% 11.11/6.23         => ( ( order_5726023648592871131at_nat @ G )
% 11.11/6.23           => ( ( bfun_nat_real
% 11.11/6.23                @ ^ [X: nat] : ( F @ ( G @ X ) )
% 11.11/6.23                @ at_top_nat )
% 11.11/6.23              = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10105_strict__mono__imp__increasing,axiom,
% 11.11/6.23      ! [F: nat > nat,N2: nat] :
% 11.11/6.23        ( ( order_5726023648592871131at_nat @ F )
% 11.11/6.23       => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10106_inj__sgn__power,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( inj_on_real_real
% 11.11/6.23          @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 11.11/6.23          @ top_top_set_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10107_log__inj,axiom,
% 11.11/6.23      ! [B: real] :
% 11.11/6.23        ( ( ord_less_real @ one_one_real @ B )
% 11.11/6.23       => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10108_pos__deriv__imp__strict__mono,axiom,
% 11.11/6.23      ! [F: real > real,F4: real > real] :
% 11.11/6.23        ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 11.11/6.23       => ( ! [X5: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X5 ) )
% 11.11/6.23         => ( order_7092887310737990675l_real @ F ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10109_inj__on__diff__nat,axiom,
% 11.11/6.23      ! [N4: set_nat,K: nat] :
% 11.11/6.23        ( ! [N3: nat] :
% 11.11/6.23            ( ( member_nat @ N3 @ N4 )
% 11.11/6.23           => ( ord_less_eq_nat @ K @ N3 ) )
% 11.11/6.23       => ( inj_on_nat_nat
% 11.11/6.23          @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 11.11/6.23          @ N4 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10110_inj__Suc,axiom,
% 11.11/6.23      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10111_inj__on__char__of__nat,axiom,
% 11.11/6.23      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10112_suminf__reindex,axiom,
% 11.11/6.23      ! [F: nat > real,G: nat > nat] :
% 11.11/6.23        ( ( summable_real @ F )
% 11.11/6.23       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 11.11/6.23         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 11.11/6.23           => ( ! [X5: nat] :
% 11.11/6.23                  ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 11.11/6.23                 => ( ( F @ X5 )
% 11.11/6.23                    = zero_zero_real ) )
% 11.11/6.23             => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 11.11/6.23                = ( suminf_real @ F ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10113_summable__reindex,axiom,
% 11.11/6.23      ! [F: nat > real,G: nat > nat] :
% 11.11/6.23        ( ( summable_real @ F )
% 11.11/6.23       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 11.11/6.23         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 11.11/6.23           => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10114_suminf__reindex__mono,axiom,
% 11.11/6.23      ! [F: nat > real,G: nat > nat] :
% 11.11/6.23        ( ( summable_real @ F )
% 11.11/6.23       => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 11.11/6.23         => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 11.11/6.23           => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10115_card_Ocomp__fun__commute__on,axiom,
% 11.11/6.23      ( ( comp_nat_nat_nat @ suc @ suc )
% 11.11/6.23      = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10116_pred__nat__trancl__eq__le,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 11.11/6.23        = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10117_uniformity__real__def,axiom,
% 11.11/6.23      ( topolo1511823702728130853y_real
% 11.11/6.23      = ( comple2936214249959783750l_real
% 11.11/6.23        @ ( image_2178119161166701260l_real
% 11.11/6.23          @ ^ [E3: real] :
% 11.11/6.23              ( princi6114159922880469582l_real
% 11.11/6.23              @ ( collec3799799289383736868l_real
% 11.11/6.23                @ ( produc5414030515140494994real_o
% 11.11/6.23                  @ ^ [X: real,Y5: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y5 ) @ E3 ) ) ) )
% 11.11/6.23          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10118_uniformity__complex__def,axiom,
% 11.11/6.23      ( topolo896644834953643431omplex
% 11.11/6.23      = ( comple8358262395181532106omplex
% 11.11/6.23        @ ( image_5971271580939081552omplex
% 11.11/6.23          @ ^ [E3: real] :
% 11.11/6.23              ( princi3496590319149328850omplex
% 11.11/6.23              @ ( collec8663557070575231912omplex
% 11.11/6.23                @ ( produc6771430404735790350plex_o
% 11.11/6.23                  @ ^ [X: complex,Y5: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y5 ) @ E3 ) ) ) )
% 11.11/6.23          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10119_rat__floor__lemma,axiom,
% 11.11/6.23      ! [A: int,B: int] :
% 11.11/6.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 11.11/6.23        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10120_less__rat,axiom,
% 11.11/6.23      ! [B: int,D: int,A: int,C: int] :
% 11.11/6.23        ( ( B != zero_zero_int )
% 11.11/6.23       => ( ( D != zero_zero_int )
% 11.11/6.23         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 11.11/6.23            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10121_le__rat,axiom,
% 11.11/6.23      ! [B: int,D: int,A: int,C: int] :
% 11.11/6.23        ( ( B != zero_zero_int )
% 11.11/6.23       => ( ( D != zero_zero_int )
% 11.11/6.23         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 11.11/6.23            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10122_Rat__induct__pos,axiom,
% 11.11/6.23      ! [P: rat > $o,Q3: rat] :
% 11.11/6.23        ( ! [A5: int,B5: int] :
% 11.11/6.23            ( ( ord_less_int @ zero_zero_int @ B5 )
% 11.11/6.23           => ( P @ ( fract @ A5 @ B5 ) ) )
% 11.11/6.23       => ( P @ Q3 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10123_Fract__less__zero__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 11.11/6.23          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10124_zero__less__Fract__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 11.11/6.23          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10125_Fract__less__one__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 11.11/6.23          = ( ord_less_int @ A @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10126_one__less__Fract__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 11.11/6.23          = ( ord_less_int @ B @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10127_Fract__le__zero__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 11.11/6.23          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10128_zero__le__Fract__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 11.11/6.23          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10129_Fract__le__one__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 11.11/6.23          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10130_one__le__Fract__iff,axiom,
% 11.11/6.23      ! [B: int,A: int] :
% 11.11/6.23        ( ( ord_less_int @ zero_zero_int @ B )
% 11.11/6.23       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 11.11/6.23          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10131_positive__rat,axiom,
% 11.11/6.23      ! [A: int,B: int] :
% 11.11/6.23        ( ( positive @ ( fract @ A @ B ) )
% 11.11/6.23        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10132_less__rat__def,axiom,
% 11.11/6.23      ( ord_less_rat
% 11.11/6.23      = ( ^ [X: rat,Y5: rat] : ( positive @ ( minus_minus_rat @ Y5 @ X ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10133_Rat_Opositive_Orep__eq,axiom,
% 11.11/6.23      ( positive
% 11.11/6.23      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10134_min__Suc__Suc,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 11.11/6.23        = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10135_min__0R,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 11.11/6.23        = zero_zero_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10136_min__0L,axiom,
% 11.11/6.23      ! [N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 11.11/6.23        = zero_zero_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10137_min__Suc__numeral,axiom,
% 11.11/6.23      ! [N2: nat,K: num] :
% 11.11/6.23        ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 11.11/6.23        = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10138_min__numeral__Suc,axiom,
% 11.11/6.23      ! [K: num,N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 11.11/6.23        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10139_inf__nat__def,axiom,
% 11.11/6.23      inf_inf_nat = ord_min_nat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10140_nat__mult__min__left,axiom,
% 11.11/6.23      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.23        ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q3 )
% 11.11/6.23        = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10141_nat__mult__min__right,axiom,
% 11.11/6.23      ! [M: nat,N2: nat,Q3: nat] :
% 11.11/6.23        ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q3 ) )
% 11.11/6.23        = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10142_min__diff,axiom,
% 11.11/6.23      ! [M: nat,I2: nat,N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 11.11/6.23        = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10143_concat__bit__assoc__sym,axiom,
% 11.11/6.23      ! [M: nat,N2: nat,K: int,L: int,R3: int] :
% 11.11/6.23        ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 )
% 11.11/6.23        = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N2 ) @ L @ R3 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10144_take__bit__concat__bit__eq,axiom,
% 11.11/6.23      ! [M: nat,N2: nat,K: int,L: int] :
% 11.11/6.23        ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N2 @ K @ L ) )
% 11.11/6.23        = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ L ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10145_min__Suc1,axiom,
% 11.11/6.23      ! [N2: nat,M: nat] :
% 11.11/6.23        ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 11.11/6.23        = ( case_nat_nat @ zero_zero_nat
% 11.11/6.23          @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N2 @ M3 ) )
% 11.11/6.23          @ M ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10146_min__Suc2,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 11.11/6.23        = ( case_nat_nat @ zero_zero_nat
% 11.11/6.23          @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N2 ) )
% 11.11/6.23          @ M ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10147_min__enat__simps_I2_J,axiom,
% 11.11/6.23      ! [Q3: extended_enat] :
% 11.11/6.23        ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 11.11/6.23        = zero_z5237406670263579293d_enat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10148_min__enat__simps_I3_J,axiom,
% 11.11/6.23      ! [Q3: extended_enat] :
% 11.11/6.23        ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 11.11/6.23        = zero_z5237406670263579293d_enat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10149_inf__enat__def,axiom,
% 11.11/6.23      inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10150_num__of__integer__code,axiom,
% 11.11/6.23      ( code_num_of_integer
% 11.11/6.23      = ( ^ [K3: code_integer] :
% 11.11/6.23            ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 11.11/6.23            @ ( produc7336495610019696514er_num
% 11.11/6.23              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 11.11/6.23              @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10151_card__le__Suc__Max,axiom,
% 11.11/6.23      ! [S2: set_nat] :
% 11.11/6.23        ( ( finite_finite_nat @ S2 )
% 11.11/6.23       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10152_divide__nat__def,axiom,
% 11.11/6.23      ( divide_divide_nat
% 11.11/6.23      = ( ^ [M6: nat,N: nat] :
% 11.11/6.23            ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 11.11/6.23            @ ( lattic8265883725875713057ax_nat
% 11.11/6.23              @ ( collect_nat
% 11.11/6.23                @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M6 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10153_gcd__is__Max__divisors__nat,axiom,
% 11.11/6.23      ! [N2: nat,M: nat] :
% 11.11/6.23        ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 11.11/6.23       => ( ( gcd_gcd_nat @ M @ N2 )
% 11.11/6.23          = ( lattic8265883725875713057ax_nat
% 11.11/6.23            @ ( collect_nat
% 11.11/6.23              @ ^ [D5: nat] :
% 11.11/6.23                  ( ( dvd_dvd_nat @ D5 @ M )
% 11.11/6.23                  & ( dvd_dvd_nat @ D5 @ N2 ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10154_upt__rec__numeral,axiom,
% 11.11/6.23      ! [M: num,N2: num] :
% 11.11/6.23        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.23         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.23            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.23         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 11.11/6.23            = nil_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10155_remdups__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 11.11/6.23        = ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10156_tl__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( tl_nat @ ( upt @ M @ N2 ) )
% 11.11/6.23        = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10157_hd__upt,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.23       => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 11.11/6.23          = I2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10158_drop__upt,axiom,
% 11.11/6.23      ! [M: nat,I2: nat,J: nat] :
% 11.11/6.23        ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 11.11/6.23        = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10159_length__upt,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 11.11/6.23        = ( minus_minus_nat @ J @ I2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10160_take__upt,axiom,
% 11.11/6.23      ! [I2: nat,M: nat,N2: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 11.11/6.23       => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 11.11/6.23          = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10161_upt__conv__Nil,axiom,
% 11.11/6.23      ! [J: nat,I2: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ J @ I2 )
% 11.11/6.23       => ( ( upt @ I2 @ J )
% 11.11/6.23          = nil_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10162_sorted__list__of__set__range,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 11.11/6.23        = ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10163_upt__eq__Nil__conv,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ( upt @ I2 @ J )
% 11.11/6.23          = nil_nat )
% 11.11/6.23        = ( ( J = zero_zero_nat )
% 11.11/6.23          | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10164_nth__upt,axiom,
% 11.11/6.23      ! [I2: nat,K: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 11.11/6.23       => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 11.11/6.23          = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10165_greaterThanLessThan__upt,axiom,
% 11.11/6.23      ( set_or5834768355832116004an_nat
% 11.11/6.23      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M6 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10166_atLeastLessThan__upt,axiom,
% 11.11/6.23      ( set_or4665077453230672383an_nat
% 11.11/6.23      = ( ^ [I3: nat,J3: nat] : ( set_nat2 @ ( upt @ I3 @ J3 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10167_atLeastAtMost__upt,axiom,
% 11.11/6.23      ( set_or1269000886237332187st_nat
% 11.11/6.23      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M6 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10168_greaterThanAtMost__upt,axiom,
% 11.11/6.23      ( set_or6659071591806873216st_nat
% 11.11/6.23      = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M6 ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10169_atLeast__upt,axiom,
% 11.11/6.23      ( set_ord_lessThan_nat
% 11.11/6.23      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10170_upt__conv__Cons__Cons,axiom,
% 11.11/6.23      ! [M: nat,N2: nat,Ns: list_nat,Q3: nat] :
% 11.11/6.23        ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 11.11/6.23          = ( upt @ M @ Q3 ) )
% 11.11/6.23        = ( ( cons_nat @ N2 @ Ns )
% 11.11/6.23          = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10171_distinct__upt,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10172_upt__0,axiom,
% 11.11/6.23      ! [I2: nat] :
% 11.11/6.23        ( ( upt @ I2 @ zero_zero_nat )
% 11.11/6.23        = nil_nat ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10173_atMost__upto,axiom,
% 11.11/6.23      ( set_ord_atMost_nat
% 11.11/6.23      = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10174_upt__conv__Cons,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_nat @ I2 @ J )
% 11.11/6.23       => ( ( upt @ I2 @ J )
% 11.11/6.23          = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10175_upt__add__eq__append,axiom,
% 11.11/6.23      ! [I2: nat,J: nat,K: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.23       => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 11.11/6.23          = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10176_upt__eq__Cons__conv,axiom,
% 11.11/6.23      ! [I2: nat,J: nat,X4: nat,Xs: list_nat] :
% 11.11/6.23        ( ( ( upt @ I2 @ J )
% 11.11/6.23          = ( cons_nat @ X4 @ Xs ) )
% 11.11/6.23        = ( ( ord_less_nat @ I2 @ J )
% 11.11/6.23          & ( I2 = X4 )
% 11.11/6.23          & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 11.11/6.23            = Xs ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10177_upt__rec,axiom,
% 11.11/6.23      ( upt
% 11.11/6.23      = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10178_upt__Suc,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.23         => ( ( upt @ I2 @ ( suc @ J ) )
% 11.11/6.23            = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 11.11/6.23        & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.23         => ( ( upt @ I2 @ ( suc @ J ) )
% 11.11/6.23            = nil_nat ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10179_upt__Suc__append,axiom,
% 11.11/6.23      ! [I2: nat,J: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ I2 @ J )
% 11.11/6.23       => ( ( upt @ I2 @ ( suc @ J ) )
% 11.11/6.23          = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10180_sum__list__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ M @ N2 )
% 11.11/6.23       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 11.11/6.23          = ( groups3542108847815614940at_nat
% 11.11/6.23            @ ^ [X: nat] : X
% 11.11/6.23            @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10181_map__Suc__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 11.11/6.23        = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10182_map__add__upt,axiom,
% 11.11/6.23      ! [N2: nat,M: nat] :
% 11.11/6.23        ( ( map_nat_nat
% 11.11/6.23          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 11.11/6.23          @ ( upt @ zero_zero_nat @ M ) )
% 11.11/6.23        = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10183_map__decr__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( map_nat_nat
% 11.11/6.23          @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 11.11/6.23          @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 11.11/6.23        = ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10184_Divides_Oadjust__div__def,axiom,
% 11.11/6.23      ( adjust_div
% 11.11/6.23      = ( produc8211389475949308722nt_int
% 11.11/6.23        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10185_card__length__sum__list__rec,axiom,
% 11.11/6.23      ! [M: nat,N4: nat] :
% 11.11/6.23        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 11.11/6.23       => ( ( finite_card_list_nat
% 11.11/6.23            @ ( collect_list_nat
% 11.11/6.23              @ ^ [L2: list_nat] :
% 11.11/6.23                  ( ( ( size_size_list_nat @ L2 )
% 11.11/6.23                    = M )
% 11.11/6.23                  & ( ( groups4561878855575611511st_nat @ L2 )
% 11.11/6.23                    = N4 ) ) ) )
% 11.11/6.23          = ( plus_plus_nat
% 11.11/6.23            @ ( finite_card_list_nat
% 11.11/6.23              @ ( collect_list_nat
% 11.11/6.23                @ ^ [L2: list_nat] :
% 11.11/6.23                    ( ( ( size_size_list_nat @ L2 )
% 11.11/6.23                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 11.11/6.23                    & ( ( groups4561878855575611511st_nat @ L2 )
% 11.11/6.23                      = N4 ) ) ) )
% 11.11/6.23            @ ( finite_card_list_nat
% 11.11/6.23              @ ( collect_list_nat
% 11.11/6.23                @ ^ [L2: list_nat] :
% 11.11/6.23                    ( ( ( size_size_list_nat @ L2 )
% 11.11/6.23                      = M )
% 11.11/6.23                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 11.11/6.23                      = N4 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10186_card__length__sum__list,axiom,
% 11.11/6.23      ! [M: nat,N4: nat] :
% 11.11/6.23        ( ( finite_card_list_nat
% 11.11/6.23          @ ( collect_list_nat
% 11.11/6.23            @ ^ [L2: list_nat] :
% 11.11/6.23                ( ( ( size_size_list_nat @ L2 )
% 11.11/6.23                  = M )
% 11.11/6.23                & ( ( groups4561878855575611511st_nat @ L2 )
% 11.11/6.23                  = N4 ) ) ) )
% 11.11/6.23        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10187_sorted__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10188_sorted__wrt__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10189_sorted__wrt__less__idx,axiom,
% 11.11/6.23      ! [Ns: list_nat,I2: nat] :
% 11.11/6.23        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 11.11/6.23       => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 11.11/6.23         => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10190_sorted__wrt__upto,axiom,
% 11.11/6.23      ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10191_sorted__upto,axiom,
% 11.11/6.23      ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10192_pairs__le__eq__Sigma,axiom,
% 11.11/6.23      ! [M: nat] :
% 11.11/6.23        ( ( collec3392354462482085612at_nat
% 11.11/6.23          @ ( produc6081775807080527818_nat_o
% 11.11/6.23            @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 11.11/6.23        = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 11.11/6.23          @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10193_prod__encode__prod__decode__aux,axiom,
% 11.11/6.23      ! [K: nat,M: nat] :
% 11.11/6.23        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 11.11/6.23        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10194_le__prod__encode__1,axiom,
% 11.11/6.23      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10195_le__prod__encode__2,axiom,
% 11.11/6.23      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10196_prod__encode__def,axiom,
% 11.11/6.23      ( nat_prod_encode
% 11.11/6.23      = ( produc6842872674320459806at_nat
% 11.11/6.23        @ ^ [M6: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N ) ) @ M6 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10197_list__encode_Oelims,axiom,
% 11.11/6.23      ! [X4: list_nat,Y: nat] :
% 11.11/6.23        ( ( ( nat_list_encode @ X4 )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( ( X4 = nil_nat )
% 11.11/6.23           => ( Y != zero_zero_nat ) )
% 11.11/6.23         => ~ ! [X5: nat,Xs2: list_nat] :
% 11.11/6.23                ( ( X4
% 11.11/6.23                  = ( cons_nat @ X5 @ Xs2 ) )
% 11.11/6.23               => ( Y
% 11.11/6.23                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10198_list__encode_Osimps_I2_J,axiom,
% 11.11/6.23      ! [X4: nat,Xs: list_nat] :
% 11.11/6.23        ( ( nat_list_encode @ ( cons_nat @ X4 @ Xs ) )
% 11.11/6.23        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10199_list__encode_Opelims,axiom,
% 11.11/6.23      ! [X4: list_nat,Y: nat] :
% 11.11/6.23        ( ( ( nat_list_encode @ X4 )
% 11.11/6.23          = Y )
% 11.11/6.23       => ( ( accp_list_nat @ nat_list_encode_rel @ X4 )
% 11.11/6.23         => ( ( ( X4 = nil_nat )
% 11.11/6.23             => ( ( Y = zero_zero_nat )
% 11.11/6.23               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 11.11/6.23           => ~ ! [X5: nat,Xs2: list_nat] :
% 11.11/6.23                  ( ( X4
% 11.11/6.23                    = ( cons_nat @ X5 @ Xs2 ) )
% 11.11/6.23                 => ( ( Y
% 11.11/6.23                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 11.11/6.23                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10200_Gcd__int__greater__eq__0,axiom,
% 11.11/6.23      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10201_Gcd__nat__eq__one,axiom,
% 11.11/6.23      ! [N4: set_nat] :
% 11.11/6.23        ( ( member_nat @ one_one_nat @ N4 )
% 11.11/6.23       => ( ( gcd_Gcd_nat @ N4 )
% 11.11/6.23          = one_one_nat ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10202_sort__upt,axiom,
% 11.11/6.23      ! [M: nat,N2: nat] :
% 11.11/6.23        ( ( linord738340561235409698at_nat
% 11.11/6.23          @ ^ [X: nat] : X
% 11.11/6.23          @ ( upt @ M @ N2 ) )
% 11.11/6.23        = ( upt @ M @ N2 ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10203_sort__upto,axiom,
% 11.11/6.23      ! [I2: int,J: int] :
% 11.11/6.23        ( ( linord1735203802627413978nt_int
% 11.11/6.23          @ ^ [X: int] : X
% 11.11/6.23          @ ( upto @ I2 @ J ) )
% 11.11/6.23        = ( upto @ I2 @ J ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10204_of__nat__eq__id,axiom,
% 11.11/6.23      semiri1316708129612266289at_nat = id_nat ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10205_Rat_Opositive__def,axiom,
% 11.11/6.23      ( positive
% 11.11/6.23      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 11.11/6.23        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10206_rcis__inverse,axiom,
% 11.11/6.23      ! [R3: real,A: real] :
% 11.11/6.23        ( ( invers8013647133539491842omplex @ ( rcis @ R3 @ A ) )
% 11.11/6.23        = ( rcis @ ( divide_divide_real @ one_one_real @ R3 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10207_cis__rcis__eq,axiom,
% 11.11/6.23      ( cis
% 11.11/6.23      = ( rcis @ one_one_real ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10208_DeMoivre2,axiom,
% 11.11/6.23      ! [R3: real,A: real,N2: nat] :
% 11.11/6.23        ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N2 )
% 11.11/6.23        = ( rcis @ ( power_power_real @ R3 @ N2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(fact_10209_of__rat__dense,axiom,
% 11.11/6.23      ! [X4: real,Y: real] :
% 11.11/6.23        ( ( ord_less_real @ X4 @ Y )
% 11.11/6.23       => ? [Q2: rat] :
% 11.11/6.23            ( ( ord_less_real @ X4 @ ( field_7254667332652039916t_real @ Q2 ) )
% 11.11/6.23            & ( ord_less_real @ ( field_7254667332652039916t_real @ Q2 ) @ Y ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 11.11/6.23      ! [X4: int,Y: int] :
% 11.11/6.23        ( ( if_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 11.11/6.23      ! [X4: int,Y: int] :
% 11.11/6.23        ( ( if_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 11.11/6.23      ! [X4: nat,Y: nat] :
% 11.11/6.23        ( ( if_nat @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 11.11/6.23      ! [X4: nat,Y: nat] :
% 11.11/6.23        ( ( if_nat @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 11.11/6.23      ! [X4: num,Y: num] :
% 11.11/6.23        ( ( if_num @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 11.11/6.23      ! [X4: num,Y: num] :
% 11.11/6.23        ( ( if_num @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 11.11/6.23      ! [X4: rat,Y: rat] :
% 11.11/6.23        ( ( if_rat @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 11.11/6.23      ! [X4: rat,Y: rat] :
% 11.11/6.23        ( ( if_rat @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 11.11/6.23      ! [X4: real,Y: real] :
% 11.11/6.23        ( ( if_real @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 11.11/6.23      ! [X4: real,Y: real] :
% 11.11/6.23        ( ( if_real @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 11.11/6.23      ! [P: real > $o] :
% 11.11/6.23        ( ( P @ ( fChoice_real @ P ) )
% 11.11/6.23        = ( ? [X3: real] : ( P @ X3 ) ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 11.11/6.23      ! [X4: complex,Y: complex] :
% 11.11/6.23        ( ( if_complex @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 11.11/6.23      ! [X4: complex,Y: complex] :
% 11.11/6.23        ( ( if_complex @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 11.11/6.23      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.23        ( ( if_Code_integer @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 11.11/6.23      ! [X4: code_integer,Y: code_integer] :
% 11.11/6.23        ( ( if_Code_integer @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: set_int,Y: set_int] :
% 11.11/6.23        ( ( if_set_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: set_int,Y: set_int] :
% 11.11/6.23        ( ( if_set_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: list_int,Y: list_int] :
% 11.11/6.23        ( ( if_list_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: list_int,Y: list_int] :
% 11.11/6.23        ( ( if_list_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 11.11/6.23      ! [X4: list_nat,Y: list_nat] :
% 11.11/6.23        ( ( if_list_nat @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 11.11/6.23      ! [X4: list_nat,Y: list_nat] :
% 11.11/6.23        ( ( if_list_nat @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: int > int,Y: int > int] :
% 11.11/6.23        ( ( if_int_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: int > int,Y: int > int] :
% 11.11/6.23        ( ( if_int_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 11.11/6.23      ! [X4: option_num,Y: option_num] :
% 11.11/6.23        ( ( if_option_num @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 11.11/6.23      ! [X4: option_num,Y: option_num] :
% 11.11/6.23        ( ( if_option_num @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 11.11/6.23        ( ( if_Pro3027730157355071871nt_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 11.11/6.23      ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 11.11/6.23        ( ( if_Pro3027730157355071871nt_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 11.11/6.23      ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 11.11/6.23        ( ( if_Pro6206227464963214023at_nat @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 11.11/6.23      ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 11.11/6.23        ( ( if_Pro6206227464963214023at_nat @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 11.11/6.23      ! [X4: nat > int > int,Y: nat > int > int] :
% 11.11/6.23        ( ( if_nat_int_int @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 11.11/6.23      ! [X4: nat > int > int,Y: nat > int > int] :
% 11.11/6.23        ( ( if_nat_int_int @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 11.11/6.23      ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 11.11/6.23        ( ( if_nat_nat_nat @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 11.11/6.23      ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 11.11/6.23        ( ( if_nat_nat_nat @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 11.11/6.23      ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 11.11/6.23        ( ( if_Pro5737122678794959658eger_o @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 11.11/6.23      ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 11.11/6.23        ( ( if_Pro5737122678794959658eger_o @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 11.11/6.23      ! [P: $o] :
% 11.11/6.23        ( ( P = $true )
% 11.11/6.23        | ( P = $false ) ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 11.11/6.23      ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 11.11/6.23        ( ( if_Pro6119634080678213985nteger @ $false @ X4 @ Y )
% 11.11/6.23        = Y ) ).
% 11.11/6.23  
% 11.11/6.23  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 11.11/6.23      ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 11.11/6.23        ( ( if_Pro6119634080678213985nteger @ $true @ X4 @ Y )
% 11.11/6.23        = X4 ) ).
% 11.11/6.23  
% 11.11/6.23  thf(conj_0,conjecture,
% 11.11/6.23      vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ).
% 11.11/6.23  ------------------------
% 11.12/6.66  % (7888)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/183Mi)
% 11.12/6.66  % (7892)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_7681 for (2995ds/2Mi)
% 11.12/6.66  % (7894)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/18Mi)
% 11.12/6.66  % (7890)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_7681 for (2995ds/27Mi)
% 11.12/6.66  % (7893)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_7681 for (2995ds/275Mi)
% 11.12/6.66  % (7889)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_7681 for (2995ds/4Mi)
% 11.12/6.66  % (7891)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/2Mi)
% 11.12/6.67  % (7892)Instruction limit reached!
% 11.12/6.67  % (7892)------------------------------
% 11.12/6.67  % (7892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.67  % (7892)Termination reason: Unknown
% 11.12/6.67  % (7892)Termination phase: shuffling
% 11.12/6.67  
% 11.12/6.67  % (7892)Memory used [KB]: 12153
% 11.12/6.67  % (7892)Time elapsed: 0.004 s
% 11.12/6.67  % (7892)Instructions burned: 2 (million)
% 11.12/6.67  % (7892)------------------------------
% 11.12/6.67  % (7892)------------------------------
% 11.12/6.67  % (7891)Instruction limit reached!
% 11.12/6.67  % (7891)------------------------------
% 11.12/6.67  % (7891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.67  % (7891)Termination reason: Unknown
% 11.12/6.67  % (7891)Termination phase: shuffling
% 11.12/6.67  
% 11.12/6.67  % (7891)Memory used [KB]: 12153
% 11.12/6.67  % (7891)Time elapsed: 0.004 s
% 11.12/6.67  % (7891)Instructions burned: 2 (million)
% 11.12/6.67  % (7891)------------------------------
% 11.12/6.67  % (7891)------------------------------
% 11.12/6.67  % (7889)Instruction limit reached!
% 11.12/6.67  % (7889)------------------------------
% 11.12/6.67  % (7889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.67  % (7889)Termination reason: Unknown
% 11.12/6.67  % (7889)Termination phase: shuffling
% 11.12/6.67  
% 11.12/6.67  % (7889)Memory used [KB]: 12281
% 11.12/6.67  % (7889)Time elapsed: 0.005 s
% 11.12/6.67  % (7889)Instructions burned: 4 (million)
% 11.12/6.67  % (7889)------------------------------
% 11.12/6.67  % (7889)------------------------------
% 11.12/6.68  % (7894)Instruction limit reached!
% 11.12/6.68  % (7894)------------------------------
% 11.12/6.68  % (7894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.68  % (7894)Termination reason: Unknown
% 11.12/6.68  % (7894)Termination phase: shuffling
% 11.12/6.68  
% 11.12/6.68  % (7894)Memory used [KB]: 12920
% 11.12/6.68  % (7894)Time elapsed: 0.020 s
% 11.12/6.68  % (7894)Instructions burned: 18 (million)
% 11.12/6.68  % (7894)------------------------------
% 11.12/6.68  % (7894)------------------------------
% 11.12/6.68  % (7896)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_7681 for (2995ds/37Mi)
% 11.12/6.68  % (7895)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/3Mi)
% 11.12/6.68  % (7897)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_7681 for (2995ds/15Mi)
% 11.12/6.69  % (7890)Instruction limit reached!
% 11.12/6.69  % (7890)------------------------------
% 11.12/6.69  % (7890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.69  % (7890)Termination reason: Unknown
% 11.12/6.69  % (7890)Termination phase: shuffling
% 11.12/6.69  
% 11.12/6.69  % (7890)Memory used [KB]: 12920
% 11.12/6.69  % (7890)Time elapsed: 0.024 s
% 11.12/6.69  % (7890)Instructions burned: 27 (million)
% 11.12/6.69  % (7890)------------------------------
% 11.12/6.69  % (7890)------------------------------
% 11.12/6.69  % (7895)Instruction limit reached!
% 11.12/6.69  % (7895)------------------------------
% 11.12/6.69  % (7895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.69  % (7895)Termination reason: Unknown
% 11.12/6.69  % (7895)Termination phase: shuffling
% 11.12/6.69  
% 11.12/6.69  % (7895)Memory used [KB]: 12153
% 11.12/6.69  % (7895)Time elapsed: 0.005 s
% 11.12/6.69  % (7895)Instructions burned: 3 (million)
% 11.12/6.69  % (7895)------------------------------
% 11.12/6.69  % (7895)------------------------------
% 11.12/6.70  % (7897)Instruction limit reached!
% 11.12/6.70  % (7897)------------------------------
% 11.12/6.70  % (7897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.70  % (7897)Termination reason: Unknown
% 11.12/6.70  % (7897)Termination phase: shuffling
% 11.12/6.70  
% 11.12/6.70  % (7897)Memory used [KB]: 12920
% 11.12/6.70  % (7897)Time elapsed: 0.017 s
% 11.12/6.70  % (7897)Instructions burned: 16 (million)
% 11.12/6.70  % (7897)------------------------------
% 11.12/6.70  % (7897)------------------------------
% 11.12/6.70  % (7898)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_7681 for (2995ds/3Mi)
% 11.12/6.70  % (7898)Instruction limit reached!
% 11.12/6.70  % (7898)------------------------------
% 11.12/6.70  % (7898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.70  % (7898)Termination reason: Unknown
% 11.12/6.70  % (7898)Termination phase: shuffling
% 11.12/6.70  
% 11.12/6.70  % (7898)Memory used [KB]: 12153
% 11.12/6.70  % (7898)Time elapsed: 0.005 s
% 11.12/6.70  % (7898)Instructions burned: 3 (million)
% 11.12/6.70  % (7898)------------------------------
% 11.12/6.70  % (7898)------------------------------
% 11.12/6.70  % (7900)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/7Mi)
% 11.12/6.70  % (7899)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_7681 for (2995ds/1041Mi)
% 11.12/6.71  % (7896)Instruction limit reached!
% 11.12/6.71  % (7896)------------------------------
% 11.12/6.71  % (7896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.71  % (7896)Termination reason: Unknown
% 11.12/6.71  % (7896)Termination phase: shuffling
% 11.12/6.71  
% 11.12/6.71  % (7896)Memory used [KB]: 13048
% 11.12/6.71  % (7896)Time elapsed: 0.028 s
% 11.12/6.71  % (7896)Instructions burned: 37 (million)
% 11.12/6.71  % (7896)------------------------------
% 11.12/6.71  % (7896)------------------------------
% 11.12/6.71  % (7900)Instruction limit reached!
% 11.12/6.71  % (7900)------------------------------
% 11.12/6.71  % (7900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.71  % (7900)Termination reason: Unknown
% 11.12/6.71  % (7900)Termination phase: shuffling
% 11.12/6.71  
% 11.12/6.71  % (7900)Memory used [KB]: 12537
% 11.12/6.71  % (7900)Time elapsed: 0.009 s
% 11.12/6.71  % (7900)Instructions burned: 7 (million)
% 11.12/6.71  % (7900)------------------------------
% 11.12/6.71  % (7900)------------------------------
% 11.12/6.72  % (7901)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/16Mi)
% 11.12/6.72  % (7902)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_7681 for (2995ds/3Mi)
% 11.12/6.72  % (7902)Instruction limit reached!
% 11.12/6.72  % (7902)------------------------------
% 11.12/6.72  % (7902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.72  % (7902)Termination reason: Unknown
% 11.12/6.72  % (7902)Termination phase: shuffling
% 11.12/6.72  
% 11.12/6.72  % (7902)Memory used [KB]: 12281
% 11.12/6.72  % (7902)Time elapsed: 0.005 s
% 11.12/6.72  % (7902)Instructions burned: 3 (million)
% 11.12/6.72  % (7902)------------------------------
% 11.12/6.72  % (7902)------------------------------
% 11.12/6.73  % (7888)Instruction limit reached!
% 11.12/6.73  % (7888)------------------------------
% 11.12/6.73  % (7888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.73  % (7888)Termination reason: Unknown
% 11.12/6.73  % (7888)Termination phase: shuffling
% 11.12/6.73  
% 11.12/6.73  % (7888)Memory used [KB]: 15095
% 11.12/6.73  % (7888)Time elapsed: 0.072 s
% 11.12/6.73  % (7888)Instructions burned: 183 (million)
% 11.12/6.73  % (7888)------------------------------
% 11.12/6.73  % (7888)------------------------------
% 11.12/6.73  % (7904)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/7Mi)
% 11.12/6.73  % (7901)Instruction limit reached!
% 11.12/6.73  % (7901)------------------------------
% 11.12/6.73  % (7901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.73  % (7901)Termination reason: Unknown
% 11.12/6.73  % (7901)Termination phase: shuffling
% 11.12/6.73  
% 11.12/6.73  % (7901)Memory used [KB]: 12920
% 11.12/6.73  % (7901)Time elapsed: 0.018 s
% 11.12/6.73  % (7901)Instructions burned: 17 (million)
% 11.12/6.73  % (7901)------------------------------
% 11.12/6.73  % (7901)------------------------------
% 11.12/6.74  % (7904)Instruction limit reached!
% 11.12/6.74  % (7904)------------------------------
% 11.12/6.74  % (7904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.74  % (7904)Termination reason: Unknown
% 11.12/6.74  % (7904)Termination phase: shuffling
% 11.12/6.74  
% 11.12/6.74  % (7904)Memory used [KB]: 12537
% 11.12/6.74  % (7904)Time elapsed: 0.010 s
% 11.12/6.74  % (7904)Instructions burned: 7 (million)
% 11.12/6.74  % (7904)------------------------------
% 11.12/6.74  % (7904)------------------------------
% 11.12/6.74  % (7905)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/3Mi)
% 11.12/6.74  % (7903)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_7681 for (2995ds/3Mi)
% 11.12/6.74  % (7906)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/4Mi)
% 11.12/6.74  % (7903)Instruction limit reached!
% 11.12/6.74  % (7903)------------------------------
% 11.12/6.74  % (7903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.74  % (7903)Termination reason: Unknown
% 11.12/6.74  % (7903)Termination phase: shuffling
% 11.12/6.74  
% 11.12/6.74  % (7903)Memory used [KB]: 12281
% 11.12/6.74  % (7905)Instruction limit reached!
% 11.12/6.74  % (7905)------------------------------
% 11.12/6.74  % (7905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.74  % (7903)Time elapsed: 0.004 s
% 11.12/6.74  % (7903)Instructions burned: 3 (million)
% 11.12/6.74  % (7903)------------------------------
% 11.12/6.74  % (7903)------------------------------
% 11.12/6.74  % (7905)Termination reason: Unknown
% 11.12/6.74  % (7905)Termination phase: shuffling
% 11.12/6.74  
% 11.12/6.74  % (7905)Memory used [KB]: 12281
% 11.12/6.74  % (7905)Time elapsed: 0.005 s
% 11.12/6.74  % (7905)Instructions burned: 3 (million)
% 11.12/6.74  % (7905)------------------------------
% 11.12/6.74  % (7905)------------------------------
% 11.12/6.74  % (7906)Instruction limit reached!
% 11.12/6.74  % (7906)------------------------------
% 11.12/6.74  % (7906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.74  % (7906)Termination reason: Unknown
% 11.12/6.74  % (7906)Termination phase: shuffling
% 11.12/6.74  
% 11.12/6.74  % (7906)Memory used [KB]: 12409
% 11.12/6.74  % (7906)Time elapsed: 0.005 s
% 11.12/6.74  % (7906)Instructions burned: 5 (million)
% 11.12/6.74  % (7906)------------------------------
% 11.12/6.74  % (7906)------------------------------
% 11.12/6.75  % (7907)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/18Mi)
% 11.12/6.76  % (7911)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_7681 for (2995ds/21Mi)
% 11.12/6.76  % (7908)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/710Mi)
% 11.12/6.76  % (7910)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_7681 for (2995ds/902Mi)
% 11.12/6.76  % (7909)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7681 for (2995ds/6Mi)
% 11.12/6.77  % (7909)Instruction limit reached!
% 11.12/6.77  % (7909)------------------------------
% 11.12/6.77  % (7909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.77  % (7909)Termination reason: Unknown
% 11.12/6.77  % (7909)Termination phase: shuffling
% 11.12/6.77  
% 11.12/6.77  % (7909)Memory used [KB]: 12409
% 11.12/6.77  % (7909)Time elapsed: 0.009 s
% 11.12/6.77  % (7909)Instructions burned: 6 (million)
% 11.12/6.77  % (7909)------------------------------
% 11.12/6.77  % (7909)------------------------------
% 11.12/6.77  % (7911)Instruction limit reached!
% 11.12/6.77  % (7911)------------------------------
% 11.12/6.77  % (7911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.77  % (7911)Termination reason: Unknown
% 11.12/6.77  % (7911)Termination phase: shuffling
% 11.12/6.77  
% 11.12/6.77  % (7911)Memory used [KB]: 12920
% 11.12/6.77  % (7911)Time elapsed: 0.016 s
% 11.12/6.77  % (7911)Instructions burned: 23 (million)
% 11.12/6.77  % (7911)------------------------------
% 11.12/6.77  % (7911)------------------------------
% 11.12/6.77  % (7907)Instruction limit reached!
% 11.12/6.77  % (7907)------------------------------
% 11.12/6.77  % (7907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.77  % (7907)Termination reason: Unknown
% 11.12/6.77  % (7907)Termination phase: shuffling
% 11.12/6.77  
% 11.12/6.77  % (7907)Memory used [KB]: 12920
% 11.12/6.77  % (7907)Time elapsed: 0.020 s
% 11.12/6.77  % (7907)Instructions burned: 19 (million)
% 11.12/6.77  % (7907)------------------------------
% 11.12/6.77  % (7907)------------------------------
% 11.12/6.78  % (7912)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7681 for (2994ds/5Mi)
% 11.12/6.78  % (7912)Instruction limit reached!
% 11.12/6.78  % (7912)------------------------------
% 11.12/6.78  % (7912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.78  % (7912)Termination reason: Unknown
% 11.12/6.78  % (7912)Termination phase: shuffling
% 11.12/6.78  
% 11.12/6.78  % (7912)Memory used [KB]: 12409
% 11.12/6.78  % (7912)Time elapsed: 0.006 s
% 11.12/6.78  % (7912)Instructions burned: 5 (million)
% 11.12/6.78  % (7912)------------------------------
% 11.12/6.78  % (7912)------------------------------
% 11.12/6.79  % (7913)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_7681 for (2994ds/6Mi)
% 11.12/6.79  % (7914)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7681 for (2994ds/377Mi)
% 11.12/6.79  % (7913)Instruction limit reached!
% 11.12/6.79  % (7913)------------------------------
% 11.12/6.79  % (7913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.79  % (7913)Termination reason: Unknown
% 11.12/6.79  % (7913)Termination phase: shuffling
% 11.12/6.79  
% 11.12/6.79  % (7913)Memory used [KB]: 12409
% 11.12/6.79  % (7913)Time elapsed: 0.008 s
% 11.12/6.79  % (7913)Instructions burned: 6 (million)
% 11.12/6.79  % (7913)------------------------------
% 11.12/6.79  % (7913)------------------------------
% 11.12/6.80  % (7915)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_7681 for (2994ds/779Mi)
% 11.12/6.81  % (7916)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_7681 for (2994ds/19Mi)
% 11.12/6.81  % (7893)Instruction limit reached!
% 11.12/6.81  % (7893)------------------------------
% 11.12/6.81  % (7893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.81  % (7893)Termination reason: Unknown
% 11.12/6.81  % (7893)Termination phase: shuffling
% 11.12/6.81  
% 11.12/6.81  % (7893)Memory used [KB]: 16502
% 11.12/6.81  % (7893)Time elapsed: 0.149 s
% 11.12/6.81  % (7893)Instructions burned: 275 (million)
% 11.12/6.81  % (7893)------------------------------
% 11.12/6.81  % (7893)------------------------------
% 11.12/6.83  % (7916)Instruction limit reached!
% 11.12/6.83  % (7916)------------------------------
% 11.12/6.83  % (7916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.83  % (7916)Termination reason: Unknown
% 11.12/6.83  % (7916)Termination phase: shuffling
% 11.12/6.83  
% 11.12/6.83  % (7916)Memory used [KB]: 12920
% 11.12/6.83  % (7916)Time elapsed: 0.019 s
% 11.12/6.83  % (7916)Instructions burned: 19 (million)
% 11.12/6.83  % (7916)------------------------------
% 11.12/6.83  % (7916)------------------------------
% 11.12/6.84  % (7917)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7681 for (2994ds/879Mi)
% 11.12/6.85  % (7918)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7681 for (2994ds/17Mi)
% 11.12/6.86  % (7918)Instruction limit reached!
% 11.12/6.86  % (7918)------------------------------
% 11.12/6.86  % (7918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.86  % (7918)Termination reason: Unknown
% 11.12/6.86  % (7918)Termination phase: shuffling
% 11.12/6.86  
% 11.12/6.86  % (7918)Memory used [KB]: 12920
% 11.12/6.86  % (7918)Time elapsed: 0.018 s
% 11.12/6.86  % (7918)Instructions burned: 17 (million)
% 11.12/6.86  % (7918)------------------------------
% 11.12/6.86  % (7918)------------------------------
% 11.12/6.89  % (7919)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7681 for (2993ds/3Mi)
% 11.12/6.89  % (7919)Instruction limit reached!
% 11.12/6.89  % (7919)------------------------------
% 11.12/6.89  % (7919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.89  % (7919)Termination reason: Unknown
% 11.12/6.89  % (7919)Termination phase: shuffling
% 11.12/6.89  
% 11.12/6.89  % (7919)Memory used [KB]: 12153
% 11.12/6.89  % (7919)Time elapsed: 0.004 s
% 11.12/6.89  % (7919)Instructions burned: 3 (million)
% 11.12/6.89  % (7919)------------------------------
% 11.12/6.89  % (7919)------------------------------
% 11.12/6.91  % (7920)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7681 for (2993ds/30Mi)
% 11.12/6.93  % (7920)Instruction limit reached!
% 11.12/6.93  % (7920)------------------------------
% 11.12/6.93  % (7920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.93  % (7920)Termination reason: Unknown
% 11.12/6.93  % (7920)Termination phase: shuffling
% 11.12/6.93  
% 11.12/6.93  % (7920)Memory used [KB]: 13048
% 11.12/6.93  % (7920)Time elapsed: 0.026 s
% 11.12/6.93  % (7920)Instructions burned: 31 (million)
% 11.12/6.93  % (7920)------------------------------
% 11.12/6.93  % (7920)------------------------------
% 11.12/6.95  % (7921)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7681 for (2992ds/127Mi)
% 11.12/6.99  % (7914)Instruction limit reached!
% 11.12/6.99  % (7914)------------------------------
% 11.12/6.99  % (7914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/6.99  % (7914)Termination reason: Unknown
% 11.12/6.99  % (7914)Termination phase: shuffling
% 11.12/6.99  
% 11.12/6.99  % (7914)Memory used [KB]: 17782
% 11.12/6.99  % (7914)Time elapsed: 0.200 s
% 11.12/6.99  % (7914)Instructions burned: 378 (million)
% 11.12/6.99  % (7914)------------------------------
% 11.12/6.99  % (7914)------------------------------
% 11.12/7.01  % (7922)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7681 for (2992ds/100Mi)
% 13.92/7.02  % (7921)Instruction limit reached!
% 13.92/7.02  % (7921)------------------------------
% 13.92/7.02  % (7921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/7.02  % (7921)Termination reason: Unknown
% 13.92/7.02  % (7921)Termination phase: shuffling
% 13.92/7.02  
% 13.92/7.02  % (7921)Memory used [KB]: 14456
% 13.92/7.02  % (7921)Time elapsed: 0.074 s
% 13.92/7.02  % (7921)Instructions burned: 128 (million)
% 13.92/7.02  % (7921)------------------------------
% 13.92/7.02  % (7921)------------------------------
% 13.92/7.04  % (7923)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_7681 for (2992ds/3Mi)
% 13.92/7.04  % (7923)Instruction limit reached!
% 13.92/7.04  % (7923)------------------------------
% 13.92/7.04  % (7923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/7.04  % (7923)Termination reason: Unknown
% 13.92/7.04  % (7923)Termination phase: shuffling
% 13.92/7.04  
% 13.92/7.04  % (7923)Memory used [KB]: 12153
% 13.92/7.04  % (7923)Time elapsed: 0.003 s
% 13.92/7.04  % (7923)Instructions burned: 3 (million)
% 13.92/7.04  % (7923)------------------------------
% 13.92/7.04  % (7923)------------------------------
% 13.92/7.05  % (7924)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_7681 for (2991ds/20Mi)
% 13.92/7.06  % (7922)Instruction limit reached!
% 13.92/7.06  % (7922)------------------------------
% 13.92/7.06  % (7922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/7.06  % (7922)Termination reason: Unknown
% 13.92/7.06  % (7922)Termination phase: shuffling
% 13.92/7.06  
% 13.92/7.06  % (7922)Memory used [KB]: 14072
% 13.92/7.06  % (7922)Time elapsed: 0.058 s
% 13.92/7.06  % (7922)Instructions burned: 101 (million)
% 13.92/7.06  % (7922)------------------------------
% 13.92/7.06  % (7922)------------------------------
% 13.92/7.06  % (7924)Instruction limit reached!
% 13.92/7.06  % (7924)------------------------------
% 13.92/7.06  % (7924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/7.06  % (7924)Termination reason: Unknown
% 13.92/7.06  % (7924)Termination phase: shuffling
% 13.92/7.06  
% 13.92/7.06  % (7924)Memory used [KB]: 12920
% 13.92/7.06  % (7924)Time elapsed: 0.016 s
% 13.92/7.06  % (7924)Instructions burned: 21 (million)
% 13.92/7.06  % (7924)------------------------------
% 13.92/7.06  % (7924)------------------------------
% 13.92/7.07  % (7926)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_7681 for (2991ds/107Mi)
% 13.92/7.08  % (7925)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_7681 for (2991ds/86Mi)
% 14.61/7.13  % (7926)Instruction limit reached!
% 14.61/7.13  % (7926)------------------------------
% 14.61/7.13  % (7926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.13  % (7926)Termination reason: Unknown
% 14.61/7.13  % (7926)Termination phase: shuffling
% 14.61/7.13  
% 14.61/7.13  % (7926)Memory used [KB]: 14072
% 14.61/7.13  % (7926)Time elapsed: 0.055 s
% 14.61/7.13  % (7926)Instructions burned: 108 (million)
% 14.61/7.13  % (7926)------------------------------
% 14.61/7.13  % (7926)------------------------------
% 14.61/7.13  % (7925)Instruction limit reached!
% 14.61/7.13  % (7925)------------------------------
% 14.61/7.13  % (7925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.13  % (7925)Termination reason: Unknown
% 14.61/7.13  % (7925)Termination phase: shuffling
% 14.61/7.13  
% 14.61/7.13  % (7925)Memory used [KB]: 13816
% 14.61/7.13  % (7925)Time elapsed: 0.054 s
% 14.61/7.13  % (7925)Instructions burned: 87 (million)
% 14.61/7.13  % (7925)------------------------------
% 14.61/7.13  % (7925)------------------------------
% 14.61/7.13  % (7908)Instruction limit reached!
% 14.61/7.13  % (7908)------------------------------
% 14.61/7.13  % (7908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.13  % (7908)Termination reason: Unknown
% 14.61/7.13  % (7908)Termination phase: Property scanning
% 14.61/7.13  
% 14.61/7.13  % (7908)Memory used [KB]: 24050
% 14.61/7.13  % (7908)Time elapsed: 0.380 s
% 14.61/7.13  % (7908)Instructions burned: 710 (million)
% 14.61/7.13  % (7908)------------------------------
% 14.61/7.13  % (7908)------------------------------
% 14.61/7.14  % (7928)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_7681 for (2991ds/448Mi)
% 14.61/7.15  % (7927)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_7681 for (2991ds/39Mi)
% 14.61/7.15  % (7929)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_7681 for (2991ds/46Mi)
% 14.61/7.17  % (7927)Instruction limit reached!
% 14.61/7.17  % (7927)------------------------------
% 14.61/7.17  % (7927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.17  % (7927)Termination reason: Unknown
% 14.61/7.17  % (7927)Termination phase: shuffling
% 14.61/7.17  
% 14.61/7.17  % (7927)Memory used [KB]: 13176
% 14.61/7.17  % (7927)Time elapsed: 0.029 s
% 14.61/7.17  % (7927)Instructions burned: 41 (million)
% 14.61/7.17  % (7927)------------------------------
% 14.61/7.17  % (7927)------------------------------
% 14.61/7.18  % (7915)Instruction limit reached!
% 14.61/7.18  % (7915)------------------------------
% 14.61/7.18  % (7915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.18  % (7915)Termination reason: Unknown
% 14.61/7.18  % (7915)Termination phase: shuffling
% 14.61/7.18  
% 14.61/7.18  % (7915)Memory used [KB]: 25585
% 14.61/7.18  % (7915)Time elapsed: 0.376 s
% 14.61/7.18  % (7915)Instructions burned: 781 (million)
% 14.61/7.18  % (7915)------------------------------
% 14.61/7.18  % (7915)------------------------------
% 14.61/7.19  % (7929)Instruction limit reached!
% 14.61/7.19  % (7929)------------------------------
% 14.61/7.19  % (7929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/7.19  % (7929)Termination reason: Unknown
% 14.61/7.19  % (7929)Termination phase: shuffling
% 14.61/7.19  
% 14.61/7.19  % (7929)Memory used [KB]: 13304
% 14.61/7.19  % (7929)Time elapsed: 0.035 s
% 14.61/7.19  % (7929)Instructions burned: 47 (million)
% 14.61/7.19  % (7929)------------------------------
% 14.61/7.19  % (7929)------------------------------
% 14.61/7.19  % (7930)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_7681 for (2990ds/98Mi)
% 15.18/7.20  % (7931)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_7681 for (2990ds/507Mi)
% 15.18/7.20  % (7899)Instruction limit reached!
% 15.18/7.20  % (7899)------------------------------
% 15.18/7.20  % (7899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.20  % (7899)Termination reason: Unknown
% 15.18/7.20  % (7899)Termination phase: shuffling
% 15.18/7.20  
% 15.18/7.20  % (7899)Memory used [KB]: 33133
% 15.18/7.20  % (7899)Time elapsed: 0.502 s
% 15.18/7.20  % (7899)Instructions burned: 1042 (million)
% 15.18/7.20  % (7899)------------------------------
% 15.18/7.20  % (7899)------------------------------
% 15.18/7.21  % (7932)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_7681 for (2990ds/149Mi)
% 15.18/7.21  % (7910)Instruction limit reached!
% 15.18/7.21  % (7910)------------------------------
% 15.18/7.21  % (7910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.21  % (7910)Termination reason: Unknown
% 15.18/7.21  % (7910)Termination phase: Property scanning
% 15.18/7.21  
% 15.18/7.21  % (7910)Memory used [KB]: 24050
% 15.18/7.21  % (7910)Time elapsed: 0.447 s
% 15.18/7.21  % (7910)Instructions burned: 904 (million)
% 15.18/7.21  % (7910)------------------------------
% 15.18/7.21  % (7910)------------------------------
% 15.18/7.21  % (7917)Instruction limit reached!
% 15.18/7.21  % (7917)------------------------------
% 15.18/7.21  % (7917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.21  % (7917)Termination reason: Unknown
% 15.18/7.21  % (7917)Termination phase: Property scanning
% 15.18/7.21  
% 15.18/7.21  % (7917)Memory used [KB]: 24050
% 15.18/7.21  % (7917)Time elapsed: 0.368 s
% 15.18/7.21  % (7917)Instructions burned: 880 (million)
% 15.18/7.21  % (7917)------------------------------
% 15.18/7.21  % (7917)------------------------------
% 15.18/7.23  % (7933)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7681 for (2990ds/39Mi)
% 15.18/7.23  % (7934)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_7681 for (2990ds/6Mi)
% 15.18/7.23  % (7935)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_7681 for (2990ds/1087Mi)
% 15.18/7.23  % (7934)Instruction limit reached!
% 15.18/7.23  % (7934)------------------------------
% 15.18/7.23  % (7934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.23  % (7934)Termination reason: Unknown
% 15.18/7.23  % (7934)Termination phase: shuffling
% 15.18/7.23  
% 15.18/7.23  % (7934)Memory used [KB]: 12409
% 15.18/7.23  % (7934)Time elapsed: 0.008 s
% 15.18/7.23  % (7934)Instructions burned: 6 (million)
% 15.18/7.23  % (7934)------------------------------
% 15.18/7.23  % (7934)------------------------------
% 15.18/7.25  % (7930)Instruction limit reached!
% 15.18/7.25  % (7930)------------------------------
% 15.18/7.25  % (7930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.25  % (7930)Termination reason: Unknown
% 15.18/7.25  % (7930)Termination phase: shuffling
% 15.18/7.25  
% 15.18/7.25  % (7930)Memory used [KB]: 14072
% 15.18/7.25  % (7930)Time elapsed: 0.056 s
% 15.18/7.25  % (7930)Instructions burned: 98 (million)
% 15.18/7.25  % (7930)------------------------------
% 15.18/7.25  % (7930)------------------------------
% 15.18/7.25  % (7936)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7681 for (2990ds/47Mi)
% 15.18/7.25  % (7933)Instruction limit reached!
% 15.18/7.25  % (7933)------------------------------
% 15.18/7.25  % (7933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.25  % (7933)Termination reason: Unknown
% 15.18/7.25  % (7933)Termination phase: shuffling
% 15.18/7.25  
% 15.18/7.25  % (7933)Memory used [KB]: 13176
% 15.18/7.25  % (7933)Time elapsed: 0.030 s
% 15.18/7.25  % (7933)Instructions burned: 39 (million)
% 15.18/7.25  % (7933)------------------------------
% 15.18/7.25  % (7933)------------------------------
% 15.18/7.27  % (7937)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_7681 for (2989ds/44Mi)
% 15.18/7.27  % (7938)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_7681 for (2989ds/432Mi)
% 15.18/7.28  % (7936)Instruction limit reached!
% 15.18/7.28  % (7936)------------------------------
% 15.18/7.28  % (7936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.28  % (7936)Termination reason: Unknown
% 15.18/7.28  % (7936)Termination phase: shuffling
% 15.18/7.28  
% 15.18/7.28  % (7936)Memory used [KB]: 13304
% 15.18/7.28  % (7936)Time elapsed: 0.034 s
% 15.18/7.28  % (7936)Instructions burned: 47 (million)
% 15.18/7.28  % (7936)------------------------------
% 15.18/7.28  % (7936)------------------------------
% 15.18/7.29  % (7932)Instruction limit reached!
% 15.18/7.29  % (7932)------------------------------
% 15.18/7.29  % (7932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/7.29  % (7932)Termination reason: Unknown
% 15.18/7.29  % (7932)Termination phase: shuffling
% 15.18/7.29  
% 15.18/7.29  % (7932)Memory used [KB]: 14711
% 15.18/7.29  % (7932)Time elapsed: 0.085 s
% 15.18/7.29  % (7932)Instructions burned: 149 (million)
% 15.18/7.29  % (7932)------------------------------
% 15.18/7.29  % (7932)------------------------------
% 15.54/7.30  % (7937)Instruction limit reached!
% 15.54/7.30  % (7937)------------------------------
% 15.54/7.30  % (7937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.30  % (7937)Termination reason: Unknown
% 15.54/7.30  % (7937)Termination phase: shuffling
% 15.54/7.30  
% 15.54/7.30  % (7937)Memory used [KB]: 13176
% 15.54/7.30  % (7937)Time elapsed: 0.029 s
% 15.54/7.30  % (7937)Instructions burned: 44 (million)
% 15.54/7.30  % (7937)------------------------------
% 15.54/7.30  % (7937)------------------------------
% 15.54/7.31  % (7940)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_7681 for (2989ds/31Mi)
% 15.54/7.31  % (7939)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7681 for (2989ds/62Mi)
% 15.54/7.31  % (7928)Instruction limit reached!
% 15.54/7.31  % (7928)------------------------------
% 15.54/7.31  % (7928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.31  % (7928)Termination reason: Unknown
% 15.54/7.31  % (7928)Termination phase: shuffling
% 15.54/7.31  
% 15.54/7.31  % (7928)Memory used [KB]: 20980
% 15.54/7.31  % (7928)Time elapsed: 0.172 s
% 15.54/7.31  % (7928)Instructions burned: 449 (million)
% 15.54/7.31  % (7928)------------------------------
% 15.54/7.31  % (7928)------------------------------
% 15.54/7.32  % (7941)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7681 for (2989ds/96Mi)
% 15.54/7.33  % (7940)Instruction limit reached!
% 15.54/7.33  % (7940)------------------------------
% 15.54/7.33  % (7940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.33  % (7940)Termination reason: Unknown
% 15.54/7.33  % (7940)Termination phase: shuffling
% 15.54/7.33  
% 15.54/7.33  % (7940)Memory used [KB]: 13048
% 15.54/7.33  % (7940)Time elapsed: 0.026 s
% 15.54/7.33  % (7940)Instructions burned: 31 (million)
% 15.54/7.33  % (7940)------------------------------
% 15.54/7.33  % (7940)------------------------------
% 15.54/7.33  % (7942)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_7681 for (2989ds/453Mi)
% 15.54/7.33  % (7939)Instruction limit reached!
% 15.54/7.33  % (7939)------------------------------
% 15.54/7.33  % (7939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.33  % (7939)Termination reason: Unknown
% 15.54/7.33  % (7939)Termination phase: shuffling
% 15.54/7.33  
% 15.54/7.33  % (7939)Memory used [KB]: 13432
% 15.54/7.33  % (7939)Time elapsed: 0.026 s
% 15.54/7.33  % (7939)Instructions burned: 62 (million)
% 15.54/7.33  % (7939)------------------------------
% 15.54/7.33  % (7939)------------------------------
% 15.54/7.35  % (7944)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7681 for (2989ds/83Mi)
% 15.54/7.35  % (7943)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_7681 for (2989ds/71Mi)
% 15.54/7.38  % (7941)Instruction limit reached!
% 15.54/7.38  % (7941)------------------------------
% 15.54/7.38  % (7941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.38  % (7941)Termination reason: Unknown
% 15.54/7.38  % (7941)Termination phase: shuffling
% 15.54/7.38  
% 15.54/7.38  % (7941)Memory used [KB]: 13944
% 15.54/7.38  % (7941)Time elapsed: 0.058 s
% 15.54/7.38  % (7941)Instructions burned: 96 (million)
% 15.54/7.38  % (7941)------------------------------
% 15.54/7.38  % (7941)------------------------------
% 15.54/7.38  % (7944)Instruction limit reached!
% 15.54/7.38  % (7944)------------------------------
% 15.54/7.38  % (7944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.38  % (7944)Termination reason: Unknown
% 15.54/7.38  % (7944)Termination phase: shuffling
% 15.54/7.38  
% 15.54/7.38  % (7944)Memory used [KB]: 13816
% 15.54/7.38  % (7944)Time elapsed: 0.036 s
% 15.54/7.38  % (7944)Instructions burned: 84 (million)
% 15.54/7.38  % (7944)------------------------------
% 15.54/7.38  % (7944)------------------------------
% 15.54/7.39  % (7946)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_7681 for (2988ds/41Mi)
% 15.54/7.39  % (7943)Instruction limit reached!
% 15.54/7.39  % (7943)------------------------------
% 15.54/7.39  % (7943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/7.39  % (7943)Termination reason: Unknown
% 15.54/7.39  % (7943)Termination phase: shuffling
% 15.54/7.39  
% 15.54/7.39  % (7943)Memory used [KB]: 13560
% 15.54/7.39  % (7943)Time elapsed: 0.046 s
% 15.54/7.39  % (7943)Instructions burned: 71 (million)
% 15.54/7.39  % (7943)------------------------------
% 15.54/7.39  % (7943)------------------------------
% 15.54/7.39  % (7945)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7681 for (2988ds/11Mi)
% 16.03/7.41  % (7945)Instruction limit reached!
% 16.03/7.41  % (7945)------------------------------
% 16.03/7.41  % (7945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/7.41  % (7945)Termination reason: Unknown
% 16.03/7.41  % (7945)Termination phase: shuffling
% 16.03/7.41  
% 16.03/7.41  % (7945)Memory used [KB]: 12920
% 16.03/7.41  % (7945)Time elapsed: 0.015 s
% 16.03/7.41  % (7945)Instructions burned: 11 (million)
% 16.03/7.41  % (7945)------------------------------
% 16.03/7.41  % (7945)------------------------------
% 16.03/7.41  % (7946)Instruction limit reached!
% 16.03/7.41  % (7946)------------------------------
% 16.03/7.41  % (7946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/7.41  % (7946)Termination reason: Unknown
% 16.03/7.41  % (7946)Termination phase: shuffling
% 16.03/7.41  
% 16.03/7.41  % (7946)Memory used [KB]: 13176
% 16.03/7.41  % (7946)Time elapsed: 0.022 s
% 16.03/7.41  % (7946)Instructions burned: 44 (million)
% 16.03/7.41  % (7946)------------------------------
% 16.03/7.41  % (7946)------------------------------
% 16.03/7.41  % (7947)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7681 for (2988ds/6Mi)
% 16.03/7.42  % (7947)Instruction limit reached!
% 16.03/7.42  % (7947)------------------------------
% 16.03/7.42  % (7947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/7.42  % (7947)Termination reason: Unknown
% 16.03/7.42  % (7947)Termination phase: shuffling
% 16.03/7.42  
% 16.03/7.42  % (7947)Memory used [KB]: 12409
% 16.03/7.42  % (7947)Time elapsed: 0.008 s
% 16.03/7.42  % (7947)Instructions burned: 6 (million)
% 16.03/7.42  % (7947)------------------------------
% 16.03/7.42  % (7947)------------------------------
% 16.03/7.42  % (7949)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7681 for (2988ds/343Mi)
% 16.03/7.43  % (7948)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7681 for (2988ds/150Mi)
% 16.03/7.44  % (7950)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_7681 for (2988ds/109Mi)
% 16.03/7.46  % (7931)Instruction limit reached!
% 16.03/7.46  % (7931)------------------------------
% 16.03/7.46  % (7931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/7.46  % (7931)Termination reason: Unknown
% 16.03/7.46  % (7931)Termination phase: shuffling
% 16.03/7.46  
% 16.03/7.46  % (7931)Memory used [KB]: 19189
% 16.03/7.46  % (7931)Time elapsed: 0.269 s
% 16.03/7.46  % (7931)Instructions burned: 508 (million)
% 16.03/7.46  % (7931)------------------------------
% 16.03/7.46  % (7931)------------------------------
% 16.03/7.48  % (7938)Instruction limit reached!
% 16.03/7.48  % (7938)------------------------------
% 16.03/7.48  % (7938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/7.48  % (7938)Termination reason: Unknown
% 16.03/7.48  % (7938)Termination phase: shuffling
% 16.03/7.48  
% 16.03/7.48  % (7938)Memory used [KB]: 20724
% 16.03/7.48  % (7938)Time elapsed: 0.209 s
% 16.03/7.48  % (7938)Instructions burned: 432 (million)
% 16.03/7.48  % (7938)------------------------------
% 16.03/7.48  % (7938)------------------------------
% 16.03/7.48  % (7951)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_7681 for (2987ds/253Mi)
% 16.62/7.50  % (7952)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7681 for (2987ds/140Mi)
% 16.62/7.50  % (7950)Instruction limit reached!
% 16.62/7.50  % (7950)------------------------------
% 16.62/7.50  % (7950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/7.50  % (7950)Termination reason: Unknown
% 16.62/7.50  % (7950)Termination phase: shuffling
% 16.62/7.50  
% 16.62/7.50  % (7950)Memory used [KB]: 14200
% 16.62/7.50  % (7950)Time elapsed: 0.066 s
% 16.62/7.50  % (7950)Instructions burned: 109 (million)
% 16.62/7.50  % (7950)------------------------------
% 16.62/7.50  % (7950)------------------------------
% 16.62/7.51  % (7948)Instruction limit reached!
% 16.62/7.51  % (7948)------------------------------
% 16.62/7.51  % (7948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/7.51  % (7948)Termination reason: Unknown
% 16.62/7.51  % (7948)Termination phase: shuffling
% 16.62/7.51  
% 16.62/7.51  % (7948)Memory used [KB]: 14711
% 16.62/7.51  % (7948)Time elapsed: 0.085 s
% 16.62/7.51  % (7948)Instructions burned: 151 (million)
% 16.62/7.51  % (7948)------------------------------
% 16.62/7.51  % (7948)------------------------------
% 16.62/7.53  % (7954)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_7681 for (2987ds/202Mi)
% 16.62/7.54  % (7953)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_7681 for (2987ds/614Mi)
% 16.62/7.55  % (7942)Instruction limit reached!
% 16.62/7.55  % (7942)------------------------------
% 16.62/7.55  % (7942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/7.55  % (7942)Termination reason: Unknown
% 16.62/7.55  % (7942)Termination phase: shuffling
% 16.62/7.55  
% 16.62/7.55  % (7942)Memory used [KB]: 21108
% 16.62/7.55  % (7942)Time elapsed: 0.219 s
% 16.62/7.55  % (7942)Instructions burned: 453 (million)
% 16.62/7.55  % (7942)------------------------------
% 16.62/7.55  % (7942)------------------------------
% 16.62/7.57  % (7949)Instruction limit reached!
% 16.62/7.57  % (7949)------------------------------
% 16.62/7.57  % (7949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/7.57  % (7949)Termination reason: Unknown
% 16.62/7.57  % (7949)Termination phase: shuffling
% 16.62/7.57  
% 16.62/7.57  % (7949)Memory used [KB]: 17270
% 16.62/7.57  % (7949)Time elapsed: 0.149 s
% 16.62/7.57  % (7949)Instructions burned: 343 (million)
% 16.62/7.57  % (7949)------------------------------
% 16.62/7.57  % (7949)------------------------------
% 16.62/7.57  % (7955)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_7681 for (2986ds/339Mi)
% 16.62/7.58  % (7952)Instruction limit reached!
% 16.62/7.58  % (7952)------------------------------
% 16.62/7.58  % (7952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/7.58  % (7952)Termination reason: Unknown
% 16.62/7.58  % (7952)Termination phase: shuffling
% 16.62/7.58  
% 16.62/7.58  % (7952)Memory used [KB]: 14456
% 16.62/7.58  % (7952)Time elapsed: 0.056 s
% 16.62/7.58  % (7952)Instructions burned: 140 (million)
% 16.62/7.58  % (7952)------------------------------
% 16.62/7.58  % (7952)------------------------------
% 16.62/7.59  % (7956)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_7681 for (2986ds/283Mi)
% 17.26/7.60  % (7957)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7681 for (2986ds/134Mi)
% 17.26/7.62  % (7951)Instruction limit reached!
% 17.26/7.62  % (7951)------------------------------
% 17.26/7.62  % (7951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/7.62  % (7951)Termination reason: Unknown
% 17.26/7.62  % (7951)Termination phase: shuffling
% 17.26/7.62  
% 17.26/7.62  % (7951)Memory used [KB]: 16247
% 17.26/7.62  % (7951)Time elapsed: 0.141 s
% 17.26/7.62  % (7951)Instructions burned: 253 (million)
% 17.26/7.62  % (7951)------------------------------
% 17.26/7.62  % (7951)------------------------------
% 17.26/7.64  % (7954)Instruction limit reached!
% 17.26/7.64  % (7954)------------------------------
% 17.26/7.64  % (7954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/7.64  % (7954)Termination reason: Unknown
% 17.26/7.64  % (7954)Termination phase: shuffling
% 17.26/7.64  
% 17.26/7.64  % (7954)Memory used [KB]: 15479
% 17.26/7.64  % (7954)Time elapsed: 0.111 s
% 17.26/7.64  % (7954)Instructions burned: 202 (million)
% 17.26/7.64  % (7954)------------------------------
% 17.26/7.64  % (7954)------------------------------
% 17.26/7.64  % (7958)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7681 for (2986ds/298Mi)
% 17.26/7.67  % (7959)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7681 for (2986ds/192Mi)
% 17.26/7.68  % (7957)Instruction limit reached!
% 17.26/7.68  % (7957)------------------------------
% 17.26/7.68  % (7957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/7.68  % (7957)Termination reason: Unknown
% 17.26/7.68  % (7957)Termination phase: shuffling
% 17.26/7.68  
% 17.26/7.68  % (7957)Memory used [KB]: 14456
% 17.26/7.68  % (7957)Time elapsed: 0.077 s
% 17.26/7.68  % (7957)Instructions burned: 135 (million)
% 17.26/7.68  % (7957)------------------------------
% 17.26/7.68  % (7957)------------------------------
% 17.26/7.68  % (7956)Instruction limit reached!
% 17.26/7.68  % (7956)------------------------------
% 17.26/7.68  % (7956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/7.68  % (7956)Termination reason: Unknown
% 17.26/7.68  % (7956)Termination phase: shuffling
% 17.26/7.68  
% 17.26/7.68  % (7956)Memory used [KB]: 18677
% 17.26/7.68  % (7956)Time elapsed: 0.094 s
% 17.26/7.68  % (7956)Instructions burned: 284 (million)
% 17.26/7.68  % (7956)------------------------------
% 17.26/7.68  % (7956)------------------------------
% 17.76/7.70  % (7961)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_7681 for (2985ds/258Mi)
% 17.76/7.70  % (7962)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_7681 for (2985ds/90Mi)
% 17.76/7.72  % (7955)Instruction limit reached!
% 17.76/7.72  % (7955)------------------------------
% 17.76/7.72  % (7955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/7.72  % (7955)Termination reason: Unknown
% 17.76/7.72  % (7955)Termination phase: shuffling
% 17.76/7.72  
% 17.76/7.72  % (7955)Memory used [KB]: 17270
% 17.76/7.72  % (7955)Time elapsed: 0.155 s
% 17.76/7.72  % (7955)Instructions burned: 340 (million)
% 17.76/7.72  % (7955)------------------------------
% 17.76/7.72  % (7955)------------------------------
% 17.76/7.74  % (7963)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_7681 for (2985ds/231Mi)
% 17.76/7.75  % (7962)Instruction limit reached!
% 17.76/7.75  % (7962)------------------------------
% 17.76/7.75  % (7962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/7.75  % (7962)Termination reason: Unknown
% 17.76/7.75  % (7962)Termination phase: shuffling
% 17.76/7.75  
% 17.76/7.75  % (7962)Memory used [KB]: 13944
% 17.76/7.75  % (7962)Time elapsed: 0.054 s
% 17.76/7.75  % (7962)Instructions burned: 91 (million)
% 17.76/7.75  % (7962)------------------------------
% 17.76/7.75  % (7962)------------------------------
% 17.76/7.76  % (7935)Instruction limit reached!
% 17.76/7.76  % (7935)------------------------------
% 17.76/7.76  % (7935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/7.76  % (7935)Termination reason: Unknown
% 17.76/7.76  % (7935)Termination phase: Property scanning
% 17.76/7.76  
% 17.76/7.76  % (7935)Memory used [KB]: 24050
% 17.76/7.76  % (7935)Time elapsed: 0.513 s
% 17.76/7.76  % (7935)Instructions burned: 1088 (million)
% 17.76/7.76  % (7935)------------------------------
% 17.76/7.76  % (7935)------------------------------
% 17.76/7.77  % (7965)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_7681 for (2984ds/458Mi)
% 17.76/7.77  % (7959)Instruction limit reached!
% 17.76/7.77  % (7959)------------------------------
% 17.76/7.77  % (7959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/7.77  % (7959)Termination reason: Unknown
% 17.76/7.77  % (7959)Termination phase: shuffling
% 17.76/7.77  
% 17.76/7.77  % (7959)Memory used [KB]: 15223
% 17.76/7.77  % (7959)Time elapsed: 0.108 s
% 17.76/7.77  % (7959)Instructions burned: 192 (million)
% 17.76/7.77  % (7959)------------------------------
% 17.76/7.77  % (7959)------------------------------
% 17.76/7.78  % (7966)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_7681 for (2984ds/31Mi)
% 17.76/7.79  % (7958)Instruction limit reached!
% 17.76/7.79  % (7958)------------------------------
% 17.76/7.79  % (7958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/7.79  % (7958)Termination reason: Unknown
% 17.76/7.79  % (7958)Termination phase: shuffling
% 17.76/7.79  
% 17.76/7.79  % (7958)Memory used [KB]: 18933
% 17.76/7.79  % (7958)Time elapsed: 0.151 s
% 17.76/7.79  % (7958)Instructions burned: 300 (million)
% 17.76/7.79  % (7958)------------------------------
% 17.76/7.79  % (7958)------------------------------
% 17.76/7.79  % (7967)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_7681 for (2984ds/297Mi)
% 18.82/7.80  % (7966)Instruction limit reached!
% 18.82/7.80  % (7966)------------------------------
% 18.82/7.80  % (7966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/7.80  % (7966)Termination reason: Unknown
% 18.82/7.80  % (7966)Termination phase: shuffling
% 18.82/7.80  
% 18.82/7.80  % (7966)Memory used [KB]: 13048
% 18.82/7.80  % (7966)Time elapsed: 0.026 s
% 18.82/7.80  % (7966)Instructions burned: 31 (million)
% 18.82/7.80  % (7966)------------------------------
% 18.82/7.80  % (7966)------------------------------
% 18.82/7.81  % (7963)Instruction limit reached!
% 18.82/7.81  % (7963)------------------------------
% 18.82/7.81  % (7963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/7.81  % (7963)Termination reason: Unknown
% 18.82/7.81  % (7963)Termination phase: shuffling
% 18.82/7.81  
% 18.82/7.81  % (7963)Memory used [KB]: 15991
% 18.82/7.81  % (7963)Time elapsed: 0.075 s
% 18.82/7.81  % (7963)Instructions burned: 231 (million)
% 18.82/7.81  % (7963)------------------------------
% 18.82/7.81  % (7963)------------------------------
% 18.82/7.82  % (7968)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_7681 for (2984ds/987Mi)
% 18.82/7.82  % (7969)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_7681 for (2984ds/182Mi)
% 18.82/7.83  % (7970)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_7681 for (2984ds/182Mi)
% 18.82/7.83  % (7961)Instruction limit reached!
% 18.82/7.83  % (7961)------------------------------
% 18.82/7.83  % (7961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/7.83  % (7961)Termination reason: Unknown
% 18.82/7.83  % (7961)Termination phase: shuffling
% 18.82/7.83  
% 18.82/7.83  % (7961)Memory used [KB]: 16119
% 18.82/7.83  % (7961)Time elapsed: 0.138 s
% 18.82/7.83  % (7961)Instructions burned: 258 (million)
% 18.82/7.83  % (7961)------------------------------
% 18.82/7.83  % (7961)------------------------------
% 18.82/7.85  % (7971)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_7681 for (2984ds/154Mi)
% 18.82/7.88  % (7953)Instruction limit reached!
% 18.82/7.88  % (7953)------------------------------
% 18.82/7.88  % (7953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/7.88  % (7953)Termination reason: Unknown
% 18.82/7.88  % (7953)Termination phase: shuffling
% 18.82/7.88  
% 18.82/7.88  % (7953)Memory used [KB]: 22771
% 18.82/7.88  % (7953)Time elapsed: 0.322 s
% 18.82/7.88  % (7953)Instructions burned: 615 (million)
% 18.82/7.88  % (7953)------------------------------
% 18.82/7.88  % (7953)------------------------------
% 18.82/7.89  % (7969)Instruction limit reached!
% 18.82/7.89  % (7969)------------------------------
% 18.82/7.89  % (7969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/7.89  % (7969)Termination reason: Unknown
% 18.82/7.89  % (7969)Termination phase: shuffling
% 18.82/7.89  
% 18.82/7.89  % (7969)Memory used [KB]: 15095
% 18.82/7.89  % (7969)Time elapsed: 0.070 s
% 18.82/7.89  % (7969)Instructions burned: 183 (million)
% 18.82/7.89  % (7969)------------------------------
% 18.82/7.89  % (7969)------------------------------
% 19.52/7.90  % (7972)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_7681 for (2983ds/79Mi)
% 19.52/7.90  % (7973)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_7681 for (2983ds/216Mi)
% 19.52/7.93  % (7970)Instruction limit reached!
% 19.52/7.93  % (7970)------------------------------
% 19.52/7.93  % (7970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/7.93  % (7970)Termination reason: Unknown
% 19.52/7.93  % (7970)Termination phase: shuffling
% 19.52/7.93  
% 19.52/7.93  % (7970)Memory used [KB]: 15223
% 19.52/7.93  % (7970)Time elapsed: 0.102 s
% 19.52/7.93  % (7970)Instructions burned: 182 (million)
% 19.52/7.93  % (7970)------------------------------
% 19.52/7.93  % (7970)------------------------------
% 19.52/7.93  % (7971)Instruction limit reached!
% 19.52/7.93  % (7971)------------------------------
% 19.52/7.93  % (7971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/7.93  % (7971)Termination reason: Unknown
% 19.52/7.93  % (7971)Termination phase: shuffling
% 19.52/7.93  
% 19.52/7.93  % (7971)Memory used [KB]: 14839
% 19.52/7.93  % (7971)Time elapsed: 0.080 s
% 19.52/7.93  % (7971)Instructions burned: 155 (million)
% 19.52/7.93  % (7971)------------------------------
% 19.52/7.93  % (7971)------------------------------
% 19.52/7.94  % (7967)Instruction limit reached!
% 19.52/7.94  % (7967)------------------------------
% 19.52/7.94  % (7967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/7.94  % (7967)Termination reason: Unknown
% 19.52/7.94  % (7967)Termination phase: shuffling
% 19.52/7.94  
% 19.52/7.94  % (7967)Memory used [KB]: 18933
% 19.52/7.94  % (7967)Time elapsed: 0.151 s
% 19.52/7.94  % (7967)Instructions burned: 297 (million)
% 19.52/7.94  % (7967)------------------------------
% 19.52/7.94  % (7967)------------------------------
% 19.52/7.94  % (7972)Instruction limit reached!
% 19.52/7.94  % (7972)------------------------------
% 19.52/7.94  % (7972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/7.94  % (7972)Termination reason: Unknown
% 19.52/7.95  % (7972)Termination phase: shuffling
% 19.52/7.95  
% 19.52/7.95  % (7972)Memory used [KB]: 13688
% 19.52/7.95  % (7972)Time elapsed: 0.050 s
% 19.52/7.95  % (7972)Instructions burned: 79 (million)
% 19.52/7.95  % (7972)------------------------------
% 19.52/7.95  % (7972)------------------------------
% 19.52/7.95  % (7975)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_7681 for (2983ds/922Mi)
% 19.52/7.95  % (7974)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7681 for (2983ds/114Mi)
% 19.52/7.96  % (7976)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_7681 for (2983ds/182Mi)
% 19.52/7.96  % (7977)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_7681 for (2982ds/164Mi)
% 19.52/7.97  % (7973)Instruction limit reached!
% 19.52/7.97  % (7973)------------------------------
% 19.52/7.97  % (7973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/7.97  % (7973)Termination reason: Unknown
% 19.52/7.97  % (7973)Termination phase: shuffling
% 19.52/7.97  
% 19.52/7.97  % (7973)Memory used [KB]: 15735
% 19.52/7.97  % (7973)Time elapsed: 0.071 s
% 19.52/7.97  % (7973)Instructions burned: 218 (million)
% 19.52/7.97  % (7973)------------------------------
% 19.52/7.97  % (7973)------------------------------
% 19.52/7.98  % (7978)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_7681 for (2982ds/50Mi)
% 19.52/8.00  % (7978)Instruction limit reached!
% 19.52/8.00  % (7978)------------------------------
% 19.52/8.00  % (7978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/8.00  % (7978)Termination reason: Unknown
% 19.52/8.00  % (7978)Termination phase: shuffling
% 19.52/8.00  
% 19.52/8.00  % (7978)Memory used [KB]: 13304
% 19.52/8.00  % (7978)Time elapsed: 0.023 s
% 19.52/8.00  % (7978)Instructions burned: 52 (million)
% 19.52/8.00  % (7978)------------------------------
% 19.52/8.00  % (7978)------------------------------
% 19.52/8.01  % (7965)Instruction limit reached!
% 19.52/8.01  % (7965)------------------------------
% 19.52/8.01  % (7965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/8.01  % (7965)Termination reason: Unknown
% 19.52/8.01  % (7965)Termination phase: shuffling
% 19.52/8.01  
% 19.52/8.01  % (7965)Memory used [KB]: 18805
% 19.52/8.01  % (7965)Time elapsed: 0.241 s
% 19.52/8.01  % (7965)Instructions burned: 458 (million)
% 19.52/8.01  % (7965)------------------------------
% 19.52/8.01  % (7965)------------------------------
% 19.52/8.01  % (7974)Instruction limit reached!
% 19.52/8.01  % (7974)------------------------------
% 19.52/8.01  % (7974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.52/8.01  % (7974)Termination reason: Unknown
% 19.52/8.01  % (7974)Termination phase: shuffling
% 19.52/8.01  
% 19.52/8.01  % (7974)Memory used [KB]: 14200
% 19.52/8.01  % (7974)Time elapsed: 0.068 s
% 19.52/8.01  % (7974)Instructions burned: 114 (million)
% 19.52/8.01  % (7974)------------------------------
% 19.52/8.01  % (7974)------------------------------
% 19.52/8.02  % (7979)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7681 for (2982ds/368Mi)
% 20.84/8.03  % (7981)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_7681 for (2982ds/267Mi)
% 20.84/8.03  % (7980)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_7681 for (2982ds/1021Mi)
% 20.84/8.05  % (7977)Instruction limit reached!
% 20.84/8.05  % (7977)------------------------------
% 20.84/8.05  % (7977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/8.05  % (7977)Termination reason: Unknown
% 20.84/8.05  % (7977)Termination phase: shuffling
% 20.84/8.05  
% 20.84/8.05  % (7977)Memory used [KB]: 14967
% 20.84/8.05  % (7977)Time elapsed: 0.087 s
% 20.84/8.05  % (7977)Instructions burned: 165 (million)
% 20.84/8.05  % (7977)------------------------------
% 20.84/8.05  % (7977)------------------------------
% 20.84/8.05  % (7976)Instruction limit reached!
% 20.84/8.05  % (7976)------------------------------
% 20.84/8.05  % (7976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/8.05  % (7976)Termination reason: Unknown
% 20.84/8.05  % (7976)Termination phase: shuffling
% 20.84/8.05  
% 20.84/8.05  % (7976)Memory used [KB]: 15223
% 20.84/8.05  % (7976)Time elapsed: 0.096 s
% 20.84/8.05  % (7976)Instructions burned: 182 (million)
% 20.84/8.05  % (7976)------------------------------
% 20.84/8.05  % (7976)------------------------------
% 20.84/8.07  % (7982)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_7681 for (2981ds/204Mi)
% 20.84/8.07  % (7983)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_7681 for (2981ds/26Mi)
% 20.84/8.10  % (7983)Instruction limit reached!
% 20.84/8.10  % (7983)------------------------------
% 20.84/8.10  % (7983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/8.10  % (7983)Termination reason: Unknown
% 20.84/8.10  % (7983)Termination phase: shuffling
% 20.84/8.10  
% 20.84/8.10  % (7983)Memory used [KB]: 13048
% 20.84/8.10  % (7983)Time elapsed: 0.023 s
% 20.84/8.10  % (7983)Instructions burned: 27 (million)
% 20.84/8.10  % (7983)------------------------------
% 20.84/8.10  % (7983)------------------------------
% 20.84/8.12  % (7984)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_7681 for (2981ds/53Mi)
% 21.17/8.15  % (7979)Instruction limit reached!
% 21.17/8.15  % (7979)------------------------------
% 21.17/8.15  % (7979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/8.15  % (7979)Termination reason: Unknown
% 21.17/8.15  % (7979)Termination phase: shuffling
% 21.17/8.15  
% 21.17/8.15  % (7979)Memory used [KB]: 17654
% 21.17/8.15  % (7979)Time elapsed: 0.132 s
% 21.17/8.15  % (7979)Instructions burned: 370 (million)
% 21.17/8.15  % (7979)------------------------------
% 21.17/8.15  % (7979)------------------------------
% 21.17/8.16  % (7984)Instruction limit reached!
% 21.17/8.16  % (7984)------------------------------
% 21.17/8.16  % (7984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/8.16  % (7984)Termination reason: Unknown
% 21.17/8.16  % (7984)Termination phase: shuffling
% 21.17/8.16  
% 21.17/8.16  % (7984)Memory used [KB]: 13304
% 21.17/8.16  % (7984)Time elapsed: 0.036 s
% 21.17/8.16  % (7984)Instructions burned: 53 (million)
% 21.17/8.16  % (7984)------------------------------
% 21.17/8.16  % (7984)------------------------------
% 21.17/8.16  % (7985)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_7681 for (2980ds/4436Mi)
% 21.17/8.16  % (7981)Instruction limit reached!
% 21.17/8.16  % (7981)------------------------------
% 21.17/8.16  % (7981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/8.16  % (7981)Termination reason: Unknown
% 21.17/8.16  % (7981)Termination phase: shuffling
% 21.17/8.16  
% 21.17/8.16  % (7981)Memory used [KB]: 18421
% 21.17/8.16  % (7981)Time elapsed: 0.133 s
% 21.17/8.16  % (7981)Instructions burned: 268 (million)
% 21.17/8.16  % (7981)------------------------------
% 21.17/8.16  % (7981)------------------------------
% 21.17/8.18  % (7986)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_7681 for (2980ds/1539Mi)
% 21.17/8.18  % (7982)Instruction limit reached!
% 21.17/8.18  % (7982)------------------------------
% 21.17/8.18  % (7982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/8.18  % (7982)Termination reason: Unknown
% 21.17/8.18  % (7982)Termination phase: shuffling
% 21.17/8.18  
% 21.17/8.18  % (7987)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_7681 for (2980ds/408Mi)
% 21.17/8.18  % (7982)Memory used [KB]: 15479
% 21.17/8.18  % (7982)Time elapsed: 0.113 s
% 21.17/8.18  % (7982)Instructions burned: 204 (million)
% 21.17/8.18  % (7982)------------------------------
% 21.17/8.18  % (7982)------------------------------
% 21.78/8.20  % (7988)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_7681 for (2980ds/5205Mi)
% 21.97/8.30  % (7968)Instruction limit reached!
% 21.97/8.30  % (7968)------------------------------
% 21.97/8.30  % (7968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.97/8.30  % (7968)Termination reason: Unknown
% 21.97/8.30  % (7968)Termination phase: shuffling
% 21.97/8.30  
% 21.97/8.30  % (7968)Memory used [KB]: 32366
% 21.97/8.30  % (7968)Time elapsed: 0.479 s
% 21.97/8.30  % (7968)Instructions burned: 988 (million)
% 21.97/8.30  % (7968)------------------------------
% 21.97/8.30  % (7968)------------------------------
% 21.97/8.31  % (7989)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_7681 for (2979ds/1913Mi)
% 21.97/8.39  % (7987)Instruction limit reached!
% 21.97/8.39  % (7987)------------------------------
% 21.97/8.39  % (7987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.97/8.39  % (7987)Termination reason: Unknown
% 21.97/8.39  % (7987)Termination phase: shuffling
% 21.97/8.39  
% 21.97/8.39  % (7987)Memory used [KB]: 18293
% 21.97/8.39  % (7987)Time elapsed: 0.213 s
% 21.97/8.39  % (7987)Instructions burned: 408 (million)
% 21.97/8.39  % (7987)------------------------------
% 21.97/8.39  % (7987)------------------------------
% 22.11/8.42  % (7975)Instruction limit reached!
% 22.11/8.42  % (7975)------------------------------
% 22.11/8.42  % (7975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.11/8.42  % (7975)Termination reason: Unknown
% 22.11/8.42  % (7975)Termination phase: Property scanning
% 22.11/8.42  
% 22.11/8.42  % (7975)Memory used [KB]: 24050
% 22.11/8.42  % (7975)Time elapsed: 0.468 s
% 22.11/8.42  % (7975)Instructions burned: 923 (million)
% 22.11/8.42  % (7975)------------------------------
% 22.11/8.42  % (7975)------------------------------
% 22.11/8.42  % (7991)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_7681 for (2978ds/4350Mi)
% 22.11/8.44  % (7992)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_7681 for (2978ds/68Mi)
% 22.11/8.48  % (7992)Instruction limit reached!
% 22.11/8.48  % (7992)------------------------------
% 22.11/8.48  % (7992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.11/8.48  % (7992)Termination reason: Unknown
% 22.11/8.48  % (7992)Termination phase: shuffling
% 22.11/8.48  
% 22.11/8.48  % (7992)Memory used [KB]: 13560
% 22.11/8.48  % (7992)Time elapsed: 0.044 s
% 22.11/8.48  % (7992)Instructions burned: 69 (million)
% 22.11/8.48  % (7992)------------------------------
% 22.11/8.48  % (7992)------------------------------
% 22.11/8.50  % (7994)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_7681 for (2977ds/358Mi)
% 22.44/8.54  % (7980)Instruction limit reached!
% 22.44/8.54  % (7980)------------------------------
% 22.44/8.54  % (7980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/8.54  % (7980)Termination reason: Unknown
% 22.44/8.54  % (7980)Termination phase: Property scanning
% 22.44/8.54  
% 22.44/8.54  % (7980)Memory used [KB]: 24050
% 22.44/8.54  % (7980)Time elapsed: 0.512 s
% 22.44/8.54  % (7980)Instructions burned: 1022 (million)
% 22.44/8.54  % (7980)------------------------------
% 22.44/8.54  % (7980)------------------------------
% 22.44/8.56  % (7995)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_7681 for (2976ds/31Mi)
% 22.44/8.59  % (7995)Instruction limit reached!
% 22.44/8.59  % (7995)------------------------------
% 22.44/8.59  % (7995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.44/8.59  % (7995)Termination reason: Unknown
% 22.44/8.59  % (7995)Termination phase: shuffling
% 22.44/8.59  
% 22.44/8.59  % (7995)Memory used [KB]: 13048
% 22.44/8.59  % (7995)Time elapsed: 0.027 s
% 22.44/8.59  % (7995)Instructions burned: 33 (million)
% 22.44/8.59  % (7995)------------------------------
% 22.44/8.59  % (7995)------------------------------
% 23.00/8.61  % (7996)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7681 for (2976ds/279Mi)
% 23.00/8.65  % (7994)Instruction limit reached!
% 23.00/8.65  % (7994)------------------------------
% 23.00/8.65  % (7994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.00/8.65  % (7994)Termination reason: Unknown
% 23.00/8.65  % (7994)Termination phase: shuffling
% 23.00/8.65  
% 23.00/8.65  % (7994)Memory used [KB]: 17526
% 23.00/8.65  % (7994)Time elapsed: 0.158 s
% 23.00/8.65  % (7994)Instructions burned: 359 (million)
% 23.00/8.65  % (7994)------------------------------
% 23.00/8.65  % (7994)------------------------------
% 23.00/8.67  % (7997)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7681 for (2975ds/258Mi)
% 23.19/8.75  % (7996)Instruction limit reached!
% 23.19/8.75  % (7996)------------------------------
% 23.19/8.75  % (7996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.19/8.75  % (7996)Termination reason: Unknown
% 23.19/8.75  % (7996)Termination phase: shuffling
% 23.19/8.75  
% 23.19/8.75  % (7996)Memory used [KB]: 18677
% 23.19/8.75  % (7996)Time elapsed: 0.140 s
% 23.19/8.75  % (7996)Instructions burned: 280 (million)
% 23.19/8.75  % (7996)------------------------------
% 23.19/8.75  % (7996)------------------------------
% 23.19/8.77  % (7998)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_7681 for (2974ds/26Mi)
% 23.19/8.79  % (7998)Instruction limit reached!
% 23.19/8.79  % (7998)------------------------------
% 23.19/8.79  % (7998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.19/8.79  % (7998)Termination reason: Unknown
% 23.19/8.79  % (7998)Termination phase: shuffling
% 23.19/8.79  
% 23.19/8.79  % (7998)Memory used [KB]: 13048
% 23.19/8.79  % (7998)Time elapsed: 0.023 s
% 23.19/8.79  % (7998)Instructions burned: 26 (million)
% 23.19/8.79  % (7998)------------------------------
% 23.19/8.79  % (7998)------------------------------
% 23.38/8.81  % (7985)First to succeed.
% 23.38/8.81  % (7997)Instruction limit reached!
% 23.38/8.81  % (7997)------------------------------
% 23.38/8.81  % (7997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.38/8.81  % (7997)Termination reason: Unknown
% 23.38/8.81  % (7997)Termination phase: shuffling
% 23.38/8.81  
% 23.38/8.81  % (7997)Memory used [KB]: 16119
% 23.38/8.81  % (7997)Time elapsed: 0.140 s
% 23.38/8.81  % (7997)Instructions burned: 258 (million)
% 23.38/8.81  % (7997)------------------------------
% 23.38/8.81  % (7997)------------------------------
% 23.38/8.82  % (7985)Refutation found. Thanks to Tanya!
% 23.38/8.82  % SZS status Theorem for DTF2THF_7681
% 23.38/8.82  % SZS output start Proof for DTF2THF_7681
% 23.38/8.82  thf(type_def_5, type, rat: $tType).
% 23.38/8.82  thf(type_def_6, type, int: $tType).
% 23.38/8.82  thf(type_def_8, type, real: $tType).
% 23.38/8.82  thf(type_def_9, type, nat: $tType).
% 23.38/8.82  thf(type_def_10, type, complex: $tType).
% 23.38/8.82  thf(type_def_11, type, product_prod_int_int: $tType).
% 23.38/8.82  thf(type_def_12, type, num: $tType).
% 23.38/8.82  thf(type_def_13, type, option_num: $tType).
% 23.38/8.82  thf(type_def_14, type, product_prod_num_num: $tType).
% 23.38/8.82  thf(type_def_15, type, code_integer: $tType).
% 23.38/8.82  thf(type_def_16, type, produc6271795597528267376eger_o: $tType).
% 23.38/8.82  thf(type_def_17, type, produc8923325533196201883nteger: $tType).
% 23.38/8.82  thf(type_def_18, type, set_fi4554929511873752355omplex: $tType).
% 23.38/8.82  thf(type_def_19, type, filter6041513312241820739omplex: $tType).
% 23.38/8.82  thf(type_def_20, type, set_fi7789364187291644575l_real: $tType).
% 23.38/8.82  thf(type_def_21, type, filter2146258269922977983l_real: $tType).
% 23.38/8.82  thf(type_def_22, type, set_real: $tType).
% 23.38/8.82  thf(type_def_23, type, set_set_nat: $tType).
% 23.38/8.82  thf(type_def_24, type, set_nat: $tType).
% 23.38/8.82  thf(type_def_25, type, set_int: $tType).
% 23.38/8.82  thf(type_def_26, type, filter_real: $tType).
% 23.38/8.82  thf(type_def_27, type, product_prod_nat_nat: $tType).
% 23.38/8.82  thf(type_def_28, type, extended_enat: $tType).
% 23.38/8.82  thf(type_def_29, type, filter_nat: $tType).
% 23.38/8.82  thf(type_def_30, type, set_Pr5085853215250843933omplex: $tType).
% 23.38/8.82  thf(type_def_31, type, set_Pr6218003697084177305l_real: $tType).
% 23.38/8.82  thf(type_def_32, type, set_o: $tType).
% 23.38/8.82  thf(type_def_33, type, set_complex: $tType).
% 23.38/8.82  thf(type_def_34, type, set_list_nat: $tType).
% 23.38/8.82  thf(type_def_35, type, set_Product_unit: $tType).
% 23.38/8.82  thf(type_def_36, type, set_char: $tType).
% 23.38/8.82  thf(type_def_37, type, char: $tType).
% 23.38/8.82  thf(type_def_38, type, set_Pr1261947904930325089at_nat: $tType).
% 23.38/8.82  thf(type_def_39, type, list_o: $tType).
% 23.38/8.82  thf(type_def_40, type, list_nat: $tType).
% 23.38/8.82  thf(type_def_41, type, list_int: $tType).
% 23.38/8.82  thf(type_def_42, type, set_Pr958786334691620121nt_int: $tType).
% 23.38/8.82  thf(type_def_43, type, set_Code_integer: $tType).
% 23.38/8.82  thf(type_def_44, type, set_rat: $tType).
% 23.38/8.82  thf(type_def_45, type, list_list_o: $tType).
% 23.38/8.82  thf(type_def_46, type, list_list_int: $tType).
% 23.38/8.82  thf(type_def_47, type, list_list_nat: $tType).
% 23.38/8.82  thf(type_def_48, type, list_list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(type_def_49, type, list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(type_def_50, type, list_complex: $tType).
% 23.38/8.82  thf(type_def_51, type, set_list_o: $tType).
% 23.38/8.82  thf(type_def_52, type, set_list_int: $tType).
% 23.38/8.82  thf(type_def_53, type, set_list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(type_def_54, type, list_P6011104703257516679at_nat: $tType).
% 23.38/8.82  thf(type_def_55, type, list_real: $tType).
% 23.38/8.82  thf(type_def_56, type, set_VEBT_VEBT: $tType).
% 23.38/8.82  thf(type_def_57, type, vEBT_VEBT: $tType).
% 23.38/8.82  thf(type_def_58, type, list_Code_integer: $tType).
% 23.38/8.82  thf(type_def_59, type, list_num: $tType).
% 23.38/8.82  thf(type_def_60, type, list_P4002435161011370285od_o_o: $tType).
% 23.38/8.82  thf(type_def_61, type, product_prod_o_o: $tType).
% 23.38/8.82  thf(type_def_62, type, list_P3795440434834930179_o_int: $tType).
% 23.38/8.82  thf(type_def_63, type, product_prod_o_int: $tType).
% 23.38/8.82  thf(type_def_64, type, list_P6285523579766656935_o_nat: $tType).
% 23.38/8.82  thf(type_def_65, type, product_prod_o_nat: $tType).
% 23.38/8.82  thf(type_def_66, type, list_P7495141550334521929T_VEBT: $tType).
% 23.38/8.82  thf(type_def_67, type, produc2504756804600209347T_VEBT: $tType).
% 23.38/8.82  thf(type_def_68, type, list_P8526636022914148096eger_o: $tType).
% 23.38/8.82  thf(type_def_69, type, list_P3744719386663036955um_num: $tType).
% 23.38/8.82  thf(type_def_70, type, list_P3126845725202233233VEBT_o: $tType).
% 23.38/8.82  thf(type_def_71, type, produc334124729049499915VEBT_o: $tType).
% 23.38/8.82  thf(type_def_72, type, list_P4547456442757143711BT_int: $tType).
% 23.38/8.82  thf(type_def_73, type, produc4894624898956917775BT_int: $tType).
% 23.38/8.82  thf(type_def_74, type, list_P7037539587688870467BT_nat: $tType).
% 23.38/8.82  thf(type_def_75, type, produc9072475918466114483BT_nat: $tType).
% 23.38/8.82  thf(type_def_76, type, list_P7413028617227757229T_VEBT: $tType).
% 23.38/8.82  thf(type_def_77, type, produc8243902056947475879T_VEBT: $tType).
% 23.38/8.82  thf(type_def_78, type, list_P7333126701944960589_nat_o: $tType).
% 23.38/8.82  thf(type_def_79, type, list_P5647936690300460905T_VEBT: $tType).
% 23.38/8.82  thf(type_def_80, type, option4927543243414619207at_nat: $tType).
% 23.38/8.82  thf(type_def_81, type, set_num: $tType).
% 23.38/8.82  thf(type_def_82, type, set_set_int: $tType).
% 23.38/8.82  thf(type_def_83, type, produc7248412053542808358at_nat: $tType).
% 23.38/8.82  thf(type_def_84, type, produc4471711990508489141at_nat: $tType).
% 23.38/8.82  thf(type_def_85, type, produc2963631642982155120at_num: $tType).
% 23.38/8.82  thf(type_def_86, type, produc3368934014287244435at_num: $tType).
% 23.38/8.82  thf(type_def_87, type, product_prod_nat_num: $tType).
% 23.38/8.82  thf(type_def_88, type, produc4411394909380815293omplex: $tType).
% 23.38/8.82  thf(type_def_89, type, produc2422161461964618553l_real: $tType).
% 23.38/8.82  thf(func_def_0, type, produc3368934014287244435at_num: $tType).
% 23.38/8.82  thf(func_def_1, type, produc4471711990508489141at_nat: $tType).
% 23.38/8.82  thf(func_def_2, type, set_fi4554929511873752355omplex: $tType).
% 23.38/8.82  thf(func_def_3, type, list_P7413028617227757229T_VEBT: $tType).
% 23.38/8.82  thf(func_def_4, type, produc2963631642982155120at_num: $tType).
% 23.38/8.82  thf(func_def_5, type, produc7248412053542808358at_nat: $tType).
% 23.38/8.82  thf(func_def_6, type, set_fi7789364187291644575l_real: $tType).
% 23.38/8.82  thf(func_def_7, type, filter6041513312241820739omplex: $tType).
% 23.38/8.82  thf(func_def_8, type, list_P7037539587688870467BT_nat: $tType).
% 23.38/8.82  thf(func_def_9, type, list_P4547456442757143711BT_int: $tType).
% 23.38/8.82  thf(func_def_10, type, list_P5647936690300460905T_VEBT: $tType).
% 23.38/8.82  thf(func_def_11, type, produc8243902056947475879T_VEBT: $tType).
% 23.38/8.82  thf(func_def_12, type, set_Pr5085853215250843933omplex: $tType).
% 23.38/8.82  thf(func_def_13, type, produc8923325533196201883nteger: $tType).
% 23.38/8.82  thf(func_def_14, type, list_P3126845725202233233VEBT_o: $tType).
% 23.38/8.82  thf(func_def_15, type, list_P7495141550334521929T_VEBT: $tType).
% 23.38/8.82  thf(func_def_16, type, filter2146258269922977983l_real: $tType).
% 23.38/8.82  thf(func_def_17, type, list_P8526636022914148096eger_o: $tType).
% 23.38/8.82  thf(func_def_18, type, option4927543243414619207at_nat: $tType).
% 23.38/8.82  thf(func_def_19, type, set_Pr6218003697084177305l_real: $tType).
% 23.38/8.82  thf(func_def_20, type, list_P3744719386663036955um_num: $tType).
% 23.38/8.82  thf(func_def_21, type, list_P6011104703257516679at_nat: $tType).
% 23.38/8.82  thf(func_def_22, type, produc9072475918466114483BT_nat: $tType).
% 23.38/8.82  thf(func_def_23, type, produc4894624898956917775BT_int: $tType).
% 23.38/8.82  thf(func_def_24, type, set_Pr1261947904930325089at_nat: $tType).
% 23.38/8.82  thf(func_def_25, type, set_Pr958786334691620121nt_int: $tType).
% 23.38/8.82  thf(func_def_26, type, produc4411394909380815293omplex: $tType).
% 23.38/8.82  thf(func_def_27, type, list_list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(func_def_28, type, list_P7333126701944960589_nat_o: $tType).
% 23.38/8.82  thf(func_def_29, type, list_P6285523579766656935_o_nat: $tType).
% 23.38/8.82  thf(func_def_30, type, list_P3795440434834930179_o_int: $tType).
% 23.38/8.82  thf(func_def_31, type, set_list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(func_def_32, type, produc334124729049499915VEBT_o: $tType).
% 23.38/8.82  thf(func_def_33, type, produc2504756804600209347T_VEBT: $tType).
% 23.38/8.82  thf(func_def_34, type, produc6271795597528267376eger_o: $tType).
% 23.38/8.82  thf(func_def_35, type, produc2422161461964618553l_real: $tType).
% 23.38/8.82  thf(func_def_36, type, product_prod_num_num: $tType).
% 23.38/8.82  thf(func_def_37, type, product_prod_nat_num: $tType).
% 23.38/8.82  thf(func_def_38, type, product_prod_nat_nat: $tType).
% 23.38/8.82  thf(func_def_39, type, product_prod_int_int: $tType).
% 23.38/8.82  thf(func_def_40, type, list_P4002435161011370285od_o_o: $tType).
% 23.38/8.82  thf(func_def_41, type, list_list_nat: $tType).
% 23.38/8.82  thf(func_def_42, type, list_list_int: $tType).
% 23.38/8.82  thf(func_def_43, type, list_VEBT_VEBT: $tType).
% 23.38/8.82  thf(func_def_44, type, set_list_nat: $tType).
% 23.38/8.82  thf(func_def_45, type, set_list_int: $tType).
% 23.38/8.82  thf(func_def_46, type, product_prod_o_nat: $tType).
% 23.38/8.82  thf(func_def_47, type, product_prod_o_int: $tType).
% 23.38/8.82  thf(func_def_48, type, list_Code_integer: $tType).
% 23.38/8.82  thf(func_def_49, type, set_VEBT_VEBT: $tType).
% 23.38/8.82  thf(func_def_50, type, set_set_nat: $tType).
% 23.38/8.82  thf(func_def_51, type, set_set_int: $tType).
% 23.38/8.82  thf(func_def_52, type, set_Code_integer: $tType).
% 23.38/8.82  thf(func_def_53, type, set_Product_unit: $tType).
% 23.38/8.82  thf(func_def_54, type, list_list_o: $tType).
% 23.38/8.82  thf(func_def_55, type, list_complex: $tType).
% 23.38/8.82  thf(func_def_56, type, set_list_o: $tType).
% 23.38/8.82  thf(func_def_57, type, product_prod_o_o: $tType).
% 23.38/8.82  thf(func_def_58, type, set_complex: $tType).
% 23.38/8.82  thf(func_def_59, type, filter_real: $tType).
% 23.38/8.82  thf(func_def_60, type, option_num: $tType).
% 23.38/8.82  thf(func_def_61, type, filter_nat: $tType).
% 23.38/8.82  thf(func_def_62, type, set_char: $tType).
% 23.38/8.82  thf(func_def_63, type, list_real: $tType).
% 23.38/8.82  thf(func_def_64, type, set_real: $tType).
% 23.38/8.82  thf(func_def_65, type, list_num: $tType).
% 23.38/8.82  thf(func_def_66, type, list_nat: $tType).
% 23.38/8.82  thf(func_def_67, type, list_int: $tType).
% 23.38/8.82  thf(func_def_68, type, vEBT_VEBT: $tType).
% 23.38/8.82  thf(func_def_69, type, set_rat: $tType).
% 23.38/8.82  thf(func_def_70, type, set_num: $tType).
% 23.38/8.82  thf(func_def_71, type, set_nat: $tType).
% 23.38/8.82  thf(func_def_72, type, set_int: $tType).
% 23.38/8.82  thf(func_def_73, type, code_integer: $tType).
% 23.38/8.82  thf(func_def_74, type, extended_enat: $tType).
% 23.38/8.82  thf(func_def_75, type, list_o: $tType).
% 23.38/8.82  thf(func_def_76, type, complex: $tType).
% 23.38/8.82  thf(func_def_77, type, set_o: $tType).
% 23.38/8.82  thf(func_def_78, type, char: $tType).
% 23.38/8.82  thf(func_def_79, type, real: $tType).
% 23.38/8.82  thf(func_def_80, type, rat: $tType).
% 23.38/8.82  thf(func_def_81, type, num: $tType).
% 23.38/8.82  thf(func_def_82, type, nat: $tType).
% 23.38/8.82  thf(func_def_83, type, int: $tType).
% 23.38/8.82  thf(func_def_84, type, archim2889992004027027881ng_rat: rat > int).
% 23.38/8.82  thf(func_def_85, type, archim7802044766580827645g_real: real > int).
% 23.38/8.82  thf(func_def_86, type, archim3151403230148437115or_rat: rat > int).
% 23.38/8.82  thf(func_def_87, type, archim6058952711729229775r_real: real > int).
% 23.38/8.82  thf(func_def_88, type, archimedean_frac_rat: rat > rat).
% 23.38/8.82  thf(func_def_89, type, archim2898591450579166408c_real: real > real).
% 23.38/8.82  thf(func_def_90, type, archim7778729529865785530nd_rat: rat > int).
% 23.38/8.82  thf(func_def_91, type, archim8280529875227126926d_real: real > int).
% 23.38/8.82  thf(func_def_92, type, binomial: nat > nat > nat).
% 23.38/8.82  thf(func_def_93, type, gbinomial_complex: complex > nat > complex).
% 23.38/8.82  thf(func_def_94, type, gbinomial_int: int > nat > int).
% 23.38/8.82  thf(func_def_95, type, gbinomial_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_96, type, gbinomial_rat: rat > nat > rat).
% 23.38/8.82  thf(func_def_97, type, gbinomial_real: real > nat > real).
% 23.38/8.82  thf(func_def_98, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_99, type, bit_and_not_num: num > num > option_num).
% 23.38/8.82  thf(func_def_100, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_101, type, bit_concat_bit: nat > int > int > int).
% 23.38/8.82  thf(func_def_102, type, bit_or_not_num_neg: num > num > num).
% 23.38/8.82  thf(func_def_103, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_104, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 23.38/8.82  thf(func_def_105, type, bit_ri7919022796975470100ot_int: int > int).
% 23.38/8.82  thf(func_def_106, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_107, type, bit_ri631733984087533419it_int: nat > int > int).
% 23.38/8.82  thf(func_def_108, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_109, type, bit_se725231765392027082nd_int: int > int > int).
% 23.38/8.82  thf(func_def_110, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_111, type, bit_se8568078237143864401it_int: nat > int > int).
% 23.38/8.82  thf(func_def_112, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_113, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_114, type, bit_se2159334234014336723it_int: nat > int > int).
% 23.38/8.82  thf(func_def_115, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_116, type, bit_se2119862282449309892nteger: nat > code_integer).
% 23.38/8.82  thf(func_def_117, type, bit_se2000444600071755411sk_int: nat > int).
% 23.38/8.82  thf(func_def_118, type, bit_se2002935070580805687sk_nat: nat > nat).
% 23.38/8.82  thf(func_def_119, type, bit_se1409905431419307370or_int: int > int > int).
% 23.38/8.82  thf(func_def_120, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_121, type, bit_se7788150548672797655nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_122, type, bit_se545348938243370406it_int: nat > int > int).
% 23.38/8.82  thf(func_def_123, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_124, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_125, type, bit_se7879613467334960850it_int: nat > int > int).
% 23.38/8.82  thf(func_def_126, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_127, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_128, type, bit_se2923211474154528505it_int: nat > int > int).
% 23.38/8.82  thf(func_def_129, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_130, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 23.38/8.82  thf(func_def_131, type, bit_se4203085406695923979it_int: nat > int > int).
% 23.38/8.82  thf(func_def_132, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_133, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_134, type, bit_se6526347334894502574or_int: int > int > int).
% 23.38/8.82  thf(func_def_135, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_136, type, bit_se9216721137139052372nteger: code_integer > nat > $o).
% 23.38/8.82  thf(func_def_137, type, bit_se1146084159140164899it_int: int > nat > $o).
% 23.38/8.82  thf(func_def_138, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 23.38/8.82  thf(func_def_139, type, bit_take_bit_num: nat > num > option_num).
% 23.38/8.82  thf(func_def_140, type, bit_un1837492267222099188nd_num: num > num > option_num).
% 23.38/8.82  thf(func_def_141, type, bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_142, type, bit_un6178654185764691216or_num: num > num > option_num).
% 23.38/8.82  thf(func_def_143, type, bit_un3595099601533988841um_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_144, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 23.38/8.82  thf(func_def_145, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_146, type, bit_un2480387367778600638or_num: num > num > option_num).
% 23.38/8.82  thf(func_def_147, type, bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_148, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 23.38/8.82  thf(func_def_149, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_150, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_151, type, code_int_of_integer: code_integer > int).
% 23.38/8.82  thf(func_def_152, type, code_integer_of_int: int > code_integer).
% 23.38/8.82  thf(func_def_153, type, code_integer_of_num: num > code_integer).
% 23.38/8.82  thf(func_def_154, type, code_nat_of_integer: code_integer > nat).
% 23.38/8.82  thf(func_def_155, type, code_num_of_integer: code_integer > num).
% 23.38/8.82  thf(func_def_156, type, comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex).
% 23.38/8.82  thf(func_def_157, type, comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real).
% 23.38/8.82  thf(func_def_158, type, comple4887499456419720421f_real: set_real > real).
% 23.38/8.82  thf(func_def_159, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 23.38/8.82  thf(func_def_160, type, complete_Sup_Sup_int: set_int > int).
% 23.38/8.82  thf(func_def_161, type, comple1385675409528146559p_real: set_real > real).
% 23.38/8.82  thf(func_def_162, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 23.38/8.82  thf(func_def_163, type, arg: complex > real).
% 23.38/8.82  thf(func_def_164, type, cis: real > complex).
% 23.38/8.82  thf(func_def_165, type, cnj: complex > complex).
% 23.38/8.82  thf(func_def_166, type, complex2: real > real > complex).
% 23.38/8.82  thf(func_def_167, type, im: complex > real).
% 23.38/8.82  thf(func_def_168, type, re: complex > real).
% 23.38/8.82  thf(func_def_169, type, csqrt: complex > complex).
% 23.38/8.82  thf(func_def_170, type, imaginary_unit: complex).
% 23.38/8.82  thf(func_def_171, type, rcis: real > real > complex).
% 23.38/8.82  thf(func_def_172, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 23.38/8.82  thf(func_def_173, type, has_de1759254742604945161l_real: (real > real) > (real > real) > filter_real > $o).
% 23.38/8.82  thf(func_def_174, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 23.38/8.82  thf(func_def_175, type, adjust_div: product_prod_int_int > int).
% 23.38/8.82  thf(func_def_176, type, adjust_mod: int > int > int).
% 23.38/8.82  thf(func_def_177, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_178, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_179, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 23.38/8.82  thf(func_def_180, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_181, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_182, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_183, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 23.38/8.82  thf(func_def_184, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_185, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_186, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 23.38/8.82  thf(func_def_187, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_188, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 23.38/8.82  thf(func_def_189, type, comm_s2602460028002588243omplex: complex > nat > complex).
% 23.38/8.82  thf(func_def_190, type, comm_s4660882817536571857er_int: int > nat > int).
% 23.38/8.82  thf(func_def_191, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_192, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 23.38/8.82  thf(func_def_193, type, comm_s7457072308508201937r_real: real > nat > real).
% 23.38/8.82  thf(func_def_194, type, semiri3624122377584611663nteger: nat > code_integer).
% 23.38/8.82  thf(func_def_195, type, semiri5044797733671781792omplex: nat > complex).
% 23.38/8.82  thf(func_def_196, type, semiri4449623510593786356d_enat: nat > extended_enat).
% 23.38/8.82  thf(func_def_197, type, semiri1406184849735516958ct_int: nat > int).
% 23.38/8.82  thf(func_def_198, type, semiri1408675320244567234ct_nat: nat > nat).
% 23.38/8.82  thf(func_def_199, type, semiri773545260158071498ct_rat: nat > rat).
% 23.38/8.82  thf(func_def_200, type, semiri2265585572941072030t_real: nat > real).
% 23.38/8.82  thf(func_def_201, type, invers8013647133539491842omplex: complex > complex).
% 23.38/8.82  thf(func_def_202, type, inverse_inverse_rat: rat > rat).
% 23.38/8.82  thf(func_def_203, type, inverse_inverse_real: real > real).
% 23.38/8.82  thf(func_def_204, type, at_bot_real: filter_real).
% 23.38/8.82  thf(func_def_205, type, at_top_nat: filter_nat).
% 23.38/8.82  thf(func_def_206, type, at_top_real: filter_real).
% 23.38/8.82  thf(func_def_207, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 23.38/8.82  thf(func_def_208, type, eventually_real: (real > $o) > filter_real > $o).
% 23.38/8.82  thf(func_def_209, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 23.38/8.82  thf(func_def_210, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 23.38/8.82  thf(func_def_211, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 23.38/8.82  thf(func_def_212, type, princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex).
% 23.38/8.82  thf(func_def_213, type, princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real).
% 23.38/8.82  thf(func_def_214, type, finite_card_o: set_o > nat).
% 23.38/8.82  thf(func_def_215, type, finite_card_complex: set_complex > nat).
% 23.38/8.82  thf(func_def_216, type, finite_card_int: set_int > nat).
% 23.38/8.82  thf(func_def_217, type, finite_card_list_nat: set_list_nat > nat).
% 23.38/8.82  thf(func_def_218, type, finite_card_nat: set_nat > nat).
% 23.38/8.82  thf(func_def_219, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 23.38/8.82  thf(func_def_220, type, finite_card_char: set_char > nat).
% 23.38/8.82  thf(func_def_221, type, finite3207457112153483333omplex: set_complex > $o).
% 23.38/8.82  thf(func_def_222, type, finite_finite_int: set_int > $o).
% 23.38/8.82  thf(func_def_223, type, finite_finite_nat: set_nat > $o).
% 23.38/8.82  thf(func_def_224, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 23.38/8.82  thf(func_def_225, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 23.38/8.82  thf(func_def_226, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 23.38/8.82  thf(func_def_227, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 23.38/8.82  thf(func_def_228, type, comp_nat_real_nat: (nat > real) > (nat > nat) > nat > real).
% 23.38/8.82  thf(func_def_229, type, id_o: $o > $o).
% 23.38/8.82  thf(func_def_230, type, id_nat: nat > nat).
% 23.38/8.82  thf(func_def_231, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 23.38/8.82  thf(func_def_232, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 23.38/8.82  thf(func_def_233, type, inj_on_real_real: (real > real) > set_real > $o).
% 23.38/8.82  thf(func_def_234, type, map_fu898904425404107465nt_o_o: (rat > product_prod_int_int) > ($o > $o) > (product_prod_int_int > $o) > rat > $o).
% 23.38/8.82  thf(func_def_235, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 23.38/8.82  thf(func_def_236, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 23.38/8.82  thf(func_def_237, type, gcd_Gcd_int: set_int > int).
% 23.38/8.82  thf(func_def_238, type, gcd_Gcd_nat: set_nat > nat).
% 23.38/8.82  thf(func_def_239, type, bezw: nat > nat > product_prod_int_int).
% 23.38/8.82  thf(func_def_240, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_241, type, gcd_gcd_Code_integer: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_242, type, gcd_gcd_int: int > int > int).
% 23.38/8.82  thf(func_def_243, type, gcd_gcd_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_244, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_245, type, abs_abs_Code_integer: code_integer > code_integer).
% 23.38/8.82  thf(func_def_246, type, abs_abs_complex: complex > complex).
% 23.38/8.82  thf(func_def_247, type, abs_abs_int: int > int).
% 23.38/8.82  thf(func_def_248, type, abs_abs_rat: rat > rat).
% 23.38/8.82  thf(func_def_249, type, abs_abs_real: real > real).
% 23.38/8.82  thf(func_def_250, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_251, type, minus_minus_complex: complex > complex > complex).
% 23.38/8.82  thf(func_def_252, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_253, type, minus_minus_int: int > int > int).
% 23.38/8.82  thf(func_def_254, type, minus_minus_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_255, type, minus_minus_rat: rat > rat > rat).
% 23.38/8.82  thf(func_def_256, type, minus_minus_real: real > real > real).
% 23.38/8.82  thf(func_def_257, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 23.38/8.82  thf(func_def_258, type, minus_minus_set_int: set_int > set_int > set_int).
% 23.38/8.82  thf(func_def_259, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 23.38/8.82  thf(func_def_260, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_261, type, minus_minus_set_real: set_real > set_real > set_real).
% 23.38/8.82  thf(func_def_262, type, one_one_Code_integer: code_integer).
% 23.38/8.82  thf(func_def_263, type, one_one_complex: complex).
% 23.38/8.82  thf(func_def_264, type, one_on7984719198319812577d_enat: extended_enat).
% 23.38/8.82  thf(func_def_265, type, one_one_int: int).
% 23.38/8.82  thf(func_def_266, type, one_one_nat: nat).
% 23.38/8.82  thf(func_def_267, type, one_one_rat: rat).
% 23.38/8.82  thf(func_def_268, type, one_one_real: real).
% 23.38/8.82  thf(func_def_269, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_270, type, plus_plus_complex: complex > complex > complex).
% 23.38/8.82  thf(func_def_271, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_272, type, plus_plus_int: int > int > int).
% 23.38/8.82  thf(func_def_273, type, plus_plus_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_274, type, plus_plus_num: num > num > num).
% 23.38/8.82  thf(func_def_275, type, plus_plus_rat: rat > rat > rat).
% 23.38/8.82  thf(func_def_276, type, plus_plus_real: real > real > real).
% 23.38/8.82  thf(func_def_277, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 23.38/8.82  thf(func_def_278, type, sgn_sgn_complex: complex > complex).
% 23.38/8.82  thf(func_def_279, type, sgn_sgn_int: int > int).
% 23.38/8.82  thf(func_def_280, type, sgn_sgn_rat: rat > rat).
% 23.38/8.82  thf(func_def_281, type, sgn_sgn_real: real > real).
% 23.38/8.82  thf(func_def_282, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_283, type, times_times_complex: complex > complex > complex).
% 23.38/8.82  thf(func_def_284, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_285, type, times_times_int: int > int > int).
% 23.38/8.82  thf(func_def_286, type, times_times_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_287, type, times_times_num: num > num > num).
% 23.38/8.82  thf(func_def_288, type, times_times_rat: rat > rat > rat).
% 23.38/8.82  thf(func_def_289, type, times_times_real: real > real > real).
% 23.38/8.82  thf(func_def_290, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 23.38/8.82  thf(func_def_291, type, uminus1482373934393186551omplex: complex > complex).
% 23.38/8.82  thf(func_def_292, type, uminus_uminus_int: int > int).
% 23.38/8.82  thf(func_def_293, type, uminus_uminus_rat: rat > rat).
% 23.38/8.82  thf(func_def_294, type, uminus_uminus_real: real > real).
% 23.38/8.82  thf(func_def_295, type, uminus1532241313380277803et_int: set_int > set_int).
% 23.38/8.82  thf(func_def_296, type, zero_z3403309356797280102nteger: code_integer).
% 23.38/8.82  thf(func_def_297, type, zero_zero_complex: complex).
% 23.38/8.82  thf(func_def_298, type, zero_z5237406670263579293d_enat: extended_enat).
% 23.38/8.82  thf(func_def_299, type, zero_zero_int: int).
% 23.38/8.82  thf(func_def_300, type, zero_zero_nat: nat).
% 23.38/8.82  thf(func_def_301, type, zero_zero_rat: rat).
% 23.38/8.82  thf(func_def_302, type, zero_zero_real: real).
% 23.38/8.82  thf(func_def_303, type, groups6621422865394947399nteger: (complex > code_integer) > set_complex > code_integer).
% 23.38/8.82  thf(func_def_304, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 23.38/8.82  thf(func_def_305, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 23.38/8.82  thf(func_def_306, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 23.38/8.82  thf(func_def_307, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 23.38/8.82  thf(func_def_308, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 23.38/8.82  thf(func_def_309, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 23.38/8.82  thf(func_def_310, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 23.38/8.82  thf(func_def_311, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 23.38/8.82  thf(func_def_312, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 23.38/8.82  thf(func_def_313, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 23.38/8.82  thf(func_def_314, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 23.38/8.82  thf(func_def_315, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 23.38/8.82  thf(func_def_316, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 23.38/8.82  thf(func_def_317, type, groups7108830773950497114d_enat: (nat > extended_enat) > set_nat > extended_enat).
% 23.38/8.82  thf(func_def_318, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 23.38/8.82  thf(func_def_319, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 23.38/8.82  thf(func_def_320, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 23.38/8.82  thf(func_def_321, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 23.38/8.82  thf(func_def_322, type, groups6381953495645901045omplex: (product_prod_nat_nat > complex) > set_Pr1261947904930325089at_nat > complex).
% 23.38/8.82  thf(func_def_323, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 23.38/8.82  thf(func_def_324, type, groups4567486121110086003t_real: (product_prod_nat_nat > real) > set_Pr1261947904930325089at_nat > real).
% 23.38/8.82  thf(func_def_325, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 23.38/8.82  thf(func_def_326, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 23.38/8.82  thf(func_def_327, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 23.38/8.82  thf(func_def_328, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 23.38/8.82  thf(func_def_329, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 23.38/8.82  thf(func_def_330, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 23.38/8.82  thf(func_def_331, type, groups3708469109370488835omplex: (complex > complex) > set_complex > complex).
% 23.38/8.82  thf(func_def_332, type, groups766887009212190081x_real: (complex > real) > set_complex > real).
% 23.38/8.82  thf(func_def_333, type, groups7440179247065528705omplex: (int > complex) > set_int > complex).
% 23.38/8.82  thf(func_def_334, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 23.38/8.82  thf(func_def_335, type, groups2316167850115554303t_real: (int > real) > set_int > real).
% 23.38/8.82  thf(func_def_336, type, groups6464643781859351333omplex: (nat > complex) > set_nat > complex).
% 23.38/8.82  thf(func_def_337, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 23.38/8.82  thf(func_def_338, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 23.38/8.82  thf(func_def_339, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 23.38/8.82  thf(func_def_340, type, groups129246275422532515t_real: (nat > real) > set_nat > real).
% 23.38/8.82  thf(func_def_341, type, groups713298508707869441omplex: (real > complex) > set_real > complex).
% 23.38/8.82  thf(func_def_342, type, groups4061424788464935467al_rat: (real > rat) > set_real > rat).
% 23.38/8.82  thf(func_def_343, type, groups1681761925125756287l_real: (real > real) > set_real > real).
% 23.38/8.82  thf(func_def_344, type, groups3417619833198082522nteger: ($o > code_integer) > code_integer > list_o > code_integer).
% 23.38/8.82  thf(func_def_345, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 23.38/8.82  thf(func_def_346, type, groups9119017779487936845_o_nat: ($o > nat) > nat > list_o > nat).
% 23.38/8.82  thf(func_def_347, type, groups4561878855575611511st_nat: list_nat > nat).
% 23.38/8.82  thf(func_def_348, type, the_int: (int > $o) > int).
% 23.38/8.82  thf(func_def_349, type, the_real: (real > $o) > real).
% 23.38/8.82  thf(func_def_350, type, if_int_int: $o > (int > int) > (int > int) > int > int).
% 23.38/8.82  thf(func_def_351, type, if_nat_int_int: $o > (nat > int > int) > (nat > int > int) > nat > int > int).
% 23.38/8.82  thf(func_def_352, type, if_nat_nat_nat: $o > (nat > nat > nat) > (nat > nat > nat) > nat > nat > nat).
% 23.38/8.82  thf(func_def_353, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_354, type, if_complex: $o > complex > complex > complex).
% 23.38/8.82  thf(func_def_355, type, if_int: $o > int > int > int).
% 23.38/8.82  thf(func_def_356, type, if_list_int: $o > list_int > list_int > list_int).
% 23.38/8.82  thf(func_def_357, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 23.38/8.82  thf(func_def_358, type, if_nat: $o > nat > nat > nat).
% 23.38/8.82  thf(func_def_359, type, if_num: $o > num > num > num).
% 23.38/8.82  thf(func_def_360, type, if_option_num: $o > option_num > option_num > option_num).
% 23.38/8.82  thf(func_def_361, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 23.38/8.82  thf(func_def_362, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_363, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 23.38/8.82  thf(func_def_364, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_365, type, if_rat: $o > rat > rat > rat).
% 23.38/8.82  thf(func_def_366, type, if_real: $o > real > real > real).
% 23.38/8.82  thf(func_def_367, type, if_set_int: $o > set_int > set_int > set_int).
% 23.38/8.82  thf(func_def_368, type, abs_Integ: product_prod_nat_nat > int).
% 23.38/8.82  thf(func_def_369, type, rep_Integ: int > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_370, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 23.38/8.82  thf(func_def_371, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 23.38/8.82  thf(func_def_372, type, nat2: int > nat).
% 23.38/8.82  thf(func_def_373, type, ring_11222124179247155820nteger: set_Code_integer).
% 23.38/8.82  thf(func_def_374, type, ring_1_Ints_complex: set_complex).
% 23.38/8.82  thf(func_def_375, type, ring_1_Ints_int: set_int).
% 23.38/8.82  thf(func_def_376, type, ring_1_Ints_rat: set_rat).
% 23.38/8.82  thf(func_def_377, type, ring_1_Ints_real: set_real).
% 23.38/8.82  thf(func_def_378, type, ring_18347121197199848620nteger: int > code_integer).
% 23.38/8.82  thf(func_def_379, type, ring_17405671764205052669omplex: int > complex).
% 23.38/8.82  thf(func_def_380, type, ring_1_of_int_int: int > int).
% 23.38/8.82  thf(func_def_381, type, ring_1_of_int_rat: int > rat).
% 23.38/8.82  thf(func_def_382, type, ring_1_of_int_real: int > real).
% 23.38/8.82  thf(func_def_383, type, inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_384, type, inf_inf_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_385, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 23.38/8.82  thf(func_def_386, type, sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_387, type, sup_sup_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_388, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 23.38/8.82  thf(func_def_389, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 23.38/8.82  thf(func_def_390, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 23.38/8.82  thf(func_def_391, type, at_infinity_real: filter_real).
% 23.38/8.82  thf(func_def_392, type, append_int: list_int > list_int > list_int).
% 23.38/8.82  thf(func_def_393, type, append_nat: list_nat > list_nat > list_nat).
% 23.38/8.82  thf(func_def_394, type, concat_o: list_list_o > list_o).
% 23.38/8.82  thf(func_def_395, type, concat_int: list_list_int > list_int).
% 23.38/8.82  thf(func_def_396, type, concat_nat: list_list_nat > list_nat).
% 23.38/8.82  thf(func_def_397, type, concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_398, type, distinct_int: list_int > $o).
% 23.38/8.82  thf(func_def_399, type, distinct_nat: list_nat > $o).
% 23.38/8.82  thf(func_def_400, type, drop_nat: nat > list_nat > list_nat).
% 23.38/8.82  thf(func_def_401, type, linord1735203802627413978nt_int: (int > int) > list_int > list_int).
% 23.38/8.82  thf(func_def_402, type, linord738340561235409698at_nat: (nat > nat) > list_nat > list_nat).
% 23.38/8.82  thf(func_def_403, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 23.38/8.82  thf(func_def_404, type, cons_int: int > list_int > list_int).
% 23.38/8.82  thf(func_def_405, type, cons_nat: nat > list_nat > list_nat).
% 23.38/8.82  thf(func_def_406, type, nil_int: list_int).
% 23.38/8.82  thf(func_def_407, type, nil_nat: list_nat).
% 23.38/8.82  thf(func_def_408, type, hd_nat: list_nat > nat).
% 23.38/8.82  thf(func_def_409, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 23.38/8.82  thf(func_def_410, type, set_o2: list_o > set_o).
% 23.38/8.82  thf(func_def_411, type, set_complex2: list_complex > set_complex).
% 23.38/8.82  thf(func_def_412, type, set_int2: list_int > set_int).
% 23.38/8.82  thf(func_def_413, type, set_list_o2: list_list_o > set_list_o).
% 23.38/8.82  thf(func_def_414, type, set_list_int2: list_list_int > set_list_int).
% 23.38/8.82  thf(func_def_415, type, set_list_nat2: list_list_nat > set_list_nat).
% 23.38/8.82  thf(func_def_416, type, set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_417, type, set_nat2: list_nat > set_nat).
% 23.38/8.82  thf(func_def_418, type, set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_419, type, set_real2: list_real > set_real).
% 23.38/8.82  thf(func_def_420, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 23.38/8.82  thf(func_def_421, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_422, type, tl_nat: list_nat > list_nat).
% 23.38/8.82  thf(func_def_423, type, nth_o: list_o > nat > $o).
% 23.38/8.82  thf(func_def_424, type, nth_Code_integer: list_Code_integer > nat > code_integer).
% 23.38/8.82  thf(func_def_425, type, nth_complex: list_complex > nat > complex).
% 23.38/8.82  thf(func_def_426, type, nth_int: list_int > nat > int).
% 23.38/8.82  thf(func_def_427, type, nth_list_nat: list_list_nat > nat > list_nat).
% 23.38/8.82  thf(func_def_428, type, nth_nat: list_nat > nat > nat).
% 23.38/8.82  thf(func_def_429, type, nth_num: list_num > nat > num).
% 23.38/8.82  thf(func_def_430, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 23.38/8.82  thf(func_def_431, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 23.38/8.82  thf(func_def_432, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 23.38/8.82  thf(func_def_433, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 23.38/8.82  thf(func_def_434, type, nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o).
% 23.38/8.82  thf(func_def_435, type, nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_436, type, nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num).
% 23.38/8.82  thf(func_def_437, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 23.38/8.82  thf(func_def_438, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 23.38/8.82  thf(func_def_439, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 23.38/8.82  thf(func_def_440, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 23.38/8.82  thf(func_def_441, type, nth_real: list_real > nat > real).
% 23.38/8.82  thf(func_def_442, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_443, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 23.38/8.82  thf(func_def_444, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 23.38/8.82  thf(func_def_445, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 23.38/8.82  thf(func_def_446, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 23.38/8.82  thf(func_def_447, type, produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o).
% 23.38/8.82  thf(func_def_448, type, product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 23.38/8.82  thf(func_def_449, type, produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 23.38/8.82  thf(func_def_450, type, product_num_num: list_num > list_num > list_P3744719386663036955um_num).
% 23.38/8.82  thf(func_def_451, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 23.38/8.82  thf(func_def_452, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 23.38/8.82  thf(func_def_453, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 23.38/8.82  thf(func_def_454, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 23.38/8.82  thf(func_def_455, type, remdups_nat: list_nat > list_nat).
% 23.38/8.82  thf(func_def_456, type, replicate_o: nat > $o > list_o).
% 23.38/8.82  thf(func_def_457, type, replicate_complex: nat > complex > list_complex).
% 23.38/8.82  thf(func_def_458, type, replicate_int: nat > int > list_int).
% 23.38/8.82  thf(func_def_459, type, replicate_nat: nat > nat > list_nat).
% 23.38/8.82  thf(func_def_460, type, replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 23.38/8.82  thf(func_def_461, type, replicate_real: nat > real > list_real).
% 23.38/8.82  thf(func_def_462, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_463, type, sorted_wrt_int: (int > int > $o) > list_int > $o).
% 23.38/8.82  thf(func_def_464, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 23.38/8.82  thf(func_def_465, type, subseqs_o: list_o > list_list_o).
% 23.38/8.82  thf(func_def_466, type, subseqs_int: list_int > list_list_int).
% 23.38/8.82  thf(func_def_467, type, subseqs_nat: list_nat > list_list_nat).
% 23.38/8.82  thf(func_def_468, type, subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_469, type, take_nat: nat > list_nat > list_nat).
% 23.38/8.82  thf(func_def_470, type, upt: nat > nat > list_nat).
% 23.38/8.82  thf(func_def_471, type, upto: int > int > list_int).
% 23.38/8.82  thf(func_def_472, type, upto_aux: int > int > list_int > list_int).
% 23.38/8.82  thf(func_def_473, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_474, type, suc: nat > nat).
% 23.38/8.82  thf(func_def_475, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 23.38/8.82  thf(func_def_476, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 23.38/8.82  thf(func_def_477, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 23.38/8.82  thf(func_def_478, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 23.38/8.82  thf(func_def_479, type, pred: nat > nat).
% 23.38/8.82  thf(func_def_480, type, semiri4939895301339042750nteger: nat > code_integer).
% 23.38/8.82  thf(func_def_481, type, semiri8010041392384452111omplex: nat > complex).
% 23.38/8.82  thf(func_def_482, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 23.38/8.82  thf(func_def_483, type, semiri1314217659103216013at_int: nat > int).
% 23.38/8.82  thf(func_def_484, type, semiri1316708129612266289at_nat: nat > nat).
% 23.38/8.82  thf(func_def_485, type, semiri681578069525770553at_rat: nat > rat).
% 23.38/8.82  thf(func_def_486, type, semiri5074537144036343181t_real: nat > real).
% 23.38/8.82  thf(func_def_487, type, semiri2816024913162550771omplex: (complex > complex) > nat > complex > complex).
% 23.38/8.82  thf(func_def_488, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 23.38/8.82  thf(func_def_489, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 23.38/8.82  thf(func_def_490, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 23.38/8.82  thf(func_def_491, type, semiri7260567687927622513x_real: (real > real) > nat > real > real).
% 23.38/8.82  thf(func_def_492, type, size_size_list_o: list_o > nat).
% 23.38/8.82  thf(func_def_493, type, size_s3445333598471063425nteger: list_Code_integer > nat).
% 23.38/8.82  thf(func_def_494, type, size_s3451745648224563538omplex: list_complex > nat).
% 23.38/8.82  thf(func_def_495, type, size_size_list_int: list_int > nat).
% 23.38/8.82  thf(func_def_496, type, size_s2710708370519433104list_o: list_list_o > nat).
% 23.38/8.82  thf(func_def_497, type, size_s533118279054570080st_int: list_list_int > nat).
% 23.38/8.82  thf(func_def_498, type, size_s3023201423986296836st_nat: list_list_nat > nat).
% 23.38/8.82  thf(func_def_499, type, size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_500, type, size_size_list_nat: list_nat > nat).
% 23.38/8.82  thf(func_def_501, type, size_size_list_num: list_num > nat).
% 23.38/8.82  thf(func_def_502, type, size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat).
% 23.38/8.82  thf(func_def_503, type, size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat).
% 23.38/8.82  thf(func_def_504, type, size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat).
% 23.38/8.82  thf(func_def_505, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 23.38/8.82  thf(func_def_506, type, size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat).
% 23.38/8.82  thf(func_def_507, type, size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat).
% 23.38/8.82  thf(func_def_508, type, size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat).
% 23.38/8.82  thf(func_def_509, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 23.38/8.82  thf(func_def_510, type, size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat).
% 23.38/8.82  thf(func_def_511, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 23.38/8.82  thf(func_def_512, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 23.38/8.82  thf(func_def_513, type, size_size_list_real: list_real > nat).
% 23.38/8.82  thf(func_def_514, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_515, type, size_size_num: num > nat).
% 23.38/8.82  thf(func_def_516, type, size_size_option_num: option_num > nat).
% 23.38/8.82  thf(func_def_517, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 23.38/8.82  thf(func_def_518, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_519, type, nat_list_encode: list_nat > nat).
% 23.38/8.82  thf(func_def_520, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 23.38/8.82  thf(func_def_521, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_522, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_523, type, nat_prod_encode: product_prod_nat_nat > nat).
% 23.38/8.82  thf(func_def_524, type, nat_set_decode: nat > set_nat).
% 23.38/8.82  thf(func_def_525, type, nat_set_encode: set_nat > nat).
% 23.38/8.82  thf(func_def_526, type, nat_triangle: nat > nat).
% 23.38/8.82  thf(func_def_527, type, root: nat > real > real).
% 23.38/8.82  thf(func_def_528, type, sqrt: real > real).
% 23.38/8.82  thf(func_def_529, type, bitM: num > num).
% 23.38/8.82  thf(func_def_530, type, inc: num > num).
% 23.38/8.82  thf(func_def_531, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 23.38/8.82  thf(func_def_532, type, neg_nu7009210354673126013omplex: complex > complex).
% 23.38/8.82  thf(func_def_533, type, neg_numeral_dbl_int: int > int).
% 23.38/8.82  thf(func_def_534, type, neg_numeral_dbl_rat: rat > rat).
% 23.38/8.82  thf(func_def_535, type, neg_numeral_dbl_real: real > real).
% 23.38/8.82  thf(func_def_536, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 23.38/8.82  thf(func_def_537, type, neg_nu6511756317524482435omplex: complex > complex).
% 23.38/8.82  thf(func_def_538, type, neg_nu3811975205180677377ec_int: int > int).
% 23.38/8.82  thf(func_def_539, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 23.38/8.82  thf(func_def_540, type, neg_nu6075765906172075777c_real: real > real).
% 23.38/8.82  thf(func_def_541, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 23.38/8.82  thf(func_def_542, type, neg_nu8557863876264182079omplex: complex > complex).
% 23.38/8.82  thf(func_def_543, type, neg_nu5851722552734809277nc_int: int > int).
% 23.38/8.82  thf(func_def_544, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 23.38/8.82  thf(func_def_545, type, neg_nu8295874005876285629c_real: real > real).
% 23.38/8.82  thf(func_def_546, type, neg_numeral_sub_int: num > num > int).
% 23.38/8.82  thf(func_def_547, type, bit0: num > num).
% 23.38/8.82  thf(func_def_548, type, bit1: num > num).
% 23.38/8.82  thf(func_def_549, type, one: num).
% 23.38/8.82  thf(func_def_550, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 23.38/8.82  thf(func_def_551, type, size_num: num > nat).
% 23.38/8.82  thf(func_def_552, type, num_of_nat: nat > num).
% 23.38/8.82  thf(func_def_553, type, numera6620942414471956472nteger: num > code_integer).
% 23.38/8.82  thf(func_def_554, type, numera6690914467698888265omplex: num > complex).
% 23.38/8.82  thf(func_def_555, type, numera1916890842035813515d_enat: num > extended_enat).
% 23.38/8.82  thf(func_def_556, type, numeral_numeral_int: num > int).
% 23.38/8.82  thf(func_def_557, type, numeral_numeral_nat: num > nat).
% 23.38/8.82  thf(func_def_558, type, numeral_numeral_rat: num > rat).
% 23.38/8.82  thf(func_def_559, type, numeral_numeral_real: num > real).
% 23.38/8.82  thf(func_def_560, type, pow: num > num > num).
% 23.38/8.82  thf(func_def_561, type, pred_numeral: num > nat).
% 23.38/8.82  thf(func_def_562, type, sqr: num > num).
% 23.38/8.82  thf(func_def_563, type, none_num: option_num).
% 23.38/8.82  thf(func_def_564, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 23.38/8.82  thf(func_def_565, type, some_num: num > option_num).
% 23.38/8.82  thf(func_def_566, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 23.38/8.82  thf(func_def_567, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_568, type, case_option_int_num: int > (num > int) > option_num > int).
% 23.38/8.82  thf(func_def_569, type, case_option_num_num: num > (num > num) > option_num > num).
% 23.38/8.82  thf(func_def_570, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 23.38/8.82  thf(func_def_571, type, map_option_num_num: (num > num) > option_num > option_num).
% 23.38/8.82  thf(func_def_572, type, size_option_num: (num > nat) > option_num > nat).
% 23.38/8.82  thf(func_def_573, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 23.38/8.82  thf(func_def_574, type, bot_bo4199563552545308370d_enat: extended_enat).
% 23.38/8.82  thf(func_def_575, type, bot_bot_nat: nat).
% 23.38/8.82  thf(func_def_576, type, bot_bot_set_int: set_int).
% 23.38/8.82  thf(func_def_577, type, bot_bot_set_nat: set_nat).
% 23.38/8.82  thf(func_def_578, type, ord_less_complex_o: (complex > $o) > (complex > $o) > $o).
% 23.38/8.82  thf(func_def_579, type, ord_less_int_o: (int > $o) > (int > $o) > $o).
% 23.38/8.82  thf(func_def_580, type, ord_less_nat_o: (nat > $o) > (nat > $o) > $o).
% 23.38/8.82  thf(func_def_581, type, ord_le549003669493604880_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 23.38/8.82  thf(func_def_582, type, ord_less_real_o: (real > $o) > (real > $o) > $o).
% 23.38/8.82  thf(func_def_583, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 23.38/8.82  thf(func_def_584, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 23.38/8.82  thf(func_def_585, type, ord_less_int: int > int > $o).
% 23.38/8.82  thf(func_def_586, type, ord_less_nat: nat > nat > $o).
% 23.38/8.82  thf(func_def_587, type, ord_less_num: num > num > $o).
% 23.38/8.82  thf(func_def_588, type, ord_less_rat: rat > rat > $o).
% 23.38/8.82  thf(func_def_589, type, ord_less_real: real > real > $o).
% 23.38/8.82  thf(func_def_590, type, ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o).
% 23.38/8.82  thf(func_def_591, type, ord_less_set_complex: set_complex > set_complex > $o).
% 23.38/8.82  thf(func_def_592, type, ord_less_set_int: set_int > set_int > $o).
% 23.38/8.82  thf(func_def_593, type, ord_less_set_nat: set_nat > set_nat > $o).
% 23.38/8.82  thf(func_def_594, type, ord_less_set_num: set_num > set_num > $o).
% 23.38/8.82  thf(func_def_595, type, ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 23.38/8.82  thf(func_def_596, type, ord_less_set_rat: set_rat > set_rat > $o).
% 23.38/8.82  thf(func_def_597, type, ord_less_set_real: set_real > set_real > $o).
% 23.38/8.82  thf(func_def_598, type, ord_less_set_set_int: set_set_int > set_set_int > $o).
% 23.38/8.82  thf(func_def_599, type, ord_le4573692005234683329plex_o: (complex > $o) > (complex > $o) > $o).
% 23.38/8.82  thf(func_def_600, type, ord_less_eq_int_o: (int > $o) > (int > $o) > $o).
% 23.38/8.82  thf(func_def_601, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 23.38/8.82  thf(func_def_602, type, ord_le704812498762024988_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 23.38/8.82  thf(func_def_603, type, ord_less_eq_real_o: (real > $o) > (real > $o) > $o).
% 23.38/8.82  thf(func_def_604, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 23.38/8.82  thf(func_def_605, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 23.38/8.82  thf(func_def_606, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 23.38/8.82  thf(func_def_607, type, ord_le4104064031414453916r_real: filter_real > filter_real > $o).
% 23.38/8.82  thf(func_def_608, type, ord_less_eq_int: int > int > $o).
% 23.38/8.82  thf(func_def_609, type, ord_less_eq_nat: nat > nat > $o).
% 23.38/8.82  thf(func_def_610, type, ord_less_eq_num: num > num > $o).
% 23.38/8.82  thf(func_def_611, type, ord_less_eq_rat: rat > rat > $o).
% 23.38/8.82  thf(func_def_612, type, ord_less_eq_real: real > real > $o).
% 23.38/8.82  thf(func_def_613, type, ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o).
% 23.38/8.82  thf(func_def_614, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 23.38/8.82  thf(func_def_615, type, ord_less_eq_set_int: set_int > set_int > $o).
% 23.38/8.82  thf(func_def_616, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 23.38/8.82  thf(func_def_617, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 23.38/8.82  thf(func_def_618, type, ord_less_eq_set_num: set_num > set_num > $o).
% 23.38/8.82  thf(func_def_619, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 23.38/8.82  thf(func_def_620, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 23.38/8.82  thf(func_def_621, type, ord_less_eq_set_real: set_real > set_real > $o).
% 23.38/8.82  thf(func_def_622, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 23.38/8.82  thf(func_def_623, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_624, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_625, type, ord_max_int: int > int > int).
% 23.38/8.82  thf(func_def_626, type, ord_max_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_627, type, ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat).
% 23.38/8.82  thf(func_def_628, type, ord_min_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_629, type, order_Greatest_nat: (nat > $o) > nat).
% 23.38/8.82  thf(func_def_630, type, order_9091379641038594480t_real: (nat > real) > $o).
% 23.38/8.82  thf(func_def_631, type, order_mono_nat_nat: (nat > nat) > $o).
% 23.38/8.82  thf(func_def_632, type, order_mono_nat_real: (nat > real) > $o).
% 23.38/8.82  thf(func_def_633, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 23.38/8.82  thf(func_def_634, type, order_7092887310737990675l_real: (real > real) > $o).
% 23.38/8.82  thf(func_def_635, type, top_top_set_o: set_o).
% 23.38/8.82  thf(func_def_636, type, top_top_set_nat: set_nat).
% 23.38/8.82  thf(func_def_637, type, top_to1996260823553986621t_unit: set_Product_unit).
% 23.38/8.82  thf(func_def_638, type, top_top_set_real: set_real).
% 23.38/8.82  thf(func_def_639, type, top_top_set_char: set_char).
% 23.38/8.82  thf(func_def_640, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 23.38/8.82  thf(func_def_641, type, power_power_complex: complex > nat > complex).
% 23.38/8.82  thf(func_def_642, type, power_8040749407984259932d_enat: extended_enat > nat > extended_enat).
% 23.38/8.82  thf(func_def_643, type, power_power_int: int > nat > int).
% 23.38/8.82  thf(func_def_644, type, power_power_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_645, type, power_power_rat: rat > nat > rat).
% 23.38/8.82  thf(func_def_646, type, power_power_real: real > nat > real).
% 23.38/8.82  thf(func_def_647, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 23.38/8.82  thf(func_def_648, type, produc851828971589881931at_num: (nat > num > num) > produc2963631642982155120at_num > produc3368934014287244435at_num).
% 23.38/8.82  thf(func_def_649, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 23.38/8.82  thf(func_def_650, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 23.38/8.82  thf(func_def_651, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 23.38/8.82  thf(func_def_652, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 23.38/8.82  thf(func_def_653, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 23.38/8.82  thf(func_def_654, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_655, type, product_Pair_int_int: int > int > product_prod_int_int).
% 23.38/8.82  thf(func_def_656, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_657, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 23.38/8.82  thf(func_def_658, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 23.38/8.82  thf(func_def_659, type, produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num).
% 23.38/8.82  thf(func_def_660, type, product_Pair_num_num: num > num > product_prod_num_num).
% 23.38/8.82  thf(func_def_661, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 23.38/8.82  thf(func_def_662, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 23.38/8.82  thf(func_def_663, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 23.38/8.82  thf(func_def_664, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 23.38/8.82  thf(func_def_665, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_666, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_667, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 23.38/8.82  thf(func_def_668, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 23.38/8.82  thf(func_def_669, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 23.38/8.82  thf(func_def_670, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 23.38/8.82  thf(func_def_671, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 23.38/8.82  thf(func_def_672, type, produc6771430404735790350plex_o: (complex > complex > $o) > produc4411394909380815293omplex > $o).
% 23.38/8.82  thf(func_def_673, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_674, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 23.38/8.82  thf(func_def_675, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 23.38/8.82  thf(func_def_676, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_677, 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).
% 23.38/8.82  thf(func_def_678, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_679, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 23.38/8.82  thf(func_def_680, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_681, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 23.38/8.82  thf(func_def_682, type, produc5414030515140494994real_o: (real > real > $o) > produc2422161461964618553l_real > $o).
% 23.38/8.82  thf(func_def_683, type, product_fst_int_int: product_prod_int_int > int).
% 23.38/8.82  thf(func_def_684, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 23.38/8.82  thf(func_def_685, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 23.38/8.82  thf(func_def_686, type, product_snd_int_int: product_prod_int_int > int).
% 23.38/8.82  thf(func_def_687, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 23.38/8.82  thf(func_def_688, type, fract: int > int > rat).
% 23.38/8.82  thf(func_def_689, type, rep_Rat: rat > product_prod_int_int).
% 23.38/8.82  thf(func_def_690, type, field_5140801741446780682s_real: set_real).
% 23.38/8.82  thf(func_def_691, type, field_7254667332652039916t_real: rat > real).
% 23.38/8.82  thf(func_def_692, type, normalize: product_prod_int_int > product_prod_int_int).
% 23.38/8.82  thf(func_def_693, type, positive: rat > $o).
% 23.38/8.82  thf(func_def_694, type, real_V2521375963428798218omplex: set_complex).
% 23.38/8.82  thf(func_def_695, type, real_V470468836141973256s_real: set_real).
% 23.38/8.82  thf(func_def_696, type, real_V3694042436643373181omplex: complex > complex > real).
% 23.38/8.82  thf(func_def_697, type, real_V975177566351809787t_real: real > real > real).
% 23.38/8.82  thf(func_def_698, type, real_V1022390504157884413omplex: complex > real).
% 23.38/8.82  thf(func_def_699, type, real_V7735802525324610683m_real: real > real).
% 23.38/8.82  thf(func_def_700, type, real_V4546457046886955230omplex: real > complex).
% 23.38/8.82  thf(func_def_701, type, real_V1803761363581548252l_real: real > real).
% 23.38/8.82  thf(func_def_702, type, real_V2046097035970521341omplex: real > complex > complex).
% 23.38/8.82  thf(func_def_703, type, real_V1485227260804924795R_real: real > real > real).
% 23.38/8.82  thf(func_def_704, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_705, type, divide1717551699836669952omplex: complex > complex > complex).
% 23.38/8.82  thf(func_def_706, type, divide_divide_int: int > int > int).
% 23.38/8.82  thf(func_def_707, type, divide_divide_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_708, type, divide_divide_rat: rat > rat > rat).
% 23.38/8.82  thf(func_def_709, type, divide_divide_real: real > real > real).
% 23.38/8.82  thf(func_def_710, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 23.38/8.82  thf(func_def_711, type, dvd_dvd_complex: complex > complex > $o).
% 23.38/8.82  thf(func_def_712, type, dvd_dvd_int: int > int > $o).
% 23.38/8.82  thf(func_def_713, type, dvd_dvd_nat: nat > nat > $o).
% 23.38/8.82  thf(func_def_714, type, dvd_dvd_rat: rat > rat > $o).
% 23.38/8.82  thf(func_def_715, type, dvd_dvd_real: real > real > $o).
% 23.38/8.82  thf(func_def_716, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 23.38/8.82  thf(func_def_717, type, modulo_modulo_int: int > int > int).
% 23.38/8.82  thf(func_def_718, type, modulo_modulo_nat: nat > nat > nat).
% 23.38/8.82  thf(func_def_719, type, zero_n356916108424825756nteger: $o > code_integer).
% 23.38/8.82  thf(func_def_720, type, zero_n1201886186963655149omplex: $o > complex).
% 23.38/8.82  thf(func_def_721, type, zero_n2684676970156552555ol_int: $o > int).
% 23.38/8.82  thf(func_def_722, type, zero_n2687167440665602831ol_nat: $o > nat).
% 23.38/8.82  thf(func_def_723, type, zero_n2052037380579107095ol_rat: $o > rat).
% 23.38/8.82  thf(func_def_724, type, zero_n3304061248610475627l_real: $o > real).
% 23.38/8.82  thf(func_def_725, type, suminf_complex: (nat > complex) > complex).
% 23.38/8.82  thf(func_def_726, type, suminf_int: (nat > int) > int).
% 23.38/8.82  thf(func_def_727, type, suminf_nat: (nat > nat) > nat).
% 23.38/8.82  thf(func_def_728, type, suminf_real: (nat > real) > real).
% 23.38/8.82  thf(func_def_729, type, summable_complex: (nat > complex) > $o).
% 23.38/8.82  thf(func_def_730, type, summable_int: (nat > int) > $o).
% 23.38/8.82  thf(func_def_731, type, summable_nat: (nat > nat) > $o).
% 23.38/8.82  thf(func_def_732, type, summable_real: (nat > real) > $o).
% 23.38/8.82  thf(func_def_733, type, sums_complex: (nat > complex) > complex > $o).
% 23.38/8.82  thf(func_def_734, type, sums_int: (nat > int) > int > $o).
% 23.38/8.82  thf(func_def_735, type, sums_nat: (nat > nat) > nat > $o).
% 23.38/8.82  thf(func_def_736, type, sums_real: (nat > real) > real > $o).
% 23.38/8.82  thf(func_def_737, type, collect_o: ($o > $o) > set_o).
% 23.38/8.82  thf(func_def_738, type, collect_Code_integer: (code_integer > $o) > set_Code_integer).
% 23.38/8.82  thf(func_def_739, type, collect_complex: (complex > $o) > set_complex).
% 23.38/8.82  thf(func_def_740, type, collect_int: (int > $o) > set_int).
% 23.38/8.82  thf(func_def_741, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 23.38/8.82  thf(func_def_742, type, collect_nat: (nat > $o) > set_nat).
% 23.38/8.82  thf(func_def_743, type, collect_num: (num > $o) > set_num).
% 23.38/8.82  thf(func_def_744, type, collec8663557070575231912omplex: (produc4411394909380815293omplex > $o) > set_Pr5085853215250843933omplex).
% 23.38/8.82  thf(func_def_745, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 23.38/8.82  thf(func_def_746, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_747, type, collec3799799289383736868l_real: (produc2422161461964618553l_real > $o) > set_Pr6218003697084177305l_real).
% 23.38/8.82  thf(func_def_748, type, collect_rat: (rat > $o) > set_rat).
% 23.38/8.82  thf(func_def_749, type, collect_real: (real > $o) > set_real).
% 23.38/8.82  thf(func_def_750, type, collect_set_int: (set_int > $o) > set_set_int).
% 23.38/8.82  thf(func_def_751, type, collect_VEBT_VEBT: (vEBT_VEBT > $o) > set_VEBT_VEBT).
% 23.38/8.82  thf(func_def_752, type, image_int_int: (int > int) > set_int > set_int).
% 23.38/8.82  thf(func_def_753, type, image_nat_int: (nat > int) > set_nat > set_int).
% 23.38/8.82  thf(func_def_754, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 23.38/8.82  thf(func_def_755, type, image_nat_real: (nat > real) > set_nat > set_real).
% 23.38/8.82  thf(func_def_756, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 23.38/8.82  thf(func_def_757, type, image_nat_char: (nat > char) > set_nat > set_char).
% 23.38/8.82  thf(func_def_758, type, image_5971271580939081552omplex: (real > filter6041513312241820739omplex) > set_real > set_fi4554929511873752355omplex).
% 23.38/8.82  thf(func_def_759, type, image_2178119161166701260l_real: (real > filter2146258269922977983l_real) > set_real > set_fi7789364187291644575l_real).
% 23.38/8.82  thf(func_def_760, type, image_real_real: (real > real) > set_real > set_real).
% 23.38/8.82  thf(func_def_761, type, image_char_nat: (char > nat) > set_char > set_nat).
% 23.38/8.82  thf(func_def_762, type, insert_int: int > set_int > set_int).
% 23.38/8.82  thf(func_def_763, type, insert_nat: nat > set_nat > set_nat).
% 23.38/8.82  thf(func_def_764, type, set_fo1517530859248394432omplex: (nat > complex > complex) > nat > nat > complex > complex).
% 23.38/8.82  thf(func_def_765, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 23.38/8.82  thf(func_def_766, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 23.38/8.82  thf(func_def_767, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 23.38/8.82  thf(func_def_768, type, set_fo3111899725591712190t_real: (nat > real > real) > nat > nat > real > real).
% 23.38/8.82  thf(func_def_769, type, set_or1266510415728281911st_int: int > int > set_int).
% 23.38/8.82  thf(func_def_770, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 23.38/8.82  thf(func_def_771, type, set_or7049704709247886629st_num: num > num > set_num).
% 23.38/8.82  thf(func_def_772, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 23.38/8.82  thf(func_def_773, type, set_or1222579329274155063t_real: real > real > set_real).
% 23.38/8.82  thf(func_def_774, type, set_or370866239135849197et_int: set_int > set_int > set_set_int).
% 23.38/8.82  thf(func_def_775, type, set_or4662586982721622107an_int: int > int > set_int).
% 23.38/8.82  thf(func_def_776, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 23.38/8.82  thf(func_def_777, type, set_ord_atLeast_nat: nat > set_nat).
% 23.38/8.82  thf(func_def_778, type, set_ord_atLeast_real: real > set_real).
% 23.38/8.82  thf(func_def_779, type, set_ord_atMost_int: int > set_int).
% 23.38/8.82  thf(func_def_780, type, set_ord_atMost_nat: nat > set_nat).
% 23.38/8.82  thf(func_def_781, type, set_ord_atMost_num: num > set_num).
% 23.38/8.82  thf(func_def_782, type, set_ord_atMost_rat: rat > set_rat).
% 23.38/8.82  thf(func_def_783, type, set_ord_atMost_real: real > set_real).
% 23.38/8.82  thf(func_def_784, type, set_or58775011639299419et_int: set_int > set_set_int).
% 23.38/8.82  thf(func_def_785, type, set_or6656581121297822940st_int: int > int > set_int).
% 23.38/8.82  thf(func_def_786, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 23.38/8.82  thf(func_def_787, type, set_or5832277885323065728an_int: int > int > set_int).
% 23.38/8.82  thf(func_def_788, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 23.38/8.82  thf(func_def_789, type, set_or1633881224788618240n_real: real > real > set_real).
% 23.38/8.82  thf(func_def_790, type, set_or1210151606488870762an_nat: nat > set_nat).
% 23.38/8.82  thf(func_def_791, type, set_or5849166863359141190n_real: real > set_real).
% 23.38/8.82  thf(func_def_792, type, set_ord_lessThan_int: int > set_int).
% 23.38/8.82  thf(func_def_793, type, set_ord_lessThan_nat: nat > set_nat).
% 23.38/8.82  thf(func_def_794, type, set_ord_lessThan_num: num > set_num).
% 23.38/8.82  thf(func_def_795, type, set_ord_lessThan_rat: rat > set_rat).
% 23.38/8.82  thf(func_def_796, type, set_or5984915006950818249n_real: real > set_real).
% 23.38/8.82  thf(func_def_797, type, ascii_of: char > char).
% 23.38/8.82  thf(func_def_798, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 23.38/8.82  thf(func_def_799, type, comm_s629917340098488124ar_nat: char > nat).
% 23.38/8.82  thf(func_def_800, type, integer_of_char: char > code_integer).
% 23.38/8.82  thf(func_def_801, type, unique3096191561947761185of_nat: nat > char).
% 23.38/8.82  thf(func_def_802, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 23.38/8.82  thf(func_def_803, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 23.38/8.82  thf(func_def_804, type, topolo4899668324122417113eq_int: (nat > int) > $o).
% 23.38/8.82  thf(func_def_805, type, topolo4902158794631467389eq_nat: (nat > nat) > $o).
% 23.38/8.82  thf(func_def_806, type, topolo1459490580787246023eq_num: (nat > num) > $o).
% 23.38/8.82  thf(func_def_807, type, topolo4267028734544971653eq_rat: (nat > rat) > $o).
% 23.38/8.82  thf(func_def_808, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 23.38/8.82  thf(func_def_809, type, topolo3100542954746470799et_int: (nat > set_int) > $o).
% 23.38/8.82  thf(func_def_810, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 23.38/8.82  thf(func_def_811, type, topolo2815343760600316023s_real: real > filter_real).
% 23.38/8.82  thf(func_def_812, type, topolo6517432010174082258omplex: (nat > complex) > $o).
% 23.38/8.82  thf(func_def_813, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 23.38/8.82  thf(func_def_814, type, topolo896644834953643431omplex: filter6041513312241820739omplex).
% 23.38/8.82  thf(func_def_815, type, topolo1511823702728130853y_real: filter2146258269922977983l_real).
% 23.38/8.82  thf(func_def_816, type, arccos: real > real).
% 23.38/8.82  thf(func_def_817, type, arcosh_real: real > real).
% 23.38/8.82  thf(func_def_818, type, arcsin: real > real).
% 23.38/8.82  thf(func_def_819, type, arctan: real > real).
% 23.38/8.82  thf(func_def_820, type, arsinh_real: real > real).
% 23.38/8.82  thf(func_def_821, type, artanh_real: real > real).
% 23.38/8.82  thf(func_def_822, type, cos_complex: complex > complex).
% 23.38/8.82  thf(func_def_823, type, cos_real: real > real).
% 23.38/8.82  thf(func_def_824, type, cos_coeff: nat > real).
% 23.38/8.82  thf(func_def_825, type, cosh_complex: complex > complex).
% 23.38/8.82  thf(func_def_826, type, cosh_real: real > real).
% 23.38/8.82  thf(func_def_827, type, cot_complex: complex > complex).
% 23.38/8.82  thf(func_def_828, type, cot_real: real > real).
% 23.38/8.82  thf(func_def_829, type, diffs_complex: (nat > complex) > nat > complex).
% 23.38/8.82  thf(func_def_830, type, diffs_int: (nat > int) > nat > int).
% 23.38/8.82  thf(func_def_831, type, diffs_real: (nat > real) > nat > real).
% 23.38/8.82  thf(func_def_832, type, exp_complex: complex > complex).
% 23.38/8.82  thf(func_def_833, type, exp_real: real > real).
% 23.38/8.82  thf(func_def_834, type, ln_ln_real: real > real).
% 23.38/8.82  thf(func_def_835, type, log: real > real > real).
% 23.38/8.82  thf(func_def_836, type, pi: real).
% 23.38/8.82  thf(func_def_837, type, powr_real: real > real > real).
% 23.38/8.82  thf(func_def_838, type, sin_complex: complex > complex).
% 23.38/8.82  thf(func_def_839, type, sin_real: real > real).
% 23.38/8.82  thf(func_def_840, type, sin_coeff: nat > real).
% 23.38/8.82  thf(func_def_841, type, sinh_complex: complex > complex).
% 23.38/8.82  thf(func_def_842, type, sinh_real: real > real).
% 23.38/8.82  thf(func_def_843, type, tan_complex: complex > complex).
% 23.38/8.82  thf(func_def_844, type, tan_real: real > real).
% 23.38/8.82  thf(func_def_845, type, tanh_complex: complex > complex).
% 23.38/8.82  thf(func_def_846, type, tanh_real: real > real).
% 23.38/8.82  thf(func_def_847, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_848, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_849, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 23.38/8.82  thf(func_def_850, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_851, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_852, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_853, type, vEBT_VEBT_high: nat > nat > nat).
% 23.38/8.82  thf(func_def_854, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_855, type, vEBT_VEBT_low: nat > nat > nat).
% 23.38/8.82  thf(func_def_856, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_857, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.38/8.82  thf(func_def_858, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_859, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.38/8.82  thf(func_def_860, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_861, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 23.38/8.82  thf(func_def_862, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_863, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 23.38/8.82  thf(func_def_864, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_865, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 23.38/8.82  thf(func_def_866, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 23.38/8.82  thf(func_def_867, type, accp_nat: (nat > nat > $o) > nat > $o).
% 23.38/8.82  thf(func_def_868, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 23.38/8.82  thf(func_def_869, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 23.38/8.82  thf(func_def_870, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 23.38/8.82  thf(func_def_871, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 23.38/8.82  thf(func_def_872, type, pred_nat: set_Pr1261947904930325089at_nat).
% 23.38/8.82  thf(func_def_873, type, fChoice_real: (real > $o) > real).
% 23.38/8.82  thf(func_def_874, type, member_o: $o > set_o > $o).
% 23.38/8.82  thf(func_def_875, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 23.38/8.82  thf(func_def_876, type, member_complex: complex > set_complex > $o).
% 23.38/8.82  thf(func_def_877, type, member_int: int > set_int > $o).
% 23.38/8.82  thf(func_def_878, type, member_list_o: list_o > set_list_o > $o).
% 23.38/8.82  thf(func_def_879, type, member_list_int: list_int > set_list_int > $o).
% 23.38/8.82  thf(func_def_880, type, member_list_nat: list_nat > set_list_nat > $o).
% 23.38/8.82  thf(func_def_881, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_882, type, member_nat: nat > set_nat > $o).
% 23.38/8.82  thf(func_def_883, type, member_num: num > set_num > $o).
% 23.38/8.82  thf(func_def_884, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 23.38/8.82  thf(func_def_885, type, member_rat: rat > set_rat > $o).
% 23.38/8.82  thf(func_def_886, type, member_real: real > set_real > $o).
% 23.38/8.82  thf(func_def_887, type, member_set_int: set_int > set_set_int > $o).
% 23.38/8.82  thf(func_def_888, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_889, type, deg: nat).
% 23.38/8.82  thf(func_def_890, type, info: option4927543243414619207at_nat).
% 23.38/8.82  thf(func_def_891, type, m: nat).
% 23.38/8.82  thf(func_def_892, type, ma: nat).
% 23.38/8.82  thf(func_def_893, type, mi: nat).
% 23.38/8.82  thf(func_def_894, type, n: nat).
% 23.38/8.82  thf(func_def_895, type, na: nat).
% 23.38/8.82  thf(func_def_896, type, summary: vEBT_VEBT).
% 23.38/8.82  thf(func_def_897, type, treeList: list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_898, type, x: nat).
% 23.38/8.82  thf(func_def_917, type, sP0: (nat > vEBT_VEBT > $o) > nat > $o).
% 23.38/8.82  thf(func_def_918, type, sP1: (nat > vEBT_VEBT > $o) > nat > $o).
% 23.38/8.82  thf(func_def_919, type, sP2: nat > list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_920, type, sP3: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_921, type, sP4: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_922, type, sP5: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_923, type, sP6: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_924, type, sP7: nat > list_VEBT_VEBT > vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_925, type, sP8: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_926, type, sP9: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_927, type, sP10: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_928, type, sP11: nat > vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_929, type, sP12: vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_930, type, sP13: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_931, type, sP14: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_932, type, sP15: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_933, type, sP16: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_934, type, sP17: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > $o).
% 23.38/8.82  thf(func_def_935, type, sP18: (option4927543243414619207at_nat > option_num > $o) > option_num > option4927543243414619207at_nat > $o).
% 23.38/8.82  thf(func_def_936, type, sP19: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_937, type, sP20: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.38/8.82  thf(func_def_938, type, sP21: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_939, type, sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 23.38/8.82  thf(func_def_940, type, sP23: list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_941, type, sP24: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_942, type, sP25: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_943, type, sP26: list_VEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_944, type, sP27: nat > list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_945, type, sP28: list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_946, type, sP29: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_947, type, sP30: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_948, type, sP31: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_949, type, sP32: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 23.38/8.82  thf(func_def_950, type, sP33: nat > nat > list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_951, type, sP34: nat > list_VEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_952, type, sP35: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 23.38/8.82  thf(func_def_953, type, sP36: nat > $o).
% 23.38/8.82  thf(func_def_954, type, sK37: (nat > vEBT_VEBT > $o) > nat > nat).
% 23.38/8.82  thf(func_def_955, type, sK38: nat > (nat > vEBT_VEBT > $o) > vEBT_VEBT).
% 23.38/8.82  thf(func_def_956, type, sK39: list_VEBT_VEBT > (nat > vEBT_VEBT > $o) > nat > nat).
% 23.38/8.82  thf(func_def_957, type, sK40: (nat > vEBT_VEBT > $o) > nat > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_958, type, sK41: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_959, type, sK42: list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_960, type, sK43: list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_961, type, sK44: vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_962, type, sK45: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_963, type, sK46: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_964, type, sK47: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_965, type, sK48: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_966, type, sK49: vEBT_VEBT > nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_967, type, sK50: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_968, type, sK51: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_969, type, sK52: nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_970, type, sK53: nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_971, type, sK54: nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_972, type, sK55: nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_973, type, sK56: nat > vEBT_VEBT > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_974, type, sK57: nat > vEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_975, type, sK58: nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_976, type, sK59: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_977, type, sK60: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_978, type, sK61: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_979, type, sK62: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_980, type, sK63: vEBT_VEBT > nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_981, type, sK64: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_982, type, sK65: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_983, type, sK66: vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_984, type, sK67: vEBT_VEBT > nat > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_985, type, sK68: vEBT_VEBT > nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_986, type, sK69: nat > list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_987, type, sK70: nat > list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_988, type, sK71: vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_989, type, sK72: vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_990, type, sK73: (list_VEBT_VEBT > $o) > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_991, type, sK74: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_992, type, sK75: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_993, type, sK76: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_994, type, sK77: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > num).
% 23.38/8.82  thf(func_def_995, type, sK78: nat > nat).
% 23.38/8.82  thf(func_def_996, type, sK79: option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_997, type, sK80: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_998, type, sK81: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > num).
% 23.38/8.82  thf(func_def_999, type, sK82: list_VEBT_VEBT > nat > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1000, type, sK83: list_VEBT_VEBT > vEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_1001, type, sK84: list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1002, type, sK85: list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1003, type, sK86: nat > nat > list_VEBT_VEBT > nat > nat > nat).
% 23.38/8.82  thf(func_def_1004, type, sK87: nat > nat > list_VEBT_VEBT > nat > nat > nat).
% 23.38/8.82  thf(func_def_1005, type, sK88: list_VEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_1006, type, sK89: nat > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_1007, type, sK90: option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_1008, type, sK91: vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1009, type, sK92: vEBT_VEBT > option4927543243414619207at_nat).
% 23.38/8.82  thf(func_def_1010, type, sK93: vEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1011, type, sK94: vEBT_VEBT > list_VEBT_VEBT).
% 23.38/8.82  thf(func_def_1012, type, sK95: vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_1013, type, sK96: vEBT_VEBT > $o).
% 23.38/8.82  thf(func_def_1014, type, sK97: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1015, type, sK98: list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1016, type, sK99: list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1017, type, sK100: vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1018, type, sK101: nat > list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1019, type, sK102: list_VEBT_VEBT > nat > nat).
% 23.38/8.82  thf(func_def_1020, type, sK103: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 23.38/8.82  thf(func_def_1021, type, sK104: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 23.38/8.82  thf(func_def_1022, type, sK105: list_VEBT_VEBT > vEBT_VEBT).
% 23.38/8.82  thf(func_def_1023, type, sK106: list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1024, type, sK107: list_VEBT_VEBT > nat > vEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1025, type, sK108: option4927543243414619207at_nat > product_prod_nat_nat).
% 23.38/8.82  thf(func_def_1026, type, sK109: list_VEBT_VEBT > list_VEBT_VEBT > nat).
% 23.38/8.82  thf(func_def_1028, type, ph111: !>[X0: $tType]:(X0)).
% 23.38/8.82  thf(f24320,plain,(
% 23.38/8.82    $false),
% 23.38/8.82    inference(avatar_sat_refutation,[status(thm)],[f23760,f23786,f23801,f24316,f24319])).
% 23.38/8.82  thf(f24319,plain,(
% 23.38/8.82    ~spl110_1),
% 23.38/8.82    inference(avatar_contradiction_clause,[status(thm)],[f24318])).
% 23.38/8.82  thf(f24318,plain,(
% 23.38/8.82    $false | ~spl110_1),
% 23.38/8.82    inference(trivial_inequality_removal,[status(thm)],[f24317])).
% 23.38/8.82  thf(f24317,plain,(
% 23.38/8.82    ($false = $true) | ~spl110_1),
% 23.38/8.82    inference(forward_demodulation,[status(thm)],[f23756,f23665])).
% 23.38/8.82  thf(f23665,plain,(
% 23.38/8.82    ($false = (vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x))),
% 23.38/8.82    inference(binary_proxy_clausification,[status(thm)],[f23663])).
% 23.38/8.82  thf(f23663,plain,(
% 23.38/8.82    ($true != ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x) | (vEBT_V5719532721284313246member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x)))),
% 23.38/8.82    inference(beta_eta_normalization,[status(thm)],[f23567])).
% 23.38/8.82  thf(f23567,plain,(
% 23.38/8.82    ($true != ((^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_VEBT_membermima @ Y0 @ Y1) | (vEBT_V5719532721284313246member @ Y0 @ Y1))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x))),
% 23.38/8.82    inference(definition_unfolding,[status(thm)],[f23489,f23355,f23427])).
% 23.38/8.82  thf(f23427,plain,(
% 23.38/8.82    (info = (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)))),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f737])).
% 23.38/8.82  thf(f737,axiom,(
% 23.38/8.82    (info = (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)))),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_736__C5_Ohyps_C_I12_J)).
% 23.38/8.82  thf(f23355,plain,(
% 23.38/8.82    (vEBT_V8194947554948674370ptions = (^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_VEBT_membermima @ Y0 @ Y1) | (vEBT_V5719532721284313246member @ Y0 @ Y1))))))),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f11806])).
% 23.38/8.82  thf(f11806,plain,(
% 23.38/8.82    (vEBT_V8194947554948674370ptions = (^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_VEBT_membermima @ Y0 @ Y1) | (vEBT_V5719532721284313246member @ Y0 @ Y1))))))),
% 23.38/8.82    inference(fool_elimination,[status(thm)],[f11805])).
% 23.38/8.82  thf(f11805,plain,(
% 23.38/8.82    ((^[X0 : vEBT_VEBT, X1 : nat] : ((vEBT_V5719532721284313246member @ X0 @ X1) | (vEBT_VEBT_membermima @ X0 @ X1))) = vEBT_V8194947554948674370ptions)),
% 23.38/8.82    inference(rectify,[status(thm)],[f1])).
% 23.38/8.82  thf(f1,axiom,(
% 23.38/8.82    ((^[X0 : vEBT_VEBT, X1 : nat] : ((vEBT_V5719532721284313246member @ X0 @ X1) | (vEBT_VEBT_membermima @ X0 @ X1))) = vEBT_V8194947554948674370ptions)),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_0_both__member__options__def)).
% 23.38/8.82  thf(f23489,plain,(
% 23.38/8.82    ((vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) != $true)),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f23091])).
% 23.38/8.82  thf(f23091,plain,(
% 23.38/8.82    ((vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) != $true)),
% 23.38/8.82    inference(flattening,[status(thm)],[f15733])).
% 23.38/8.82  thf(f15733,plain,(
% 23.38/8.82    ~((vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    inference(fool_elimination,[status(thm)],[f15732])).
% 23.38/8.82  thf(f15732,plain,(
% 23.38/8.82    ~(vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    inference(rectify,[status(thm)],[f10250])).
% 23.38/8.82  thf(f10250,negated_conjecture,(
% 23.38/8.82    ~(vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    inference(negated_conjecture,[status(cth)],[f10249])).
% 23.38/8.82  thf(f10249,conjecture,(
% 23.38/8.82    (vEBT_V8194947554948674370ptions @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',conj_0)).
% 23.38/8.82  thf(f23756,plain,(
% 23.38/8.82    ($true = (vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x)) | ~spl110_1),
% 23.38/8.82    inference(avatar_component_clause,[status(thm)],[f23755])).
% 23.38/8.82  thf(f23755,definition,(
% 23.38/8.82    spl110_1 <=> ($true = (vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x))),
% 23.38/8.82    introduced(definition,[new_symbols(naming,[spl110_1])],[avatar_definition])).
% 23.38/8.82  thf(f24316,plain,(
% 23.38/8.82    ~spl110_8),
% 23.38/8.82    inference(avatar_contradiction_clause,[status(thm)],[f24315])).
% 23.38/8.82  thf(f24315,plain,(
% 23.38/8.82    $false | ~spl110_8),
% 23.38/8.82    inference(trivial_inequality_removal,[status(thm)],[f24314])).
% 23.38/8.82  thf(f24314,plain,(
% 23.38/8.82    ($false = $true) | ~spl110_8),
% 23.38/8.82    inference(forward_demodulation,[status(thm)],[f23779,f23664])).
% 23.38/8.82  thf(f23664,plain,(
% 23.38/8.82    ($false = (vEBT_V5719532721284313246member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x))),
% 23.38/8.82    inference(binary_proxy_clausification,[status(thm)],[f23663])).
% 23.38/8.82  thf(f23779,plain,(
% 23.38/8.82    ((vEBT_V5719532721284313246member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x) = $true) | ~spl110_8),
% 23.38/8.82    inference(avatar_component_clause,[status(thm)],[f23778])).
% 23.38/8.82  thf(f23778,definition,(
% 23.38/8.82    spl110_8 <=> ((vEBT_V5719532721284313246member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    introduced(definition,[new_symbols(naming,[spl110_8])],[avatar_definition])).
% 23.38/8.82  thf(f23801,plain,(
% 23.38/8.82    ~spl110_9 | spl110_8),
% 23.38/8.82    inference(avatar_split_clause,[status(thm)],[f23566,f23778,f23782])).
% 23.38/8.82  thf(f23782,definition,(
% 23.38/8.82    spl110_9 <=> ((vEBT_V5719532721284313246member @ (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))))) = $true)),
% 23.38/8.82    introduced(definition,[new_symbols(naming,[spl110_9])],[avatar_definition])).
% 23.38/8.82  thf(f23566,plain,(
% 23.38/8.82    ((vEBT_V5719532721284313246member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x) = $true) | ((vEBT_V5719532721284313246member @ (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))))) != $true)),
% 23.38/8.82    inference(definition_unfolding,[status(thm)],[f23488,f23427])).
% 23.38/8.82  thf(f23488,plain,(
% 23.38/8.82    ((vEBT_V5719532721284313246member @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true) | ((vEBT_V5719532721284313246member @ (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))))) != $true)),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f23132])).
% 23.38/8.82  thf(f23132,plain,(
% 23.38/8.82    ((vEBT_V5719532721284313246member @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true) | ((vEBT_V5719532721284313246member @ (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))))) != $true)),
% 23.38/8.82    inference(ennf_transformation,[status(thm)],[f23076])).
% 23.38/8.82  thf(f23076,plain,(
% 23.38/8.82    ((vEBT_V5719532721284313246member @ (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))))) = $true) => ((vEBT_V5719532721284313246member @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    inference(fool_elimination,[status(thm)],[f23075])).
% 23.38/8.82  thf(f23075,plain,(
% 23.38/8.82    (vEBT_V5719532721284313246member @ (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))))) => (vEBT_V5719532721284313246member @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    inference(rectify,[status(thm)],[f8])).
% 23.38/8.82  thf(f8,axiom,(
% 23.38/8.82    (vEBT_V5719532721284313246member @ (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))))) => (vEBT_V5719532721284313246member @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062)).
% 23.38/8.82  thf(f23786,plain,(
% 23.38/8.82    spl110_9 | spl110_2),
% 23.38/8.82    inference(avatar_split_clause,[status(thm)],[f23699,f23758,f23782])).
% 23.38/8.82  thf(f23758,definition,(
% 23.38/8.82    spl110_2 <=> ((vEBT_VEBT_membermima @ (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))))) = $true)),
% 23.38/8.82    introduced(definition,[new_symbols(naming,[spl110_2])],[avatar_definition])).
% 23.38/8.82  thf(f23699,plain,(
% 23.38/8.82    ((vEBT_VEBT_membermima @ (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))))) = $true) | ((vEBT_V5719532721284313246member @ (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))))) = $true)),
% 23.38/8.82    inference(binary_proxy_clausification,[status(thm)],[f23698])).
% 23.38/8.82  thf(f23698,plain,(
% 23.38/8.82    (((vEBT_VEBT_membermima @ (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))))) | (vEBT_V5719532721284313246member @ (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)))))) = $true)),
% 23.38/8.82    inference(beta_eta_normalization,[status(thm)],[f23559])).
% 23.38/8.82  thf(f23559,plain,(
% 23.38/8.82    (((^[Y0 : vEBT_VEBT]: ((^[Y1 : nat]: ((vEBT_VEBT_membermima @ Y0 @ Y1) | (vEBT_V5719532721284313246member @ Y0 @ Y1))))) @ (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))))) = $true)),
% 23.38/8.82    inference(definition_unfolding,[status(thm)],[f23452,f23355])).
% 23.38/8.82  thf(f23452,plain,(
% 23.38/8.82    ((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))))) = $true)),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f19232])).
% 23.38/8.82  thf(f19232,plain,(
% 23.38/8.82    ((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))))) = $true)),
% 23.38/8.82    inference(fool_elimination,[status(thm)],[f19231])).
% 23.38/8.82  thf(f19231,plain,(
% 23.38/8.82    (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ x @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ x @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),
% 23.38/8.82    inference(rectify,[status(thm)],[f12])).
% 23.38/8.82  thf(f12,axiom,(
% 23.38/8.82    (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ x @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ x @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_11_assms_I3_J)).
% 23.38/8.82  thf(f23760,plain,(
% 23.38/8.82    spl110_1 | ~spl110_2),
% 23.38/8.82    inference(avatar_split_clause,[status(thm)],[f23568,f23758,f23755])).
% 23.38/8.82  thf(f23568,plain,(
% 23.38/8.82    ($true = (vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ x)) | ((vEBT_VEBT_membermima @ (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))))) != $true)),
% 23.38/8.82    inference(definition_unfolding,[status(thm)],[f23492,f23427])).
% 23.38/8.82  thf(f23492,plain,(
% 23.38/8.82    ((vEBT_VEBT_membermima @ (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))))) != $true) | ((vEBT_VEBT_membermima @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    inference(cnf_transformation,[status(thm)],[f23126])).
% 23.38/8.82  thf(f23126,plain,(
% 23.38/8.82    ((vEBT_VEBT_membermima @ (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))))) != $true) | ((vEBT_VEBT_membermima @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    inference(ennf_transformation,[status(thm)],[f18374])).
% 23.38/8.82  thf(f18374,plain,(
% 23.38/8.82    ((vEBT_VEBT_membermima @ (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))))) = $true) => ((vEBT_VEBT_membermima @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x) = $true)),
% 23.38/8.82    inference(fool_elimination,[status(thm)],[f18373])).
% 23.38/8.82  thf(f18373,plain,(
% 23.38/8.82    (vEBT_VEBT_membermima @ (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))))) => (vEBT_VEBT_membermima @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    inference(rectify,[status(thm)],[f9])).
% 23.38/8.82  thf(f9,axiom,(
% 23.38/8.82    (vEBT_VEBT_membermima @ (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))))) => (vEBT_VEBT_membermima @ (vEBT_Node @ info @ deg @ treeList @ summary) @ x)),
% 23.38/8.82    file('/export/starexec/sandbox/tmp/tmp.GhAPYOlALz/DTF2THF_7681.p',fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062)).
% 23.38/8.82  % SZS output end Proof for DTF2THF_7681
% 23.38/8.82  % (7985)------------------------------
% 23.38/8.82  % (7985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.38/8.82  % (7985)Termination reason: Refutation
% 23.38/8.82  
% 23.38/8.82  % (7985)Memory used [KB]: 29807
% 23.38/8.82  % (7985)Time elapsed: 0.644 s
% 23.38/8.82  % (7985)Instructions burned: 1658 (million)
% 23.38/8.82  % (7985)------------------------------
% 23.38/8.82  % (7985)------------------------------
% 23.38/8.82  % (7887)Success in time 2.575 s
%------------------------------------------------------------------------------